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ϕe, 3)/2 respectively.Performance indices are used to evaluate the contributions of the concrete and steel components to the ultimate strengths of CFST slender beam-columns and to quantify the strength reduction caused by the section and column slenderness, loading eccentricity and initial geometric imperfections. These performance indices can be used to investigate the cost effective designs of CFST slender beam-columns under biaxial loads.The steel contribution ratio is used to determine the contribution of the hollow steel tubular beam-column to the ultimate strength of the CFST slender beam-column under axial load and biaxial bending, which is given bywhere Pn is the ultimate axial strength of the CFST slender beam-column and Ps is the ultimate axial strength of the hollow steel tubular beam-column, which is calculated by setting the concrete compressive strength f′c to zero in the numerical analysis while other conditions of the hollow steel tubular beam-column remain the same as those of the CFST beam-column. The effects of local buckling are taken into account in the determination of both Pn and Ps.The concrete contribution ratio quantifies the contribution of the concrete component to the ultimate axial strength of a CFST slender beam-column. The slender concrete core beam-column without reinforcement carries very low loading and does not represents the concrete core in a CFST slender beam-column. Portolés et al. is an inverse of the steel contribution ratio and may not accurately quantify the concrete contribution. To evaluate the contribution of the concrete component to the ultimate axial strength of a CFST slender beam-column, a new concrete contribution ratio is proposed as that the concrete contribution to the ultimate axial strength of a CFST slender beam-column is the difference between the ultimate axial strength of the CFST column and that of the hollow steel column.The ultimate axial strength of a CFST short column under axial loading is reduced by increasing the section and column slenderness, loading eccentricity, and initial geometric imperfections. To reflect on these effects, the strength reduction factor is defined aswhere Po is the ultimate axial strength of the column cross-section under axial compression. The ultimate axial strengths of Pn and Po are determined by considering the effects of local buckling of the steel tubes.This paper has presented a new multiscale numerical model for the nonlinear inelastic analysis of high strength thin-walled rectangular CFST slender beam-columns under combined axial load and biaxial bending. At the mesoscale level, the inelastic axial load-strain and moment-curvature responses of column cross-sections subjected to biaxial loads are modeled using the accurate fiber element method, which accounts for the effects of progressive local buckling of the steel tube walls under stress gradients. Macroscale models together with computational procedures have been described that simulate the axial load-deflection responses and strength envelopes of CFST slender beam-columns under biaxial bending. Initial geometric imperfections and second order effects between axial load and deformations are taken into account in the macroscale models. New solution algorithms based on the Müller's method have been developed and implemented in the numerical model to obtain converged solutions.The computer program that implements the multiscale numerical model developed is an efficient and powerful computer simulation and design tool that can be used to determine the structural performance of biaxially loaded high strength rectangular CFST slender beam-columns made of compact, non-compact or slender steel sections. This overcomes the limitations of experiments which are extremely expensive and time consuming. Moreover, the multiscale numerical model can be implemented in frame analysis programs for the nonlinear analysis of composite frames. Steel and concrete contribution ratios and strength reduction factor proposed can be used to study the optimal designs of high strength CFST beam-columns. The verification of the numerical model and parametric study are given in a companion paper Influence of the intramedullary nail preparation method on nail's mechanical properties and degradation rateWhen it comes to the treatment of long bone fractures, scientists are still investigating new materials for intramedullary nails and different manufacturing methods. Some of the most promising materials used in the field are resorbable polymers and their composites, especially since there is a wide range of potential manufacturing and processing methods. The aim of this work was to select the best manufacturing method and technological parameters to obtain multiphase, and multifunctional, biodegradable intramedullary nails. All composites were based on a poly(-lactide) matrix. Either magnesium alloy wires or carbon and alginate fibres were introduced in order to reinforce the nails. The polylactide matrix was also modified with tricalcium phosphate and gentamicin sulfate. The composite nails were manufactured using three different methods: forming from solution, injection moulding and hot pressing. The effect of each method of manufacturing on mechanical properties and degradation rate of the nails was evaluated. The study showed that injection moulding provides higher uniformity and homogeneity of the particle-modified polylactide matrix, whereas hot pressing favours applying higher volume fractions of fibres and their better impregnation with the polymer matrix. Thus, it was concluded that the fabrication method should be individually selected dependently on the nail's desired phase composition.The obvious advantages of intramedullary osteosynthesis, such as: a good stabilization of bone fragments guaranteeing elasticity of the fixation, minimal damage of the surrounding tissue and low surgical risk, make it a significant and valuable method of long bone fracture treatment One of the first attempts at applying resorbable materials for intramedullary osteosynthesis was undertaken by Saikku-Bäckström et al. in 2004 -lactide (PLA96). The work was performed using intramedullary nails with SR-PLA96 applied together with Kirschner wires, which were implanted in the fractures of the femoral bone neck of large animals (sheep).The manufacturing and processing methods used in creating polymer composites are key in the control of mechanical properties. Such parameters as homogeneity, interphase bond strength, and distribution of modifiers can be changed depending on the type, volume fraction, and properties of applied additives This work constitutes an attempt at the development of intramedullary nails made of resorbable polylactide reinforced with resorbable magnesium alloy wires or long fibres (alginate and carbon fibres were used). All the applied phases demonstrate the ability of full or partial (in the case of carbon fibres) degradation. It has already been proven by the authors that carbon fibres, after their fragmentation, are able to assimilate with the bone tissue and, moreover, stimulate its growth (the apatite's nucleation begins at the surface of the fibres) In this work, different multiphase, biodegradable intramedullary nails were manufactured using three various methods. The applied methods were: forming from solution, injection moulding and hot pressing. Authors focused on assessing the influence of the particular fabrication method and its technological parameters on the mechanical properties and degradation behaviour of the nails.The following materials were used to manufacture composite nails:-lactide (PLA) — Ingeo™ 3051D, NatureWorks® LLC;long carbon fibres (CF) — Toho Tenax America, HTS 5631 (tensile strength of 4.3 GPa, Young's modulus of 238 GPa and elongation of 1.8%);long calcium alginate fibres (Alg) — Department of Material and Commodity Sciences and Textile Metrology of Lodz University of Technology. The fibres were formed by the wet solution method applying a 7.4% sodium alginate solution in water. The solidification and tension process was performed in a 3% CaCl2 bath (fibre diameter of 17 μm, tensile strength of 220.8 MPa, Young's modulus of 12.7 GPa);magnesium alloy wires (Mg) — Leibniz University of Hannover, Institute of Materials Science. The wires differed in diameter and a composition of an alloy:MgII — dMgII
= 0.97 mm, magnesium alloy with the content of: aluminium 3%, lithium 9%, and calcium up to 1%;MgIII — dMgIII
= 0.5 mm, magnesium alloy containing the main elements: aluminium 5.5–6.5%, zinc 0.8–1.5% and the trace elements up to 1%: lithium, rare earth metals (an alloy addition obtained as rare earth metal ore), and calcium;tricalcium phosphate (TCP) — Sigma-Aldrich® (Ca3(PO4)2
≥ 96.0%);gentamicin sulfate (GS — gemtamicini sulfas) — Interforum Pharma wholesaler in Krakow.Two main groups of composite nails can be specified:PLA reinforced with CF and Alg fibres — to map the anatomic structure of the bone, the fully degradable alginate fibres were placed inside the intramedullary nails, while the partially degradable carbon fibres were placed outsidePure PLA nails and PLA modified with TCP and GS were tested as referenceThree different methods were used to manufacture designed composite nails: forming from solution (S), injection moulding (IM) and hot pressing (HP). The nails were fabricated in two sizes:small nails suitable for rabbit femoral bone — 2.5 mm in diameter, 100 mm long;large nails suitable for human forearm bone — 4.5 mm in diameter, 150 mm long.Polymer solution was prepared by dissolving PLA in dichloromethane CH2Cl2 (POCH) (40 g/100 ml), and then adding gentamicin sulfate distributed in 100 ml of the same solvent. In the next step alginate fibres were preliminary saturated with the PLA + GS solution and pulled through 1 mm cylindrical form to create the nail's core. After the solvent evaporated, a carbon outer layer was formed — alginate core was covered with uniaxially oriented carbon fibre rovings. The whole sample was then saturated with the polymer solution and pulled through a 2.5 mm cylindrical form (it was repeated three times).Samples were left overnight to allow the solvent to evaporate and after that samples were cut into 100 mm nails (2.5 mm in diameter).Nails of the following phase composition were obtained by forming from solution: PLA + CF + Alg + GS (S) — polylactide matrix modified with carbon fibres (20 wt.%), calcium alginate fibres (20 wt.%) and gentamicin (12 mg per implant) (Using the injection moulding method, pure polymer or polymer with tricalcium phosphate nanoparticles and/or gentamicin powder (dependent of the nails' phase composition) was plasticized at 160–170 °C and then injected in a vertical screw injection moulder (MULTIPLAS).Small nails (2.5 mm in diameter, 100 mm long) of the following phase composition were obtained by injection moulding:PLA (IM) — polylactide nail, reference samplePLA + CF + Alg + GS (IM) — polylactide matrix modified with carbon fibres (10 wt.%), calcium alginate fibres (10 wt.%) and gentamicin (12 mg per implant) (Alginate (inner) and carbon fibre (outer layer) cores were prepared by saturating the fibres with the PLA + GS solution (prepared as above) and drawing through a 1 mm cylindrical form. Prepared cores were then placed in a 2.5 mm in diameter mould and the injection moulding of homogenized polymer granulate/gentamicin powder was performed.PLA + Mg + GS (IM) — polylactide matrix modified with MgII and MgIII wires and gentamicin (12 mg per implant) (The first step in the fabrication of the Mg-modified nails was etching of the magnesium alloy wires. The wires were immersed in an etching solution (19 g 100% acetic acid, 5 g sodium nitrate (V), 100 ml distilled water) for 30 s, then rinsed with distilled water and dried in a dryer for 20 min at 70 °C. The MgIII wire was then twisted around a MgII wire and they were both placed in the mould, completing the injection process.Large nails (4.5 mm in diameter, 150 mm long) of the following phase composition were obtained by injection moulding:PLA + TCP + GS (IM) — polylactide matrix modified with tricalcium phosphate (5 wt.%) and gentamicin (20 wt.%)PLA + MgII
+ GS (IM) — polylactide matrix modified with two twisted MgII wires and gentamicin (20 wt.%).Two etched (as described previously) and twisted MgII wires were placed in the mould. A mixture of polymer granulate and gentamicin powder was injected.Large nails (4.5 mm in diameter, 150 mm long; suitable for a human forearm bone) of the following phase composition were obtained by hot pressing.PLA + TCP + GS (HP) — polylactide matrix modified with tricalcium phosphate (5 wt.%) and gentamicin (20 wt.%)The PLA granulate mixed with TCP and GS was poured into the form and heated to 145 °C. The forms were then pressed under 5 MPa in a hydraulic press.PLA + MgII
+ GS (HP) — polylactide matrix modified with two twisted MgII wires and gentamicin (20 wt.%)Two etched (as described previously) and twisted MgII wires were placed in the form, then the PLA granulate mixed with GS was added. The sample was heated to 145 °C and pressed under 5 MPa in a hydraulic press.PLA + CF (HP) — polylactide matrix modified with 1D carbon fibres (40 wt.%)The carbon fibre rovings were interlayered with the polymer granulate in the form, which was then heated to 165 °C and pressed under 5 MPa in a hydraulic press.PLA + CF + Alg (HP) — polylactide matrix modified with 1D calcium alginate fibres (20 wt.%) and 1D carbon fibres (20 wt.%)The calcium alginate fibres and carbon fibre rovings were interlayered with the polymer granulate in the form. In the next step the form was heated to 165 °C and samples were pressed under 5 MPa in a hydraulic press.PLA + CF + Alg + TCP + GS (HP) — polylactide matrix modified with 1D calcium alginate fibres (20 wt.%), 1D carbon fibres (20 wt.%), tricalcium phosphate (5 wt.%) and gentamicin (20 wt.%)The calcium alginate fibres and carbon fibre rovings were interlayered with the polymer granulate mixed with TCP particles and GS powder. In the next step the form was heated to 165 °C and samples were pressed under 5 MPa in a hydraulic press.The nails were incubated in distilled water at 37 °C for 12 weeks. Mass to volume ratio was set to 1 g/50 ml. The tests included the measurements of pH (Elmetron CP-411, 0.01 pH accuracy) and conductivity (Elmetron CC-411, 0.1 μS/cm accuracy) changes of the incubation fluids. All tests were triplicated.Mass changes of the nails were also analyzed. Samples were weighed on RADWAG PS 360/C/2 (± 0.001 g). Mass loss values were calculated according to the following equation:The measurements were taken after 24, 48 and 96 h in the first week and then — once per week.The mechanical properties (bending strength and Young's modulus) of the obtained nails were determined using the three point bending test according to the PN-EN ISO 14125:2001 and PN-EN ISO 178. The tests were performed on a universal testing machine Zwick 7000 type 1435, compatible with the TestXpert v.8.1 program, with the deformation rate of 2 mm/min. The mechanical tests were conducted on initial samples as well as on samples after 8 and 12 weeks of incubation. Summary statistics were calculated and are presented as the median value. The error bars represent standard deviations.Scanning Electron Microscopy (SEM) was used to observe the microstructure of the obtained composite materials, the distribution of their phases and the state of interphases, as well as the changes in microstructure taking place during incubation. The tests were performed using Nova 200 NanoSEM electron microscope (FEI Company) on initial samples and those incubated in distilled water for 8 and 12 weeks.The nails were manufactured using three methods: forming from solution, injection moulding and hot pressing. The first two methods were used to obtain smaller nails adapted to the dimensions of a rabbit's femoral bone (2.5 mm in diameter and 100 mm long). Due to the technological difficulties, it was impossible to obtain such small nails by hot pressing. Hence, the hot pressed nails were larger: 4.5 mm in diameter and 150 mm in length, which corresponds to the dimensions of intramedullary nails used in a human forearm bone. In order to assess the influence of the preparation method on the properties of the implant, large nails adapted to a forearm bone were also produced by injection moulding.The technological parameters (temperature, plasticization time in high temperature methods, solution concentration and homogenization technique in the forming from the solution method) were selected experimentally. The difficulties were as follows: the presence of bubbles in the hot pressing method, the degradation of the polymer manifested by increased brittleness as a result of too high temperature of the process, the agglomeration of fillers, the difficulty to impregnate fibres, excessive shrinkage and bubbles appearing while solvent vaporized in the forming from the solution method. Due to the occurring difficulties, it was not possible to obtain all the phase contents of the nails in the particular methods. The work presents the results achieved once the technology was optimized.Samples obtained by forming from solution and injection moulding were incubated in distilled water in 37 °C. The changes of incubation fluids' pH and conductivity values were analyzed. Significant differences in the behaviour of particularly fabricated materials in the water environment were noted (A) was observed in the case of the samples modified with magnesium alloy wires obtained by injection moulding (PLA + Mg + GS(IM)). Already after the fourth day of incubation, the pH reached its maximum and maintained the pH = 10 level for the whole period of twelve weeks' incubation. Increases in conductivity values were also observed (B). Those significant changes resulted from the corrosion of magnesium and the release of Mg2 + ions of basic character Despite significant pH and conductivity changes, the degradation of Mg wires – even after the 12th week of incubation – was not visible in the microstructure of the nails (). SEM cross-section images showed very good adhesion at the wire–matrix interphase in the case of Mg-reinforced nails. The incubation of the material in distilled water did not cause any significant changes in the character of the interphase. Both after 8 and 12 weeks, no cracks or fissures were observed, which could have appeared as a result of the polymer's degradation or the corrosion of Mg wires. Good adhesion was assured by etching the wire surface before the nail moulding. In this way, a significant change in the wire surface microstructure was achieved (). The etching removed minor impurities, loosely bounded fragments and made the surface porous. Lack of microstructural changes proved that the degradation process was neither advanced nor rapid, and the PLA matrix properly protected the wires. The corrosion probably affected only those areas of wires that have not been covered properly with the polymer during the injection, e.g. their endings.The pH changes observed for the carbon and alginate fibre-reinforced nails were not significant. A slight pH decrease (to the levels of 6–) was recorded only after the first incubation day and then pH remained at a neutral level. The initial decrease was a result of the gentamicin release, which was confirmed by Morawska-Chochol et al. Differences resulting from the type of fabrication method were visible in ion conductivity variations (B). The conductivity values changed the most in the case of PLA + CF + ALG + GS(S) nails formed from solution, whereas they were almost half as small in the case of analogical nails obtained by injection moulding (IM). This can be explained by the fact that the polymer matrix in nails formed from solution did not assure proper protection against degradation of alginate fibres. Particular fibrous phases were differently arranged depending on manufacturing methods of the nail. When forming from solution, the fibres were present in the whole PLA matrix volume. As a result, fibre–polymer matrix interphases were present not only in the volume of the nails, but also on their surface. This facilitated water diffusion into the nails and the release of degradation products into the environment. In contrast, the nails that were obtained by injection moulding had only a fibrous core and the outer layer was a compact polymer matrix. This made fluid penetration into the nails more difficult.These conclusions are confirmed by the SEM images () — the microstructure of the nails formed from solution significantly loosened during incubation time. After 8 weeks, empty spaces appeared among the fibres in both carbon and alginate reinforced nails. The nails obtained by injection moulding were affected by such changes after 12 weeks of incubation.The above observations concerning the nail degradation were confirmed by their mass changes (). The highest decrease in mass value is visible for the PLA + CF + Alg + GS(S) nails formed from solution and it can be explained by the degradation of the alginate fibre core. In nails obtained by injection moulding (both with carbon and alginate fibres and with magnesium wires) mass loss values are significantly lower. As it was mentioned earlier, the microstructure of outer parts of those nails was much more compact, hence inner phases of composites were better protected from the influence of aqueous environment of incubation fluids.Mechanical tests indicated that each of the applied reinforcements positively influenced the mechanical properties of the nails (). The highest increase in strength values was observed for the PLA + Mg + GS(IM) and PLA + CF + Alg + GS(IM) nails obtained by injection moulding. However, significant scattering of results in the case of fibre-reinforced nails attests to the lack of repeatability. In the injection moulding method, the introduction of carbon fibres into the polymer matrix significantly improved the bending strength of the composite (the average increase of 70%, but considering the best obtained result — over 100%), as well as its Young's modulus (about 150% increase). The analogise composite obtained by forming from solution (PLA + CF + Alg + GS(S)) showed lesser improvement in mechanical parameters (strength increase of 20%), even though the fibre volume fractions were doubled as compared to the nails obtained by injection moulding. Most likely, it was a consequence of the sample forming technique and weak fibre–matrix interphases coming from insufficient impregnation of the fibres with polymer solution. Weak fibre–matrix interphase did not assure the appropriate transfer of stresses on the fibres and caused its rapid delamination.In contrast, good adhesion of the polylactide matrix to the Mg wire surface (discussed above and presented in ) ensured stability of Mg-nail mechanical properties during the first 12 weeks of incubation. The decrease in mechanical parameters was observed only after this time period (After the 8th week, the strength values of the PLA + CF + Alg + GS nails, independent of the forming method, were reduced by about 50%. This resulted from the degradation of alginate fibres in the nail core. Furthermore, the nails became deformed during incubation. shows the photographs of macroscopic changes in the nails after 12 weeks of incubation in distilled water. The deformation was connected with the difficulty in the axial positioning of the core (containing the fibres) in the PLA matrix, as it shifted during the injection to the bottom of the mould.The mechanical tests performed on hot pressed, larger-sized nails corresponding to nails used to stabilize forearm bone fractures showed a significant advantage of the composites reinforced with carbon fibres. With the addition of subsequent modifying phases, that is: alginate fibres, tricalcium phosphate nanoparticles and gentamicin particles, the strength of the nails decreased gradually. However, even the most complex composite nails (PLA + CF + Alg + TCP + GS nails) were still stronger (over 200 MPa) than the nails discussed above obtained by injection moulding or formed from solution (). In the case of the nails with fibrous reinforcement, the bending strength was much higher than for bone tissue (120 MPa). This value should be sufficient to ensure long bone fracture stabilization B) was close to the value of the Young's modulus of the bone (10–40 GPa) In the case of the other composites, the strength of nails obtained by injection moulding was higher, which was especially evident for the nails with Mg wires. This was connected with the more homogeneous distribution of ceramic and drug particles in the polymer matrix after the injection. In contrast, in the hot pressing method, the particles formed agglomerates and despite the pressing, there were some local pores left.It was demonstrated that the fabrication method of polymer-based nails significantly affects their mechanical properties and degradation behaviour. With the first method, forming from solution, it was challenging to fabricate samples with reproducible properties. Injection moulding assured higher uniformity and homogeneity of the polymer matrix containing ceramic and antibiotic particles in the case of Mg-reinforced nails. The final method — hot pressing, was the most applicable for the fibre-reinforced nails, as it allowed for using higher volume fractions of fibres and their better impregnation with the polymer matrix. This study showed that the fabrication method of novel polymer-based nails should be individually selected depending on desired phase composition of the nails.Effects of additives on dual-layer hydrophobic–hydrophilic PVDF hollow fiber membranes for membrane distillation and continuous performanceThe advantages of the implementation of dual-layer hydrophobic–hydrophilic hollow fiber membranes for membrane distillation (MD) have been highlighted in this work. The effects of incorporating methanol as a non-solvent additive and self-synthesized fluorinated silica (FSi) particles as a hydrophobic modifier on the resultant membrane morphology and MD performance were investigated. Employing a 3.5 wt% sodium chloride solution at 80 °C, the highest direct contact membrane distillation (DCMD) flux of 83.40±3.66 kg/(m2
h) and separation factor higher than 99.99% were attained for the membrane spun with methanol additive. Moreover, the stability of the dual-layer hydrophobic–hydrophilic hollow fiber membrane has been demonstrated through continuous DCMD experiments for 5 days. The separation factor was maintained higher than 99.99% for the membrane spun with methanol additive, verifying the suitability of the dual-layer hydrophobic–hydrophilic hollow fiber membrane configuration for desalination processes. The morphological transformation of the outer membrane surface from a porous agglomerated globule structure into a denser interconnected globule structure may be accounted for by the stability improvement of the membrane spun with methanol additive. On the other hand, it was found that an enhanced hydrophobicity of the membrane spun with FSi particles did not result in an improvement of the membrane stability. The existence of the hydrophilic hydroxyl group on the FSi particle surface may favor the occurrence of membrane wetting.► Application of dual-layer hydrophobic–hydrophilic hollow fiber membranes in MD is proven advantageous. ► Incorporation of methanol additive improves membrane stability under continuous MD operation. ► Addition of methanol transforms the morphology from porous agglomerated globule into denser interconnected globule. ► Membrane hydrophobicity is enhanced with FSi particles additive. ► The existence of the hydrophilic hydroxyl group on the surface of FSi particles may induce membrane wetting.Water crisis, which is defined as shortage in the availability of fresh water resources relative to its demand, has been considered as one of the most important issues in this century. As the world population continually increases, water shortage is predicted to become more severe in the future (). Water crisis is also exacerbated by the limited availability of fresh water resources on earth. From the total amount of 1360 million km3 of water on earth, only about 37 km3 comprises fresh water. The amount of accessible fresh water is further reduced to around 0.126 km3 as the rest of the fresh water is stored in inaccessible ground water or locked in icecaps (). To overcome these problems, desalination processes have received great attention as an alternative route for fresh water production from saline water.). The highly fluctuating crude oil price towards higher prices further reduces their competitiveness. On the other hand, reverse osmosis (RO) process is limited by the saline water concentration and fouling (). Among various attempts to develop more versatile desalination processes, MD process, an old technology that was firstly patented by , stands out and receives worldwide attention. MD operability at a lower temperature and pressure has made it outstanding compared to conventional desalination processes (). Furthermore, the feasibility of MD to be coupled with solar () or low-grade heat sources intensifies its attractiveness (The working principle of MD is the utilization of a porous hydrophobic membrane as a physical barrier between the hot feed side, where an aqueous solution is evaporated, and the distillate side, where the transported water vapor is condensed. Obviously, membrane hydrophobicity plays an important role in ensuring that only water vapor gets transported across the membrane while inhibiting the penetration of liquid feed. Based on this concept, a total rejection of non-volatile solutes can be theoretically achieved in MD (). In addition to water repellency property, MD membranes should also exhibit 2 main features: (1) low thermal conductivity to reduce conductive heat loss and (2) low transport resistance towards diffusion of vapor molecules to enhance permeation flux. These features require membrane scientists to exclusively design membranes with desirable morphological and transport properties.Awareness of the coupling effect between mass and heat transfer phenomena is essential in designing membranes for the MD process (). A good membrane should maximize the extent of mass transport, yet minimize the extent of heat transport. Thus, compared to other membrane separation processes, the membrane parameters may have different effects on MD performance (flux and separation). Considering mass transfer alone, the relation between membrane parameters and the resultant MD flux can be written as follow (where N is the molar flux, r is the membrane mean pore size, α is a constant factor that equals 1 for the Knudsen diffusion and 2 for viscous flow, ε is the membrane porosity, δm is the membrane thickness, and τ is the membrane tortuosity. According to Eq. , a thinner membrane is favorable for mass transfer as it reduces resistance for the transport of water vapor. On the contrary, a thinner membrane increases conductive heat loss through the membrane matrix (). It was reported that by modeling the competing effect between mass and heat transports, an optimum membrane thickness was estimated to be in the range of 30–60 μm (The hydrophobic–hydrophilic membrane configuration for MD was first introduced by . Tailoring membrane thickness within the optimized range becomes possible with this configuration as the hydrophilic sub-layer beneath can provide mechanical support. Following this, there have been a number of publications on the fabrication of hydrophobic–hydrophilic membranes using various methods. Modification of cellulose acetate membranes by a radiation graft polymerization method was reported by while modification of cellulose nitrate membranes by a plasma polymerization method was reported by . However, the additional modification step required by both approaches moderates their competitiveness. One-step fabrication of hydrophobic–hydrophilic composite membrane was proposed by were the first to propose the fabrication of hydrophobic–hydrophilic hollow fiber membranes by a dual-layer co-extrusion spinning technology. By increasing thermal conductivity properties of the hydrophilic sub-layer with the aid of graphite particles and multi-wall carbon nanotubes (MWNT), enhanced the MD flux of the hydrophobic–hydrophilic hollow fiber membranes.Depending on the degree of severity, membrane wetting was classified into four categories, i.e. non-wetting, surface wetting, partial wetting, and fully wetting (). In the case of surface wetting, the interface of the liquid and vapor is shifted inward of the membrane cross section. Nevertheless, distillate with a high purity can be produced as long as the gaseous gap between the feed and the distillate is maintained. As the MD operation continues, the feed and distillate solutions may penetrate deeper, resulting in a partial membrane wetting. In the case of partial wetting, the MD operation can be continued if the majority of the pore channels are dried though a gradual decline of the distillate purity is normally observed. Membrane wetting has been regarded as one of the major barriers for the industrial implementation of MD process (). Thus, research efforts have been devoted to the development of MD membranes with better wetting resistance. However, at present, most of the developed membranes still suffer certain degree of wetting.Several mechanisms were proposed to explain the wetting phenomenon: (1) membrane fouling and scaling (), (2) a large gap between hydraulic pressure at the opposing sides of the membrane (), (3) formation of bigger membrane pores under high pressures (), and (4) oxidation of hydrophobic groups on the membrane surface to form hydrophilic chemical moieties, such as carbonyl and hydroxyl groups (). The longest MD operation of a single-layer polypropylene (PP) hollow fiber membrane in which RO permeate was employed as a feed was reported by . It was found that during the 3 years' operation time, the membrane surfaces are firstly wetted and as the MD operation continues, the liquid penetrates deeper towards the membrane cross-section, resulting in the flux decay and separation performance deterioration.According to previously explained wetting mechanisms, a thinner membrane may be more prone towards wetting and hence, questions may arise on the applicability of hydrophobic–hydrophilic membranes for MD application. Interestingly, based on the authors' best knowledge, the wetting propensity of hydrophobic–hydrophilic membranes under long-term MD operation has not been investigated by any researchers. Therefore, the objectives of this study are as follows: (1) to design the dual-layer hydrophobic–hydrophilic hollow fiber membranes with suitable morphological and transport properties by understanding the mechanism of phase inversion process; (2) to explore the effects of methanol as a weak non-solvent additive and fluorinated silica particle as a hydrophobic modifier on the membrane formation, membrane morphology, and the resultant MD performance; and (3) to investigate the stability and wetting resistance of the fabricated dual-layer hydrophobic–hydrophilic hollow fiber membranes under continuous DMCD operation.Commercial polyvinylidene fluoride (PVDF) HSV 900 was purchased from Arkema Inc. while commercial polyacrylonitrile (PAN) was kindly provided by Prof. Juin-Yih Lai and Prof. Hui-An Tsai from Chung Yuan Christian University of Taiwan. Both PVDF and PAN powders were dried at 60 °C overnight under vacuum before using. Hydrophilic cloisite NA+ clay particles were purchased from Southern Clay Products. N-methyl pyrrolidone (NMP) as a solvent, methanol (MeOH) as a non-solvent, and ethylene glycol (EG) as a pore-forming additive were purchased from Merck. Heptadecafluoro-1,1,2,2-tetrahydrodecyl)triethoxysilane (FOS) and tetraethyl orthosilicate (TEOS) for the synthesis of FSi particles were supplied by ABCR and Sigma Aldrich, respectively. Ethanol from Merck and aqueous ammonium hydroxide (28–30%) from Sigma Aldrich were used as a solvent and a catalyst for the synthesis of FSi particles, respectively. Sodium chloride was purchased from Merck and deionized (DI) water was produced by a Milli-Q unit from Millipore. All of the chemicals were of reagent grade and used as received.The synthesis procedure of FSi particles was derived with modifications from the method described by . The method consists of five steps. Firstly, TEOS (5 ml) together with FOS (1.32 ml) was dissolved in ethanol (25 ml) under stirring at room temperature. Next, DI water (1 ml) was added dropwise and then, an aqueous ammonium hydroxide solution (5 ml) was fed into the reaction mixture under an intensive stirring. Afterwards, the mixture was continuously stirred for 12 h to allow the hydrolysis, polycondensation, and fluorination reactions of the reactants to occur. Next, the unreacted FOS and TEOS molecules were removed by filtering the resultant particles using the PTFE membrane filter with the average pore size of 0.22 μm from Millipore. The retained particles were dispersed in ethanol and then the dispersion was subsequently filtered. The filtering and washing procedure was repeated three times before the FSi particles were finally dried at 70 °C under vacuum for 48 h. The reactions route for synthesis of the FSi particles is presented in The structure of FSi particles was observed by scanning electron microscopy (SEM) on a JEOL JSM-5600LV unit. The samples for SEM were prepared by drying a dilute dispersion of the FSi particles in ethanol on a carbon coated copper grid. The size distribution of the FSi particles was analyzed using a dynamic light scattering technique on a Zetasizer Nano system. The fluorination on the silica particles was confirmed by X-ray photoelectron spectrometry (XPS) and Fourier transform infrared spectroscopy (FTIR) analyses. The XPS analysis was conducted on a Kratos AXIS Ultra DLD spectrometer with the source of a monochromatised AlKα. The functional groups on FSi particles were identified by an IR method on a Bio-Rad FTIR FTS 135 over the range of 700–4000 cm−1 with the total of 16 scans for each sample. The samples for FTIR were prepared by mixing the ground silica particles (2 mg) and KBr (98 mg) and then, the mixtures were compressed to form the pellets.A polymer solution was prepared by dissolving the dried PVDF powder (12 wt%) in NMP (88 wt%) under vigorous stirring until a homogeneous solution was attained. The polymer solution was then casted with a casting knife of 250 μm thickness on a glass plate, followed by immersion in coagulant baths containing pure water or different compositions of water/methanol. Afterwards, the as-cast membranes were transferred into water for solvent exchange. After 3 days of solvent exchange, the membranes were freeze dried for further characterizations. Flat sheet membranes casted in the pure water coagulant were labeled as FM-0, membranes casted in the mixture of 40/60 wt% methanol/water coagulant were labeled as FM-40, and membranes casted in the mixture of 80/20 wt% methanol/water coagulant were labeled as FM-80.). The detailed dope compositions and spinning parameters are summarized in The rheological properties of polymer solutions were studied using an advanced rheological extension system (ARES) from Rheometrics Scientific. The shear viscosity was measured using a 25 mm cone-and-plate geometry at 25 °C with the shear rate in the range of 1–100 s−1.The membrane morphologies were observed by SEM on a JEOL JSM-5600LV unit. The membrane cross-sectional images were obtained by immersing and fracturing membranes in liquid nitrogen. The samples were coated with platinum using a JEOL-JFC-1300 coater before analysis.The measurement of the membrane maximum pore size was conducted with a CFP-1500 AE capillary flow porometer from Porous Materials Inc. (PMI). The membrane maximum pore size was calculated based on the lowest pressure at which the gas flow was detected as the Porewick™-impregnated membrane was pressurized with nitrogen gas. The overall membrane porosity was calculated from the ratio of the pore volume to the total volume of the membrane. The membrane pore volume was determined by measuring the increment on the membrane mass before and after being fully impregnated with kerosene.The mechanical properties in terms of strain at break, tensile stress at break, and Young's modulus for hollow fiber membranes were characterized with an Instron tensiometer (Model 5542) from Instron Corp. at room temperature. The fiber was clamped at both ends with an initial gauge length of 50 mm. A constant elongation rate of 50 mm/min was fixed for all measurements. For each spinning condition, the average value obtained from at least five samples was reported.DCMD experiments were carried out using a laboratory scale MD unit, whose details have been described in our previous works (). Membrane modules were prepared by assembling 10 fibers inside a 3/8" polypropylene fitting with the modules length fixed at 10 cm. To match typical seawater salinity, a saline solution with 3.5 wt% of sodium chloride (NaCl) was prepared and employed as the MD feed. The typical conductivity of the feed solution was 50.93 mS/cm. The feed inlet temperature was varied between 50±0.5 °C and 80±0.5 °C and circulated through the shell side of the modules with a flow velocity of 1.4 m/s. The DI water employed as the circulated distillate was cooled down to 17±0.5 °C and flowed co-currently through the lumen side of the hollow fiber membranes with a flow velocity of 0.7 m/s.For continuous DCMD experiments, the DCMD unit was operated 24 h per day until a total operating period of 120 h for each module was attained. The feed inlet temperature was fixed at 80±0.5 °C and other operating conditions were similar to those described above. This high feed temperature was selected to induce a noticeable performance difference between the various membranes tested as a high temperature gap between feed and distillate was reported to facilitate membrane wetting (). The collected distillate was recycled back to the feed tank to maintain the salinity of the feed.The concentrations of NaCl in the feed and distillate solutions were determined by a Lab 960 conductivity meter from Schott Instruments. The separation factor (β) and water vapor permeation flux (Jv) were calculated using the following equations:where Cd and Cf correspond to the concentrations of NaCl in the distillate and feed solutions, respectively, Mw is the mass of the transported water vapor (kg), n represents the number of hollow fiber membranes assembled in one module, do refers to the outer diameter of the hollow fiber membrane (m), L is the effective module length (m), and t indicates the sampling time (h).The membrane thermal efficiency (EE) is defined as the ratio of the latent heat utilized for evaporation of water from the feed to the overall heat transported through the membrane. In a well insulated MD unit where the distillate is circulated in the fibers lumen side, the overall heat can be calculated from the enthalpy change of the distillate as follows:EE=JvΔHvAJvΔHvA+hm(Tfm−Tdm)A=JvΔHvAνdCd(Tdo−Tdi)where A is the effective membrane area (m2), ΔHv corresponds to the latent heat of evaporation (J/kg), hm is the membrane heat transfer coefficient (W/K m2), Tfm and Tdm refer to the temperatures of membrane surface at the shell side and lumen side (K), respectively, νd indicates the distillate flow rate (kg/s), Cd is the distillate specific heat (J/kg K), and Tdi and Tdo refer to the temperatures of the distillate at the module inlet and outlet (K), respectively.. It can be observed that different membrane cross-sectional morphologies can be developed by altering the coagulant composition. Membranes casted with pure water or 40/60 wt% methanol/water possess 2 types of morphology: (1) finger-like macrovoid near the top surface and (2) cellular structure near the bottom surface. The macrovoid structure can be fully eliminated when the methanol content is increased to 80 wt%. This structural distinction indicates the occurrence of different precipitation rates during phase inversion, which can be explained using the concept of solubility parameter. The solubility parameters of polymer, solvent, and non-solvents employed in this work are summarized in ). The difference in solubility parameter between polymer and non-solvents increases in the order of 80/20 wt% methanol/water<40/60 wt% methanol/water<water. Normally, a larger gap in the solubility parameter favors the occurrence of an instantaneous demixing (i.e. a fast precipitation rate) and hence, membranes with finger-like macrovoid structures are formed (). The inhibition of the coagulant intrusion into the casted film resulting from the suppression of water activity with increasing methanol content could be another plausible reason for the observed structural distinction (The phase inversion is also affected by a mutual diffusion between solvent and non-solvent. Selection of a non-solvent with a high diffusivity towards the solvent is beneficial to accelerate the demixing process and vice versa (), the diffusivities of non-solvents towards NMP as the solvent follow the order 80/20 wt% methanol/water<40/60 wt% methanol/water<water. These results show that from both kinetic and thermodynamic aspects, the addition of methanol as a weak non-solvent in the coagulant favors the occurrence of delayed demixing (i.e. a slow precipitation rate), resulting in membranes with a macrovoid-free structure. A macrovoid-free structure is desirable for MD application as proposed by our research group () because it possesses a higher resistance towards wetting. This hypothesis was later confirmed by under long-term DCMD operation. Therefore, a mixture of methanol/water with methanol content of 80 wt% is selected as the standard external coagulant for the fabrication of dual-layer hydrophobic–hydrophilic hollow fiber membranes.Another significant finding is that the incorporation of methanol in the coagulant also causes transformation of membrane morphology from cellular to globules that can be apparently observed from the images of membranes top surface and cross section (). PVDF as a semi-crystalline polymer has been reported to undergo two types of demixing process: (1) liquid–liquid demixing process that develops membranes with cellular morphology in which the pores are formed from the polymer-lean phase while the membrane matrix is formed from the polymer-rich phase and (2) solid–liquid demixing process that develops membranes with interlinked semi-crystalline particles morphology (). Therefore, it can be concluded that the addition of methanol into water coagulant can thermodynamically and kinetically decelerate the precipitation process and hence, provide sufficient time for the solid–liquid demixing process to occur. The formation of a membrane with a globules structure can enhance the membrane surface porosity and roughness, leading to an abrupt increase of the membrane contact angle as presented in . This result is in agreement with the work done by To ensure a non-wetting characteristic under MD operation, the ideal material for MD membranes is required to possess a low free surface energy. In this respect, polytetrafluoroethylene (PTFE) with a low free surface energy of 18.5 mN/m and polyethylene (PE) of 20–25 mN/m are preferable compared to PVDF with a surface energy of 30.3 mN/m (). However, polyethylene has a low melting point, while PTFE is difficult to be processed. PVDF is more processable as it can be dissolved in common organic solvents and hence, membrane fabrication by the non-solvent induced phase inversion process is possible. In order to lower surface energy, we attempt to incorporate self-synthesized FSi particles into the outer layer of the dual-layer PVDF hollow fiber membrane. The SEM image and particle size distribution of FSi particles are illustrated in . The resultant particles are spherical in shape with an average diameter of 800 nm. The XPS analysis on the particle surface reveals the presence of carbon (C), oxygen (O), fluorine (F), and silicon (Si) elements as summarized in . Comparison of molar ratio between FSi particles (NC/NO/NF/NSi=28.26/26.41/33.71/11.63) and FOS molecule (NC/NO/NF/NSi=45.2/9.7/41.9/3.2) allows roughly estimation for the contribution of FOS and TEOS molecules on the resultant FSi particles. FOS and TEOS molecules contribute to around 23% and 77%, respectively, of the Si compound on the surface of FSi particles, which is higher than the initial FOS/TEOS ratio of 17/83. A similar fluorine enriched particle surface phenomenon was also reported by shows the morphology of dual-layer PVDF hollow fiber membranes with various formulations for the outer layer spinning solution while the composition of the inner layer spinning solution is fixed. From the cross-sectional images, it is apparent that all membranes exhibit a similar morphological feature with a macrovoid-free globular structure in the hydrophobic outer layer while the hydrophilic inner layer comprises a layer of macrovoids near the inner edge. The formation of macrovoids in the inner layer is possibly caused by the incorporation of an internal coagulant (bore fluid) with higher water content of 40 wt%. Moreover, the formation of macrovoids is also triggered by the addition of EG into the inner layer spinning solution, which possesses a good affinity with the water coagulant (). In MD processes employing dual-layer hydrophobic–hydrophilic membranes, only the hydrophobic layer is responsible for the separation while the hydrophilic layer is intended to be fully wetted with the circulating distillate. The presence of a porous hydrophilic supporting layer mitigates the occurrence of temperature polarization at the distillate side as PVDF was reported to have a lower heat conductivity compared to water (). Therefore, the formation of a layer of macrovoids in the hydrophilic layer is favorable as a higher volume percentage can be occupied by the more conductive liquid water (Despite the differences in thermodynamic characteristics of the outer layer (hydrophobic) and inner layer (hydrophilic), the two layers are tightly adhered to each other as can be observed from the images of membranes outer edge in . The strategy to form the delamination-free dual-layer hollow fiber membranes in this work is by selecting PVDF as a major polymeric compound for both outer and inner layer spinning solutions. Consequently, both layers are thermodynamically compatible, allowing the counter-diffusion process between both layers to occur during phase inversion (). The formation of dual-layer hollow fiber membranes with a delamination-free structure is desirable for MD as the hydrophilic inner layer can provide a uniform mechanical support for the thinner hydrophobic outer layer.A close observation of the images of the outer layer-outer membrane surface in reveals that there is a significant decrease in the average globule size when additives are added into the outer layer spinning solution. The outer layer-outer surface of the DL-0 membrane spun from a binary PVDF/NMP mixture shows an agglomerated globules structure with the individual globule having an average diameter of 0.714±0.102 μm. On the other hand, when methanol is added into the spinning solutions, the outer surface morphology of DLM-0 membrane shows an interconnected globules structure with the individual globule having a smaller average diameter of 0.357±0.051 μm. This structural distinction can be attributed to the different phase inversion period. Generally, the diameter of spherulitic globules corresponds to the time available for solid–liquid demixing; for instance, a shorter time results in the formation of a smaller globule. Considering the thermodynamic aspect of the phase inversion process, the addition of methanol into the spinning solution accelerates the phase inversion period by shifting the initial composition closer to the gelation line. Moreover, the addition of methanol also reduces the spinning solution viscosity () and thus, kinetically accelerates the inward diffusion of the external coagulant towards the nascent fibers. As a result, the DLM-0 membrane undergoes faster phase inversion than the DL-0 and has a smaller globule size. In contrast to the diluting effect of a pure methanol additive, the spinning solution of the DLM-5 membrane becomes more viscous when a dispersion of FSi particles in methanol is added as shown in . Nevertheless, the outer surface morphology of the DLM-5 membrane shows a similar globule size to that of the DLM-0 membrane, suggesting that the thermodynamic aspect is possibly more dominant in the phase inversion process evaluated in this work.The advancing contact angle, maximum pore size, and porosity of the as-spun membranes with and without additives are summarized in . The advancing contact angle increases when the additives are incorporated into the spinning solution. The DLM-5 membrane exhibits the highest advancing contact angle of 139.84±2.15° owing to the positive contribution of a low surface tension fluorocarbon compound from FSi particles. The XPS analysis shown in indicates the presence of Si element. This result verifies the existence of FSi particles on the DLM-5 membrane surface. On the other hand, a reduction of membrane porosity and maximum pore size () is observed when methanol (DLM-0) or methanol and FSi particles (DLM-5) are incorporated into the spinning solutions. The effect is more pronounced for the DLM-5 membrane possibly due to its higher total solid loading in the outer layer spinning solution compared to the DL-0 and DLM-0 membranes. Moreover, the effects of additives on the membrane mechanical properties are tabulated in . In general, all membranes fabricated in this study possess high Young's modulus, which is typically observed on the mixed matrix polymeric membrane and inorganic additive. As reported by , the addition of methanol into the dope solution reduces the Young's modulus due to the suppression of globules–globules interactions by facilitation of short-range crystallization. On the contrary, the incorporation of the FSi particles increases the Young's modulus owing to the reinforcement effect of the silica particles. Equipped with high contact angle, small maximum pore size, and stronger mechanical properties, DLM-5 membrane possesses the potential for application in MD operation as those membrane features may ensure non-wetting characteristic and membrane stability under long-term operation (The resultant DCMD flux as a function of the feed inlet temperature is presented in . The general trend where the water vapor flux increases exponentially with increasing feed inlet temperature is observed. This is due to the fact that the water vapor pressure increases exponentially with increasing temperature, resulting in an increment of driving force for water vapor transport. Comparison of the DCMD fluxes between the membrane fabricated in this work and literature data is tabulated in . The resultant DCMD flux outperforms other previously reported hollow fibers (). It is important to mention that the comparably high flux reported by was achieved through application of a triple layer membrane configuration in which a thin layer of sponge-like structure is sandwiched between two thick layers of finger-like macrovoids. The relatively high fluxes achieved for all membranes fabricated in this study are most likely resulted from a low barrier for water vapor transport resulting from the application of hydrophobic–hydrophilic dual-layer membrane strategy. Moreover, the separation factor higher than 99.98% and thermal efficiency higher than 70% (feed inlet temperature of 80 °C) are achieved for all membranes tested.At the feed inlet temperature of 80 °C, the highest water vapor flux of 83.40±3.66 kg/(m2
h) is achieved for the DLM-0 membrane whereas comparable fluxes of 77.00±2.54 kg/(m2
h) and 74.89±3.10 kg/(m2
h) are achieved for the DLM-5 and DL-0 membranes, respectively. Referring to membrane characterizations in , even though the DL-0 membrane possesses the thinnest hydrophobic functional layer, biggest maximum pore size, and highest overall porosity, the DL-0 membrane achieves the lowest DCMD flux. The plausible reason is that the thick hydrophilic supporting layer of the DL-0 membrane may facilitate temperature polarization at the distillate side, which causes the distillate temperature increment at the interface between hydrophobic outer layer and hydrophilic inner layer. Hence, the driving force for water vapor transport is subsequently declined. This result suggests the eminence of designing the dual-layer hollow fiber membrane with the lesser thickness of the hydrophilic supporting layer to minimize the negative contribution of temperature polarization at the distillate side. As for the DLM-5 membrane, the moderate DCMD flux obtained can be mainly accounted to its smallest maximum pore size and lowest overall porosity as summarized in Through investigation of the membrane performance during short-term DCMD experiments, the applicability of the dual-layer hydrophobic–hydrophilic membrane for MD processes has been demonstrated. However, it is more convincing for the industrial end-users to implement the dual-layer hydrophobic–hydrophilic membrane strategy if the membrane stability is also investigated during long-term operation. For this purpose, a continuous DCMD experiment for all dual-layer hydrophobic–hydrophilic hollow fiber membranes fabricated in this work was conducted over a period of 120 h. The resultant fluxes and separation factors of continuous DCMD operations are plotted in that a gradually declining flux with increasing operation time is observed for all membranes. However, this flux decay phenomenon should not be solely associated to the incorporation of the thin hydrophobic functional layer of the dual-layer hydrophobic–hydrophilic membrane. A thorough review on MD literatures reveals that a similar phenomenon was also observed on single-layer membranes fabricated from PVDF or even from materials with a lower free surface energy, such as polypropylene (PP) and PTFE (). It is suggested that the permeation flux decay is attributed to the wetting of the membrane surface pores. Consequently, the interface of the liquid and vapor is shifted inwards of membrane cross section, facilitating temperature polarization and suppressing the MD process efficiency.Besides, even though the membrane separation factors are slightly reduced with increasing operation time, a separation factor higher than 99.98% can be maintained throughout the entire experiments for all membranes as shown in . The intensity of reduction of membrane separation factor allows roughly estimation of the progressivity of partial membrane wetting. As mentioned earlier, the membrane with the highest contact angle and smallest maximum pore size generally possesses the highest resistance towards wetting. However, this may not be the case for the DLM-5 membrane as it displays the lowest separation factor and correspondingly, the highest rate of partial membrane wetting. It is important to note that the scaling inducing wetting phenomenon might not be the reason for the surface and partial wetting observed in this work. The membrane outer surface images before and after continuous experiments presented in reveal that the membranes outer surface remains clean of scaling. Moreover, both XPS and SEM–EDX analyses on the membrane surfaces confirm the presence of only minuscule amounts of sodium and chloride elements (the data are not shown here). To explain this opposing trend, FTIR analyses were conducted on the FSi particles. For comparison purposes, FTIR analyses were also conducted on the SiO2 particles, which were solely synthesized from TEOS without the addition of FOS. The resultant FTIR spectra are shown in and the corresponding functional groups are tabulated in reveal the existence of the peak for Si–OH group (wavenumber: 957 cm−1) for both FSi and SiO2 particles with a significantly lower intensity for the FSi particles. This result indicates that the presence of the hydrophilic hydroxyl group on FSi particles might be responsible for the slightly higher tendency of partial wetting observed on the DLM-5 membrane. As for the DL-0 membrane, the high rate of the partial membrane wetting might be caused by the presence of the big pores on the membrane surface as can be observed from the SEM image in . On the other hand, a separation factor higher than 99.99% can be maintained for the DLM-0 membrane, evidencing its highest resistance towards the partial membrane wetting. The synergism of the high permeation flux and the membrane stability encountered on the DLM-0 membrane signifies (1) the feasibility of the dual-layer hydrophobic–hydrophilic hollow fiber membrane for MD application and (2) the importance of an exclusively designed membrane for MD process.The following conclusions can be drawn from this work:In attempts to improve the efficiency of MD process, the implementation of dual-layer hydrophobic–hydrophilic hollow fiber membrane has been proven to be advantageous. The resistance for the transport of water vapor is reduced mainly due to the utilization of a thin hydrophobic functional layer. Accordingly, the highest permeation flux of 83.40±3.66 kg/(m2
h) and a separation factor higher than 99.99% are attained for the membrane spun with methanol additive (DLM-0). In addition, the formation of hydrophilic inner layer with lesser thickness and macrovoids structure contributes to the flux increment owing to the mitigation effect on temperature polarization at the fiber lumen side.The stability of the dual-layer hydrophobic–hydrophilic hollow fiber membrane has been proven through the continuous DCMD performance test. The prominent membrane characteristics to establish a steady performance have been identified as a macrovoid-free structure and hydrophobicity of the functional layer, as well as an optimized pore size on membrane surface and a delamination-free structure on the interface of the dual-layer hollow fiber membrane.The incorporation of FSi particles dispersion in methanol into the outer layer spinning solution of the DLM-5 membrane elevates membrane hydrophobicity as evidenced by the contact angle increment. Nevertheless, the hydrophobicity enhancement is not accompanied by the improvement of membrane resistance towards wetting. The existence of the unreacted Si–OH group on the particle surface might be responsible for this opposing phenomenon. On the other hand, the addition of solely methanol into the outer layer spinning solution of the DLM-0 membrane is found to promote membrane resistance towards wetting, which can be attributed to the formation of a denser membrane surface.Increased interest in normal faults and extended terranes has led to the development of an increasingly complex terminology. The most important terms are defined in this paper, with original references being given wherever possible, along with examples of current usage.Available online at www.sciencedirect.com - -0l -0 o.o ScienceDirect JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 2011, 18(11): 07-11 Production of Nitrogen-Bearing Stainless Steel by Injecting Nitrogen Gas SUN Li-yuanâ€�â€˜ , LI Jing-sheâ€™ , ZHANG Li-fengâ€™ , YANG Shu-fengâ€�â€™ , CHEN Yong-fengâ€�â€™ (1. School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, China; Technology, Rolla 65401, Missouri, USA) 2. Department of Materials Science and Engineering, Missouri University of Science and Abstract: To replace nickel-based stainless steel, a nitrogen-bearing stainless steel was produced to lower the produc- tion cost stemming from the shortage of nickel recourses. Thermodynamic model to calculate the saturated nitrogen content in the stainless steel was developed and the model was validated by experimental measurements performed with a high temperature induction furnace. Nitrogen gas under constant pressure was injected into the molten steel with a top lance. Thus, the nitrogen was transferred to the molten stainless steel. The effects of chemical composi- tion, temperature, superficial active elements and nitrogen flow rate on the transfer of nitrogen to the steel were in- vestigated and discussed. The results showed that the dissolution rate of nitrogen in the molten steel increases with a higher temperature and larger nitrogen flow rate but decreases significantly with an increase in the content of surface- active elements. Alloying elements such as chromium and manganese having a negative interaction coefficient can in- crease the dissolution of nitrogen in the molten steel. It was also proposed that the primary factor affecting the final saturated nitrogen content is temperature rather than the dissolved oxygen content. Key words: nitrogen-bearing stainless steel; nitrogen; thermodynamic modeling Nickel is one of the most widely used alloying elements, especially for the stainless steels. Nickel changes body-centered-cubic crystal lattice to face- centered-cubic crystal lattice that was named austen- ite. Austenitic stainless steel shows better proper- ties such as plasticity, solderability and toughness. With the increase of nickel price, more and more studies have been carried out to find the potential al- loying elements for stainless steel to replace nickel. Nitrogen is a potential element for this purpose. Re- searches showed that in addition to rapidly austen- itizing the stainless steel, nitrogen also enlarges and stabilizes the austenite phase regionâ€�]. With the rapid growth of stainless steels production, the ni- trogen-bearing stainless steel has attracted more and more attention recently for their high strength and excellent corrosion resistanceC2â€™. However, it is dif- ficult to produce the nitrogen-bearing steel since ni- trogen is a gas element and has a low solubility in the steel. Hence, efficiently increasing the dissolu- tion of nitrogen in steel is one of the main concerns for the production of nitrogen-bearing steels. Alloying nitrogen at a .normal pressure can be performed either by alloy addition or by gas injec- tion. Blowing nitrogen gas into the steel is a more economic and advisable method since the nitrogen- bearing alloy is quite expensive and may contain im- purities that are detrimental to the steel. A number of investigations have been reported on the solubility of nitrogen gas in pure ironC3] but few are for stain- less steels. In order to find out a cheap and efficient way to dissolve more nitrogen in stainless steels, the feasibility to directly inject nitrogen gas into the steel was in- vestigated in the present study. The effects of steel chemical composition, temperature, superficial ac- tive element-dissolved oxygen and nitrogen flow rate on the dissolution of nitrogen in the steel were ex- perimentally investigated using a high temperature induction furnace. A thermodynamic model was also developed for the dissolution reaction of nitrogen in the steel. Foundation Item: Item Sponsored by National Natural Science Foundation of China (51074021) ; Doctoral Programs Foundation of Ministry of Biography:SUN Li-yuan(1985-1, Female, Doctor; Education of China (200800080016) E-mail: sunliyuanustb@l63. com; Received Date: December 8, 2010 -8- Journal of Iron and Steel Research, International Vol. 18 1 Experimental Method The chemical composition of the stainless steels used is given in Table 1. The steel samples were melted in a 50 kg induction furnace and the tempera- ture was measured. The experimental set-up is shown in Fig. 1. The nitrogen gas was injected to the molten steel using a quartz tube as a lance from the top of the molten steel. After the steel was com- pletely melted, the molten steel was sufficiently de- oxidized by adding enough Si-Ca alloys and A1 lumps. The first steel sample was taken using a quartz tube to analyze the initial content of nitrogen and oxygen. After that, nitrogen gas was injected into the molten steel with a certain flow rate. During gas injection process, other five steel samples were taken with certain time intervals and the content of ni- Table l Chemical composition of steels used in present study (mass percent, %) C Si Mn P S Cr Ni Steel grade Steel-I 0. 130 0. 650 14. 9 0.030 0. 030 16. 3 2.00 Steel-I1 0. 130 0. 600 13. 5 0. 026 0. 023 16. 1 1. 66 Nitrogen n blomiw Rotameter I .- Induction coil 0 0 0 0 0 0 0 0 0 0 0 Fig. 1 Schematic diagram of experimental set-up trogen in the samples was analyzed. 2 gen Content in Stainless Steels Thermodynamic Model for Saturated Nitro- A thermodynamic model to calculate the satu- rated nitrogen content in the molten stainless steel was developed based on previous re~earches[~-~â€™. Factors such as temperature, alloy composition, and the second-order interaction coefficient of alloying elements such as chromium and manganese were taken into account. The dissolution reaction of nitrogen in steel can be expressed by 1 -N, <g>=[N] 2 (1) When nitrogen dissolves in the liquid iron under a low pressure, it obeys the Sievertsâ€™s The equilibrium constant of the reaction can be expressed by where, fN is the activity coefficient of nitrogen; wN is the nitrogen concentration in equilibrium state; PN2 is the nitrogen partial pressure; and Po is the standard atmosphere pressure, P,=l. 013 25 X lo5 Pa. Eqn. (2) can be rewritten into (3) Table 2 lists the interaction coefficient of differ- ent alloying elements in pure iron at 1873 KC4]. If the concentrations of chromium and manganese in the steel are as high as 14%-18%, a first-order in- teraction coefficient for activity calculation is not ac- curate enough. The second-order interaction coeffi- cients fi and rk should be used. Then, the activity coefficient can be expressed by 1 1gWN = Tlg(PN/Po ) + 1gKN -1gfN Table 2 First-order interaction coefficient of alloying elements in pure iron at 1873 K j C Si Mn S P 0 Mo Ni Cr cu eh 0.13 0.047 -0.02 0.007 0.045 0.05 -0.011 0.01 -0.047 0.009 lgfN = x(& WJ + (4) The value of fi and $ depends on temperature T as Eqn. (5) fi=1.52T-â€™-5. 3X10-4, ~=--2.3463T-â€™fO.0011 (5) The activity coefficient of nitrogen at temperature fN,T=(3 280T-â€™-0. 75)fN.l 873 (6) Several researchers have studied the dissolution reaction of nitrogen in meltC48-9â€™ and the reaction T can be expressed by the Chipman formulaC4â€™ equilibrium constant can be derived as lgKN=-l88.052T-â€™--1.17 (7) Then, the saturated nitrogen content can be cal- culated by Issue 11 Production of Nitrogen-Bearing Stainless Steel by Injecting Nitrogen Gas -9- 3 Results and Discussion 3. 1 Effect of steel composition Two grades of stainless steels were used, as shown in Table 1, under the same melting condi- tions. The dissolution of nitrogen in Steel-I was ap- parently higher than that in Steel-11, as shown in Fig. 2 (a). In Fig. 2 (a), the scatters are the experi- mental data, the solid curve is the regression of the experimental data, and the dotted curve is the ex- trapolation of the regression equation. Steel-I has more alloying elements that decrease the activity co- efficient of nitrogen in the steel. The alloying ele- ments of chromium and manganese have a negative interaction coefficient (e'N < 0) which promotes the interaction between the alloy and nitrogen and causes a higher solubility of nitrogen. It indicates that Steel-I has a higher rate of nitrogen increase than Steel-11. In order to evaluate the effect of experimental parameters on the solubility of nitrogen in the steel, the saturated (cT - - - - - - - - - - - d -- 0.642 / 0 nitrogen content is calculated by Eqn. ( 8) , which corresponds to the horizontal dotted line in Fig. 2. The dotted curve, the extrapolation of the measure- ment, shows that the nitrogen change rate gradually approaches to zero, at which nitrogen reaches the saturated value. The calculation by Eqn. (8) agrees roughly with the extrapolation of experimental re- sults. Steel-I has a smaller fN than Steel-I1 (fN,steetl = 0. 104, fN,steel.ll=O. 117) and thus a greater trend to dissolve nitrogen. Although manganese is a weak el- ement for the formation of austenite, it can well sta- bilize austenite for its contribution to the dissolution of nitrogen-a powerful austenite former in the molten steel. If a certain amount of manganese is added with nitrogen into the steel, it will cause much lower consumption of nickel. Since the alloying elements have a great influ- ence on the solubility and dissolution rate of nitrogen in the molten steel, it is better to add and well dis- perse the alloys first and then inject nitrogen gas. 0 20 40.. 160 180 0 20 40 160 180 200 Timelmin Influence of steel composition (a), dissolved oxygen (b) , temperature (c> and Fig. 2 nitrogen gas flow rate (d) on nitrogen content in molten steel 3.2 The experiments were carried out using Steel-I1 at 1873 K with the same amount of Ca-Si powder addition and nitrogen flow rate of 25 L min-' , but with varied dissolved oxygen content. For the first Effect of initial dissolved oxygen heat, the Ca-Si powder was added and the deoxida- tion was completed before nitrogen gas was injected, and the dissolved oxygen content was 0.0042%. For the second heat, 50 g FeO powders were added during the melting process, which raised the dis- 10 Journal of Iron and Steel Research, International VOl. 18 1 820 1 a70 1920 TIK 0.015 wc,=16.3%; ~~"'14.9%; PN~ =Po. Fig. 3 Influence of oxygen content on nitrogen content in Steel-I P 0.010 3.3 Effect of temperature -3 solved oxygen to 0.013%. As shown in Fig. 2 (b) , with initial oxygen content of 0.004 2%, there was a steep increase of nitrogen content during the first 6 min of nitrogen injection, and after that, the rate of nitrogen increase slowed down. The first heat (with initial oxygen concentration of 0. 004 2 % ) has higher overall final nitrogen content and higher ni- trogen increase rate than the second heat (with ini- tial oxygen concentration of 0.013%). The thermo- dynamic prediction shows that the initial dissolved oxygen content has little effect on the final nitrogen content in the steel, as shown in Fig. 3. This implies that the dissolved oxygen only affects the kinetic condition for the nitrogen transfer in the steel rather than the thermodynamic condition. The dissolved oxygen remarkably affects the speed to reach the fi- nal saturated nitrogen [Fig. 2 (b)] but affects little the value of the final saturated nitrogen in the steel (Fig. 3). The dotted curve in Fig. 2 (b) showed that the nitrogen in the first heat reached saturation within a shorter time than that in the second heat. It means that the dissolution rate of nitrogen in the steel decreased significantly with the increase of the dissolved oxygen, which was a surfaceactive element. The surfaceactive element significantly keeps nitrogen from being dissolved in the molten steel. Hence, it is very important to complete the deoxidation before injecting nitrogen gas into the molten steel. 0.60 - a L.min-' - / 0.55 0.50 0.45 lution of nitrogen when the nitrogen content is lower than a critical value, which is because the higher temperature provides a better kinetic transfer condi- tion. The dissolution of nitrogen in the molten steel is endothermic and thus higher temperature favors the reaction at the beginning stage. Furthermore, the random molecular motion is more vigorous at higher temperature, which reduces the viscosity and increases the fluidity of the molten steel, and thus favors the mass transfer. After the nitrogen reaches a critical value, the dissolution rate of nitrogen at lower temperature became larger than that at higher temperature. At lower temperature, the steel had higher final saturated nitrogen, as predicted by ther- modynamic model [Eqn. (8) and Fig. 2 (c)]. The change of nitrogen solubility in the molten steel with temperature can be obtained from Eqn. (8). The two heats have a close value of lgf,,, 873 K, approx- imately -0. 931. Then, if PN2 =Po, Eqn. (8) gives 2 865.628 - 1. 868 T lgWN = (9) Thus, the final saturated nitrogen varies in- versely with temperature, implying lower equilibrium nitrogen content at higher temperature. It also can be seen from Fig. 3 that the primary factor affecting the final saturated nitrogen content is temperature rather than the dissolved oxygen content. 3.4 Effect of gas flow rate In order to investigate the effect of gas flow rate, different experiments were performed for Steel-I1 at 1873 K with the same amount of Ca-Si powder addition and dissolved oxygen concentration of 0.002% -0. 003%. Fig. 2 (d) shows that larger nitrogen flow rate produced larger nitrogen content and the rate of nitrogen increase was much higher, especially during the first 6 min, as shown in Fig. 4. 0.020 I Issue 11 Production of Nitrogen-Bearing Stainless Steel by Injecting Nitrogen Gas ' 11 However, in the last several minutes of experiment, the increase rate of nitrogen for the heat with gas flow rate of 8 L min-' was decreased and even low- er than the heat with gas flow rate of 0. 6 L * min-'. For the heat with gas flow rate of 0. 6 L min-', the increase rate of nitrogen firstly increased with time and then decreased with time after reaching a critical value. Larger nitrogen gas flow rate pro- duces the larger contact area of nitrogen with the molten steel, higher stirring power and faster mix- ing, and thus generates a better kinetic condition for the transfer of nitrogen in the molten steel. Besides, too large gas flow rate may push away the slag at the top and the molten steel will touch the air, which will induce serious reoxidation. Thus, the gas flow rate should have an optimum value. 4 Conclusions 1) Larger nitrogen flow rate favors the dissolu- tion of nitrogen in the molten steel. 2) The dissolution rate of nitrogen to the mol- ten steel significantly decreases if the steel contains a certain amount of surface-active elements, such as the dissolved oxygen, and the nitrogen gas should be injected into the molten steel after fully deoxida- tion while the dissolved oxygen has a little effect on the final nitrogen content in the steel. 3) The dissolution rate of nitrogen in the mol- ten steel increases with the increase in temperature, but higher solubility of nitrogen can be obtained at lower temperature. 4) For the two grades of stainless steels in this study, it is hard to reach the saturated nitrogen con- tent in the feasible refining time under atmospheric pressure. References : Speidel M 0. Nitrogen Containing Austenitic Stainless Steels [J]. Mat-wiss. u. Werkstoiftech, 2006, 37(10): 875. Speidel M 0. New Nitrogen-Bearing Austenitic Stainless Steels With High Strength and Ductility [J]. Metal Science and Heat Treatment, 2005, 47(11/12): 489. Balachandran G, Bhatia M L, Ballal N B, et al. Some Theoret- ical Aspects on Designing Nickel Free High Nitrogen Austenitic Stainless Steels [J]. ISIJ Internationa1,'2001, 41(9) : 1018. Chipman J, Corrigan D A. Prediction of the Solubility of Nitro- gen in Molten Steel [J]. AIME Trans, 1965, 233(4): 1249. Rawers J C, Kikuchi M. Nitrogen Concentration in FeCr-Mn Alloys [J]. Journal of Materials Engineering and Performance, 1993, 2(5): 651. Rawers J C, Gokcen N A. High-Temperature, High-pressure Nitrogen Concentration in FeCr-Mn-Ni Alloys [J]. Steel Re search, 1993, 64(2): 110. LI Hua-bing, JIANG Zhou-hua. Thermodynamic Calculation Model of Nitrogen Solubility in Molten Stainless Steel [J]. Journal of Northeastern University: Natural Science, 2007, 28 (5) : 672 (in Chinese). Satir-Kolorz A H, Feichtinger H K. On the Solubility of Nitro- gen in Liquid Iron and Steel Alloys Using Elevated Pressure [J]. Z Metallkd, 1991, 82(9): 689. Pehlke R D, Elliott J F. Solubiiity of Nitrogen in Liquid Iron Alloys [J]. AIME Trans, 1960, 218(6): 1088. (Continued From Page 6) [lo] Natsui Shungo, Ueda Shigeru, FAN Zheng-yun, et al. Sensi- tivity Analysis of Physical Parameters in Discrete Element Method Compared With Blast Furnace Cold Model Experi- ments [J]. Tetsu-to-Hagane, 2010, 96(1): 1 (in Japanese). Natsui Shungo, Ueda Shigeru, Oikawa Masashi, et al. Opti- mization of Physical Parameters of Discrete Element Method for Blast Furnace and Its Application to the Analysis on Solid Motion Around Raceway [J]. ISIJ International, 2009, 49 Ueda Shigeru, Natsui Shungo, FAN Zheng-yun, et al. Influ- [ll] (9) : 1308. [l2] ences of Physical Properties of Particle in Discrete Element Method on Descending Phenomena and Stress Distribution in Blast Furnace [J]. ISIJ International, 2010, 50(7): 981. Shimizu Masakata, Yamaguchi Arata, Inaba Shin-ichi, et al. Dynamics of Burden Materials and Gas Flow in the Blast Fur- nace [J]. Tetsu-to-Hagane, 1982, 68(8): 936 (in Japanese). Nouihi Taihei, Sato Takeshi, Sato Michitaka, et al. Stress Field and Solid Flow Analysis of Coke Packed Bed in Blast Furnace Based on DEM [J]. ISIJ International, 2005, 45 (10): 1426. [13] [14] se rate of nitrogen for the heat with gas flow rate of 8 L min-' was decreased and even low- er than the heat with gas flow rate of 0. 6 L * min-'. For the heat with gas flow rate of 0. 6 L min-', the increase rate of nitrogen firstly increased with time and then decreased with time after reaching a critical value. Larger nitrogen gas flow rate pro- duces the larger contact area of nitrogen with the molten steel, higher stirring power and faster mix- ing, and thus generates a better kinetic condition for the transfer of nitrogen in the molten steel. Besides, too large gas flow rate may push away the slag at the top and the molten steel will touch the air, which will induce serious reoxidation. Thus, the gas flow rate should have an optimum value. 4 Conclusions 1) Larger nitrogen flow rate favors the dissolu- tion of nitrogen in the molten steel. 2) The dissolution rate of nitrogen to the mol- ten steel significantly decreases if the steel contains a certain amount of surface-active elements, such as the dissolved oxygen, and the nitrogen gas should be injected into the molten steel after fully deoxida- tion while the dissolved oxygen has a little effect on the final nitrogen content in the steel. 3) The dissolution rate of nitrogen in the mol- ten steel increases with the increase in temperature, but higher solubility of nitrogen can be obtained at lower temperature. 4) For the two grades of stainless steels in this study, it is hard to reach the saturated nitrogen con- tent in the feasible refining time under atmospheric pressure. References : Speidel M 0. Nitrogen Containing Austenitic Stainless Steels [J]. Mat-wiss. u. Werkstoiftech, 2006, 37(10): 875. Speidel M 0. New Nitrogen-Bearing Austenitic Stainless Steels With High Strength and Ductility [J]. Metal Science and Heat Treatment, 2005, 47(11/12): 489. Balachandran G, Bhatia M L, Ballal N B, et al. Some Theoret- ical Aspects on Designing Nickel Free High Nitrogen Austenitic Stainless Steels [J]. ISIJ Internationa1,'2001, 41(9) : 1018. Chipman J, Corrigan D A. Prediction of Production of Nitrogen-Bearing Stainless Steel by Injecting Nitrogen GasTo replace nickel-based stainless steel, a nitrogen-bearing stainless steel was produced to lower the production cost stemming from the shortage of nickel recourses. Thermodynamic model to calculate the saturated nitrogen content in the stainless steel was developed and the model was validated by experimental measurements performed with a high temperature induction furnace. Nitrogen gas under constant pressure was injected into the molten steel with a top lance. Thus, the nitrogen was transferred to the molten stainless steel. The effects of chemical composition, temperature, superficial active elements and nitrogen flow rate on the transfer of nitrogen to the steel were investigated and discussed. The results showed that the dissolution rate of nitrogen in the molten steel increases with a higher temperature and larger nitrogen flow rate but decreases significantly with an increase in the content of surface-active elements. Alloying elements such as chromium and manganese having a negative interaction coefficient can increase the dissolution of nitrogen in the molten steel. It was also proposed that the primary factor affecting the final saturated nitrogen content is temperature rather than the dissolved oxygen content.Biography: SUN Li-yuan (1985–), Female, DoctorUncertainty quantification of the factor of safety in a steam-assisted gravity drainage process through polynomial chaos expansionUncertainty quantification of the factor of safety in a steam-assisted gravity drainage process through polynomial chaos expansionThe factor of safety (FoS) is a measure of the operational safety of a reservoir and is defined as the ratio of the yield strength to the applied effective stress. In the steam assisted gravity drainage (SAGD) process, maintaining the caprock FoS within the prescribed limits during the operation is crucial in adhering to safe operational standards. Deformations associated with the development of the steam chamber in the reservoir affect the FoS of the caprock significantly. With a limited number of well-logs, precise quantification of heterogeneity in petrophysical and geomechanical parameters is a challenge in coupled reservoir-geomechanics modelling; this, along with nonlinearity in the process dynamics, gives rise to non-Gaussian uncertainties in the pore pressure/temperature, which poses severe challenges in reservoir control and optimization. The large scale nature of the reservoir imposes computational complexity in uncertainty quantification through first-principles modelling; hence, a data-driven methodology using the results from first-principles simulations is valuable. In this work, a data-driven polynomial chaos expansion (PCE)-based proxy model is developed from sequentially coupled reservoir-geomechanics simulation. Proper orthogonal decomposition (POD) combined with the PCE yields a proxy model which can provide a quick and accurate estimation of caprock FoS along with quantifying its uncertainty.Uncertainty and imprecision are unavoidable in all engineering problems, and two types of uncertainty quantification (UQ) can be carried out in model-based optimal policy computation as shown in a: forward UQ and reverse UQ. Forward UQ deals with transferring input and parametric uncertainties to the outputs of the system and reverse UQ deals with propagating the input and output sensor uncertainities (noise) to the states (). This work deals with the former case for the factor of safety (FoS) in a steam assisted gravity drainage (SAGD) process as the output, with high parametric uncertainty in the reservoir permeability (). SAGD is a large scale nonlinear distributed parameter system spread across a vast geographical area and the limited availability of well logs to sample the heterogeneity makes it even more complex in UQ. Monte Carlo simulation () is a widely used method that is simple to implement but is computationally intensive, requiring a prohibitively large number of sampling points to apply effectively to SAGD (). Hence, we propose a computationally affordable technique, polynomial chaos expansion (PCE), that requires a handful of sampling points to achieve reasonable UQ of the FoS ( is the most widely used recovery technique for oil sands. Two parallel wells, the injector at the top and the producer at the bottom, run in parallel. The injector well injects steam into the reservoir, mobilizing the bitumen to flow down due to gravity to the producer. The development of the steam chamber applies a vertical stress field on the caprock, which is an impermeable layer preventing the high pressure oil and gas from escaping to the surface. The FoS () is a measure of the stability of the caprock and is computed as a function of the stress state and shear strength of the caprock layer. Numerically, it should be greater than 1 to assure caprock integrity. Caprock rupture incidents such as Joslyn () have proved the importance of caprock surveillance in SAGD operations and precisely quantifying the uncertainties in the FoS is essential to monitor it. The stress field on the caprock layer is mainly a function of reservoir pore parameters like pressure, temperature, well bottom hole pressure (well BHP) and the reservoir petrophysical parameters (mainly permeability). In this work, to have a parsimonious PCE representation, we only consider two of the factors affecting the stress field of the caprock, i.e. the well BHP and the reservoir permeability, since these two quantities directly determine the steam chamber shape in the reservoir and the FoS of the caprock layer. We chose well BHP as the input because it is a prime manipulated variable in SAGD reservoir operation. The permeability was chosen as the representative random variable as it is the petrophysical property that governs the reservoir flow and geomechnical profile the most, and is the one that is constantly updated in the sequential coupling between the reservoir and geomechanical simulations. b shows the functional representation of the FoS as a function of the well bottom hole pressure as input (U), and the petrophysical parameters (ξ). An explicit form of this functional relationship (f) is not directly available; hence, we are left with the option of analyzing this relationship through data obtained from a first-principles reservoir flow simulator CMG-STARS (), which is used to compute stress and strain (explained in detail in the next section). This work will present this simulator data-based technique to obtain a PCE model for the FoS. All of the computations are carried out in MATLAB (PCE was introduced as a homogeneous chaos by Weiner and is derived from the Cameron-Martin theorem to represent a random process in terms of orthogonal polynomials of standard random variables (). As pointed out earlier, PCE is computationally efficient compared to Monte Carlo-based techniques (). PCE represents a random process as an infinite series of the products of orthogonal polynomials of standard random variables (RV) as basis functions and deterministic weighing coefficients:Y is the random process of interest, yi are the deterministically computable weighting coefficients and ψi(ξ) are the orthogonal polynomials of RV ξ (basis functions) of order i. The recurrence relations of the orthogonal polynomials can be used to generate them and within a defined interval, they make an orthogonal basis for a defined inner product. The first N terms are considered depending upon the required accuracy. The most commonly used orthogonal polynomials include, but are not limited to, Hermite, Legendre and Chebyshev polynomials () refers to decomposing a given field (function) into orthogonal counterparts; this is practically equivalent to the singular value decomposition (SVD) () for our case where the simulator FoS data is spatiotemporal data (also referred to as snapshots) (). The POD expansion allows us to estimate the spatial variation in the snapshots of FoS by decomposing the field into a set of basis functions and singular values (SVs). The SVs capture the variability present in the field hierarchically from the highest to the lowest (component-wise), and the variability in the spatiotemporal FoS data can be captured by the first few dominant SVs. Owing to this feature of the SVD, we consider the SVs of the FoS as the representatives of the uncertainty and model them with PCE while keeping the corresponding basis intact.The organization of the paper is as follows: describes the SAGD system and the details of the sequentially coupled reservoir-geomechanics simulator setup and the obtained data format. explains the analysis techniques, followed by providing the corresponding results and discussion. provides conclusions and future directions.This section describes the details of the simulation framework and the tools used in the data generation and visualization. To start with, we describe the details of the sequentially coupled simulation platform, which consists of CMG-STARS for reservoir flow simulation and FLAC3D for computing stress and strain. A sequential coupling platform facilitates the study of the effect of geomechanics and in turn the FoS in a SAGD process. This platform enables to visualize the interactions between flow and deformation response in subsurface modelling in the SAGD process ( shows the flow chart of the coupled reservoir-geomechanics simulation and the use of the PCE model for UQ. The pore pressure and temperature obtained from CMG-STARS are used to compute the stress and strain through FLAC3D. This information is transformed into the updates in the petrophysical parameters of the reservoir, and the pore pressure and temperature are re-computed with the updated parameters and the loop goes on (refer A wellpad of MacKay River oil sand area is selected and applied in the coupled platform with geomechanical and reservoir models. The schematic of the reservoir model with the permeability distribution and the geomechanical model under consideration is shown in , respectively. A total of 6 well pairs operate in the pad with well spacing of 100 m. The grid size and numbers vary in different formations to retain the inherent heterogeneity due to the sedimentation process. The Wabiskaw and McMurray formations are included in both the reservoir and geomechanical model, and the Till, Clearwater, and Devonian formation are only included in the geomechanical model for computational efficiency, as the flow response in these three formations can be ignored due to the low permeability. The injectors open from day 1 for preheating of the cold bitumen near the wellbore and the producers open in 150 days for production; hence, for the purpose of modelling, data from day 160 and onwards is considered. The caprock region, which is the region of interest in this study, corresponds to the Clearwater formation, and the reservoir corresponds to the Wablskaw and McMurry formations; the rest is the under and over burdens. A pseudorandom binary sequence (PRBS) input for the well BHP for injectors and producers is designed to provide excitation to the system and generate suitable data for the purposes of modelling and identification. The designed PRBS frequency range is between three to six months, sufficient enough to capture the variability in the FoS due to the well BHP. In this work, the variability in the FoS data is due to the uncertainty in the petrophysical and geomechanical parameters and the input PRBS of the bottom hole pressures. The PCE model developed serves as the UQ tool in both inputs and the parameters.Here, we present the steam chamber evolution at different instants of time. a–c showing the 3D steam chamber at t=1, 10 and 25 (time frames) , respectively. Each time frame corresponds to 100 days of operation. The spread of the steam chamber across the reservoir and the heterogeneity in the permeability is clearly seen in the figure.Working with PCE requires the generation of an ensemble of realizations of the random process of interest. In our case, it is the FoS realizations and the corresponding well BHP input. Since we consider working with a two-dimensional reservoir problem in this work, we conduct a single heterogeneous three-dimensional simulation and use each two-dimensional slice perpendicular to the well direction (XZ) as a separate realization. This approach is better as it considers the cross-flow terms capturing the true dynamic flow behaviour during the SAGD process, and is therefore our preferred approach for creating 2D realizations. To summarize, 200 XZ frames along the Y direction of the 3D model are used as 200 2D realizations to construct the ensemble. demonstrates the formatting procedure to obtain the 2D realizations from a 3D simulation. shows the average change of the permeability across all the realizations at t=1 (c), respectively. In sequential coupling, the permeability distribution is updated at each time step. The permeability distributions presented in are the ‘posterior’ permeability distributions obtained after the updates, which will be used in the PCE model development. presents the modelling work flow. The first three columns to the left in the figure show the realizations of the reservoir permeability {Ξk}1200, the corresponding reservoir pressure and/or temperature fields computed from CMG-STARS and the FoS field realizations computed from the sequentially coupled FLAC3D data (refer to for more details on sequential coupling), respectively, at any instant of time t. The singular value decomposition of the FoS realizations yields basis {Uk}1200 and {Vk}1200 and the ensemble of singular values (SVs) {Sr,k}r=1,k=1r=6,k=200. The SV ensemble acts as the ‘representative’ of the FoS field, and is used as the output of the PCE model of the underlying FoS field.After obtaining the stress data from FLAC3D, the FoS can be computed for every grid point usingwhere σmax and σmin are the maximum and minimum stress component of the stress tensor, respectively. Pp is the pore pressure, C is the cohesion and ϕ is the friction angle. All of these variables are directly available from the coupled simulations to compute the FoS.SVD decomposes a given matrix into a product of two basis vectors and the matrix of SV. SVD hierarchically captures the total variance in the data into the basis vectors scaled by the matrix of SVs (highest to lowest). In essence, the ratio of the magnitude of a particular SV to the sum of all SVs is proportional to the relative magnitude of the variance captured by it. Also, each SV along with its basis can be used contsruct a low rank approximation of the original data and the highest SV gives the matrix 2-norm of the original data. It is in this context that we call the SVs as the representatives of the original data (in our case, the FoS field). SVD has been used extensively in data analysis both in deterministic, stochastic and spatiotemporal frameworks (). We use the SVD for two purposes in our work. First, we use it to analyse the FoS field to determine how many SVs and corresponding basis vectors are required to reconstruct the field accurately. Secondly, we use the SVD on the reservoir permeability field realizations to quantify or to find a set of representatives of a particular realization to be used in building a PCE model.The FoS data D is four dimensional (spatial dimension: 200 × 200 × 6 grid blocks, with 29 time frames) and is considered as 200 realizations of a frame of dimension 200 × 6 with data available at 29 time instants (see ). The SVD for a particular realization Ξk of the frame at any time instant {t}129 is given byU(t), V(t) are orthogonal matrices and Σ(t) is a diagonal matrix at any time frame t, with the SVs of D arranged in descending order. These basis vectors capture the variance in the data in the least squares sense and their corresponding SVs quantify the contribution of each basis vector. The ratio Σi=irσiΣi=i6σi quantifies the percentage of variance captured by the first r SVs (out of 6 in our case). To keep the computational cost of building the PCE model low, we choose the first r SVs and fit a PCE model for each of them. Out of the r SVs, the first SV (S1) is the most important as it quantifies the 2-norm of the corresponding frame, which can be effectively taken as a representation of that frame.The reservoir permeability realizations Ξ1−200 are analyzed similarly; here, the data D is also four-dimensional (spatial dimensions 200 × 200 × 35 over 29 time frames) and is viewed as 200 realizations of frames of dimension 200 × 35 at 29 time instants (see ). The SVD for a particular realization Ξk of the frame at any time instant {t}129 is given by:D200×35(t)=U200×35(t)Σ35×35(t)V35×35′(t)Here, we choose the first r dominant SVs to represent the kth realization Ξk. explains the application of SVD in representing a realization Ξk by its dominant SVs (ξk1,ξk2…ξkr). This procedure helps us to represent a 2D permeability field by a sequence of SVs, which is useful in computing the PCE model. It is worthwhile to mention that the Ξk represents the ‘posterior permeability’ of the sequential coupling process.After computing the SV distribution of the FoS field over its realizations for every instant of time {Sr(t)}1r, we can develop a PCE model for each Sr(t) as a function of the well BHP (μ) as the input and the permeability vector (ξ) as the parametric uncertainty at every instant of time (refer ). The parametric uncertainty ξ incorporates the intrinsic heterogeneity in the permeability, the error in computing the permeability field due to the limited availability of well logs and the uncertainty arising in the sequential coupling. The input variable μ is assumed to have a uniform distribution and is expanded with a sequence of Legendre polynomials that are orthogonal on a scaled interval [0, 1]. The uncertain parameters ξi (representatives) are normalized by scaling them as standard normal variables and expanded with a sequence of Hermite polynomials on the interval [−∞,∞]. The output variable of interest, Sr (SVs of the FoS), is expanded as a combination of the polynomials as follows:Sr(t)=f1(t)H1(ξ)+⋯+fr+1(t)L1(μ)+⋯+fi(t)Hj(ξ)Lk(μ)+⋯ represents the general PC expansion, where i represents the number of terms considered (based on truncation of ), and j and k are the order of the polynomials H and L, respectively. The PCE coefficients fi(t) are computed from the process data {Sr,k}r=1,k=1r=6,k=200, permeability data {Ξk}200 and the input μ for every t using regression and collocation methods ( describes the details of the implementation of the PCE modelling. The realizations are split into modelling and validation data, with PCE coefficients being computed over all the modelling realizations and the developed PCE model then being tested over the validation realizations to check the modelling adequacy. If the model’s accuracy in validation is not satisfactory, the number of terms, the order of the polynomial basis, and the combination of the polynomials are changed; the new PCE model is rebuilt and checked again for adequacy over the validation realizations. This process is repeated until an adequate model is found. Regression analysis indices such as the error sum of squares (SSE), the coefficient of determination (R2) and the adjusted coefficient of determination (Radj2) are used as the metrics for model adequacy.A pair of polynomials, f(x) and g(x), are said to be orthogonal in an interval [a, b] ifwhere < f, g > denotes the inner product of f(x) and g(x). A sequence of such orthogonal polynomials can be generated for a given interval [a, b] using their recurrence relationship. gives the Hermite and Legendre orthogonal polynomials of order 1–4 and their respective roots over the intervals [−∞,∞] and [0, 1]. The orthogonal polynomials can be generated using the Python library ORTHPOL A set of randomly chosen 100 permeability realizations are used for training the PCE model and the other 100 realizations are used for validating it. at every grid block for all realizations over time. Now we need a scalar measure of FoS for every frame to mathematically compare its magnitude with other frames and at other instants of time. For this purpose, we propose two schemes to obtain a scalar measure: in the first, we find the minimum FoS over all the grids points in a frame and call it the representative of that frame. In the second, the first SV (S1) of the FoS field (which represents the matrix 2-norm of the field) is normalized by dividing it by the 2-norm of a matrix of ones of the dimension of the frame (200 × 6). shows the evolution of the minimum FoS (first measure) of every frame over all realizations and time. Similarly, shows the evolution of the normalized highest SV (second measure) over realizations and time. These two visualizations present the two different scalar measures (representatives) of the FoS of a frame over all realizations and time. The trend in both of the representations is similar; the FoS measure decreases with time and the variation across the realizations increases over time. visualizes exact locations of occurrence of the minimum FoS in the X direction over all realizations (Y) (reported with X, Y and Z grid numbers). a, b and c show the variation at t=1, t=10 and t=25, respectively. At each X location, the minimum FoS always occurs at the bottom layer of the caprock (at Z=6, the layer right above the reservoir). This is expected as the closeness of the steam chambers influences the FoS of the bottom of the caprock stronger than the other regions of the caprock. Also, it is interesting to note that the location of the minimum FoS is confined to the middle zone of X where the six well bores are placed.The SV decomposition of the permeability field Ξ over all the realizations and time shows that only first three dominant SVs are good enough to capture most of the variance, as shown in . The ratio Σi=13ξiΣi=i35ξi, considering three of the total SVs averaged over all realizations and time, is 0.4912, which means the first three SVs capture 49.12% of the total variance in the permeability; this implies 3 random variables ξ1, ξ2 and ξ3 can characterize the permeability field covering 49.12% of the total variance. Hence, every kth realization of the permeability field Ξk at an instant of time t is characterized by the set {ξk1ξk2ξk3μt}, where the random variable μ represents the input (well BHP). shows the SVs (S1…S6) of the FoS frame over all the realizations and time. The ratio Σi=i2SiΣi=i6Si considering two of the total SVs averaged over all realizations and time, is 0.9995, and if only the first SV is considered, the ratio becomes S1Σi=i6Si=0.9985. That means the first SV captures over 99% of the total variance in the FoS data. This justifies the choice of three random variables to characterize the permeability: even though they capture only 49.12% of its variance, the corresponding variance of the FoS that is captured is over 99%.Once the number of SVs to be considered for the FoS field is decided, we can use the averaged basis over all the realizations U(t) and V(t) and reconstruct the FoS field from only two out of six SVs. demonstrate this process at t=1, t=10 and t=25, respectively. c) show the actual FoS field, the reconstructed FoS field with the first two dominant SVs and the reconstruction error = [actual frame - reconstructed frame], respectively, at time instants 1, 10 and 25. In all of the cases, the Frobenius norm of the error frame ‖E‖F is reported as a metric to evaluate the reconstruction error. The Frobenius norm is defined as ∥E∥F=(Σi=16Σj=1100\|eij\|2)1/2, where eij is the error at each grid point. ‖E‖F is quite low at the start, increases later then and seems to saturate. The number of SVs and the effectiveness of the technique are deemed to be satisfactory, since ‖E‖F is relatively small at all times.The SVs {Sr}16 of all realizations of permeability are computed and normalized as a standard Gaussian random variable ξ between [−∞,∞] for all time. The well BHP input is normalized as a standard uniform random variable μ between [0, 1]. The realizations are characterized by ξ and μ with the first three dominant SVs of the permeability field; this means that the set {ξr1, ξr2, ξr3, μt} represents a particular realization Ξr. give the PCE expansions for {Sr}16 of first and second order, respectively, in terms of μ, ξ1, ξ2 and ξ3. Each of the terms in the expansion and the corresponding estimated coefficients are tabulated in . The model coefficients fi are computed using regression or collocation methods. The regression coefficients are estimated by performing least squares regression of the PCE model over all the modelling realizations and computing fi over them. In the collocation method, specific realizations are chosen as the collocation points and fi is computed over them. The Gaussian quadrature technique () is used to choose the collocation points. It suggests that the collocation points be chosen as the roots of the next higher order polynomials used in the PCE model. The collocation points (realizations) in terms of representative SVs for the first and second order PCE model are obtained through the roots of the second and third order polynomials, respectively (see ). A combination of higher order polynomial roots (eg. roots of H3 in ξ1, ξ2, ξ3) are used as the collocation points and the corresponding realization and FoS are chosen as the collocating realization to find fi.Sr(t)=f1(t)H1(ξ1)+f2(t)H1(ξ2)+f3(t)H1(ξ3)+f4(t)L1(μ)Sr(t)=f1(t)H1(ξ1)+⋯+f4(t)H2(ξ1)+⋯+f8(t)H1(ξ1)H1(ξ2)+⋯+f11(t)L2(μ)As pointed out earlier, S1 is the most important SV; hence, we show representative approximations for S1. The coefficients fi(t) for models of order 1, 2 and 3 computed using regression and collocation at times t=10 and t=25 are tabulated in show the validation results of PCE for S1 for order 1, 2 and 3, respectively, for time t=10. The validation data distribution and the scatter plots are shown side by side for easier visualization. Each point in the scatter plot corresponds to a realization {Ξk}1100. Similarly, show the validation results of PCE for S1 for models of order 1, 2 and 3, respectively, for time t=25. The R2, Radj2 and the sum of square error SSE for each case is shown in along with the coeffficients. It is worth mentioning that each of the first, second and third order models have only one term (polynomial basis term in μ) of their respective order capturing the effect of the input. This is because the input being the same for all realizations restricts the model to have only one μ basis term in order to consistently estimate its corresponding coefficient in the PCE model. Lower SSE and the higher R2 values are the indicators of the effectiveness of a model and it is evident that they increase with an increase in the model order. It is interesting to note that collocation-based models perform comparably in many cases to their regression counterparts, given the fact that the collocation coefficients are estimated only from a few chosen points. However, the regression-based PCE models provide superior performance overall. The adjusted coefficient of determination (Radj2), which accounts for model accuracy but also penalizes extra degrees of freedom, indicates that the second order PCE models provide the best performance.To completely validate the best performing PCE order 2 model, we will use it to replicate the validation realizations of the representative FoS over all times ( we can reconstruct the FoS field with 99.85% accuracy using only the first SV, the second order PCE model is used to reconstruct S1, through which we can reconstruct the validation realizations of the representative FoS at all times. a, b and –c show the minimun FoS surface for the actual validation realizations, reconstructed minimum FoS surface reconstructed using PCE order 2 model and the error between them, respectively. The Frobenius norm of the reconstruction error is also reported. The error is highest when the steam chamber is dynamic and not fully established, i.e. around the middle part of the lifetime; the variation may also be due to the heterogeneity in the Y direction (over realizations). Overall, due to the low ‖E‖F, we can conclude that the PCE order 2 model has good performance.Another important feature of the PCE model is the ability to obtain explicit representation for the moments such as mean and variance of the underlying random process (FoS represented by Sr). Consider the PCE model of , and take moments on both sides of the equation:M[Sr(t)]=M[f1(t)H1(ξ1)]+⋯+M[f4(t)H2(ξ1)]+⋯+M[f8(t)H1(ξ1)H1(ξ2)]+⋯+M[f11(t)L2(μ)]Here, M stands for any of the moments; the left hand side of the equation denotes the moment on the representative FoS (Sr) expressed in terms of the moments of the individual terms in the right hand side. But we know that the individual terms (basis functions) in the PCE are polynomials of the standard random variables, which can be easily computed using their moment generating functions. Also, the orthogonality of the basis functions forces the moments of the cross terms to zero. As an example, consider the usual operation of the reservoir, where the value of the well BHP input μ is specified, but the randomness in the permeability is unknown and represented by standard zero-mean normal variables ξ1, ξ2 and ξ3. Now the problem of quantifying the uncertainty in FoS (S1) is carried out by computing the moments of the PCE model. Below are the mean and variance computed for a first order PCE model at t=10 using the discussed procedure.M[S1]=M[−0.74ξ1]+M[−0.35ξ2]+M[−0.04ξ3]+M[−0.01(μ−0.5)]Mean[S1]=M[−0.74ξ1]+M[−0.35ξ2]+M[−0.04ξ3]+M[−0.01(μ−0.5)]Mean[S1]=−0.01(μ−0.5)]Since ξ1, ξ2 and ξ3 are zero mean, this means that the mean value of S1 is governed by the deterministic input, in other words, the mean uncertainty in FoS is due to the input. Similarly, we can compute the variance.Variance[S1]=V[−0.74ξ1]+V[−0.35ξ2]+V[−0.04ξ3]+V[−0.01(μ−0.5)]Variance[S1]=(−0.74)2+(−0.35)2+(−0.04)2+(−0.01(μ−0.5))2 quantify the uncertainty in S1 due to the input μ. These equations can be valuable from the perspective of designing a controller to control the FoS. As these equations quantify the uncertainty in FoS due to the input, these can be used in formulating a robust optimization problem often used in designing model predictive controllers (). Also, the polynomial chaos expansion method provides a systematic way to identify and incorporate non-Gaussian distributions in reservoir forecasting.In this work, we proposed two measures to quantify the caprock factor of safety based on the minimum FoS value and the normalized singular value of the FoS frame. The location of the weakest point (minimum FoS) in the caprock was also tracked and presented. We then demonstrated a framework to propagate the uncertainty in the petrophysical parameters and the well BHP of a SAGD process to the factor of safety of the caprock. We have proposed a computationally efficient technique to quantify uncertainty using singular value decomposition coupled with polynomial chaos expansion requiring a handful of realizations compared to Monte Carlo techniques requiring thousands of realizations. The uncertainty in petrophysical parameters was modelled by three representative Gaussian random variables and the input by one random variable with uniform distribution. PCE models of order 1, 2 and 3 were developed with regression and collocation approaches, the models were compared using various performance measures and a second order PCE model was chosen as the optimum. The model was used to reconstruct the representative FoS and the results were validated. Quantifying uncertainty in the FoS with respect to inputs and the permeability was demonstrated by determining the moments of the representative distributions.Ajay Ganesh: Conceptualization, Methodology, Formal analysis, Visualization, Writing - original draft. Bo Zhang: Methodology, Data curation, Writing - review & editing, Resources. Richard J. Chalaturnyk: Supervision, Project administration, Funding acquisition. Vinay Prasad: Conceptualization, Supervision, Funding acquisition, Writing - review & editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Investigation on TIG welding of SiCp-reinforced aluminum–matrix composite using mixed shielding gas and Al–Si fillerUsing He–Ar mixed gas as shielding gas, the tungsten inert gas (TIG) welding of SiCp/6061 Al composites was investigated without and with Al–Si filler. Welded joint with filler were submitted to tensile tests. The microstructure and fracture morphology of the joint were examined. The results show that adding 50 vol.% helium in shielding gas improves the arc stability, and seams with high-quality appearance are obtained when the Al–Si filler is added. In addition, the interface reaction between SiC and matrix is greatly suppressed when using Al–Si filler. The microstructure of the welded joint displays non-uniformity with many SiC particles distributing in the weld center. The average tensile strength of weld joints with Al–Si filler is 70% above that of the matrix composites under annealed condition.Aluminum–matrix composites have wide applications, e.g. in the aerospace and automobile industries, due to their high specific strength, rigidity, wear resistance and good dimensional stability compared with unreinforced alloys In recent years, the results of much research work have been published proposing the application of solid-state bonding techniques (diffusion bonding, friction welding, etc.) to solve those problems Fusion welding is the most flexible and versatile welding technology. Extensive investigation on welding of SiC particle-reinforced aluminum–matrix composites with high-power laser beam and electron beam has been conducted This paper describes an experimental research on the TIG weldability of SiC-reinforced 6061 aluminum alloy protected with helium–argon mixed gas.Parent composite was a 6061 aluminum alloy reinforced with 15 vol.% SiC particles with an average size of 10 μm. Material which was produced by steer casting was received as a plate in annealed state after hot rolling forms with thickness of 3 mm. The tensile strength of the parent composite in annealed state is 271 MPa. For welding, the material was made into specimens with the dimensions of 60 mm × 30 mm × 3 mm by wire cutting. Prior to welding, the specimens were polished with abrasive paper and were thoroughly washed with acetone to clean greasy dirt and impurities.The joint structure without groove was adopted in the welding process. As shown in , a hold-down strip was used to prevent the displacement of samples; the red copper pallet had the effect of accelerated cooling for the weld. The penetration rate and root shape of the seam were controlled by the concave trough in the pallet.The specimens were welded applying single electric arc discharge on one face with filler of Al–Si alloy, using a multifunction TIG WSE-315 welding machine by manual welding. The composition of the filler metal is listed in . An AC square-wave current of about 60 A was adopted. The diameters of tungsten electrode and injecting nozzle were 2.5 mm and 7 mm, respectively. The electric arc was always generated in a mixture gas of helium and argon using a gas flow of 115 ml/s. The purities of helium and argon were 99.99%. The welding parameters were selected to achieve complete penetration of the molten pool through the specimen thickness. The welding speed (18 cm/min) and the arc length (4 mm) were constant for all the welding tests. The angle between the blowtorch, filler and specimens were in the ranges of 75–80° and 10–15°, respectively.Both parent composites and welded ones were machined in the form of tensile test specimens as shown in . The tensile test of specimens was conducted on a universal testing machine at a nominal applied strain rate of 1.0 mm/min. The fracture surfaces were examined by scanning electron microscopy (SEM). The microstructure of the welded joint was examined by OLYMPUS optical microscopy.The mixture ratio of helium and argon was changed in the range of 0–100% to observe the electric arc shape and the shielding effect. The results show that the stability of the electric arc increases with the raising of helium in the gas flow. However, the stability of the electric arc decreases when the ratio of helium is higher than 60%, as shown in Compared with air, the argon has played a good role of protection and stable electric arc in the welding process, owing to heavier density, smaller heat capacity ratio and heat conductivity. In contrast to argon, the helium has higher ionization potential and heat conductivity. Under the same welding current and arc length, the helium has higher arc voltage and provides higher power. In addition, the higher energy density and focused arc column of helium arc result in a deeper penetration of weld. Therefore, adding of a doping helium gas in the shielding gas improves not only the arc stability but also provides the seams with high-quality appearance and prevents oxidation of the specimens and welding spatter on the specimens shows the appearance of TIG weld joint without filler using a shield gas of 50 vol.% helium. From , we can see that the abutting joint line (indicated by arrowhead) is clearly observed. The ripple appearance, often found in aluminum welding, did not form and bad semblance of welded seam was obtained. The fused slag and bulge are obviously seen on the seam surface. The reasons for these phenomena lie in the enormous difference in the physical and chemical properties of SiC particles and aluminum alloy matrix.It is well known from numerous previous studies ) occurs between them to form an acicular aluminum carbide and free silicon:The reaction product Al4C3 is also unstable in wet environments because it undergoes rapid hydrolysis causing corrosion of the composite. Moreover, the other reaction product, Si, may generate Al–Si eutectic aggregates both in the particle/matrix interfaces and in the grain boundary matrix, decreasing the ductility of the composite The Al–Si filler was used to improve the fluidity of the welding pool. shows the weld appearance with Al–Si filler. Compared with , we can see that the weld formation with filler is evidently improved and the fish scale weld ripple forms. From , we know that the filler contains 12 wt.% Si. When the Al–Si filler was added into the molten pool, the Si content in the weld pool was obviously increased. Hence, the Gibbs free energy of Si was visibly increased and the harmful interface reaction was greatly depressed, due to the activity of Si being raised also compares the appearance of welds with Ar gas and Ar–He mixed gas. It can be observed that the width of the weld using Ar–He mixed gas ((a)). It is attributing to the higher concentration of the arc with Ar–He mixed gas.The microstructures of the joint are compared in (a) demonstrates the acicular reaction product of Al4C3 in weld with Al–Si filler, however, in (b), the acicular Al4C3 have not been found in the weld without Al–Si filler. The result indicates that the addition of Al–Si filler is helpful to obtain a high-quality appearance and restrains the interface reaction between reinforcement and matrix. These experimental results are agreed with that in the literature shows the microstructures of the welded joint with Al–Si filler, including heat-affected zone, fusion area and weld zone. From the figure, it can be seen that no harmful needle-like Al4C3 is formed in the weld zone and in the vicinity of the weld junction. Moreover, the drawbacks, such as gas porosity and oxidation are barely seen. However, the microstructure of the weld joint is inhomogeneous, as shown in (b). Exquiaxed grains and many SiC particles are found in the weld center; columnar crystals and a lower number of SiC particles can be found in the bond zone. The microstructure in the weld top has few SiC particles and mainly consists of Al and Si, as shown in the top part of (b). In contrast, numerous SiC particles are found in the weld center, weld bottom and bond zone. The above results demonstrate that the distribution of the reinforcement phase in the three parts of the weld is inhomogeneous, resulting from the non-uniform composition in the fused bath.The maximum tensile strength of the weld joints with Al–Si filler is 240 MPa. It is about 88% of the matrix composites under annealed condition and the average tensile strength of the three weld joints is about 70% of the matrix. The breaking points of the tensile test specimen mainly lie in the heat-affected zone. shows the fracture morphology of the tensile-tested specimens with high-quality welding joint. As shown in (b), it can be seen that almost all of the SiC particles are covered with a coating of aluminum–matrix, indicating the excellent interfacial bonding between SiC particles and matrix in the parent composites. Moreover, ductile regions with near-featureless non-circular dimples, called “tear ridges” and voids ((a) and (b)) were frequently observed. These are the signs of plastic deformation; therefore, the fracture mechanism of the investigated specimen with Al–Si filler mainly belongs to the ductile rupture.Adding of a doping helium gas in the shielding gas improves not only arc stability but also provides the seams with high-quality appearance.Compared weld formability of composites with and without Al–Si filler, the high-quality appearance welded seam is obtained when the Al–Si filler added. In addition, the harmful interface reaction between SiC particles and aluminum–matrix is greatly depressed. However, the microstructure of the welding joint has evident non-uniformity.The maximum tensile strength of the welded joints with Al–Si filler is about 88% and the average value is 70% of that for the matrix composites under annealed condition. The fracture mechanism of the said specimen with Al–Si filler mainly belongs to the ductile rupture.The role of structure defects in the deformation of anthracite and their influence on the macromolecular structureThe impacts of stress on the physical and optical properties of coals are well recognized, while the influence on the chemical structure is seldom considered. In the light of mechanochemistry research that mechanical force can act on the molecule directly to initiate or accelerate reactions by deforming the chemical bonds, it is meaningful to consider how stress works on the macromolecule of coals. In this work, some insights are given based on anthracites with different tectonic deformation from Qinshui Basin, Shanxi Province, China. The deformation degree was measured by bireflectance (Ro,max
− Ro,min), and the macromolecular structure was characterized by Raman spectroscopy. For samples from the same colliery, there is a positive relationship between Raman area ratio AD/AG and bireflectance, suggesting that the deformation of anthracite is related with the generation of structure defects at the atomic scale. Further quantum chemistry calculations demonstrate that accompanying the generation of one Stone-Wales (SW) defect (induced via in-plane rotation of C-C bond by 90°), the molecular geometries of anthracite, such as chemical bonds and angles, change. The deviation of atoms from their equilibrium geometries reflects the local force distribution and transfers 303.48 kJ/mol mechanical energy into chemical energy. These changes allow chemical bonds to adjust to the applied stress without breakage, so that anthracite will accommodate plastic deformation. Additionally, the existence of SW defect slightly reduces the energy needed to produce carbon monoxide from carbonyl in anthracite. The current study helps to understand the potential influence of stress on the chemical structure evolution of coals.The chemical structure evolution of coals is the foundation for understanding coalification and the accompanying volatile To determine the macromolecular structure response of coals under stress, in our previous study, we performed deformation experiments on anthracite In this study, using a series of tectonically deformed anthracites from Qinshui Basin, Shanxi Province, China, we continue to investigate the relation between structure defects and deformation. Structure defects are revealed by Raman spectroscopy, which is a widely-used method to characterize structure defects in carbonaceous materials Samples were collected from Wangtaipu Colliery and Sihe Colliery in the Qinshui Basin, Shanxi Province, China. Wangtaipu Colliery is in the eastern margin of Qinshui basin (a). The main coal-bearing strata in Wangtaipu Colliery range from Carboniferous to Permian, which strike NE and dip NW with an angle of 4–5°. Coal seam No. 15 in the lower Taiyuan Formation of the Upper Carboniferous is the main minable coal seam in the XV5306 working face. Normal fault DF133 and a nearby normal fault (here we name it DF133′) are found in the north-eastern of the working face (b). DF133 strikes 97°, dips 7° with an angle of 80°, and DF133′ strikes 84°, dips 354° with an angle of 80°. They both have a stratigraphic displacement of 1.6 m. Wangtaipu samples were collected near faults DF133 and DF133′. Sihe Colliery is in the south-eastern Qinshui Basin (a). Coal seam No. 3 in the Shanxi Formation of the Lower Permian is the main minable seam. The structure characteristics of the W2301 working face are mainly controlled by the anticline in the west and the reverse fault DF9 in the east (c). The DF9 has a stratigraphic displacement of 6 m and dips 265° with an angle of 15–35°. Sihe samples were collected from these two local deformed regions. Samples from the anticline are named by S-Z, and from the DF9 are named by S-D. General information of the samples is summarized in Collected samples are quite soft and can be broken easily by hand (). Primary structures, such as the bedding plane, in most samples were damaged. Instead, tectonically induced features, such as friction surfaces, crumple, and exogenous fractures can be observed in these tectonically deformed coals (Due to low strength of deformed coals, it is difficult to make oriented samples. Therefore, reflectance measurements were performed on polished grain blocks using the Zeiss Axio Imager M1m photometer microscope with reflected, monochromatic, and polarized light (oil immersion) in Henan Polytechnic University. After calibrating the photometric system, vitrinite reflectance were continuously measured as the stage was rotated through 360°. At each measurement point, an apparent maximum reflectance (R′max) and an apparent minimum reflectance (R′min) were recorded. About 200 measurement points were selected on one specimen, usually on banded telocollinite. On the basis of collected data, the maximum (Ro,max) and minimum vitrinite reflectance values (Ro,min) were calculated using Kilby’s method Raman spectra of the samples were examined in-situ by a Jobin Yvon HR640 instrument with microscopy, equipped with 50× objective in Tsinghua University. A 532 nm Nd-YAG laser was used as the illumination source. The laser power was controlled to 2.5 mW to avoid thermal alteration of the sample. Spectra were collected at room temperature for 10 s over the spectral range of 700–2200 cm−1, covering the first-order region (1000–1800 cm−1). Considering the heterogeneity of coal, for each sample Raman spectra were collected from three different locations.Samples from Wangtaipu Colliery are of similar Ro,max (4.3%), which fall into the category of anthracite B according to ISO11760 (Classification of coals). The a reveals that there is a negative correlation between Ro,min and bireflectance. The increase of bireflectance with the decrease of Ro,min is viewed as the beginning of pre-graphitization, which usually occurs at Ro,max
> 6.0% The Ro,max values of Sihe samples range from 3.00 to 4.32%, which are mainly anthracite C (according to ISO11760), except that sample S-D-4 (Ro,max
= 4.32%) is the anthracite B. According to the burial of anticline is about 15 m deeper than the reverse fault, so if Ro,max is only influenced by temperature, Ro,max values of S-Z samples should be similar or a little higher than S-D samples. However, there is no such a relation, indicating that Ro,max values are also influenced by tectonic stress. The Ro,min and bireflectance values vary from 2.27 to 3.35% and 0.73 to 1.12%, respectively. The b indicates that both Ro,min and bireflectance show a good positive correlation with Ro,max, suggesting that for Sihe samples, the variations in the vitrinite optical properties are mainly caused by stress. Similar with Wangtaipu samples, samples from Sihe Colliery with a higher bireflectance also show more obvious tectonic stress influences. For example, sample S-D-1 (bireflectance = 1.12%) displays obvious friction surface and the coal is very soft, which can be broken into powder by hand; by contrast, sample S-Z-2 (bireflectance = 0.82%) is hard and integral, and cannot be broken by hand.a shows the Raman spectra of collected samples. Two major bands respectively at 1350 and 1600 cm−1 are identified. A minor band at about 1230 cm−1 is also visible, which is more obvious in Sihe samples than in Wangtaipu samples. To obtain detailed and fine data of Raman spectra, a curve-fitting procedure was performed following Sadezky et al. a, four bands are assigned to the first-order Raman spectra. They are the G band at ∼1597 cm−1 (Lorentzian profile), D band at ∼1338 cm−1 (Lorentzian profile), D3 band at ∼1499 cm−1 (Gaussian profile), and D4 band at ∼1237 cm−1. The curve fits of the sample S-D-3 are shown in the b as an example. Results of all fitting data (peak position, amplitude, area, and wide) are listed in the Supplementary Material II.The G band corresponds to the E2g symmetrical stretching vibration mode in the polyaromatic structure b shows that for the perfect graphene, only G band (near 1580 cm−1) exists in the first-order region; while for the defective graphene, D band appears in approximately the same region (near 1350 cm−1) as in anthracite. Direct observations of the layered structure in coals from HRTEM reveal that aromatic layers exist as fringes with tortuosity a, the D4 band in Wangtaipu samples (Ro,max
= 4.3%) is not as obvious as that in Sihe samples (Ro,max
= 3.0–4.3%).The D and G band intensity ratio is widely used for characterizing the defect degree in coals and related materials ). Samples from different collieries are of different geological age and maturity. The maturity degree shows that overall, for samples from the same colliery, with the increase of bireflectance, structure defects increase. Since the bireflectance reflects the deformation degree of samples from the same colliery, so can be interpreted that deformation is closely related with structure defects generation. This result agrees with results obtained from previous deformation experiments, which indicated that compared with brittle deformed anthracite (with no or little plastic deformation), ductile deformed coals were characterized by high structure defects Anthracite is a high-rank coal, and its macromolecular structure mainly consists of polycyclic aromatic hydrocarbons (PAH) that exist as aromatic layers To explain the potential role of structure defects in the deformation of anthracite, quantum chemistry calculations were performed on a macromolecule fragment which was selected from the anthracite atomic model proposed by Pappano et al. a shows the structure of this fragment. It is composed of thirteen aromatic rings and a hydrogenated aromatic ring. A carbonyl is linked at the periphery of the hydrogenated aromatic ring. The carbon content is 94.01%, the hydrogen content is 3.01%, and oxygen content is 2.98%. Structure defects are constructed by rotating the C-C bond of 90°, so that four hexagons are transformed into two pentagons and a pair of heptagons (blue highlights in b). Macromolecule fragment (a) and (b) have the same molecular structural formula and bonding types. All calculations were performed using the Gaussian 09 program. The geometries were optimized using the density functional theory (DFT) B3LYP/6-31G (d, p) method. With the generation of structure defects, molecular geometries, such as bond lengths and bond angles, change. As shown in the , compared with the molecule (a), all C-C and C-O bond lengths in the molecule (b) change, with some being stretched and some being compressed, making the molecule (b) a strained one. The deviation of atoms from their equilibrium geometry reflects the local force distribution and transforms some mechanical energy into chemical energy. In the absence of the SW defect, the total system energy is −1685.637 a.u. After four non-hexagon rings are generated, the total system energy is improved to −1685.522 a.u. That is, accompanying one SW defect generation, 0.115 a.u (303.48 kJ/mol) energy is stored in the molecule. Calculations suggest that with the generation of structure defects, chemical bonds can adjust themselves to the applied force by changing their geometries without breakage, so samples will display plastic deformation, instead of fracturing. With the increase of structure defects, since chemical bonds have more chances to adapt themselves to the stress, deformation degree gradually increases. Otherwise, if there is no structure defect generation, the mechanical stress will directly break chemical bonds and result in the macroscopic fractures.The weakest bonds in the molecule (a) and (b) are the C-C bonds linked with carbonyl carbon, i.e. C1-C2 and C1-C3 (yellow highlights in ), the breakage of which will result in the formation of carbon monoxide (CO). Mechanochemistry research proves that mechanical stress can break chemical bonds directly by stretching the molecules . The energy and geometry optimization at each deformation state was still calculated at the B3LYP/6-31G level of DFT. The c shows that for the molecule without defect, the required energy continues to increase as the distance of C1 and C4 atom increases, leading to a maximum required energy of 846.37 kJ/mol at the distance of 3.795 Å; further elongation of the distance to 4.270 Å breaks the C1-C2 and C1-C3 bonds. In contrast, the molecule with SW defect shows a maximum required energy of 815.60 kJ/mol, indicating that the energy needed to produce CO from carbonyl is slightly reduced by the existence of even only one SW defect (c). Though the energy was not calculated continuously and the maximum required energy does not exactly equal the activation energy, it is safe to infer that the existence of SW defect can reduce the energy barrier of CO generation from the macromolecule of anthracite. The reduced energy barrier is probably caused by the variations in the initial reactant energy and molecule geometry. As mentioned in the calculations, the reactant energy is increased by 303.48 kJ/mol accompanying the generation of SW defect. The a and b indicate that the C1-C2 bond length decreases from 1.520 to 1.500 Å, and the C1-C3 bond length increases from 1.476 to 1.482 Å. The bond angle between them also changes from 118.1 to 116.2°. The influence of structure defects on the macromolecular structure suggests that stress can facilitate the chemical structure evolution and result in greater chemical structure variations in coals, which is supported by previous Fourier Transform Infrared spectroscopy (FTIR) and 13C Nuclear Magnetic Resonance (13C NMR) investigations. The FTIR and 13C NMR results indicate that with the increase of deformation degree, from brittle to ductile deformation, aliphatic carbons gradually decrease and aromatic carbons increase, implying the pre-evolution of coal structure under stress The macromolecular structure response of anthracite under stress was investigated using anthracites with different tectonic deformation from three deformation zones in Wangtaipu and Sihe Colliers of the Qinshui Basin, Shanxi Province, China. The following results are obtained:For samples from the same colliery, using bireflectance (Ro,max
− Ro,min) to measure the deformation degree and Raman spectroscopy to reveal the macromolecular structure characteristics, there is a positive relationship between Raman area ratio AD/AG and bireflectance, in agreement with results we have obtained in previous deformation experiments. Both results support that the deformation of anthracite is related with the generation of structure defects at the atomic scale;Quantum chemistry calculation shows that accompanying the generation of one Stone-Wales (SW) defect (induced via in-plane rotation of C-C bond by 90°), the molecular geometries of anthracite, such as chemical bonds and angles, change. The deviation of atoms from their equilibrium geometries reflects the local force distribution and transfers some (303.48 kJ/mol) mechanical energy into chemical energy. In this way, chemical bonds adjust to the applied stress without breakage, so anthracite will accommodate plastic deformation, instead of fracturing;The existence of even only one SW defect can slightly reduce the energy needed to produce carbon monoxide from carbonyl in anthracite. This influence is attributed to the changes in the reactant energy and geometry caused by SW defect. The result suggests that stress can facilitate the chemical structure evolution in coals.Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.fuel.2017.05.085Influence of dye doping on the structural, spectral, optical, thermal, electrical, mechanical and nonlinear optical properties of -histidine hydrofluoride dihydrate crystalsStructural, optical, NLO and other properties of Rhodamine-B (dye) doped -histidine hydrofluoride dihydrate (RLHHF) crystals have been investigated in this work. RLHHF crystals were grown by the slow evaporation technique at room temperature. The results of single X-ray diffraction reveal the orthorhombic system of RLHHF crystal with a non-centrosymmetric space group P21 21 21. Various diffracting planes of the grown crystal were identified from the powder X-ray diffraction study. Fourier transform infrared spectral analysis was used to identify the functional groups present in the crystal. The optical transmittance spectrum was recorded for powder RLHHF sample and the transmittance observed is about 85% in visible region with a lower cut-off wavelength at 237 nm. The fluorescence emission spectrum shows the emission is in the yellow region. The presence of various elements in the crystal was analyzed using EDAX technique. Mechanical hardness, stiffness constant, and yield strength were estimated by the Vickers microhardness technique. Thermal studies were carried out to discuss the thermal stability and various decomposition stages of the material. The dielectric constant, dielectric loss and AC conductivity of the title material were calculated at different temperatures and frequencies to analyze the electrical properties. By Kurtz-Perry technique, SHG measurement was carried out and it is observed that the SHG efficiency of the powdered RLHHF sample increases as the particle size increases.Recent research shows that the frequency conversion is one of the important methods to extend the useful wavelength range of laser -histidine is used as it is the most basic amino acids among others. These amino acids form a significant number of salts that contain different organic and inorganic acids and posses NLO properties. In these materials, the efficiency of high SHG conversion is observed compared to the standard KDP materials -histidine based semi organic NLO crystals like -histidine hydrofluoride dihydrate (LHHF) Dye inclusion crystals are used for the application of solid-state lasers. The dye molecule is incorporated into the water-soluble crystals in order to address many drawbacks that occurred in other solid materials such as working media for lasers since dyes do not interact with oxygen and water In the present investigation, the growth and characterization of RLHHF crystal are reported for the first time. The grown crystals are subjected to X-ray diffraction studies, FT-IR studies, EDAX studies, UV–vis-NIR spectral studies, fluorescence studies, thermal studies, dielectric studies, Vickers microhardness studies, and SHG studies.-Histidine hydrofluoride dihydrate (RLHHF) was prepared by dissolving -histidine (Merck), hydrofluoric acid (Merck) taken in the ratio of 1:1 in double-distilled water and 0.1 mole% Rhodamine-B is added to this solution. The prepared solution was stirred to get the homogeneous mixture, it was filtered and allowed for evaporation at room temperature. The synthesized RLHHF was purified by successive recrystallization processes.To grow a bulk single crystal of RLHHF, the prepared solution of RLHHF was taken in a beaker closed with a perforated cover. The solvent could evaporate slowly. The microbes have not been observed during the growth of the crystal, probably due to the presence of hydrofluoric acid (HF) which acts destructively on the growth of microbes. RLHHF crystal was harvested from the mother solution with a growth period of 31 days. The pink color of the RLHHF crystal indicates that the dopant (Rhodamine-B) has entered into the lattice of LHHF crystal. The photograph of the as-grown crystal is shown in . It is mentioned here that the undoped -histidine hydrofluoride dihydrate (RLHHF) crystal is colourless The grown crystal of RLHHF was subjected to single-crystal XRD analysis to find the cell parameters by employing Bruker AXS Kappa Apex-II single crystal CCD X-ray diffractometer with MoKα (0.71073 Å) radiation. From the single crystal XRD data, it is observed that RLHHF crystallizes in the orthorhombic crystal system with the non-centrosymmetric space group P21 21 21. shows the lattice parameter values of RLHHF crystal. From the literature, it is found that the lattice parameters of RLHHF crystal are slightly altered in comparison with undoped -histidine hydrofluoride dihydrate crystal (LHHF) and the crystal structure is observed to be the same for both dye-doped and undoped crystals The crystalline nature of the RLHHF was analyzed by powder XRD analysis. For this analysis, the grown crystal was crushed into a fine powder and subjected to analysis by an XPERT PRO diffractometer with CuKα (λ=1.5418 Å) radiation. The sample was scanned over the range of 10–80° at a scan rate of 2°/ minute. The recorded powder XRD pattern of RLHHF is shown in . The recorded diffraction peaks (h k l) values are indexed by the Powder-X software package. The well-defined sharp diffraction peaks reveal that the RLHHF crystals are of good crystalline quality.FT-IR study is used to identify the functional groups of the grown crystal. The FT-IR spectrum of RLHHF crystal was recorded in the region 4000–400 cm−1 with a Perkin Elmer FT-IR spectrometer (Model: Spectrum RXI) using KBr pellet technique and is shown in The stretching frequency around 3447 cm−1 clearly indicates the OH stretching of the carboxylic acid group and the presence of hydrogen bonding and the water molecule in the crystal lattice O group gives its stretching frequency around 1668 cm−1. The peaks at 1503 and 1429 cm−1 are assigned to the symmetric bend of NH3+ and symmetric mode of –COO−.The torsional NH oscillation of NH3+is obtained at 540 cm−1. The various functional groups associated with the grown crystal are presented in Linear optical studies provide the information on the linear optical parameters like transmittance, absorbance, optical band gap, reflectance, linear refractive index, extinction coefficient, etc. The UV–vis-NIR transmission spectrum of the powdered sample of RLHHF was recorded in the range 190–1100 nm using Perkin Elmer (Lambda 35) spectrometer. As RLHHF crystal is an anisotropic material, the absorbance of this sample depends on the relative orientation of the crystal to the incident beam and hence the transmittance spectrum was recorded for the powdered sample. The recorded optical transmission spectrum is shown in . Low absorption in the entire visible and near-infrared region is observed with the lower cut-off wavelength at 237 nm. Using the formula Eg = 1240/λ nm, the bandgap energy of RLHHF crystal is calculated to be 5.23 eV. As the RLHHF crystal shows good transmission, it is appropriate to employ in optical devices -histidine hydrofluoride dihydrate crystal (LHHF) crystal (at 220 nm) Fluorescence is the phenomenon in which electronic states of solids are excited by light of particular energy and the excitation energy is released as light shows the recorded fluorescence spectrum for the title material. From the broad emission peak was observed at 579 nm. Using the relation Eg = 1240/λ eV, the energy band gap was calculated to be 2.14 eV. The results show that RLHHF has yellow fluorescence emission. The fluorescence emission is due to electron-donating group NH2 and electron acceptor group COOH of Rhodamine-B in the grown crystal The energy dispersive X-ray (EDAX) spectrum of the RLHHF crystal was recorded using Vega 3 Tescan model scanning electron microscope and the results are displayed in ), it is clear that Rhodamine-B doped LHHF crystal contains the elements such as C, O, N, F and Cl. The composition of various elements is shown in . Thus, from the result, it is confirmed that the doped element (Cl) has entered into the lattice of the RLHHF crystal. It is to be mentioned here that the element hydrogen cannot be identified by the EDAX method.Microhardness studies were carried out at room temperature using Shimadzu hardness tester. Microhardness, work hardening coefficient, yield strength and stiffness constant are some of the important mechanical properties. The Vickers microhardness number (Hv) was calculated using the relation Hv = 1.8544 p/d2 where p is applied load and d is the average diagonal length of indentation impression. shows the variation of Hv as a function of applied load varying from 25 to 300 g on the RLHHF crystal. It is seen from the that, Hv increases with the increase of load. The plot of log p against log d is shown in The work hardening coefficient (n) of the RLHHF crystal was ascertained by the least-square fit method. The ‘n’ value of RLHHF crystal was found to be 2.61. Onitsch and Hanneman The elastic stiffness constant (C11) of RLHHF crystal is calculated using Wooster's empirical relation It is observed that the values of the yield strength of the RLHHF crystal increase with the applied load and hence the grown crystal has high mechanical strength. Due to the release of the internal for loads above 300 g, indentation cracks developed on the smooth surface of the crystal. The observed values of stiffness constant and yield strength indicate that the binding forces between the ions in the crystal are strong The thermogravimetric (TG) and differential thermal analysis (DTA) were carried out simultaneously using SDT Q 600 V 20.9 Build 20 thermal analyzer in the temperature range 50–800 °C in the nitrogen atmosphere at a heating rate of 20 °C/min. The thermograms of RLHHF crystal are displayed in From the TG curve, it is noticed that there is no weight loss up to 90 °C and multi-stages of weight loss are observed. There is no endothermic and an exothermic peak before the decomposition point (90 °C). It reveals that there is no phase transition and no decomposition occurs up to decomposition point Dielectric constant and dielectric loss factor measurements were performed using the parallel plate capacitor at different temperatures up to 120 °C using an Agilent 4284A LCR meter at different frequencies ranging from102 to 106 Hz. Defect-free and transparent crystals were selected for the dielectric measurements. The dielectric constant (εr) and dielectric loss (tanδ) were estimated for varying frequencies under different temperature slotsfrom30 to120 °C. The variations of dielectric constant and dielectric loss of the sample with frequency at different temperatures are shown in . From the results, it is observed that both dielectric constant and loss factor decrease as the frequency increases and these values increase as the temperature increases. This can be explained based on polarization and conduction processes, which are involved when an electric field is applied to the crystal. At the lower frequency, we obtained a higher value of dielectric constant which may be associated with the presence of four polarizations namely space charge, ionic, orientation and electronic polarization. However, its low value at high frequencies can be related to the loss of significance of these polarizations that decreases gradually. The higher values of εr with lower frequencies can be explained by the space charge polarization The AC conductivity (σac) was calculated using the relation σac= 2πf ε0 εr tan δ where f is the frequency of the applied field ε0 is the permittivity of free space (8.85 × 10−12 C2 N−1 m−2), εr is the dielectric constant and tan δ is the dielectric loss of the sample. In , the frequency dependence of ac conductivity at various temperatures is shown.It is seen that at a given temperature, the magnitude of conductivity is high at high frequencies which is normal dielectric behavior. The electrical conduction in the dielectric is mainly a defect-controlled process in the low- temperature region. At any particular temperature, Gibb's free energy of a crystal is minimum certain fractions of ions leave the normal lattice. As temperature increases more and more defects are produced, which in turn increases the conductivity The nonlinear optical (NLO) property was determined using powder Kurtz and Perry . The SHG intensity increases linearly with the increase in particle size till 355 µm and above this range, the intensity gets deviated from the linearity and starts attaining saturation. This property of particle size dependency of SHG intensity is observed in phase matchable crystals. Hence from the obtained result, RLHHF crystal is an efficient candidate in frequency doubling applications and as a parametric oscillator The novel dye (rhodamine B) doped semiorganic crystal of RLHHF was successfully RLHHF from the water solvent by the slow solvent evaporation method. As reported in the literature, the undoped -histidine hydrofluoride dihydrate crystal is observed to be colourless. But the title sample rhodamine-B doped -histidine hydrofluoride dihydrate (RLHHF) crystal is slightly pink in colour. The grown crystal has been characterized by single crystal XRD method and also the powder XRD study was carried out and the obtained diffracted peaks were indexed. Various functional groups of grown crystals were identified from FT-IR spectral analysis. The various elements present in the crystal were identified by EDAX analysis. The title material has yellow color fluorescence emission at 579 nm. The dielectric constant and dielectric loss of the RLHHF crystal decreases exponentially with frequency. The AC conductivity was found to be high at high frequencies and high temperatures. Comparing to the thermal stability of unodped -histidine hydrofluoride dihydrate sample, the thermal stability of Rhodamine-B doped -histidine hydrofluoride dihydrate crystal is slightly less. It is observed that the work hardening coefficient of unodped -histidine hydrofluoride dihydrate crystal is 1.43 and this value is more for Rhodamine-B doped -histidine hydrofluoride dihydrate (RLHHF) crystal. It is found that the UV cut-off wavelength of RLHHF crystal (at 237 nm) is more than that of LHHF crystal (at 220 nm). The second-order nonlinear optical property (SHG) was confirmed by the emission of green light radiation and SHG efficiency of the RLHHF sample was measured as the function of particle size. The plateau region for large particle size gives an indication that RLHHF crystal is a phase-matchable material. Owing to all these properties, RLHHF crystal may be a potential material for photonic and electro-optic device applications.V. Kathiravan: Investigation, Methodology, Writing - original draft, Project administration. G. Satheesh kumar: Methodology, Conceptualization, Data curation. S. Pari: Writing - original draft, Writing - review & editing. P. Selvarajan: Writing - original draft, Writing - review & editing.Copyright to the above work (including without limitation, the right to publish the work in whole, or in part, in any and all forms) is hereby transferred to Journal of Molecular Structure, to ensure widest dissemination and protection against infringement of it.Influence of halloysite nanotube on hydration products and mechanical properties of oil well cement slurries with nano-silicaExcellent physical and chemical properties of halloysite nanotube make it potential to reinforce cement composites. In this study, effects of halloysite nanotube on mechanical properties of oil well cement were investigated. The results showed that the compressive and flexural strength of cement with 3% halloysite nanotube was increased by 40.8% and 49.2%, respectively and the elasticity modulus decreased by 20.01% after curing for 28 days, which demonstrated that halloysite nanotube cement had high strength and good toughness. TG-DTA, SEM, XRD, MIP tests were carried out to study the hydration products and microstructure changes in cement samples after adding halloysite nanotube. Optimized hydration products, lower permeability up to 38.82%, cross-linking and denser microstructure all contributed to excellent mechanical properties of oil well cement with halloysite nanotube.Portland cement is the most commonly used oil well cement. In petroleum industry, oil well cement is typically utilized to fill the annular space of the casing and rock formation, isolate complicated layers, support the casing and protect it from corrosive fluids Among all the nanomaterials, nanosilica is the most concerned due to its excellent pozzolanic properties and many studies have been done about the effect of nanosilica on the on the properties of cement slurries Another promising candidate to improve properties in cementitious materials is halloysite nanotube because of its high surface area, excellent mechanical properties, low cost and natural existence In the present study, the mechanical properties of oil well cement with different dosage of halloysite nanotube were measured. Thermal analyses, hydration products composition and microstructure were studied to explore the enhancement mechanism using TG-DTA, XRD and SEM, respectively. Porosity and gas permeability are important indicators for durability for cement based materials, the influences of halloysite nanotube on pore structure and gas permeability of oil well cement were also investigated.Ordinary commercial G grade oil well Portland cement was used, and the chemical compositions of cement are presented in . 1.5% nano-silica as replacement for cement was used. Halloysite nanotube (HNT) was provided by Nanyu material Co. Ltd., Hebei province of China and the transmission electron microscope, scanning electron microscope morphologies and thermal gravimetric curve of HNT are shown in . The physical properties of nano-silica and halloysite nanotube used are listed in . It is noted that HNT is stable before 400 ℃ and can be used in high-temperature oil wells. To ensure the fluidity of oil well cement pastes, a poly-carboxylate (PC) dispersing agent was used to improve the dispersion of nano-materials, as the addition of materials of high surface area could increase the water demand obviously.In order to explore the influences of halloysite nanotube on the mechanical properties of oil well cement pastes, five different cement samples containing 0, 1, 2, 3 and 4% halloysite nanotube were prepared. 1.5% nano-silica as replacement for all the 5 cement samples was used to promote cement hydration and 0.3% PC dispersing agent was used to ensure good rheology behavior. The mix composition of oil well cement slurries are shown in , which can produce about 600 mL cement pastes.Oil well cement pastes were prepared according to the Chinese standard GB/T 19139-2012. Firstly, halloysite nanotube and nano-silica were adequately dry mixed with oil well cement for 20 min before preparing cement pastes. Secondly, water and PC dispersing agent were added to a shear mixer orderly. Then, the shear mixer was turned on so that the water and the dispersant mix evenly. Thirdly, the dry blend was added to the mixer at low speed (4000 r/min) for 15 s and continuously mixed at high speed (12,000 r/min) for an additional 45 s. Then, the prepared cement pasts were used for rheology test and cured into square specimens (50.8 × 50.8 × 50.8 mm3) and rectangular specimens (40.0 × 40.0 × 160.0 mm3) for compressive and flexural strength test, respectively. The samples were kept in molds at 90 °C with 100% relative humidity at 3,7 and 28 days for test.Rotary rheometer (ZNN-D6, CHANDLER, USA) was used to measure the rheology behavior. The rheology tests were conducted after 5 min of mixing of the cement slurries and the slurries were kept at 90 °C with a heating chamber. The rheology parameters including yield stress and plastic viscosity were determined from the average shearing rate value of upload (ф3, ф6, ф100, ф200, ф300, ф600) and download (ф600, ф300, ф200, ф100, ф6, ф3) of the increase rotation of the rheometer.The compressive and flexural properties were severally measured by an electronic hydraulic tester at a crosshead speed of 400 N/s and a motorized 3-point-bending testing apparatus at a crosshead speed of 0.02 mm/min. The cement cores (φ1 in. × 2 in., as seen in , prepared from the 50.8 × 50.8 × 50.8 mm3 square specimens using a coring experiment) were used to measure elasticity modulus using a triaxial rock mechanics testing system (TAW-1000, Changchun Instrument Co. Ltd, China) at a constant loading rate of 2 kN/min with confining pressure of 20 MPa. In order to ensure the accuracy of mechanical performance test results, there were 5 samples tested for each test data and the standard deviation values are shown.Thermal gravity and differential thermal analyser (TG-DTA, SHIMADZU DTG-60, Japan) was utilized to test the cement hydration degree and calcium hydroxide content for the control, H1, H2, H3 and H4 samples curing at 3, 7 and 28 days. The samples were heated from room temperature to 1000 °C with the heating rate of 10 °C/min. XRD microanalysis (BRUKER D8, German) was utilized to determine the hydration products of the control and H3 samples curing at 28 days with a scanning rate of 0.02 s−1 in a 2ϴ range of 10–60°. In order to get deeper insights into the effect of halloysite nanotube on calcium hydroxide contents, 17–20° range of small angle diffraction is investigated for control and H3 samples at 1, 3, 7 and 28 days. Scanning electron microscopy (HITACHI SU8010, Japan) was utilized to observe the microstructure of control sample and cement with halloysite nanotube. Mercury intrusion porosimetry was utilized to compare the pore structures of control sample and cement with halloysite nanotube. The permeability measurement apparatus (Core Lab, CMS-300, USA) was used to measure the gas permeability of control and H3 cement samples. The sample should be vacuum dried for 4 h before mercury porosimetry and gas permeability testing.The rheological properties of the fresh state cement slurries are extremely important for the oil-well cement completion when nanomaterials are present in the paste composition. The rheological properties of halloysite nanotube cement slurries are familiar with Bingham model, and yield stress and plastic viscosity of samples containing halloysite nanotube are shown in . The yield stress and plastic viscosity both increased. The probable reason for the results is that halloysite nanotubes possess high surface area which need more water to lubricate the surface and the irregular nanotube shape of halloysite nanotubes tends to form a network structure inside the cement slurry, which impedes the flow of cement slurry. The flowability of oil well cement samples with halloysite nanotubes are also investigated. As seen in , the flowability decreased as the dosage of nanotube was increased. According to the results, 1–3% of halloysite nanotubes can be applied in oil well cement, because cement engineering requires that the flowability of cement paste should be larger than 18 cm. shows the compressive strength and flexural strength of the control, H1, H2, H3 and H4 samples. The results show that the addition of 2–3% halloysite nanotube was more effective in reinforcing the mechanical properties compared with the control samples and Farzadnia et al. (a), the compressive strength of H3 was increased by 35.5%, 41.8% and 40.8% after curing 3, 7 and 28 days, respectively. As seen in (b), the flexural strength of H2 and H3 were increased by 42% and 49.2% by comparing with control cement respectively after curing 28 days. The above results indicate that halloysite nanotubes can improve the compressive and flexural strength of cement significantly. The high compressive and flexural strength of set cement respectively means that the set cement has a strong ability to resist stressing and bending failure. Allalou et al. In order to investigate the influences of halloysite nanotube on the toughness on oil well cement, triaxial loading tests were done. The triaxial stress-strain curves for control and enhanced cement at 28 days are shown in shows the elastic modulus and peak strain results of control cement and cement with halloysite nanotube under triaxial confining pressure of 20 MPa. The results display that the peak strain of oil well cement samples increases while the elastic modulus decreases with the addition of halloysite nanotube. Therefore, the halloysite nanotube can improve the toughness of oil well cement to some extent under loading condition and reinforcement effects with different dosage of halloysite nanotube are significantly different as shown in . When the dosage of halloysite nanotube is increased to 3%, the peak stress and peak strain of hardened cement paste is increased by 18.85% and 48.59%, respectively. The elasticity modulus of H3 sample is decreased by 20.01% compared to the control sample. The triaxial results indicate that oil well cement with halloysite nanotube can exhibit a higher strength and a better toughness in the case of force. The above results showed that oil well cement with halloysite nanotube possess excellent mechanical properties including high strength and good toughness. In the following sections, thermal behavior, chemical composition and microstructure and gas permeability would be investigated, which may explain the mechanical results to some degree. shows the TG-DTA curves for control, H1, H2, H3 and H4 samples curing at different ages. Although the pure halloysite nanotube has a significant mass loss in the temperature range between 0 and 500 °C, it has been involved in cement hydration and its effect on the mass loss of hardened cement paste is limited. The mass loss of hardened cement paste is mainly due to the loss of water and decomposition of hydration products. The weight loss below 105 °C is mainly attributed to the escape of evaporation water existed in voids and capillaries of cement. When the cement samples continue to be exposed at temperature which rises to 1000 °C, the non-evaporable water and hydration products lose gradually shows the non-evaporable water content of cement with halloysite nanotube at different ages. As the curing age increases, the hydration degree and non-evaporable water content of cement increase. It's remarkable that the addition of the nanotubes increased the non-evaporable water content of cement distinctly. One reason for the result may be that the halloysite nanotube promotes cement hydration effectively. Another reason may be attributed to the loss of water contained between layers of halloysite nanotube which is along with expansion of the nanotube. The calcium hydroxide content can be calculated by the difference of the weight of cement under the heat at temperature of 400 °C and 500 °C, and shows the calcium hydroxide content of cement with halloysite nanotube at different ages. According to the results, in control sample the CH content at 3 and 7 days was higher than that of samples with halloysite nanotube. This may be attributed to the tardy reaction of nano-silica with calcium hydroxide than halloysite nanotube in the early period of hydration process. The CH contents of the control samples curing at 7 days and 28 days were quite close, which could be explained that the added nano-silica exert pozzolanic effect to form calcium silicate hydrate at a later time, which consumed a certain amount of calcium hydroxide. It can be seen that at 28 days the amount of calcium hydroxide was also less in sample with halloysite nanotube. This is further evidence that it has a positive hybrid behavior to exert pozzolanic effect when both halloysite nanotube and nano-silica both exist. compares the XRD patterns of control and H3 samples cured for 28 days, and there was no new diffraction peak occurred due to the addition of halloysite nanotubes. It’s remarkable that the intensity of the diffraction peak at about 18° which represent CH crystal of H3 cement is obviously reduced compared to the control cement. For further analysis of the differences, 17–20° range of small angle diffraction is investigated for control and H3 samples at 1, 3, 7 and 28 days, as shown in . The peak intensity of calcium hydroxide is determined by its crystal size and content. The crystal size is investigated by the analysis of XRD by full-width at half maximum (FWHM), and calculated according to Debye-Scherrer equation where D is the crystal size (nm); K is Scherrer constant 0.89; γ is X radiation wavelength, which is a constant value of 0.1549 nm; B is FWHM of the sample; θ is the diffraction Angle (rad).As the CH crystal size results shown in , there are little difference among the CH crystal size of control and H3 samples. Other research has also studied about the effect of nanomaterials on the CH crystal size. On one hand, nanomaterials can accelerate hydration process ), CH content increases with age in the first week, but a week later the increase in CH content is not significant as nano-silica exerted pozzolanic effect which consumed part of calcium hydroxide. The results are consistent with the conclusions obtained from thermal gravity and differential thermal analysis. For H3 samples (), amount of CH at 1 day is close to that at 3 days which may mean halloysite nanotubes consume most of calcium hydroxide from hydration reaction. But after 3 days, CH content is increased which may be explained that the reaction rates between halloysite nanotube and calcium hydroxide slow down. Consumption of CH increases again from 7 days to 28 days which may attribute to pozzolanic effect of nano-silica in cement specimen. By comparing , it can be seen that the amount of calcium hydroxide at all ages was less in cement with halloysite nanotube. Farzadnia et al. By comparing SEM of H3 and control samples in , microstructure of samples with 3% halloysite nanotube was much denser while control sample had relative loose structure. Hexagonal calcium hydroxide could be obviously seen in control sample but not seen in H3 sample. The results could be explained by several reasons: Firstly, the nanosized particles of halloysite nanotube can fill up nano-scale and micro-scale voids of hardened cement paste. Secondly, high surface area of halloysite nanotube can accelerate the hydration process and improve the formation of hydration products. A large amount of SiO2 on the outside surface of halloysite nanotube may participate in a secondary hydration reaction with calcium hydroxide to form C-S-H which is good for strength of cement matrix. Finally, expansion of halloysite nanotube may happen because there is a certain amount of water entrapped between its layers, which may result in further filling up in capillary pores of hardened cement paste. In order to further study the effect of halloysite nanotube on the microstructure of cement, SEM for H3 samples curing at different ages are shown in . Spheres of nano-silica coated with oil well cement can be seen in samples at 1 day and 3 days, but not seen in samples at 7 days and 28 days. Again, it proves that nano-silica participate in the reaction in later period. In addition, crosslinking and net-work structure which can restrict micro-crack to occur and bridge cracks hence reinforce cement matrix, can be found in samples with halloysite nanotube. The main reasons for this phenomenon may be that the nanotube shape and hydroxyl groups on the surface of halloysite nanotube react with cement composites.It is well known that cement composite is a kind of porous material and contains a large number of voids and capillaries, which may be negative for mechanical properties of cement material. The pore size distribution curves of control cement (C) and enhanced cement with 3% halloysite nanotube (H3) are shown in . According to the result, there is a narrow and high peak at about 90 nm and most pores are distributed between 80 and 100 nm for the control sample. Meanwhile, the curve of cement with halloysite nanotube is more wide and lower, and the pore size mainly ranges from 50 to 90 nm, which indicates that the enhanced cement with halloysite nanotube has fewer, smaller and more uniform pore structure. As seen in , the average pore size of enhanced cement decreased from 18.4 to 15.8 nm and the porosity decreased by 20.3% compared with the control cement. The effect of halloysite nanotube on the gas permeability of cement was also investigated. Adding 3% halloysite nanotube decreased gas permeability from 0.0085 to 0.0052 mD, and the fall was up to 38.82%. The results may be ascribed to the filling effect, accelerating hydration and expansion of halloysite nanotube, which together lead to a denser structure.According to the results and discussion in the present study, the enhancement mechanisms of halloysite nanotube effect on oil-well cement are summarized. Firstly, the nanosized particles of halloysite nanotubes may filled up the nano and micro voids which lead to that oil-well cement with halloysite nanotubes possess a denser microstructure comparing with the control sample. Secondly, the halloysite nanotubes may form cross-linking structure with cement composites due to their tubular structure. The functional groups on the surface of halloysite nanotube such as OH– The following conclusions may be drawn from the current study:Incorporation of 3% halloysite nanotube increased the compressive and flexural strength by 40.8% and 49.2%, and decreases the elasticity modulus by 20.01% after curing 28 days, which demonstrated halloysite nanotube cement had high strength and good toughness.Results from TG-DTA and XRD showed higher rate of hydration process and more consumption of CH to form C-S-H, which may be attributed to the high surface area and available SiO2 on the surface of halloysite nanotube.Denser microstructure could be observed from SEM of halloysite nanotube cement, which may be mainly because of higher hydration degree and the nanosize particles and expansion of halloysite nanotube filling up the pores of cement samples. Cross-linking structure could be also seen because of the nanotube shape and hydroxyl groups on the surface of halloysite nanotube.Oil well cement samples with halloysite nanotube possess lower gas permeability. Gas permeability of cement samples with 3% halloysite nanotube was reduced by a minimum of 38.82% compared with the control samples.Optimized hydration products, lower permeability, cross-linking and denser microstructure all contributed to high strength and good toughness of oil well cement with halloysite nanotube.Huiting Liu: Conceptualization, Data curation and analysis, Writing - review & editing. Jianzhou Jin: Conceptualization, Funding acquisition, Supervision. Yongjin Yu: Project administration, Resources, Supervision. Huimin Liu: Visualization, Writing - review & editing. Shuoqiong Liu: Conceptualization, Supervision. Jiyun Shen: Investigation, Methodology. Xiujian Xia: Data curation, Formal analysis. Hongfei Ji: Software, Validation.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.The influence of boundary conditions on the loading of rectangular plates subjected to localised blast loading – Importance in numerical simulationsA series of localised blast loading experiments are performed in order to understand how the experimental set-up influences the impulse imparted to a plate. The imparted impulse is measured using a ballistic pendulum. The experimental results show that for both rigid and deformable plates the impulse measured by a ballistic pendulum increases as the height of the boundary (clamps) increases. Significantly, it is found that although the measured impulse varies as a function of the boundary height, the plate deformation is unchanged. This suggests that not all of the impulse measured by the ballistic pendulum resulted in plate deformation. Therefore, in numerical and analytical modelling, the total impulse from the ballistic pendulum should not simply be applied as a centrally localised pressure load.Numerical simulations of localised blast loading in combination with the aforementioned experimental results are used to develop a localised blast loading model. The loading model is a simplified pressure loading model which only imparts the deformation causing impulse as opposed to the total ballistic pendulum impulse. The model is validated using an independent set of localised blast load experiments on clamped mild steel plates. Results obtained using a published localised blast load model are also compared.impulse density profile as function of radius and charge massTraditionally, in numerical modelling, a localised blast load has been represented by a constant pressure load acting over an area equivalent to the charge or burn diameter A variation of this method was presented by Bimha ) where the blast load was represented by a constant pressure acting over the charge area with the pressure decaying to the edge of the plate. Based on comparison with experimental plate deflection profiles the decay constant was found for variations in charge radius as a function of plate radius/width. In a further variation of this method, Balden and Nurick The preceding localised blast load models use the measured ballistic pendulum impulse to determine the magnitude of the pressure profile. This ensures that the total measured experimental impulse is applied impulsively to the plate in the form of a pressure load. These methods assume that the total impulse measured by the ballistic pendulum is transferred to the plate as a centrally localised load. The focus of this paper is to investigate this assumption in order to determine the proportion of the measured ballistic pendulum impulse responsible for plate deformation. The results of this investigation are used to develop a localised blast load model. The loading model is used in a finite element model of clamped rectangular plates subjected to localised blast loading. A comparison of the finite element results with an independent set of experiments on clamped rectangular plates provides a validation of the loading model.An alternative is to model the explosive using a program such as AUTODYN ), then a priori knowledge of how the impulse is imparted to the plate is not required. The geometry in the simulation will allow any physical phenomena to be reproduced and the impulse will be imparted as in the experiment. Axi-symmetric or 3-dimensional models can be used but 3-dimensional models greatly increase the computational expense. Experiments such as rectangular plate experiments cannot be reduced to axi-symmetric models and therefore, for practical reasons, developing a simple validated pressure loading model is advantageous.The paper begins by describing an experimental investigation to determine the effect of the presence of clamps (boundaries) and clamp height on both rigid and deformable plates for localised blast loading. The rigid plate tests are used to determine the effect of clamping arrangement on impulse transfer as measured by a ballistic pendulum. The effect of the varying impulse transfer is subsequently investigated in terms of plate deformation. Axi-symmetric numerical simulation results from AUTODYN are used to develop a pressure loading model which is applied to rectangular plates and compared with an independent set of experiments. The results of the investigation into the effect of the clamping arrangement are incorporated in the loading model. The results of the proposed loading model are compared with the results obtained using a published A series of experiments are performed in order to gain further insight into localised blast loading of rectangular plates. The experiments are as follows:To determine the effect of the boundary height (clamp height) on the impulse transferred for a given charge mass.To determine the impulse transferred to the exposed area of the plate only with no boundary effects.To determine the effect of the boundary height (clamp height) on the deformation of the plate for a given charge mass. shows the layouts used to determine the effect of clamp height (for a constant charge mass) on impulse transfer and deformation. In all cases with an exposed area the breadth (B) is 120 mm and the length (L) is 200 mm. The total plate dimensions are 260 mm × 300 mm. Tests with charge masses of 8 g, 12 g and 15 g (excluding the 1 g leader) are performed with either no clamps, one clamp or two clamps on the loaded side of the plate (additional charge masses are tested with two clamps). Each clamp is 16 mm in height. The charge diameter is kept constant at 40 mm which in this case results in a charge diameter to plate breadth ratio of one-third. As a result of the diameter being held constant the charge height increases with increasing charge mass. For the 8 g, 12 g and 15 g charge masses the calculated nominal charge heights are 4.0 mm, 6.0 mm and 7.5 mm, respectively. The clamp assembly is attached to a ballistic pendulum which measures the total transferred impulse (see The rigid exposed area plate tests are performed with a charge mass of 15 g (excluding the 1 g leader). The rigid exposed area plate is of the same size as the exposed area of the deformable plates and the plate is sufficiently offset from the pendulum attachments so as to ensure no direct blast loading of the pendulum, as shown in The experimental impulse versus mass of explosive results of the localised blast load tests performed on rigid plates with varying clamp heights is shown in . The rigid plate results are compared with previous deformable plate results to show that the measured ballistic pendulum impulse is independent of plate deformation. The single clamp rigid plate results (•) correspond to the previous single clamp deformable plate (♦) trends. Another important point is that the various trend lines clearly show that for the same charge mass the impulse recorded on the pendulum varies as a function of clamp height. Increasing clamp height results in increased transfer of impulse to the ballistic pendulum and therefore the effect of clamp height (experimental configuration) needs to be taken into account.For the cases where there is no clamp height, both sets of data show a reduced impulse as compared with clamped plate tests. The results of the exposed area rigid plate tests (□) are also shown in and the trend is below the rigid plate tests (▴) with no clamp. This is due to the reduced area of the exposed area plate tests compared to the plate tests with no boundary. These tests give an indication of the impulse transferred to the plate with no clamp effects and no direct loading on top of the clamps. This information is necessary to determine how much extra impulse is transferred to the plates as a result of the clamps.To get a quantitative idea of the effect of the clamps and clamp height, the trends of the 15 + 1 g case are examined. Taking the one clamp height case as a baseline the increase (decrease) in impulse for the other cases is given asIt is clear that when using the measured ballistic pendulum impulse to apply a load either analytically or numerically, the experimental configuration used to obtain the impulse value needs to be considered with great care.It has been established that for the same charge mass significantly different impulse measurements are possible depending on the boundary conditions used in the experiment. The next step is to determine whether for the same charge mass, the variation in impulse results in a variation in midpoint deflections for deformable plates.The deformable plate impulses as a result of varying clamp heights are compared with the rigid plate results at a charge mass of 15 + 1 g as shown in (a). The grouping of the deformable plate results corresponds to the grouping of the rigid plate results for varying clamp heights. There is no trend of the deformable plates transferring more impulse than the rigid plates and vice versa. For the current deformable plate experiments it is again shown that, within experimental variation, deformable plates do not produce different impulse transfers when compared with rigid plates.The plate midpoint deflections versus the measured impulse for the various clamp heights at a constant charge mass of 15 + 1 g are shown in (b). The experimental results indicate that even though there is a large variation in impulse transferred to the ballistic pendulum due to the varying clamp heights, the plate midpoint deflections are unaffected. Therefore for a given charge mass the clamp height greatly affects the measured impulse transfer but has no effect on the plate midpoint deflection. This suggests that not all the impulse measured by the ballistic pendulum results in plate deformation. This result is extremely important when representing the blast load with a simplified impulsive pressure load for analytical and numerical work. Even though the impulse measured by the ballistic pendulum is a true measure of the impulse being transferred through the plate, the total measured impulse cannot simply be applied as a centrally localised impulsive pressure load. As a result of the clamps, the applied impulse must be reduced to take account of the measured impulse which does not cause deformation.Localised blast loading simulations are performed using AUTODYN-2D v6.1, a state of-the-art nonlinear dynamics modelling and simulation software package The localised blast loading simulations are performed axi-symmetrically in AUTODYN-2D. The reason for using an axi-symmetric model as opposed to a 3-dimensional model is to reduce computational costs. The axi-symmetric model is used to characterise how the impulse density varies as a function of distance from the blast centre and to gain insight into the effect of the interaction between the blast wave and the boundary (clamps). A simplified pressure loading model is sought to replace the 3-dimensional modelling of the explosive and plate interaction within reasonable limits of accuracy.The AUTODYN model used to obtain pressure histories from the rigid plate test is shown in . The “rigid plate” is modelled by not specifying a boundary condition at the edge of the air zone. This allows no transmission of material and acts as a rigid boundary. The reflected pressure on the “rigid plate” is measured using gauge points in the air cell on the edge of the air zone. Transmission boundaries are included at the outer edges of the mesh. These boundaries are sufficiently far away from the plate so that the majority of the loading on the plate is complete before any material is lost through the transmission boundaries. The majority of the central load transfer is assumed to be complete within approximately 40 μs ((d)) and the explosive products have not yet reached the boundary (The size of the Eulerian cells is approximately 0.5 mm × 0.5 mm. The air is modelled using the ideal gas law and the explosive (PE4 = C4) is modelled using the JWL equation of state and are obtained from the material library in AUTODYN The detonation is modelled using a programmed burn where the detonation front travels at a constant detonation velocity of 8193 m/s for PE4 . Detonation is initiated at the end of the leader furthest from the plate and the detonation front travels as a planar wave along the leader. After reaching the end of the leader the detonation progresses into the explosive disc automatically using the programmed burn algorithm.The rigid plate simulation results for charge masses of 8 + 1 g, 12 + 1 g and 15 + 1 g are shown graphically in for various clamp heights. The results follow the same trend as the experimental results with an increase in impulse recorded for an increasing clamp height at a constant charge mass. To get a quantitative idea of the effect of the clamps and clamp height, the trends of the 15 + 1 g case are examined for the numerical model. Taking the one clamp height case as a baseline, the increase (decrease) in impulse for the other cases is given as (rectangular plate experimental values are given in parenthesis)Exposed area only: −33.3% (−10.0%) (trend not shown in The exposed area only and the no clamps case have slightly different impulses because the no clamps case has a larger area than the exposed area only case. Localised blast loading is not uniform and therefore the ratio of impulse of the exposed area only and the no clamps cases is not directly proportional to their respective areas. It is, however, useful to compare the no clamps case with the clamped cases because there is some loading on the top surfaces of the clamps and this area is included in the no clamps case.The increase in impulse for an increase in clamp height is more severe for the numerical results due to the fact that they are axi-symmetric and that the radius is taken as the half-width of the rectangular plate. The entire boundary of the axi-symmetric plate is close to the centre of the localised blast load as opposed to the rectangular plate where only the half-width boundaries are close. The axi-symmetric plate using the half-width as a radius gives an upper bound of the effect of boundary conditions on impulse transfer. Since only a trend of the effect of clamp height is sought the upper bound is sufficient. Direct comparisons between rectangular and axi-symmetric plates should not be made from this choice.For the axi-symmetric plates with clamps, as the explosive products expand radially they are met in all directions by a clamp face perpendicular to the radial expansion. This constraint is equal in all directions and does not allow a relief of pressure as is the case with the rectangular plates used in the experiments. For the rectangular plates, only the explosive products interacting with the closest point on the shortest and longest boundaries do so at right angles. Explosive products interacting with other points along the boundaries do so at acute angles which will result in lower reflected pressures and therefore lower impulse transfer. shows the pressure build-up due to the clamped boundary. The pressure build-up acts on the plate near the boundary after most of the pressure has receded above the plate with no clamp. This lingering pressure, although of relatively low magnitude, acts over a long duration and therefore increases the total impulse transferred to the plate. Graphs of the intermediate impulse density profiles are shown in . The impulse density is defined as the impulse per unit area. The impulse density at the centre of the plate has almost reached a maximum by the time the impulse density begins to increase at the boundary as shown in (b) and (c). The reflected pressure from the clamp travels back and forth across the plate and gradually adds more impulse. This is seen in the final impulse density profile in (f) where the plate with two clamps has a slightly higher impulse density than the plate with a single clamp which in turn has a higher impulse density than the plate with no clamp.In order to compare the rectangular experimental impulse results with the axi-symmetric numerical impulse results, the axi-symmetric impulse density results are mapped onto the quarter-rectangular layout as shown in . The impulse is calculated by creating a rectangular grid of 1 mm × 1 mm square “elements” and multiplying the area of each element by its impulse density. The impulse density of each element is determined by calculating its distance from the plate centre and using the distance to find the impulse density from the AUTODYN impulse density profile with no clamps. An example of the impulse density profile obtained from AUTODYN is shown in Once the impulse acting on each element is known the impulses are summed over the rectangle to obtain the total impulse (which is multiplied by 4). shows a graph comparing the experimentally obtained impulses with the numerically obtained impulses. The trend of the numerical impulses obtained from AUTODYN is below the experimental impulses. Given the necessary simplifications and approximations required to model this complicated event the numerical trend is nevertheless acceptable. Halving the element size in the region adjacent to the plate and using double precision as opposed to the usual single precision AUTODYN processor resulted in no change in the simulation results.Axi-symmetric impulse density profiles obtained from the 8 + 1 g, 12 + 1 g and 15 + 1 g AUTODYN simulations with no clamps are each fit (using a least-squares minimisation method) with a function of the form given in Eq. . The function is purely a curve-fit and no physical meaning is attached. Any function which can fit the impulse density profile could be used. The 15 + 1 g case is shown in (a). The AUTODYN fits are shifted up slightly so that the impulse they produce over the quarter-rectangular layout () matches their respective experimental impulses (exposed area only). The shift to match the experimental impulse is shown in (b) for the 15 + 1 g case (the shift is barely noticeable but nevertheless increases the impulse by approximately 7.7%). The 15 + 1 g case is chosen as a baseline impulse density function. The baseline function is multiplied by a scaling factor which is varied until the difference between the scaled baseline function and the 12 + 1 g experimentally matched function is minimised. The process is repeated for the 8 + 1 g case. The scale factors are plotted as a function of charge mass (including the 1 g leader) in The linear trend allows the scale factor to be determined for any charge mass in the range 8 + 1 g to 15 + 1 g. It is not known how far the linear trend can be extrapolated on either side of the range; this needs to be further investigated. The scale factor trend and the baseline function allow the impulse density distribution to be determined for any charge mass in the specified range. This means that by simply specifying the charge mass, the impulse density distribution which corresponds to the correct experimental impulse can be found. The baseline function (the 15 + 1 g case) is given asI∗(r)=(Ih∗−Il∗)(1−exp(s1(rinI−r)s3))+I1∗forr≤rinII∗(r)=(Il∗−I0∗)exp(s2(r−rinI)s4)+I2∗forr>rinIwhere r (mm) is the distance from the centre and the constants used to fit the function are given in . The scaled impulse density function, using the trend from The results of scaling the baseline impulse density function are shown in for the 8 + 1 g and 12 + 1 g cases, respectively. The results show that by multiplying the baseline function by a simple scaling factor, the impulse density distribution from the experimentally corrected AUTODYN simulations can be matched.In order to validate the scaled impulse density function, an independent set of experiments are performed on 3 mm thick, monolithic single-clamped mild steel plates with an exposed area of 120 mm × 200 mm. The chemical composition of the commercial quality mild steel plates is given in . The plate material mechanical properties are characterised based on tensile tests and Split Hopkinson Pressure Bar (SHPB) tests. The behaviour at quasi-static (8 × 10−4
s−1), intermediate (8 × 10−2
s−1) and dynamic (2.6 × 103
s−1) strain rates is characterised.The quasi-static and intermediate results are obtained using an iterative experimental/numerical method in which the tensile tests are simulated and the material properties adjusted until the experimental force–deflection curves are matched. A more detailed description of this method is given by Bao and Wierzbicki (a). The high temperature response is based on high strain rate, high temperature results of a similar mild steel as presented by Gilat and Wu The strain rate effects are characterised based on a strain of 0.1. The strain rate effects are additive as opposed to multiplicative and therefore the strain rate effect causes a parallel shift of the flow stress curve. With a multiplicative strain rate model, such as Johnson–Cook The final form of the material model is similar to that of Zhao σ(ɛ˙p)=σref[Cln(ɛ˙pɛ˙0p)+C1(ɛ˙pɛ˙0p)1/C2]The coefficients used in the material model are summarised in . The coefficients cp and η are the specific heat and inelastic heat fraction (Taylor–Quinney coefficient), respectively. 100% of the plastic work is assumed to be converted into heat.A graphical summary of the material response at various strain rates is given in . The tensile test results at quasi-static and intermediate strain rates are only presented up to the Ultimate Tensile Stress (UTS).The finite element program ABAQUS/Explicit v6.56 (a). Appropriate symmetry boundary conditions are included on the symmetry edges. A rigid clamp is placed at the boundary and a clamping force is applied. The plate is meshed using 3-dimensional continuum 8-node linear brick elements with reduced integration and hourglass control (C3D8R). The clamps are meshed using 4-node 3-dimensional discrete rigid brick elements (R3D4). Hard contact with separation allowed is defined between the clamp and the plate. Tangential behaviour is included with a friction coefficient of 0.5. Simulating an actual clamp as opposed to simply constraining the nodes at the boundary allows slight pull-in of the plate which is more realistic where the pressure profile is applied for a duration equal to the burn time, tb, which is calculated as the charge radius divided by the detonation velocity. The burn time equals 2.44 μs in this case. The pressure load is applied using a Fortran coded VDLOAD user-subroutine in ABAQUS/Explicit v6.56. The extent of the deformation for a 15 + 1 g charge mass is shown in (b) where the final midpoint deflection is more than 10 times the plate thickness.The experimental results for midpoint deflection are shown in together with a selection of simulation results and good correlation is achieved. Since the midpoint deflections are a necessary but insufficient condition of validation the deflection profile is also verified. shows the experimental and numerical deflection profiles for a 13 + 1 g and a 16 + 1 g charge mass. The simulation results, which correlate well with the experimental midpoint deflection trends and deflection profiles, validate the pressure loading profile and the scaled applied impulse.A localised blast load pressure model was developed by Bimha where P0
= central pressure, a
= charge radius, r
= position along radius and R
= plate outer radius. The decay constant, k, obtained using a combined experimental/numerical method is given byThe units for the decay constant given in Eq. are m−1. For an a/R ratio of one-third the decay constant is 148.3 m−1. The central pressure is found by substituting Eq. and solving for P0 (the impulse is known). P(r,t) is the pressure distribution as a function of radius and time (in this case the pressure is constant in time and the time is taken as the burn time, tb).. The Bimha model and results are compared with the proposed impulse function and the proposed function shows better correlation in terms of plate deflection profile. It is interesting to note that good correlation is only achieved for the Bimha model in which the applied impulse has been scaled to the exposed area only impulses. The results show that the simple Bimha model provides a relatively accurate prediction in terms of plate deflection profile. It could therefore be used as a localised pressure loading model on condition that the impulse is scaled correctly to remove non-deformation causing impulse.A series of experiments have been performed to determine the effect of the presence of clamps and clamp height on impulse transfer for both rigid and deformable plates under localised blast loading. An increase in clamp height in the experiments was found to increase the impulse measured by the ballistic pendulum. Deformable plate experiments with varying clamp height showed that the additional impulse due to the clamps did not influence the deformation of the plate. This implies that not all the impulse measured by a ballistic pendulum necessarily contributes to plate deformation. This is an extremely important result and has implications for localised load representation in numerical simulations and analytical modelling. Previous empirical results in terms of impulse and corresponding damage numbers need to be interpreted in terms of the experimental set-up in which they were obtained. In other words, previous empirical results implicitly contain the effect of using a single clamp (used in the majority of cases).Axi-symmetric simulations with AUTODYN were used to develop a pressure loading model which only takes into account the impulse which results in plate deformation and not the entire impulse as measured by a ballistic pendulum. The loading model was applied to rectangular plates and excellent correlation with experiments was achieved for plate midpoint deflection and plate deflection profile. The results of the loading model were compared with the results of a published localised loading model and the proposed model was found to correspond better with experimental results. When used with only the deformation causing impulse, the loading model by Bimha It is noted that only one experimental configuration (one load diameter and plate size) has been investigated in this work. The significance of the results obtained suggests that the work needs to be extended to include various charge stand-offs and diameters and various plate configurations. The effect of clamping arrangement also needs to be investigated for uniform blast loads.Effect of a pre or postweld heat treatment on microstructure and mechanical properties of an AA2050 weld obtained by SSFSWThe effects of a pre- or post-weld heat treatment on the microstructure and the mechanical properties of a sound stationary shoulder friction stirred AA2050 weld are compared.For both samples, the texture of the area located just under the zone deformed by the shoulder friction is similar and characterized by B and B̅ ideal shear components. In addition, whatever the sample, the nugget presents a lower thermal stability than the base material.Some differences are also worthy to be highlighted. Compared to the specimen with a post-welding treatment, the pre-treated sample possesses slightly greater grain sizes across the nugget depth. Concomitantly, other features are evidenced, namely a larger zone affected by the shoulder forging action, a smaller Al lattice parameter close to the top surface of the weld, the presence of Guinier–Preston zones resulting in a lower thermal stability, a smaller microhardness undermatching and a lower uniform deformation.Conventional rotational shoulder friction stir welding (FSW) was patented in 1991 by TWI. For the case of thick joints, the presence of a thermal gradient along the depth of the joints during the process entails heterogeneous microstructure and properties as shown in a previous paper This drawback was at the origin of stationary shoulder friction stir welding (SSFSW) which was proposed in order to improve the homogeneity of the microstructure along the nugget's depth. This pretty new process was first developed for temperature resistant metals (like titanium) or alloys with a low thermal conductivity Only few works on SSFSW are reported in the literature despite its numerous advantages. The studies are dealing with various welds whose nature differs from the present one (). The process was also applied to thin plates compared to the present case.In the current study, SSFSW was used in order to butt weld an AA2050 15 mm thick plate, which presents a rather low thermal conductivity among the aluminum alloys. The thermal conductivity at 20 °C of the T3 state is only of 76.6 W/mK for the 2050 alloy. Such a value must actually be compared with the close to 230 W/mK thermal conductivity of many aluminum alloys The aim of the current work is thus twofold:1) to investigate the effect of the aging step position, i.e. before or after SSFSW, on the microstructure and the mechanical properties of 15 mm thick joints and2) to explore if the SSFSW process is beneficial to the welding of thick Al–Cu–Li plates.The base material is a AA2050 aluminum alloy, belonging to the new Airware® alloys of the Al–Cu–Li family with the chemical composition range indicated in 15 mm thick plates (400 mm*200 mm) in a T3 + aged state or in a T3 state were abutted and joined perpendicularly to the rolling direction. FSW was conducted under a mean axial effort of 20–22 kN with a clockwise rotation rate of 400 rpm and at a welding speed of 100 mm/min. The tool made of the MP159 (35.7 wt.%Co, 25.5 wt.%Ni, 19 wt.%Cr, 9 wt.%Fe, 7 wt.%Mo, 3 wt.%Ti, 0.6 wt.%Nb, 0.2 wt.%Al) alloy was located at the faying interface. It was 0.5° tilted backwards. The tool comprised a 21.5 mm-diametered stationary shoulder prolonged by a pin. This 10 mm long pin was a left hand threaded truncated flute tool with 10 mm diameter at the root (). The backing plate was made of XC48 steel. Two superposed passes with air cooling down to room temperature in-between were performed one on each surface of the plate. The welding direction of the second pass was inverted so that the advancing side (AS) after the first pass remains the advancing side after the second pass.An aging for a few tens of hours at a close to 150 °C temperature was then carried out on the joint produced with the T3 material, which gives rise to the specimen referred to as the post-treated sample. The specimen aged in the aforesaid conditions and before welding is on the contrary designated as the pre-treated sample. The T3 state was obtained following the patented parameters defined in Both samples were stored at room temperature for several months after welding or artificial aging before their analysis to warrant that their characterization be made on a stable state at room temperature.The micro and nanostructure of the nugget of both samples and of the base material were compared. This investigation was conducted in (Y, Z) plane views () taken at various depths i.e. 1, 4 or 8 mm from the top surface of the second pass. After polishing, the various sections were characterized by X-ray diffractometry (XRD) in a Bragg–Brentano configuration by using a cobalt Kα radiation (λKα
= 1.78901 Å). The samples have also been etched for 20 s with the Keller's reagent (3 mL HNO3, 6 mL HCl, 6 mL HF, 150 mL H2O) so as to visualize the various features of the nuggets and to determine the mean grain size by means of the Image J® software with light micrographs. Scanning electron microscopy (SEM) was carried out to analyze the roughness of the free surface of the joints. Electron Back Scattered Diffraction/Scanning Electron Microscopy (EBSD/SEM) was also performed in order to identify the crystallographic textures at the aforesaid depths in the nugget centre. The specimens for EBSD were prepared by mechanical polishing down to 1 μm and then by electropolishing in a 25 vol.% nitric acid–75 vol% methylic alcohol solution at a temperature between − 10 and 13 °C with a voltage of 12 V and a current density between 0.17 and 1.15 A.cm− 2. The analyses were recorded with a step size of 1 μm. The accuracy of crystal orientations determined by means of a silicon monocrystal is 0.25°. For transmission electron microscopy (TEM) under a 200 kV accelerating voltage, thin foils were mechanically polished down to a thickness of 50 μm. The foils were then electropolished in the solution used for the EBSD samples preparation at a temperature between − 9 and − 4 °C with a voltage of 12.5 V and a current density in-between 18.1 and 22.6 A/cm2. They were finally ion milled with two 3 keV argon ion beams with a ± 6° angle of incidence for 15 min. Differential scanning calorimetry (DSC) analyses were also performed on the base material and on specimens sampled in the nuggets at the aforementioned depths, i.e. at 1, 4 and 8 mm from the top surface by using a Netzsch DSC 404C® apparatus. The experiments were conducted on samples of 16 mg with a heating rate of 10 °C/min under argon in an alumina crucible.Some Vickers microhardness tests were performed on the transverse sections of the nugget under a 50 g load applied for 15 s.Only the features of the joint generated by the second pass will be analyzed in the following. depicts the aspect of the plate surface after SSFSW. Whatever the sample, the surface is rather smooth even if some periodic linear features parallel to the travel direction of the tool can be observed (see b). They are due to the shoulder friction over the plate surface and more precisely to the roughness of the shoulder and/or to some dust or foreign particles which could have been dragged on the surface during the tool advance. Besides, and in spite of the reduced processing temperature, some traces of adhesive wear can be noticed on the surface. The height of these asperities remains lower than the relief of the semi-rings generated by a rotational shoulder for which one example is shown in a previous paper ) as it was already the case for the same alloy welded with a rotational shoulder As expected, the nugget bottom of the first pass has experienced the stirring action of the second pass. At the second pass nugget bottom, the pile-up of onion rings is obvious (see , the pile-up of onion rings is also visible close to the top surface, which definitely differs from the case of a rotational shoulder. In the latter case, the rotational movement of the shoulder as well as the pressure exerted on it governs the deformation of the area just beneath the shoulder which originates the shoulder shear flow zone. This shoulder flow zone hinders the upflow movement of the material chips cut by the pin up to the top surface b also shows the overall material displacement from the advancing side (AS) towards the retreating side (RS) close to the top surface of the joint. It is worth noticing that this material flow occurs over a larger depth than that of zone I.In addition, the turbulent interface or remnant joint line – which originates from the presence of remaining oxides – is also visible in b. Its serrated morphology is due to the helical down flow movement of the material led by the pin. In addition, the remnant line is shifted towards the AS, which agrees with a global displacement of material towards the retreating side.Finally, some equally spaced linear features can be distinguished more particularly on the AS of the nugget of the post-treated sample. These features are indicated by white arrows in b. Their number (about 12 for one nugget) is greater than the close to 10 pin threads number. It is worth noting that the dots on these lines are curiously located at the interfaces between two successive onion peels. It is therefore suspected that these features originate from periodic tool vibrations. depicts the EBSD maps of the transverse cross-sections from the top surface of the second pass. For both samples, the evolution of crystal orientations is similar across the nugget depth and for the second pass. Except the zone of pass overlapping at plate mid-thickness, two zones must be distinguished because of their different textures.As already shown by Prangnell in another joint ) near the top surface. The thickness of this zone is close to 200 μm thick in the present case. In this zone, the pole figures as well as the sections of the orientation distribution functions (ODFs) indicate that the crystallographic texture is not simple. The thickness of zone I is slightly greater for the pre-treated than for the post-treated sample. Conversely, below this area, zone II exhibits a close to < 111 > perfect fiber texture (For each sample, the plane sections at φ2
= 0° and 45° of the ODFs are on the contrary the same irrespective of the analyzed zone, either I or II (). This result proves that it is the pin motion which governs the texture even close to the shoulder. In accordance with this interpretation, shows that zone II presents only the fiber texture while this preferred orientation is not single in zone I.The direct interpretation of the ODF sections drawn in shows that the textures at a φ2 Euler angle equal to 45° are predominantly very close to the B 11̅2110 and B̅1̅12̅1̅1̅0 ideal shear texture components. According to the ODF sections at φ2
= 0°, no other A1, A2 or C shear texture components are identified whatever the zone In addition, the strict analysis of the ODFs sections shows that, in accordance with the cubic symmetry of the aluminum lattice, the samples are orthotropic According to the areas analyzed by EBSD, the fraction covered by the low angle boundaries (LABs) (with a misorientation between 2 and 15°) over the total boundary length amounts to 87% for the pre-treated sample (vs. 89% in case of post-treatment) while the frequency of high angle boundaries (HABs) (misorientation greater than 15°) is 13% for the pre-treated sample (vs. 11% for the post-treated sample). The HABs are uniformly distributed along the X–Y transverse cross-section.As it is the case of joints obtained by conventional friction stir welding, dynamic recrystallization occurs in the nugget during SSFSW. As a consequence, equiaxed grains are observed at all depths within both nuggets. Their mean size estimated at the different depths on the (X–Y) transverse cross sections views are summarized in . In both nuggets, the grain size diminishes along the depth (). In addition, whatever the depth, the grain size is similar in both samples.It is also worth noting that the size of the grains in the nugget remains smaller than the 55.2 μm mean size of the plate-shaped grains in the T3 + aged base material is deduced from the XRD analyses. It enables to compare the lattice parameter of aluminum at the different depths within the nugget of the second pass in both joints with the lattice parameter of the base material.Irrespective of the sample, and in contradiction with the possible existence of residual tensile stresses at least in the pre-treated sample ) which originates many kinds of precipitates, it very likely contributes to a reduction of the Al lattice parameter resulting from the dissolution of Cu rich precipitates during FSW. As demonstrated in the following, the T1 compounds are for instance dissolved during joining.At the joints mid-depth, i.e. at the depth of 8 mm, the aluminum lattice parameter amounts to the same value in both samples. Concerning the two other depths, the samples are differing from each other. More particularly, near the top surface, the lattice parameter of the pre-treated sample is more reduced than that of the post-treated nugget. According to the generation of residual tensile stresses in a friction stirred weld The X-ray diffraction patterns of the base material and at the different depths in the nuggets of the two samples are displayed in . The pre-treated sample seems to present fewer peaks than the post-treated sample.It is worthy to emphasize that the present study does not aim to a thorough investigation of the precipitation states at each depth. The interpretation of the XRD patterns is indeed quite ticklish, because of the complexity of the system due to the numerous alloying elements which entails multifarious natures of the potential precipitates and to the miscellaneousness of their distributions. Nevertheless, a phase is considered as definitely present in the sample when at least one Bragg peak in the XRD pattern can only be attributed to this compound. Using this procedure, the precipitates at the origin of most of the numerous peaks have been identified by direct comparison with their published crystallographic data. The origin of some very few peaks in is on the contrary not solved. Due to the complexity of the alloy chemical composition, some substitution of elements within more usual compounds, with resulting changes of their lattice parameters, are a priori expected. Further dedicated work remains necessary to elucidate this problem. Despite this drawback, the XRD analysis leads to the main following conclusions:Θ′ (Al2Cu) and T2 (Al5CuLi3) are for sure identified in the base material and at every depth in both nuggets.TB (Al7Cu4Li) exists at 1, 4 and 8 mm in the post-treated sample and at 1 and 4 mm in the pre-treated sample whereas its signal is weak at 8 mm in the latter sample. This phase is not identified in the base material.β′ (Al3Zr) is evidenced in the nugget of the post-treated sample and at 4 mm in the pre-treated sample. Its presence is also suspected at 1 and 8 mm in the pre-treated sample and in the base material.S (Al2CuMg) was identified in both nuggets and its formation is suspected in the base material.Finally, in the pre-treated sample, only traces of T1 (Al2CuLi) are found at 1 and 8 mm while they are not apparent at a depth of 4 mm. Conversely, in the post-treated sample this T1 (Al2CuLi) compound is detected at 4 and 8 mm and not formally identified at 1 mm. It however exists in the base material.To complete the XRD analyses, the precipitation states were investigated at the TEM finer and more local scale in the base material as well as in the joints (). The observations are essentially focused on the T1 (Al2CuLi) phase which is known to be the main strengthening precipitate in AA2050 alloys First, the base material contains many precipitates, among which the longest plate shaped Al20Cu2Mn3 precipitates arrowed in a. The volume fraction occupied by this compound is however reduced as it was not detected by the more statistical volumetric X-Ray diffraction. Some smaller T1 (Al2CuLi) precipitates with a width of 20 nm and a length over the [100–500 nm] range are also identified (b). Their nature was proved by electron diffraction (not supplied here). Other usual precipitates were detected such as some few tens nanometers diametered disk-shaped β′ (Al3Zr), nanometric plate shaped Θ′ (Al2Cu) and submicrometric diametered disk-shaped S (Al2CuMg). EDX analyses further confirmed their nature.By way of contrast, no T1 (Al2CuLi) phase was observed by TEM in the pre-treated sample, may be because of the very local feature of the analyses or of the slow kinetics of formation of the T1 (Al2CuLi) phase during natural aging after FSW, and despite the presence of many dislocations (b–e–g–h) which are known to promote the T1 formation. The white arrows in d–g further indicate Al20Cu2Mn3 plate-shaped precipitates. c also shows θ′ (Al2Cu) precipitates (marked by black arrows).In opposition with the previous case, some 100 nm long by 5–10 nm wide T1 (Al2CuLi) precipitates are detected at the different depths after the post-treatment (b–c–d–f–g–i). These particles which can be formed in presence of dislocations ( b-c-f) are indicated by white arrows for the finest ones in c and g. The T1 (Al2CuLi) phase is also observed inside the subgrains and at the sub-boundaries ( b). Some θ′ (Al2Cu) precipitates, indicated by black arrows in a–d and f, the precipitates density is higher at 8 mm than at the two other depths for the pre-treated sample. Concerning the post-treated sample, this conclusion seems less obvious ( shows that whatever the analyzed depths and the sample, the density of precipitates remains lower than in the T3 + aged base material.In summary, the T1 (Al2CuLi) phase is more often observed in the base material and in the post-treated sample than in the pre-treated sample. show the DSC curves of the base material and at the various depths of the nuggets in the pre- and post-treated samples. supplies further information about the endothermal or exothermal nature and the onset temperatures of the various thermal events.Four peaks can be distinguished on the DSC curve of the base material, the first one is endothermal whereas the following three ones are exothermal (). According to the literature data dealing with an Al–5.3%Cu–1.3%Li–0.4%Mg–0.4%Ag alloy in a T3 state and thus with a microstructure expected to be close to the present one, and tested in the same heating conditions in an aluminum crucible For the different zones in the nugget of both samples, the global aspect of DSC curves is the same as that of the base material.It is worth noting that peaks 1 and 4 are only evident in the pre-treated sample irrespective of the depth. This existence of peak 1 indicates the obvious dissolution of GP zones in the pre-treated sample which was naturally aged after welding.Moreover, peak 2 exists in both joints and at every depth.For the pre-treated sample at the depth of 1 mm and in accordance with the precipitates dissolution, expected from the low value of the Al lattice parameter (), the last three peaks are more marked than at the other depths. This result indicates more pronounced precipitations induced by the DSC heat input. puts into evidence that for any nugget and at any depth, the phase transformations corresponding to peaks 1 (when it is visible) and 2 happen more rapidly than in the base material. By way of contrast, the phase transformations corresponding to the two other peaks (when peak 4 is obvious) rather occur with the same or a slightly slower kinetics than in the base material.The sensitivity to thermal grain growth was further investigated along the nuggets' depth. For both samples, the mean grain size of the specimens which have experienced the DSC thermal cycle was around 15, 10 and 7 μm at the depths of 1, 4 and 8 mm, respectively. The comparison of the latter values with those of measured before the DSC analyses proves that the 10 °C/min heating up to 450 °C entails a slight grain growth in particular at the depth of 8 mm which has experienced the two successive tool paths corresponding to the first and second pass. The quasi absence of grain growth at a depth of 1 mm is consistent with the high fraction of LABs detected by EBSD (Section in Results part). The presence of precipitates has also very probably contributed to the grain size stability at this depth. shows that the nugget's microhardness is lower in the post-treated than in the pre-treated sample. Then, the undermatching is lower in the pre-treated sample. In addition, the hardness gradient is less pronounced along the nugget's depth and along the transverse direction at the different depths of the pre-treated joint. It gives the impression that the nugget as well as the HAZ is larger in the pre-treated than in the post-treated sample.At last, it is worth noting that the softest zone corresponds to the nugget's bottom. summarizes the tensile properties of the joints as well as the location of the final fracture area. By referring to the ultimate tensile strength of the base material, the joint efficiency amounts to 71% for the pre-treated sample vs. 75% for the post-treated sample. With regard to tensile elongation, the value of the joint efficiency is 55% and 59% for the pre-treated and the post-treated sample, respectively. In accordance with the localization of the tensile specimens in the joints and the hardness maps (), the differences are quasi inexistant between both joints.) with a low grain growth since the cooling time is decreased. A similar observation has already been reported for 5 mm thin joint of 2219-T6 Concerning the crystals orientations along the depth of the current nuggets, two zones are distinguished, a first one which extends over the first 200 μm beneath the top surface (zone I) and a second one (zone II) below zone I (As far as the upper part of the nugget is concerned, zone I results from the forging effect of the shoulder which is far less extended than in the case of a conventional rotational shoulder where the heat input due to the shoulder increases the malleability of the material and entails a deeper shoulder flow zone Conversely, the texture of zone II indicates the existence of a < 111 > preferential orientation parallel to the normal direction of the joint. The B 11̅2110 and B̅1̅12̅1̅1̅0 ideal shear texture components are further consistent with the literature data Comparing the evolutions of textures along the nugget depth of the pre- and post-treated samples (), the different extent of the shoulder affected zone near the top surface is very likely linked to the material microstructure before welding. At room temperature, the hardness of the material in the T3 + aged condition, i.e. 175 HV0.05, is higher than that of the T3 state (125 HV0.05), because of the precipitation of the T1 (Al2CuLi) phase during the artificial aging. As previously said, the T1 (Al2CuLi) phase is the major strengthening precipitate in 2050 alloy Due to this difference of mechanical strength, friction stir welding of the pre-treated sample should require a more important work in order to deform the material, which generates a heat input slightly greater than for the case of the post-treated sample. Such a modification is supposed to be the more marked with a stationary shoulder that it is known to bring less heat than a conventional rotational one. As a consequence, and in accordance with the current results (), the extent of the zone affected by the shoulder forging action (zone I) is slightly more important in the pre-treated sample. In addition, in this area, the T1 (Al2CuLi) particles are actually dissolved (a, b, c) because of the FSW deformation. This phenomenon agrees with the diminution of Al lattice parameter at the top surface of the pre-treated sample (). The greater Al matrix lattice parameter measured in this zone for the post-treated sample is due to aging which favors the precipitation of at least the T1 (Al2CuLi) phase. This assumption is also consistent with the higher hardness of the post-treated compared to the pre-treated sample (mean value of 140 HV0.05 vs 120 HV0.05, respectively) in zone I. More rigorously, instead of the hardness at room temperature, the flow laws of both materials at the welding temperature should have rather been considered in order to be more confident about the difference of heat input between both materials. In addition, the greater heat input required for the welding of the pre-treated sample is also consistent with the softening of the weld, which is laterally more extended (along the Y direction) than for the post-treated sample (). In the latter case, the post-welding treatment very likely generates phase transformation such as the formation of strengthening precipitates.As suggested by the diminution of grain size along the nugget depth, the use of a stationary shoulder only enables to reduce but not to suppress the gradient of heat input and hence of homologous temperature (defined as the ratio between the welding temperature and the absolute melting temperature) between the top and the bottom of the nugget, all the more that the AA2050 alloy presents a rather low thermal conductivity among the Al alloys. Some microhardness fluctuations remain along the nugget depth. These local variations agree with the TEM, DRX observations and DSC analyses according to which, the precipitation states discontinuously vary within the nugget. All these observations suggest a miscellaneous deformation generated by the pin along the depth.With regard to microhardness, it is worthy to note that given the grain sizes summarized in and according to the Hall–Petch relationship for aluminum alloys ) is therefore essentially due to the different precipitation states along the nugget. According to the present XRD and TEM results, the T1 (Al2CuLi) phase is however not the single cause of strengthening.Compared to the post-treated sample, in the pre-treated sample, the microhardness undermatching is lower because of the difference of thermal history of the two materials. Except of the expected higher welding heat input, the hardness of the pre-treated sample has to do with its T3 + aged state before welding and to natural aging subsequent to SSFSW. In the case of the post-treated sample, welding was on the contrary performed with a T3 state.The microstructure after welding (grain size, precipitation) evolves along the nugget's depth and in the case of the post-treated sample, despite the lack of data immediately after welding, the final aging seems to amplify the differences of behavior along the nugget (). The more important softening of the nugget's bottom in the post-treated sample actually corresponds to the softening of the T3 state during FSW. The subsequent post-welding treatment has indeed almost no effect on the microhardness The difference of hardness between both base materials is essentially linked to the larger volume fraction of the T1 (Al2CuLi) strengthening precipitates in the T3 + aged state. According to the elevated temperature and deformation necessary for FSW, to the decrease of the Al matrix lattice parameter (), it can be naturally assumed that a part of the T1 (Al2CuLi) phase is dissolved in the nugget during FSW. The dissolution is more pronounced at the weld top as the reached temperature is higher than at the joint bottom and as the present aluminum alloys possess a rather low thermal conductivity. The effect of local temperature on dissolution seems indeed to be predominant compared to the effect of the faster cooling rate close to the top surface since larger grain sizes are observed at this place (). Besides, post-welding treatment should have promoted the precipitation of the T1 (Al2CuLi) phase, which does not seem to be the case since the nugget's bottom of the pre-treated sample remains harder than that of the post-treated sample. As a consequence and as suggested by the similar amplitude of peak 2 in the DSC curves at a depth of 8 mm for both joints (), the amount of T1 (Al2CuLi) phase remains lower than at the other depths. This proves two things. First, the microstructure is heterogeneous along the nuggets' depth, although this feature is far less exacerbated than in another AA 2050 joint obtained with a rotational shoulder c at 8 mm) and of traces of T1 (Al2CuLi) precipitates. The major part of lithium in solid solution in aluminum and resulting from the dissolution of T1 (Al2CuLi) phase during SSFSW was therefore consumed to form in particular TB (Al7Cu4Li) and T2 (Al6CuLi3) compounds at the nugget's bottom. According to the time-temperature-precipitation diagram of a similar alloy It is the reason why the post-welding treatment is not effective on the T1 (Al2CuLi) phase precipitation at this location. The DSC curves also prove that a temperature of 200 °C, higher than that used during the aging treatment, is required for the precipitation of T1 (Al2CuLi) phase to go on.At last, the marked difference in undermatching at the nugget bottom between both specimens establishes that the pre-weld treatment must be preferred to the post-weld treatment.As far as the thermal stability of the joints is concerned (), the pre-treated sample is less stable (up to 114.9 ± 2.0 °C) than the base material (up to around 159 °C) while the post-treated sample is more stable (up to 223.5 ± 1.1 °C) than the base material.In the first case, the deformation generated during SSFSW favored a faster kinetics of phase transformation, in particular of the GP zones dissolution and of the T1 (Al2CuLi) phase precipitation. In agreement with the literature The enhanced stability of the post-treated sample is associated with the absence of detection of an endothermal peak corresponding to the dissolution of GP zones. The (Al–Cu) Guinier Preston zones observed in the pre-treated sample have very likely been formed during the natural aging after SSFSW. Conversely, the absence of GP zones in the post-treated sample may be due either to the aging which promotes the precipitation of the T1 (Al2CuLi) phase by consuming the Al and Cu atoms formerly contained in the GP atom clusters or to the previous formation of θ′ (Al2Cu) from GP zones.Besides, neither natural aging nor post-weld aging enable to complete the precipitation of the T1 (Al2CuLi) phase in the joints, as suggested by the DSC curves (The joint coefficients of both welds are quite similar and the choice of the pre- or post-welding treatment depends on the selected criteria for the applications. Indeed the pre-treatment leads to a slightly larger grain size along the nugget, a larger zone affected by the forging action of the shoulder, a less thermally stable joint, a lower undermatching of the nugget and a more homogeneous hardness in the nugget. Nevertheless, the 2050 alloy is most often used in the T8 peak aged condition, a heat treatment optimized to the base metal. The better condition would therefore primary result in an overall strength in the welding line closer to the base metal in the T8 condition.For time consuming and cost saving reasons, instead of carrying out one pass on each side of the plates to butt join 15 mm thick AA2050 plates, one pass on a single side seems more suitable. This requires increasing both pin length and diameter as well as the rotation speed. For the same reasons, the use of a bobbin tool with stationary shoulders A change of pin shape may also be better suited: for instance, the use of a cylindrical probe instead of a truncated one may be favorable to the strain and heat input homogeneization along the depth.To summarize, the use of a stationary shoulder leads to sound AA2050 alloy welds. Besides, this process is beneficial in order to reduce the gradient of grain size along the nugget's depth of the joints. It is however insufficient to totally suppress the heterogeneousness of the microstructure in the nugget of 15 mm thick plates. The joint's hardness is non constant along the depth since the hardness of AA2050 is governed by precipitation.The aging was performed either before or after friction stir welding and the effect of this modification of process was investigated on both the microstructure and the properties of the joints. The joints coefficients of both welds are quite similar and the choice of the pre- or post-welding treatment depends on the selected criteria for the applications. Indeed the pre-treatment leads to a slightly larger grain size along the nugget, a larger zone affected by the forging action of the shoulder, a less thermally stable joint, a lower undermatching of the nugget and a more homogeneous hardness in the nugget.Besides, both joints are similar with regard to the B and B̅ ideal shear texture components and to the almost perfect (111) fiber texture in the zone below the area affected by the forging action of the shoulder as well as to the nature of the phases detected in the nuggets.First-principles study on the stability and properties of β-SiC/Mn+1AlCn (M=Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta; n=1,2) interfacesIn this work, first principles calculations are performed to investigate the structural, electronic, and mechanical properties of the interface between β-SiC ceramics and Mn+1AlCn (M = Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta; n = 1,2) phases, with particular focus on Ti3AlC2 and Ti2AlC. The interface between the β-SiC(111) and Tin+1AlCn (0001) (n = 1,2) surfaces is most likely a stable interface because of the small misfit in lattice constants. Six different interface models between β-SiC(111) and Tin+1AlCn(0001) are examined. The optimized interfacial distances are determined using the universal binding energy relation method, and then each model is fully relaxed to calculate work of adhesion. By comparison, it is determined that the junctions connecting the C-terminated SiC(111) and Ti-terminated Tin+1AlCn(0001) surfaces are the most stable structures. Then the electronic structures for this interface model of Ti3AlC2/SiC are analyzed from the density of states, atomic charges, total electron densities and electron density difference. The elastic moduli are also computed in this study, and the data show that the mechanical properties for the composite Tin+1AlCn/SiC slab are between those of bulk Tin+1AlCn and β-SiC, with enhanced plasticity. Finally, the results for β-SiC/Tin+1AlCn are extended to study the interfacial stabilization of β-SiC ceramics and the wider class of Mn+1AlCn phase coatings (M = Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta; n = 1,2). It is found that SiC ceramics may be effectively joined by Mn+1AlCn with stable interfacial chemical bonding, which provides a theoretical basis for the effective junction in SiC composites.Silicon carbide fiber-reinforced silicon carbide-matrix composites (SiC/SiC) are well known as potential structural materials in nuclear reactors and fusion systems for their excellent performance in high temperature resistance against radiation-induced fracture, creep and corrosion in hot steam []. For light water reactor (LWR) fission power applications, in particular, the ceramic claddings composed of SiC/SiC fibrous composite, are attractive because of their potential to achieve satisfactory damage tolerance under severe accident conditions [SiC/SiC composites have been developed for decades since their discovery in the 1970s. At present, the strength of joining SiC ceramics to its composites is one of the crucial challenges limiting their industrial use, which causes the manufacture of these materials with a large size or a complicated shape to be still difficult and expensive []. Several technologies have either been established or are currently being considered promising for joining SiC ceramics to SiC/SiC composites [], such as thin foils of reactive metals junction [], spark plasma sintering (SPS) without titanium junction []. Among these junction phases, MAX phases are nano-layered ceramics with hexagonal crystalline structures with the generic formula of Mn+1AXn, where M stands for a transition metal, A represents an element from the IIIA or IVA groups and X is either carbon or nitrogen. Depending on the value of the n index, the MAX phases are divided into three general categories: 211, 312 and 413 groups []. Because of the dual behaviors of metals and ceramics, MAX phases have become an attractive industrial choice for joining ceramics, including SiC/SiC composites.So far, more than 70 different pristine or alloying Mn+1ACn (M = Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, etc.; A = Al, Si, Ge, S, etc.; n = 1,2,3) phases have been synthesized []. Interestingly, the MAX phases are marked by both their uniqueness and uniformity as a constellation. The difference in the transition metal element renders different reactivity under exfoliation toward the fabrication of their two-dimensional derivatives, MXene []. However, they also show similarity in structure and chemical bonding features because of coinciding layered atomic stacking patterns. The Ti3AlC2 and Ti2AlC phases have been the most widely investigated, both by experiment and theory [], as the representative structures in many pioneering works. Therefore, one may take the junction of Tin+1AlCn(n = 1,2)/β-SiC as an example to investigate the structural, electronic and mechanical properties of the interface between SiC ceramics and the Mn+1AlCn phase coating.In this paper, first-principles methods are used to explore the structures and characteristics in the corresponding interfacial interactions for the Tin+1AlCn(n = 1,2)/SiC interface. By comparing lattice parameters along different surfaces between SiC and Tin+1AlCn, it is found that the lattice parameters of the SiC(111) surface match those of the Tin+1AlCn(0001) surface. The most stable configurations of Tin+1AlCn/SiC(111) are thus determined, and the mechanisms behind the formation of stable configurations are tentatively accounted for by analyzing the electronic and mechanical properties. Finally, the most stable interface between SiC ceramics and other Mn+1AlCn coatings are investigated.First-principles calculations are performed with the plane-wave CASTEP codes based on the density functional theory (DFT) []. Vanderbilt ultrasoft pseudo potentials are exploited with a 500 eV plane wave cutoff energy []. After comparing the accuracy of bulk β-SiC and Tin+1AlCn(n = 1,2) properties as predicted by different exchange-correlation functions, we adopted the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional []. The interface models are constructed by connecting slabs of SiC and the MAX phase. To model the physics of a joint with bulk-like characteristics, the layered junction structure must be sufficiently thick. Hence, the models for M3AlC2 or M2AlC consist of 20 or 16 atomic layers, with 8 layers for SiC and the rest for M3AlC2 or M2AlC. A 9 × 9 × 1 k-point mesh is used in our interface Brillouin zone (BZ) []. All of our interface models are relaxed until the forces on each atom are smaller than 0.03 eV/Å, and the stress is smaller than 0.05 GPa. The maximum atom displacement is set as 0.001 Å. A vacuum layer of 50 Å is used perpendicular to the interface, eliminating the interactions of neighboring layers.The Ti3AlC2 and Ti2AlC phases have a hexagonal structure with the P63/mmc space group, and β-SiC has a cubic crystal structure. To verify the accuracy of the exchange-correlation potentials used herein, ground state calculations are carried out to optimize the single crystal structures with three different exchange-correlation functions: the local density approximation (LDA) with the Ceperley-Alder-Perdew-Zunger (CAPZ) parameterization, and the PBE and Perdew-Wang (PW91) functions under GGA. The results are listed in , together with previous theoretical results and experimental data for comparison [Compared with experimental data, the lattice parameters are consistently underestimated by the LDA method, for all three compounds. For example, the a lattice constant of the Ti3AlC2 compound is underestimated by approximately 2%. GGA calculations show better agreement with the experimental data relative to LDA, with similar results for both PBE and PW91 functions. In particular, the GGA-PBE exchange-correlation potential shows slightly better consistency with the experiments, and some related computational works also discover the same tendency []. Therefore, we will focus on the following calculations with GGA-PBE exchange-correlation potential.The essential factor to determine the interface stability between ceramics and metals is the comparability of their lattice parameters. Scanning tunneling microscopy (STM) images show a 6 × 6 reconstruction of the β-SiC(111) surface annealed at 1150–1200 °C, which means that the β-SiC(111) surface is a readily accessible interface in the experiments []. The Ti3AlC2(0001) surface has also been found stable, as demonstrated by the fact that the etching direction of Ti3SiC2 and Ti3AlC2 in HF(hydrofluoric acid) solution at room temperature is preferentially parallel to the (0001) plane [From our calculation, the lattice parameters of Ti3AlC2(0001), Ti2AlC(0001) and SiC(111) are 3.072, 3.063 and 3.044 Å, respectively. Therefore, the SiC(111) surface can match that of the Tin+1AlCn (0001) (n = 1,2) surface with only a 1% misfit. This value is smaller than that of WC/TiC (4.8%), which has previously been determined to be stable, indicating that the formation of a stable Tin+1AlCn (0001)/SiC(111) interface is potentially achievable [In regard to the slab structures, models containing vacuum along the c axis have been built for both SiC(111) and Tin+1AlCn(0001) (n = 1,2). For the SiC(111) slab, 8 atom layers have been found to be suitable based on previous work by Schuck and Stoller []. As the Ti3AlC2 and Ti2AlC slabs are ternary layered ceramic structures, we use 12 atom layers thickness for the Ti3AlC2(0001) slab and 8 layers for the Ti2AlC(0001) slab as in our previous work [], both consisting of two unit cells along the c lattice direction, for presenting the bulk-like characteristics in the interior. This choice is consistent with the work of Zhang and Wang, which suggested that the appropriate super cell of the Ti3AlC2(0001) slab should contain approximately two unit cells []. Therefore, the current structural model is reasonable with the two slabs thick enough to prevent the unreasonable interference of the surfaces in the model.In this work, six models for the interface configurations of Ti3AlC2(0001)/SiC(111) with different atomic contacts are considered as shown in . Models 1 and 2 are the interfaces formed by the C-terminated Ti3AlC2(0001) and the C-terminated or Si-terminated SiC(111); Models 3 and 4 are the interfaces between Ti-terminated Ti3AlC2 and SiC terminated by C or Si atoms, respectively; and Models 5 and 6 are the interfaces between Al-terminated Ti3AlC2 and SiC terminated by C or Si atoms. To estimate the optimized interface distance between the two slabs, the dependence of interfacial energy on slab separation is evaluated using the universal binding energy relation (UBER) method [], and then these models of optimized distances are fully relaxed. It has been shown that this scheme can enhance both the computing efficiency and the accuracy of work of adhesion. In this study, a similar scheme is also adopted for Ti2AlC(0001)/SiC(111), as in our previous work, in order to elucidate the interfacial structures and energetics [To determine the energetically stable Ti3AlC2(0001)/SiC(111) interface structures, we calculate the work of adhesion (Wad) of the interface for all six models:Wad=ESiC(111)+ETi3AlC2(0001)−ETi3AlC2(0001)/SiC(111)A,where A is the interface area and Wad is the work of adhesion of the interface defined as the reversible work per unit area required to separate an interface into two free surfaces; this quantity can be used to predict the interface stability [, ESiC(111), ETi3AlC2(0001) and are the total energies of the relaxed SiC(111) and Ti3AlC2(0001) slab and the optimized Ti3AlC2 (0001)/SiC(111) junction structure, respectively. The Wad value for Ti2AlC (0001)/SiC(111) is calculated in a similar manner with Ti2AlC(0001) replacing Ti3AlC2(0001).The procedure to obtain Wad involves two steps. First, the approximately optimized interface distance by the UBER method is predicted from a series of unrelaxed models with different interface distances (d0), and then Wad of these models are calculated using Eq. . The UBER curves of the Wad dependence on d0 for Ti3AlC2(0001) and SiC(111) are plotted in , by which the “optimal” d0 for the rough estimation of maximum Wad can be obtained. In the second step, starting from the “optimal” d0, interfacial structures are fully optimized and the corresponding Wad is computed using Eq. . By examination on the structures, it can be found that the change in geometries of the structure caused by full relaxation in the second step is actually limited. Taking Model 3 as an example, the variation for the α axial angle is 1.3%, and those for β and γ are nearly zero, indicating that the shape of the lattice is substantially maintained. As for the lattice parameters, there is only 0.1% change in lattice parameter in the a(b) direction, and the lattice variation in the c direction is 0.2% relative to the UBER determined Ti3AlC2/SiC slab. Finally, inspection on the interatomic distances inside both Ti3AlC2 and SiC slabs indicates that the bond distances are nearly unchanged. On the whole, the geometries obtained using the UBER method are close to the optimized junction structures, and thus the optimization efficiency is improved.The Wad values and structural parameters of the Ti3AlC2/SiC junctions are listed in , which shows that the lattice parameters of the six models of Ti3AlC2/SiC range from 3.06 to 3.09 Å. With the lattice parameter of 3.072 and 3.044 Å for Ti3AlC2(0001) and SiC(111), respectively, the stable interface structures can be formed with little lattice strains. The largest calculated Wad (most favorable) is for Model 3 (7.67 J/m2). This suggests that the stable interface between the Ti-terminated Ti3AlC2 and C-terminated SiC is the most probable bonding pattern between SiC and Ti3AlC2. In comparison with the work of adhesion for other ceramic junction materials—such as 5.56 J/m2 for the interface between TiC(111) and TiN(111) [], and 6.39 J/m2 for Fe(100) and W(100) []—the maximum work of adhesion from our calculations exhibits an apparently higher value. The Wad of C-terminated Ti3AlC2(0001) and C-terminated SiC(111) has the second highest value (6.89 J/m2) in , which may be a reflection of the fact that the CC interaction may also generate a stable interface of Ti3AlC2(0001)/SiC(111). For this reason, the interfaces between Ti-terminated Ti3AlC2(0001) and C-terminated SiC(111) and between C-terminated Ti3AlC2(0001) and C-terminated SiC(111) are the two potential stable configurations of Ti3AlC2/SiC.The work of adhesion of Ti2AlC(0001)/SiC(111) is revisited in this work, and the recalculated data are shown in . From the calculation, the interface between C-terminated SiC(111) and Ti-terminated Ti2AlC(0001) is again the highest of all six types of interface, with a Wad value of 6.06 J/m2, which coincides with that of the Ti3AlC2(0001)/SiC(111) interface. The joining between C-terminated Ti2AlC(0001) and C-terminated SiC(111) is also found important with a Wad of 5.41 J/m2. Therefore, the results for Ti2AlC/SiC follow a trend similar to that for Ti3AlC2/SiC and SiC ceramics might be effectively joined by both Ti2AlC and Ti3AlC2. In Section , the Wad values of β-SiC and Mn+1AlCn (M = Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta; n = 1,2) are calculated using the corresponding two stable models in order to evaluate the interface stabilization of Mn+1AlCn and β-SiC.To interpret the theoretical results of this work, the optimized interface structure of C-terminated SiC(111) and Ti-terminated Ti3AlC2(0001) is further studied from its electronic structure. The bond length between the terminal C atom and the adjacent Ti atom is 2.421 Å (Ti-3 to C-3), which is comparable to (slightly weaker than) the interatomic spacing of CTi in the Ti3AlC2(0001) structure of 2.071 Å (Ti-1 to C-1), as illustrated in Ti chemical bond formed in the interface between SiC(111) and Ti3AlC2(0001). The variation of atomic charges from the slabs of each separate component (Ti3AlC2 and SiC) to the optimized junction structure (Ti3AlC2/SiC) has been computed using Mulliken analysis [. From these results, a remarkable Mulliken charge transfer of approximately 0.45e from the Ti and 0.43e to the C atom in the interface can be identified, clearly proving that a CTi chemical bond is formed in the interface of SiC(111) and Ti3AlC2(0001). The charge of the Al atom is close to zero in both the Ti3AlC2 slab and the interface structure, meaning that the Al layer is relatively weakly bonded with the Ti atom layers, consistent with the fact that the Al layer is a transition layer of the structure and can be stripped. For the atoms residing one unit cell away from the interface, the charge difference between the slab and the interface structure is almost zero, demonstrating that the slab thickness is large enough to represent the influence of junction between two materials on separate crystal structures.To Whom It May Concern: gain insight into the bonding mechanisms of the Ti3AlC2/SiC interface, the density of states (DOS) and the partial density of states (PDOS) for Model 3 [C-terminated SiC(111) and Ti-terminated Ti3AlC2(0001)] are calculated, with the results shown in . The interface model exhibits metal characteristics indicated by the overlapping of the DOS with the Fermi level. The electrons in p and d orbitals provide the most significant contribution to the DOS near the Fermi level. The strong hybridization between Ti-d and C-p can be observed from −5 to −3 eV, indicating TiC bonding. In order to resolve whether this comes from the interface, the Ti3AlC2 interior structure, or both, the layer density of states (LDOS) for each atom are listed in , providing further insight into the electronic properties of the interface and interior structure for Ti3AlC2. It can be seen that hybridization occurs for C-3 of SiC and Ti-3 of Ti3AlC2 from −5 to −3 eV. At the same time, there is another hybridization that occurs for Ti-2 and C-2 from −10 to −5 eV. The results indicate that TiC bonding occurs both in the interface and in the interior structure of Ti3AlC2.The total electron density and the electron density difference of the interface have also been calculated, as shown in . These contour plots show the changes in electron distribution by forming chemical bonds in Ti/C-terminated Ti3AlC2/SiC, and help to identify the types and strength of chemical bonds. (a) shows that there is hardly any overlap of electron clouds for Ti and C atoms in the interface, meaning that the bonding in the interface was strongly ionic. For Ti atoms away from the interface, obvious electron overlap with C atoms can be found, which may be an indication of the slightly electrovalent bond contribution. This is probably a result from the different TiC bond distances. Overall, it should be mentioned that the slab structure is mainly stabilized by ionic bonding via electron localization function (ELF) calculations. This implies that the interface may be strengthened from the slight increase in ionic bonding contribution since ionic bonds are free of angular dependence and allow better flexibility of interfacial bonding especially for high-temperature applications. From the electron density difference, it can be seen that the Ti atoms of Ti3AlC2 are electron donating whereas the C atoms of SiC gain electrons as shown in (b). Interestingly, the interfacial Ti atoms can be seen to exhibit some of the characteristics of metallic bonds with the enrichment of electron density near the interface Ti atoms. This is consistent with the DOS plot showing that the energy of Ti-d electrons are in a wide range, −5–7 eV.With the interface bonding well studied, the elastic mechanical properties of the junctions between SiC and Ti3AlC2 or Ti2AlC are next investigated. The elastic constants of bulk β-SiC, Ti3AlC2, Ti2AlC and the most stable interface structures of Ti3AlC2/SiC and Ti2AlC/SiC are determined theoretically in this work. As mentioned in Section , the Ti3AlC2 and Ti2AlC phases have a hexagonal structure with the P63/mmc space group, and the β-SiC phase forms into a cubic crystal structure. So there are six elastic stiffness constants—C11, C12, C13, C33, C44 and C66—for the perfect crystals of Ti3AlC2 and Ti2AlC [] with five independent parameters since C66=(C11C12)/2. Meanwhile, the β-SiC perfect bulk has three independent stiffness constants: C11, C12 and C44 []. The three Born stability criteria for the cubic system are well known: C11C12>0, C11+2C12 > 0 and C44 > 0. For the most stable structures of the Ti3AlC2/SiC and Ti2AlC/SiC slabs, Cij can be defined as [] having 21 independent elastic stiffness constants in the stiffness matrix:Cij=[C11C12C13C14C15C16C22C23C24C25C26C33C34C35C36C44C45C46C55C56C66]For triclinic crystals, the elastic stiffness constants Cij should satisfy the following formula [C11+C22+C33+3(C44+C55+C66)-(C12+C13+C23)>0Using straightforward calculations, the elastic stiffness constants Cii for the most stable structures of the Ti3AlC2/SiC and Ti2AlC/SiC slabs are determined to satisfy the above mechanical stability criteria, which means that the Ti3AlC2/SiC and Ti2AlC/SiC slabs indeed have the mechanical stability in terms of elastic stiffness constants.The theoretical polycrystalline elastic modulus for the bulk β-SiC,Ti3AlC2, Ti2AlC and the most stable interfacial structures of Ti3AlC2/SiC and Ti2AlC/SiC can be calculated by their independent elastic stiffness constants Cij, using the equations corresponding to different lattice systems []. There are two approximation methods to calculate the crystalline modulus, namely, the Voigt method [], which can represent the upper and lower limits of the true polycrystalline mechanical properties. The bulk modulus (B) and the shear modulus (G) are the arithmetic mean values of the Voigt (BV, GV) and Reuss (BR, GR) modulus, and thus they are calculated as follows [Young's modulus (E) and Poisson's ratio (ν) are the two important physical quantities that describe the elastic behavior of materials under uniaxial strain by definition. Materials with higher Poisson's ratios generally possess better plasticity. The Young's modulus E and Poisson's ratio ν are determined as follows [The calculated mechanical properties are listed in . The elastic moduli for the Tin+1AlCn(n = 1,2)/SiC slab structures are between those for the perfect bulk SiC and Tin+1AlCn, which indicates that their elastic mechanical properties are stronger than those of the perfect bulk Tin+1AlCn but weaker than those of perfect bulk SiC. Nevertheless, the Poisson's ratio ν for the junction structures are higher than that of their bulk counterparts, indicating that they have higher plasticity compared with bulk β-SiC, Ti3AlC2 and Ti2AlC. Since plasticity is important for determining materials behavior, especially at high temperatures, this suggests that the interfacial interactions between SiC and MAX phases may enhance the serving performance of SiC composites. Finally, the B/G ratio describes the ductility (or brittleness) of a material; the B/G values of 1.08, 1.10, 1.15, 1.20 and 1.17 for the β-SiC, Ti3AlC2, Ti2AlC, Ti3AlC2/SiC and Ti2AlC/SiC, respectively, show that Ti3AlC2/SiC and Ti2AlC/SiC still behave in a brittle manner as the B/G ratio is ＜1.7, though better than their bulk materials. For this reason, methods strengthening the SiC fiber from ductility should be further explored beyond the formation of interphase using MAX phases.To recap, we have found that the interfaces between Ti-terminated Tin+1AlCn and C-terminated SiC (Model 3) or between C-terminated Tin+1AlCn and C-terminated SiC (Model 1) are the most likely to be formed in experiments. To further extend the current study, we consider the interfacial stabilization of Mn+1AlCn/SiC (M = Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta; n = 1,2). First, the lattice parameters of Mn+1AlCn(0001) and SiC(111) are investigated using the first-principles method, leading to the results listed in . The lattice parameters (a) for 211 and 312 MAX phases of the same M atom present almost the same results and thus show structural similarity as forming M2AlC/SiC and M3AlC2/SiC junctions. However, it can also be seen that the lattice constants vary from 2.84 to 3.31 Å for different M's. As indicated earlier, the interface stability between ceramics and metals can be reflected by the comparability of their lattice parameters. Through preliminary inspection, one may presume that the interfacial stabilization of some Mn+1AlCn(0001) (M = Ti, V, Nb, Ta, Mo; n = 1,2)/SiC(111) is better than that of others.Two models for Mn+1AlCn(0001)/SiC(111) are fully relaxed analogous to Model 1 and Model 3 for Ti3AlC2(0001)/SiC(111) shown in . The lattice parameters of Mn+1AlCn(0001)/SiC(111) present a trend to approach the average of the two bulk constituents, such as 3.32 Å for Sc3AlC2(0001) reduced to 3.18 Å for Sc3AlC2/SiC, and 2.84 Å for Cr3AlC2(0001) increased to 2.96 Å for Cr3AlC2(0001)/SiC. Surprisingly, the work of adhesion for Mn+1AlCn(0001) and SiC(111) are not as the prediction solely from the misfit between the separate slabs and most Mn+1AlCn/SiC(111) show good interfacial stabilization. This indicates that the bonding in the interface overcomes the misfit between the slabs for most cases. The Wad values for the interface between M-terminated Mn+1AlCn(0001) and C-terminated SiC (Model 3) are not always higher than the values between C-terminated Mn+1AlCn(0001) and C-terminated SiC(111) (Model 1). For Sc3AlC2, Hf3AlC2, Sc2AlC, Hf2AlC, and Ta2AlC MAX phases, the CC interfacial interactions are stronger than M–C. In particular, the strongest bonding in the interface for all Mn+1AlCn/SiC(111) lies in Ti3AlC2/SiC with a Wad of 7.67 J/m2, and the Wad of the CC interface for Ti3AlC2/SiC posted the second highest value among all of CC interfaces for Mn+1AlCn/SiC(111) (Sc3AlC2/SiC has the strongest CC interface), which indicates that Ti3AlC2 is a good candidate for SiC joining. Moreover, the Sc3AlC2, Ti3AlC2 and Ta3AlC2 MAX phases are also capable of bonding strongly to SiC with a Wad of more than 7 J/m2. The most stable interface for M2AlC/SiC is formed by Sc2AlC in Model 1. Interestingly, all of the M2AlC phases appear to have less interfacial strength than that of the M3AlC2 phase and this is consistent with the fact that the 312 MAX phases are more stable than the 211 MAX phases. Based on all of the current data, we can conclude that SiC ceramics can be joined effectively with a variety of Mn+1AlCn phases via interfacial chemical bonding.We have performed first-principles calculations to investigate the junctions’ structure between β-SiC ceramics and Mn+1AlCn (M = Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta; n = 1,2) MAX phases. In order to determine the most stable Mn+1AlCn/SiC interface structures, the Ti3AlC2/SiC slab is taken as an example and the work of adhesion is evaluated. Six interfacial models were considered, with different atomic stacking contacts. The interfaces between the C-terminated SiC(111) and the Ti-terminated Tin+1AlCn (0001) (n = 1,2) surfaces show the highest Wad, and are thus considered stable. This most stable interface structure of the Ti3AlC2/SiC slab is chosen to study its electronic properties and elastic modulus. By investigating electronic properties such as the density of states, electron density, and charge density difference, we find that the bonding of the interface atoms shows stronger ionic characteristics than those in the bulk. The elastic moduli show that the mechanical properties for the structure Ti3AlC2/SiC and Ti2AlC/SiC are between the bulk Ti3AlC2 or Ti2AlC and β-SiC bulk, with enhanced plasticity. All stable interfaces [Ti-terminated Mn+1AlCn(0001) and C-terminated SiC or C-terminated Mn+1AlCn(0001) and C-terminated SiC] between Mn+1AlCn(0001) and SiC(111) have been investigated computationally. Most of these Mn+1AlCn(0001)/SiC(111) structures show good interfacial stabilization, suggesting that SiC ceramics may be joined effectively with MAX phases via interfacial chemical bonding.The authors declare that they have no conflict of interest, and all the authors have approved the final version of the manuscript.MT data inversion and sensitivity analysis to image electrical structure of Zagros collision zoneMagnetotelluric (MT) data from 46 stations on a 470-km-long profile across the Zagros fold-thrust belt (ZFTB) that marks the Arabia-Eurasia collision zone were inverted to derive 2-D electrical resistivity structure between Busher on the coast of Persian Gulf and Posht-e-Badam, 160 km north east of Yazd. The model includes prominent anomalies in the upper and lower crust, beneath the brittle-ductile transition depth and mostly related to the fluid distribution and sedimentary layers beneath the profile. The conductivities and dimensions of the fault zone conductors (FZCs) and high conductivity zones (HCZs) as the major conductive anomalies in a fault zone conceptual model vary significantly below the different faults accommodated in this region. The enhanced conductivity below the site Z30 correlates well with the main Zagros thrust (MZT), located at the western boundary of Sanandaj-Sirjan zone (SSZ) and known as the transition between the two continents. The depth extent of the huge conductor beneath the south west of the profile, attributed to the thick sedimentary columns of the Arabian crust, cannot be resolved due to the smearing effect of the smoothness constraint employed in the regularized inversion procedure and the sensitivity of MT data to the conductance of the subsurface.We performed different tests to determine the range of 2-D models consistent with the data. Our approach was based on synthetic studies, comprising of hypothesis testing and the use of a priori information throughout the inversion procedure as well as forward modeling. We conclude that the minimum depth extent of the conductive layer beneath the southwest of the profile can be determined as approximately deeper than 15 km and also the screening effect of the conductive overburden is highly intense in this model and prevents the deep structures from being resolved properly.Modern continent-continent collision zones are considered as active laboratories for testing different geodynamic models and explaining the nature of continental growth (). Located at the tectonic crossroads of the Alpine-Himalayan belt, Zagros collision zone is initiated due to the closure of Neotethys Ocean and a long-lasting convergence between Arabian (as a Gondwanian-derived fragment) and Eurasian plates (). However, reliable data on the lithospheric structure of Zagros is scarce and many geological and tectonic aspects of this region remain poorly known or disputed (Fluid content and thermal structure of the crust and upper mantle are the most important factors characterizing the rheology in collision zones. They are also the key parameters controlling electrical conductivity of subsurface structures. MT sounding being sensitive to electrical conductivity contrasts is among geophysical deep sounding methods capable of constraining rhological properties of the crust and mantle and can aid our understanding of deformation mechanisms at collision zones (Here we present 2-D inversion results as well as different sensitivity analysis of MT data from Zagros collision zone.MT data inversion obtained from minimizing the misfit of calculated model responses and observed data (Φd) is considered as an inherently ill-posed nonlinear modeling problem. Its mathematically unique solution is hindered by wrong physical assumptions (ex. dimensionality of the subsurface geoelectrical structure), systematic and statistical data errors as well as improper parameterization of the model space (). A standard approach to solve the non-uniqueness of the MT inversion result is introduction of a smoothness constraint (Φm) as a regularizing term in the inversion objective function (where: Φd=∑idiobs−dicalmaxd^iεdiobs2 and Φ1m=∫∇→m→−m→02dA, Φ2m=∫∇2m→−m→02dA.Penalizing some predefined properties of the model space which are unacceptable (ex. model roughness, calculated as the norm of model parameter gradients (Φ1m) or Laplacian (Φ2m)), this term stabilizes the inversion, prevents geologically un-resolvable structures from being appeared in the final model and adopt the smoothest model as the inversion solution. The lagrange multiplier (τ) is a trade-off parameter, controlling the relative weight given to the data fit (Φd)and model smoothness (Φm). di,d^i,ε represent ith measured data, their corresponding errors and error-floor, respectively.However, the result does not resemble the true earth more accurately than any other models fitting the data. It's an extreme model in the sense of giving the lower bound on the number of required structures (Numerical experiments employing synthetic data representing real situations where sharp conductivity contrasts exist (ex. conductive fluids released from the slab beneath the volcanic arc in a subduction zone) indicated that the tradeoffs inherent in the smoothness assumption make it difficult to resolve those boundaries as well as the details of the conductive structures (). Sensitivity tests employing a combination of imposed features and tear zones (where smoothing assumption is locally cancelled out) in the inversion starting model are essential to determine the range of models consistent with the data which demonstrate the intricacies of model structures, more accurately (). However, comparing to the smooth inversion results these models are obtained through a more subjective procedure as the regions of imposed features and tear zones are predefined by the modeler (Numerous MT profiles recorded for oil exploration in Iran do not penetrate the crust beyond the 10 km depth. The only MT work to date conducted in Zagros using broadband MT (BBMT) systems with sufficient penetration depth was performed as a research project at the institute of geophysics, university of Tehran in 2009 April and May (). The topographic map with all sites in the measurement area is depicted in . The profile traverses the main morphological units of the Zagros collision zone: Zagros Fold thrust Belt (ZFTB), Sanandaj-Sirjan zone (SSZ), central domain (CD) and central Iranian micro continent (CIMC). In this paper, we reassess this data set and present 2D inversion results and perform an extensive sensitivity study to characterize uncertainties in the calculated models.In order to investigate necessary (but not sufficient) condition for two dimensional modeling of Zagros MT data, we calculated the β skewness values, based on the phase tensor method (). Measuring the phase tensor's asymmetry produced by 3D structures, β skew angles describe the significance of 3-D effects in the MT regional responses. The results are presented in . The background color shows that at all sites and for most of the periods β values are below the threshold for a 3D case (<±5°), coinciding well with the low values of phase sensitive (b, c respectively). Accordingly, the data set may be regarded as two dimensional, in general. Furthermore, a comparision between different results show that anomalous regions are more restricted on the pseudosection of β skew angles, implying the fact that they are immune from galvanic distortion effects and mostly produced by 3-D structures.The phase tensor approach provides estimates of regional strike for all periods at each station. Telluric currents in TE mode typically flows parallel to geological features. Accordingly, additional information from induction vectors as well as geological and geophysical data are conventionally used to resolve the 90° ambiguity inherent in phase tensor analysis and assign the TE and TM modes, properly. Due to the high level noises contaminated the measured vertical magnetic fields, induction vectors were useless in this study area and we resolved the strike ambiguity based on regional geology. We performed a close inspection of strike values at different sections of the profile and for different period bands. The results () suggest a regional strike angle of N45°W at the long periods of the northeastern part of the profile beneath CIMC, UDMA, CD and SSZ as well as ZFTB until station Z39 which coincides well with the ZFTB trend as the main geologic structure in this region. Since MT data have a small sampling area at short periods and are more sensitive to the localized structures, the pattern of strike across the profile seems more scatter at this period range. The observed complexity of the strike directions at short periods may reflect a low station density throughout the profile. Except the last three stations in the southwestern part of the profile, strike direction is consistantly between 30°–45° west of the geographic north for short priods while the strike is variable between N30°E and N20°W for longer periods. The more complex geology as seen in the southwestern part of the profile provides an explanation for the inconsistent strike directions.Furthermore, an early investigation of the dataset based on the approach propsed by evinced that the RMS misfit between the measured impedances for all stations and periods with those of an ideal 2D model is minimal when the strike direction is equal to N45°W (Despite the difficulties in finding a common strike angle for all sites and periods through such a long profile, traversing numerous geological environments, we conclude that based on the majority of the measured impedances as well as regional geology, an azimuth of 45° west of north could roughly be distinguished as a preferable strike direction for the regional conductivity structure.Winglink interpretation software, employing non-linear conjugate gradient (NLCG) algorithm of for regularized inversion has been adopted for further investigations. The frame work of the whole inversion modelings consisted of the following settings:1) TE and TM mode impedances, expanding throughout six decade period of 0.0039–1448.2 s were recalculated at the optimized strike angle and used in the inversion procedure. 2) Data interpolation was prohibited and only the station data were used throughout the modelings. 3) Data errors were used if existing, differently 10% resistivity and 5% (= 1.4°) phase error values were set for the input data. 4) A higher weight was assigned to the phase data to reduce the influence of the static shift. Error floors were set to 20% for apparent resistivities and 5% (= 1.4°) for phases, i.e. data errors larger than these thresholds remained unchanged while smaller errors were raised to these values. 5) Vertical magnetic transfer functions were excluded from the inversion procedure, due to the insufficient quality. 6) The models indicating subsurface electrical resistivity distribution are presented on a grid consisting of 320 and 60 cells in y and z directions, respectively. 7). A regularization functional, penalizing the integral of model laplacian, weighted by a standard grid Laplacian operator was used in the inversion procedure. 8) Numerous initial experiments employing the phase data (immune from static shift effects) were conducted to determine the proper values for regularization parameters controlling the trade-off between data misfit and model spatial smoothness (τ), the weighting parameters controlling vertical compared to horizontal smoothness (α), the depth variation of smoothness (β) and also horizontal and vertical block dimensions used for weighting functions. The results () suggest that the premier values for these parameters are: 2, 1, 1 and H/V = 500/500, respectively. 9) Static shift coefficients were not included as free parameters for neither TE nor TM mode inversions.Individual TE and TM mode impedances as well as their joint inversions were undertaken. Our joint inversion approach was based on modeling of the TM phase data at first and then adjoining TE phase, TM resistivity and TE resistivity, sequentially. The inversion outcomes () clearly show inconsistencies aroused due to the different sensitivities of the two independent modes (). While inherently inductive TE mode data are sensitive to the currents flowing along the strike of the conductor and can make even thin vertical conductors, like fault zones, to be observed at the surface, TM mode data are galvanic in nature and quite invisible to these structures (The most prominent features in the TE mode model are highly conductive regions near the faults, especially vertical and northeastward dipping conductive zones close to the MZT and HZF faults (c). It also exhibits a much resistive lower crust, beneath the Iranian plate. The inversion of the TM mode impedances results in a well data fit of 1.27. The upper and lower crust appears heterogeneous with much higher conductivities in the central part of the profile than at either end (The inclusion of the Persian Gulf as a-priori information in the starting model to investigate the sensitivity of MT data to this major off-profile conductor, represented minor effects on the inversion result and by fixing the resistivity of sea water, unrealistic high conductance was generated beneath the SW end of the profile and the coast.In order to check the consistency of the results with a more resistive crust, a resistive layer along the entire subsurface and extended into the lithospheric mantle depth was used in the starting model. The result does not improve the misfit significantly (RMS = 1.92) and the major resistive and conductive features had similar shapes but extended to deeper parts. Accordingly in subsequent numerical experiments all of the starting models were 100 Ωm half spaces for the whole dataset.Diverse experiments performed to test the consistency of the resolved structures and confine the maximum extent of the significant features are divided in five categories:I) the joint TE and TM inversion model was manipulated and used as inversion starting models. show the model where all the conductive or resistive structures have been removed. They were used as starting models and allowed to evolve through the inversion procedure, where the closest model to the starting model was looked for. This strategy confines the starting district of the inversion, causes the algorithm to work more efficiently close to the global minimum and spotlights undetected or poorly constrained features (c, d) suggest that: i) the main features in a) are data supported and their shapes do not change significantly through the sensitivity studies (even the hooked like conductor extended beneath the sites z40-z32 is a persistent feature in different models). ii) However this procedure reduces the size of resistive structure extended between sites 50–40 at the crustal depths (d). iii) The upper crustal resistors remain disconnected. iv) a thin conductive layer has been resolved beneath the sites z24–z19 (d). Due to the sparse lateral sampling provided by a site spacing of about 10 km, joint inversion of TE and TM impedances (a) could not find this structure continuous. Although imposing the conductor as a continuous feature is accepted by the inversion in this part of the model, but further numerical experiments show that for the southwestern part of the profile this is not the case and the presence of a continuous structure is completely ruled out by the numerous faults accommodated in this region.II) In a second set of tests, we started with the a, b) and introduce the tear zones throughout their respective resistive or conductive structures. This scheme would cause the smoothing constraint to be collapsed in these regions and encourage the inversion to find solutions with sharp conductivity contrasts at the edges of the tear zones () to improve the accuracy of inversion model in natural situations where different conductivities are juxtaposed (ex. Fault zones where fluids are extracted into the brittle crust). It is clear from the results (e, f) that the tear zone inversions recover the resistive/conductive structures with high conductivity gradients at their boundaries without aggravating the data fit. However this scenario has also restricted the upper crustal extension of the huge resistor beneath sites z49–z45(III) The robustness of major features in the resistivity model was evaluated using the constrained inversions, according to the strategies suggested by . In the first group of experiments, the significance of major conductive features was examined using variations of the starting models in regions containing the conductors. The resistivities of these areas were constrained to their surroundings and made firm throughout the inversion procedure. The results are presented with a larger section than that of the profile coverage to consider the influence of the off profile structures ()). The impedance phase responses of these models at sites located above the constrained regions are also compared with those of unperturbed models (). In the second inversion tests, outside of a rectangular region extending from − 75 to 575 km profile distance and from the surface to a depth of 125 km were constrained to 100 Ωm and fixed during the inversion, in addition to the conductive zones. These tests allow us to evaluate whether the off profile features can reproduce the effect of the major conductors.Although by constraining a region throughout the HCZ1 area in the depth range 10–60 km (outlined with a rectangular crosshatched area) to 1000 Ωm, an overall RMS misfit of 1.92 was achieved and only at the site Z49 the phase responses were affected (the first column of the ), but note that the inversion model exhibit extremely low resistivities in the vicinity of the constrained zone (b). This suggests that the inversion tries to reestablish the HCZ1 as a distinct conductive body, pushed eastward when compared to the original model.c) was constrained to contain a resistivity of 1000 Ωm in the area of the HCZ2 conductor. The result indicates that the inversion has mostly attempted to compensate the originally contained conductance by resolving conductive features off the profile. However, when the influence of the area outside of the profile is restricted by fixing its resistivity to that of the starting model, the HCZ2 is resolved as a well defined conductor, pushed upward, comparing to the original model in the a). Examining the impedance phase responses with those of the unconstrained inversion, it becomes obvious that data misfit is degraded (the middle column in Finally, the upper crustal conductor, beneath the MZT was tested by constraining the resistivity in this area to 1000 Ωm. In this case the data fit was worse (RMS > 2.15) and a continuous conductive zone was restored beneath the constrained region. Similar to the above mentioned tests, the inversion tries to compensate the original model conductance by resolving high conductivities outside of the profile. The inspection of the phase sounding curves also suggests that the absence of the FZC has degraded the data fit (the third column in IV) In the next step, constrained inversions were performed to find the shallowest depth, permitted by the data, for the bottom of the conductor beneath the southwest of the profile. MT data are mainly sensitive to the conductance and the top of a conductive layer while insensitive to its bottom. So if the resistivity model was replaced bellow a given depth with a resistive half space, data misfit would not be affected by the resistive region. Shifting the top of the resistive basement to the shallower depths until the data misfit increases significantly, one can find the shallowest bottom of the conductive layer (and consequently its minimum conductance) allowed by the data (). In the starting model of the next inversions, we fixed the bottom of the resistivity model, beneath 100 km depth with a 1000 Ωm half space and moved its top to the shallower depths at 50, 40, 30, 15 and 10 km. Consider that similar structures to the a) are resolved at the shallow part of the models, data misfit for each model is also presented. It's evident that the data misfit is independent of basement location for the depths > 15 km. Although the depth to the resistor basement does not have physical significance, but it determines the minimum conductance required by the data which is useful for MT data interpretation (Integrated conductance from the surface to the resistive basement is shown in . It shows a general decreasing trend from SW to NE along the profile. The minimum conductance reaches the values of about 10,000 S, beneath the southwestern part of the profile. These high crustal conductances are coincident with the values observed at the other active collisions (V) Despite the screening effect of the upper crustal conductive layer beneath the south-west of the profile, suggested for such situations that the forward responses of the smooth inversion model (a) to be computed and manipulated with the Gaussian noises and used as input data for the subsequent inversions with extra synthetic stations added along the profile. This strategy is helpful to find out whether the deeper structures could be resolved with better data quality and station coverage or if the lack of resolution is an inherent characteristic of the model.We applied this technique for the Zagros profile data and assumed synthetic stations with 2 km spacing throughout the profile. The results of the smooth inversion of these synthetic data are presented in . It appears that the smooth inversion does reproduce resistive and conductive structures equivalent to that of (a). The equivalence of the model classes indicates that the screening effect of the conductive overburden is highly intense in this model and prevents deep structures from being resolved properly.In the previous section we performed different numerical experiments to test the consistency of significant conductive and resistive features and the dependencies on starting models and inversion parameters. Despite its higher value of data misfit, we prefer now to base our interpretation on inversion model 5a that was obtained without a priori information and focus on its crustal part.Fault zone electrical conductivities measured by MT method at seismogenic depths are functional to deduce the existence and distribution of fluids within the brittle portion of the crust (). The most significant conductors imaged in the model 5a can be divided in three categories:Fault zone conductors (FZCs), High conductivity zones (HCZs) and near surface conductive layers along profile towards southwest and northeast (noted as C1 and C2 in the High conductivities resolved beneath the major faults at the upper crust characterize saline fluids circulating within the damage zone of the faults. Such a model coincides well with earlier fault zone model (). The width and depth extent of FZCs vary at different faults along the Zagros profile. At the southwestern part of the profile beneath ZFF and KF faults as well as the main Zagros thrust (MZT), the anomalous zones of high conductivities are extended to middle crust. While the conductors beneath BF, KZF, SPF and MFF faults are confined to the zones centered on their respective faults and extended from the surface to a depth of 2–6 km. In contrast, the FZCs at the HZF and DF faults are weakly revealed both in terms of conductivity and depth extent.The most prominent structure obtained from MT data in the middle part of the profile is a deep hooked like high-conductivity zone (HCZ2) extended in 15–40 km depth range between HZF and MZT faults. Another HCZ is also extended beneath KF fault. Mineralized fluids within an interconnected porosity network could be considered for the resolved conductivities of the HCZs. These structures are located beneath the brittle-ductile transition zone in Zagros (). The HCZs likely represent ductile deformation regions with long-lasting hydraulic permeability (Thickness variation of the sedimentary cover across the Zagros (), different modes of decoupling between the basement and this sedimentary cover (), numerous N-S and E-W trending basement faults and variable inversion rate of the normal basement faults of the Arabian passive margin during the collision between Arabia and Eurasia () have made the configuration of the sedimentary basins along the profile significantly different.The thick conductive layer at the SW end of the profile can be attributed to the lower Cambrian to Pliocene sedimentary sequence of the Arabian platform. Furthermore, massive Neogene sediments of the central domain (CD) could be responsible for near surface thin conductive layer imaged in the upper crust of the NE part of the profile, as documented by An early modeling approach was carried out by employing the reduced data base Occam algorithm (REBOCC, ) to invert the determinant as well as the TE and TM modes of the same data set of Zagros profile. Major features are in good agreement with the a). In both models the Arabian upper crust seems more conductive than the Eurasian's one with a sharp conductivity contrast between them, located beneath the site Z30 and coinciding well with the surface location of MZT fault (known as the suture between the two continents). Furthermore, thick sedimentary rocks of the Arabian plate (extended beneath the sites Z56 to Z50) as well as the neogenic sediments beneath the sites Z26–Z19 are equally well resolved in both models. However, small discrepancies are observed over the anomalous bodies. These discrepancies are caused by the different inversion parameter values as well as strategies used by these algorithms to penalize the data misfit and regularization terms in the inversion objective function (eq. ). The major difference between REBOCC and NLCG (employed in the present study) algorithms is that the Lagrange multiplier (τ in eq. ) is determined from a search process in REBOCC while in the NLCG, it is pre-chosen (Laterally uniform deep resistive structure obtained by is probably associated with the followings: i) while MT data are generally insensitive to the deep resistive structures they used an inversion a-priori model composed of a resistive half space (with 1000 Ωm resistivity) located at the 40 km depth. ii) TE mode resistivities were almost excluded from the inversion procedure by assigning a very high error floor of 90% (the TE mode data are generally more sensitive to deep structures ()). iii) weights on horizontal smoothing constraint were five time greater than the weights on vertical smoothing constraint.A two dimensional smooth inversion model has been derived for an MT data set recorded along a transect perpendicular to the Zagros fold thrust belt. The result indicates distinct resistive and conductive features within the crust which are in general agreement with conductivity structure expected in a collision zone.Although the smoothness constraint involved in MT inversion objective function is a solution for the non-uniqueness of the problem, but the result dose not resemble the true earth more accurately than any other models fitting the data and sensitivity studies are essential to increase the reliability of structures resolved in the model. We performed sensitivity studies based on various forward and inverse modeling in combination with different a priori models, synthetic data sets and tear zones in the inversion procedure.Introducing tear zones throughout the main conductive and resistive structures of the model does not change the inversion result significantly. Constrained inversions show that neither of the major conductive structures can be removed from the model. Furthermore, another set of constrained inversions evince that the MT data require a minimum crustal conductance of 10 kS beneath SW of the profile.High conductance beneath the Zagros profile are attributed to the near surface sedimentary layers, fault zone conductors in the brittle portion of the crust and high conductivity zones beneath the brittle-ductile transition zone.Discontinuously reinforced metal matrix composite (DRMMC)Correlation between matrix residual stress and composite yield strength in PM 6061Al–15 vol% SiCwUpon relieving residual stress (RS) by means of isothermal annealing, it is observed that the RS and the yield strength (YS) of a 6061Al alloy follow a linear relationship. In contrast, two regimes are observed for a SiC-reinforced composite: firstly the YS decreases at constant RS, then the RS relaxes at constant YS.Discontinuously reinforced metal matrix composite (DRMMC)Discontinuously reinforced metal matrix composites (DRMMCs), such as Al alloys reinforced by SiC, are being increasingly used in structural applications because of their enhanced mechanical properties with respect to the corresponding unreinforced matrix. These properties are strongly dependent on the microstructure and highly influenced by the presence of residual stress (RS) Knowledge of the RS state in industrial components is important since it may have a great influence on their behaviour in service. Moreover, the component fabrication implies the application of thermo-mechanical processes (extrusion, rolling, etc.) and treatments (surface peening, pre-straining, heat treatments, etc.). These are able to affect both the mechanical properties and the final RS state of alloys and DRMMCs The aim of this work was to correlate the relaxation of the matrix RS in a 6061Al–15 vol% SiCw composite and in its unreinforced 6061Al alloy with the variation of their yield strength (YS), and observe the conditions under which the first is possible while avoiding the second. Both variations were induced by means of heat treatments, bringing the materials from a T6 (fully hardened) condition, through several isothermal treatments at 300 °C, to an over-aged condition, OA (100 h treatment).The materials studied, a 6061Al–15 vol%SiCw composite and its 6061Al alloy matrix, were prepared by a powder metallurgical (PM) route The stress-relieving heat treatments were also tailored to obtain different mechanical properties at each treatment stage. The composite and the unreinforced alloy were first brought to the fully hardened (T6) condition, and then aged at 300 °C for different treatment times, up to an over-annealed (OA) condition.The T6 treatment consisted of a solution treatment at 520 °C for 90 min followed by water quenching plus annealing at 146 °C for 16 h. The reference alloy had to be annealed for 56 h to achieve a similar precipitation state as the composite matrix. The longer annealing time in the reinforced material is due to the accelerated ageing phenomenon Intermediate heat treatments consisted of holding the samples at 300 °C for 0.5, 1, 2, 5 and 9 h. The OA condition was achieved by annealing at 300 °C for 100 h and furnace cooling. It has been already reported Compression tests were carried out in a computer controlled SERVOSIS (class 1) testing machine at a strain rate of 10−4
s−1. Cylindrical samples (13 mm high with 6.5 mm diameter) were used for both compressive tests and neutron diffraction (ND).The RS in all precipitation states, from T6 to OA, was studied by neutron diffraction, ND. The ND experiments were carried out on the diffractometer D1A at the ILL, Grenoble, France, and the calculation procedure to evaluate stresses from diffraction data are fully reported elsewhere, see Refs. shows two examples (after 0 and 0.5 h annealing at 300 °C following the T6 heat treatment) of stress–strain curves for composite E219 and the alloy E220. The variation of the YS is clearly visible for both materials. The YS of the composite and the unreinforced matrix (evaluated at 0.2% strain, see Ref. where τ is the relaxation time, σ∞ is the asymptotic value and σ0 is the total range of stress variation. shows the decay of the YS as a function of the treatment time. lists the values of τ, σ∞ and σ0 for both materials. The strength of the composite is always higher than that of the unreinforced matrix. As can also be seen, although the rate of decrease is the very similar in both materials (i.e., τYSE219≈τYSE220), the magnitude of the YS drop (σ0) is significantly larger in the unreinforced alloy than in the composite.A similar analysis was carried out on the RS. The rule of mixtures (ROM) was applied to separate the macro (index M) and micro (index m) stress from the total (phase specific, index T) stress, according to The hydrostatic component of stress σH was calculated as the average between the axial, radial and hoop components. Since ND measurements were carried out at the centre of each sample, we could assume σrad
=
σhoop and getThe phase-specific RS, as calculated from the ND strain measurements, are fully reported in Ref. for both materials. Both macro and micro-hydrostatic RS relax as a function of the ageing time in both the E219 composite matrix and the E220 unreinforced alloy. Their behaviour can be again described through an exponential decay, Eq. . The corresponding fit parameters are listed in shows that the RS of the composite and the unreinforced alloy are radically different after the OA treatment. The RS in the composite relaxes towards a stable value (σ∞
≈ 105 MPa of the total-RS), whereas in the unreinforced alloy the RS virtually disappears (σ∞
≈ 20 MPa), . For both matrix and reinforcement, the axial deviatoric component of the micro-RS does not relax (see Ref. The YS of the composite is always higher than that of the unreinforced alloy due to the strengthening effect of the whisker, . This effect is based on the higher density of dislocations in composites (the geometrically necessary dislocations, GNDs, are always pinned at the particle/matrix interface) and on the load transfer phenomenon The annealing treatment activates diffusion processes in the matrix, by which the precipitation state changes, leading to changes in the mechanical properties of the 6061Al alloy. In the 6061Al alloy, the precipitation sequence is β″ → β′ → β (Mg2Si), of which only the latter is stable. The precipitates grow, reducing the number of particles, but increasing their average size. In this situation the dislocations can move more easily making plastic flow easier and consequently reduce the YS. In fact, the Orowan’s mechanism ) of the unreinforced alloy relaxes almost to zero in a very short time, whereas that in the composite is only partially reduced in a longer time. This behaviour is very different from that of the YS relaxation.By separating the total stress of the composite in macro and micro-stresses, according to the ROM (Eq. ), we observe an exponential decay also of the micro-RS, but with a very small total variation. The GNDs created during the cooling process cannot be annihilated by any annealing treatment ). As in the case of the YS, the drop of the macro-RS in the composite is much smaller than that in the unreinforced matrix. This is related to the more stable dislocation structure of the composite and to its smaller thermal expansion coefficient (CTE), caused by the presence of the ceramic reinforcement. It is well established that the RS increases with the CTE. In parallel to this, also the RS relaxation appears to increase with the CTE. the total (σT), macro-(σM) and micro-(σm) RS resulting after each treatment are plotted as a function of the corresponding YS. For the unreinforced alloy there is a linear dependence between macro-RS and YS. This is to be expected, because for E220 they relax at a similar rate, see The RS vs. YS curves of E219 show, however, two well-defined regions, In fact, they relax at very different rates. The YS relaxes faster than the RS (). Initially, with short heat-treatment times, a variation of the strength takes place, independent from the residual stress. While the RS is still large, the yield strength drops rapidly to its minimum value. Successively, the RS decreases while the yield strength has already relaxed and remains basically constant. The result is a logarithmic-type variation, very different from the linear behaviour observed for E220.The decrease of E220 YS with annealing at 300 °C is only due to the growth and coalescence of precipitates in the matrix. The more the precipitates grow, the lower the strength and the less inhibited the dislocations motion In E219 the YS is also influenced by the presence of the reinforcement, via the load transfer mechanism and the higher dislocation density with respect to E220. This is why the range of YS variation (σ0) is larger in E220: the GNDs at the particle/matrix interface form back after each cooling process. This implies that while in the alloy one can arbitrarily annihilate dislocations by means of suitable heat treatments, in the composite we would always get a minimum amount of them. This means that the difference between the dislocation densities in E219 and E220, Δρ, is such thatThe YS of E219, however, decreases approximately at the same rate as in E220. This similarity can be attributed to the fact that the precipitation kinetics at 300 °C is the same in the composite and in the alloy With short-time heat treatments, the effect of the precipitates on the YS is immediate, while that of the whiskers is mainly to lock the RS via the GNDs. Therefore, shows that the slope of the RS vs. YS curve is much smaller in E219 than in E220: the residual stress relaxes more slowly than the yield strength. Then, after relatively long treatment time, the slope increases and the RS relaxes dramatically, while the YS is essentially constant. This occurs until the RS reaches a minimum. In fact, there is an accumulation of points at the end of each curve in E219. As mentioned before, a minimum value of the RS is present in E219, because a certain amount of dislocations are still locked and cannot move and annihilate: they are the GNDs The relationship between the matrix residual stress and the yield strength in PM 6061Al–15 vol%SiCw has been studied. In order to achieve both stress relief and microstructural changes, samples were treated to a fully hardened (T6), to a severe over annealed (OA, at 300 °C) condition, and at different annealing times. The most relevant conclusions are:The presence of the reinforcement leads to higher YS in the composite matrix than in the unreinforced alloy, after every annealing treatment at 300 °C.The YS relaxation time (τYS) is very similar in the unreinforced alloy and in the composite. This implies that relaxation is mainly driven by the solid solution precipitation kinetics in the matrix. The small difference between the relaxation times can be attributed to the more rapid recovery in the alloy than in the composite.The YS relaxation (σ0) is more pronounced in the unreinforced alloy than in the composite. Again, the faster recovery (dislocation annihilation and redistribution) in the alloy than in the composite is responsible for this.The residual stress in the unreinforced alloy relaxes almost completely with annealing. The RS and the YS relaxations occur at a similar rate: a linear dependence is found between them in the whole range of stress variation. This implies that the precipitation sequence (β″ → β′ → β) is the rate-controlling process of RS relaxation in the 6061Al alloy. Upon annealing, the precipitates coalesce and the dislocations are able to move more freely, relaxing the residual stress but decreasing the YS proportionally.In the composite, the relaxation times of the YS and the matrix RS are clearly different. In fact, both the precipitation and the reinforcement determine the value of the YS. Upon annealing, the hindrance to dislocation motion represented by the precipitates (Orowan’s mechanism) decreases drastically, but the contribution of the reinforcement related mechanisms (the GNDs) remains. Schematically, there is a double-linear dependence between YS and matrix RS. Firstly, the yield strength decreases steeply while the RS is still locked by the GNDs, then, when the YS has decreased to its minimum, the RS relaxes, accumulating at a minimum. This implies that it is not possible to relieve the RS without substantially decreasing the material performance, at least by means of heat treatments at 300 °C.The macro-RS relaxes less and more slowly in the composite than in the unreinforced alloy. This is because the dislocations motion in the matrix is more inhibited in the former. Moreover, part of the composite macro-RS does not relax.Nanosized TiN–SBR hybrid coating of stainless steel as bipolar plates for polymer electrolyte membrane fuel cellsIn attempt to improve interfacial electrical conductivity of stainless steel for bipolar plates of polymer electrolyte membrane fuel cells, TiN nanoparticles were electrophoretically deposited on the surface of stainless steel with elastic styrene butadiene rubber (SBR) particles. From transmission electron microscopic observation, it was found that the TiN nanoparticles (ca. 50 nm) surrounded the spherical SBR particles (ca. 300–600 nm), forming agglomerates. They were well adhered on the surface of the type 310S stainless steel. With help of elasticity of SBR, the agglomerates were well fitted into the interfacial gap between gas diffusion layer (GDL) and stainless steel bipolar plate, and the interfacial contact resistance (ICR), simultaneously, was successfully reduced. A single cell using the TiN nanoparticles-coated bipolar plates, consequently, showed comparable cell performance with the graphite employing cell at a current density of 0.5 A cm−2 (12.5 A). Inexpensive TiN nanoparticle-coated type 310S stainless steel bipolar plates would become a possible alternate for the expensive graphite bipolar plates as use in fuel cell applications.Currently, metallic materials like stainless steels are being expected to compose bipolar plates for polymer membrane electrolyte fuel cells (PEFC) because of their superiority against carbon-based materials in respect of mechanical reliability, gas impermeability and mass productivity. Most of commercial metallic materials, however, are not free from corrosion under the PEFC environments even in the case of type 304 stainless steel Several treatment methods for metallic bipolar plates have been reported: gold plating In order to realize surface coating of stainless steel with such elastic electro-conductive agglomerates, we adopted electrophoretic deposition (EPD). EPD applies a DC electric field to deposit suspended particles on a substrate In this paper, we would like to report the PEFC performance with type 310S stainless steel bipolar plates coated with nanosized TiN–SBR via EPD. The TiN-coated and as-polished type 310S stainless steels were evaluated through polarization tests in the simulated PEFC environments and single cell operation.Type 310S stainless steel was employed as the base material. The chemical composition of the specimen is described in . The stainless steel plates were machined into a square (20 mm × 20 mm × 2 mm) and mounted into epoxy resin for polarization tests. The surfaces were finished using diamond paste polisher (6 μm) and cleaned ultrasonically in hexane for 15 min.TiN–SBR coating on type 310S stainless steel surface was carried out by EPD process. The suspension was composed by 0.064 mass% of TiN (50 nm, Wako), 0.24 mass% of emulsified SBR (M
= 110,000–260,000 g mol−1, NIHON Zeon) and 2-propanol. Prepared suspension was ultrasonically homogenized for 10 min. EPD treatments under a constant voltage (500 V) were controlled using a DC power supply (NC-1011, NIHON EIDO).Powder X-ray diffraction (Rigaku RINT-2200) using Cu Kα radiation was used to identify the crystalline phase of the coating layer. XRD data were obtained at 2θ
= 30–80°. Transmission electron microscopy (TEM, H-800, Hitachi) was used to observe the ultrasonically treated TiN nanoparticles and SBR in a suspension state. ICR was measured as a function of compaction force followed by a four-terminal method between the TiN-coated specimen and carbon paper as the GDL.Polarization tests were carried out in a PTFE lined cell, which was filled with 0.05 M SO42−
+ 2 ppm F− containing aqueous solution (pH 2.3, 200 ml), saturated with either Ar (transient mode: at −100 mV, which was suggested by Borup et al. A plate of stainless steel (80 mm × 80 mm × 6 mm) was machined into a bipolar plate with serpentine flow field according to the NEDO report by JARI After cell operations, the surfaces of the TiN-coated type 310S stainless steel were analyzed by XPS (ULVAC-PHI 5600) with a monochromatic Al Kα source. The take-off angle of the emitted photoelectrons was adjusted to 45° for the surface observation. Depth scale for sputtering was calibrated relative to anodically formed SiO2 standard layers. The sputter rate was determined to be 2.7 nm min−1 for the Ar-ion gun. shows TEM photographs of the SBR, TiN nanoparticles and microparticles with spherical SBR particle dispersed ultrasonically in propanol before the EPD treatment. Observed particle size of the SBR was around 600 nm in diameter with spherical morphology in b presents the bright-field image of TiN nanoparticles (average particle size: 50 nm) adhered on the spherical SBR particle. Majority of the TiN nanoparticles shows square shape. The TiN nanoparticles completely cover the SBR, and the agglomerate size of TiN and SBR is estimated to be around 600–700 nm, which is similar to that of the SBR particle. It is imagined that the TiN nanoparticles encapsulate the elastic binder (SBR) particle. The flexible structure with help of SBR particles would be advantageous as interfacial filler. The image of TiN microparticle with SBR is exhibited in c. The observed TiN particles approximate to 1 μm in size and are irregular in shape. It seems that the microscale TiN particles are connected point to point by SBR particles which are marked by arrows in c. Apparently, each TiN particle has no flexibility. shows XRD patterns of the TiN nanoparticles coated on the type 310S stainless steel with different EPD treatment time. Irrespective of EPD treatment time, typical fingerprint peaks of the stainless steel are clearly seen, as marked by triangle. Diffraction intensity of the TiN nanoparticles is quite lower in a. On the contrary, EPD treatment for 10 min gives rise to a clear appearance of simple cubic structured-TiN with Fm3m space group [JCPDS: #381420]. The calculated lattice parameter of the TiN was 4.24 Å by a least square method. TiN particles could be deposited on stainless steel by EPD without SBR. However, such TiN layer could be peeled off easily. The hybrid layer of TiN and SBR sufficiently adheres to stainless steel after heat treatment at 353 K and passed a peeling test by tape. We also examined the peeling test for the TiN nanoparticles coated on the type 310S stainless steel without the SBR binder obtained by the same EPD method. The TiN coating layer was readily peeled off from the stainless steel, indicating the SBR binder plays an important role to make a strong adhesion of the electro-conducting TiN nanoparticles on the surface of the steel. In lithium battery industries, the elastic SBR is one of common binders for electrodes materials that should be coated on metallic current collector foils. Thus, adhesion of SBR on the surface of the type 310S stainless steel would be strong enough. Therefore, it is found that TiN nanoparticles with elastic SBR were well deposited on the surface of type 310S stainless steel. shows relation of ICR between TiN nanoparticle-coated type 310S stainless steel and carbon paper GDL as a function of EPD time. The measurement method was referred from the literature shows ICR between the type 310S stainless steel covered with TiN of different particle sizes and GDL. The treatment time was 30 s. Obviously, the ICR of the TiN-coated type 310S stainless steel is smaller than that of as-polished, irrespective of TiN particle size. The results are similar to those reported by Cho et al. shows schematic drawings of interfaces between GDL and stainless steel before and after TiN–SBR coating. Stainless steel has air-formed oxide layers on the surface. Even though the thickness of oxide layers is thin (several nanometers), it obstructs the interfacial electron transfer. Another factor which would affect the interfacial conductivity is real contact area. The surface roughness would directly influence the contact resistance, as suggested by Kraytsberg et al. a), leading to an increase of ICR. Similarly, if the TiN nanoparticles without SBR are coated on grooves that are formed during surface polishing, the coated surface would hardly contact with the carbon fiber GDL, remaining as resistance. For this reason, relatively higher ICR value was obtained for the SBR-free TiN nanoparticle coating. Introduction of TiN–SBR layers onto the stainless steel would fill such empty gaps, as shown in b. The spherical morphology of the SBR particle would be changed at higher applying force (200 N cm−2) due to its elastic property (b). Hence, the contact area between stainless steel and GDL would be enlarged with help of electro-conducting TiN with SBR filler. Simultaneously, it gives rise to significantly decreased contact resistance, as presented in , especially when the EPD time was 30 s. Hereafter, EPD treatment was carried out using the TiN nanoparticles together with SBR binder and the process time was fixed to 30 s. shows the current density versus time curves for the TiN-coated type 310S stainless steel in 0.05 M SO42−
+ 2 ppm F− solutions (pH 2.3) at 353 K. We tested at two potentials, −100 mV (SCE) with Ar gas purge (PEFC anodic environment), and +600 mV (SCE) with air purge (PEFC cathodic environment) a shows the results at −100 mV simulating the PEFC anodic environment. As can be seen in a, the transient current decays very fast in the early stage for the as-polished and TiN-coated ones. The fast decay of the current density is ascribed to the formation of the passive film on the surface of the type 310S stainless steel. As soon as the whole surface is covered with the passive film, the needed current density for retaining the passivation is very low. The current density, finally, reached close to zero for the TiN–SBR hybrid coated samples. On the other hand, negative value was seen for the as-polished. As suggested by Wang et al. b, the current density stabilized and approached close to zero after 2000 s. In the inset of b, the TiN-coated type 310S stainless steel exhibited much lower current density, compared with that of the as-polished. The TiN nanoparticles hybrid coating with flexible SBR by the simple EPD treatment is promising to improve the corrosion resistance both at −100 mV and +600 mV in our experiments. shows comparison of ICR values before and after polarization tests between samples and carbon paper as a function of compaction force. As can be seen from a, the as-polished type 310S stainless steel after polarization at −100 mV showed a little increase in ICR, whereas that at +600 mV had about 10 times higher resistance. Generally, stainless steel is covered with passive films based on iron and chromium oxides. The passive film becomes thicker after polarization, which is also associated with changes in the chemical composition of the surface film b, the ICR value before polarization was about 10 times lower than that of as-polished. Even after polarization at −100 mV or +600 mV, negligible increase was seen. The ICR value for the TiN-coated type 310S stainless steel is comparable to that for the graphite at higher pressure (200 N cm−2) in b. It is believed that the presence of electro-conducting TiN nanoparticles with flexible SBR binder provides better contact between stainless steel and GDL at higher load (200 N cm−2) because the particle shape of elastic SBR can be changed by the compaction, as described in b. These combinational functions of TiN nanoparticles as electron conductor and SBR as a binder and a filler, contributed to the significantly improved corrosion resistance and reduced ICR properties.The TiN-coated and the as-polished type 310S stainless steels were employed as the bipolar plates for PEFC. For the operations, carbon paper was used as GDL. presents initial i–V characteristics of three kinds of single cells: the as-polished, the TiN-coated type 310S stainless steel and graphite bipolar plates. In an open circuit state, the TiN-coated sample showed cell voltage of 0.98 V, which is comparable to that of graphite employing cell (0.96 V). On the contrast, the as-polished type 310S stainless steel employing cell showed the lowest voltage (0.91 V) at that state. With increasing current to 0.1 A cm−2, the corresponding operation voltages of the cells decreased to around 0.8 V. Even though the applied current density was 0.5 A cm−2 (12.5 A), the TiN-coated bipolar plates employing cell presented similar i–V properties to graphite employing cell (0.68 V). For the case of as-polished type 310S stainless steel employing cell, it had lower voltage at 0.1 A cm−2 (0.75 V), compared with other two cells in . The voltage at 0.5 A cm−2 (12.5A) was 0.56 V, which is approximately 0.12 V lower than other two cells in , the TiN nanoparticle-coated type 310S stainless steel exhibited the similar ICR value to graphite, which is much lower than that observed in the as-polished. This proves that the lower ICR results in higher cell voltage. shows time variation of the cell voltage for the three single cells shown in . The higher cell voltages were maintained through the operation for the graphite and TiN-coated type 310S stainless steel bipolar plates employing cells in . The voltage decay was 55 mV and 44 mV, respectively, for the cells throughout the operation. The as-polished type 310S stainless steel bipolar plates employing cell showed 0.501 V after 300 h. The voltage decay observed was around 60 mV, which is the highest among three cells in Such a poor cell performance is not surprising for the as-polished type 310S stainless steel bipolar plates employing cell when carbon paper was used as the GDL, as suggested by Kraytsberg et al. a. The non-contact area remains as resistance. Therefore, the ICR value is higher and the corresponding operation voltage is also relatively lower during the operation. For case of TiN-coated type 310S stainless steel bipolar plates, the interfacial gap would be filled well with the nanosized TiN–SBR hybrid. The TiN nanoparticles, therefore, have good contact with carbon fibers of GDL. Electron pathway is also continuously connected by TiN nanoparticles, which is supported by the SBR filler, point by point from the surface of stainless steel to beneath of the carbon fiber. This, in turn, induces a decrease in the ICR so that the corresponding cell voltage, finally, becomes higher, compared with the as-polished case.After the operations, i–V characteristics were measured again in , the TiN-coated type 310S stainless steel bipolar plates employing cell showed improved properties. i–V profiles were similar to those observed in The operated cells were carefully disassembled and the ribs from bipolar plates were sampled for XPS analysis to investigate the chemical state of TiN coating layer. shows XPS spectra of TiN on the surface of type 310S stainless steel bipolar plate for the anode side after cell operation. The spectra were compared with those of as-coated one. As can be seen in a, the outer surface coated with TiN nanoparticles exhibited peaks related to TiO2 and TiN around 458.5 eV and 455.8 eV, respectively a. Further sputtering to 48 s (ca. 2 nm) presented that the inner surface was almost composed by TiN compound and TiO2-related peaks were barely detected. The similar to tendency was also observed in the anode side in TiN coating layers were carefully peeled off from the rib surfaces for further observation by TEM. The TiN nanoparticles presented square-shaped morphology with smooth edge lines in , the similar morphology is obviously observed. This means that TiN nanoparticles were not dissolved even after the operation for 300 h. shows XPS spectra for the TiN-coated surface of the type 310S stainless steel bipolar plate for the cathode side after cell operation. Similar to the anode parts, TiO2 peaks were seen in the outer surface. Again, sputtering to 12 s (ca. 0.5 Å) obviously gave rise to the appearance of TiN. By further sputtering, the intensity of TiN became much stronger than that of TiO2. The original particle shapes of TiN were almost maintained upon the cell operation in . It can be concluded, therefore, that TiN particles are stable enough under the PEFC environments even in size of 50 nm.To reduce the ICR of passivating metallic bipolar plates, type 310S stainless steel was coated by nanosized TiN–SBR via an electrophoretic deposition. The conductive TiN nanoparticles adhered on the flexible SBR provide pathways for the electrons transportation. The favorable contact, therefore, supported by the electro-conducting TiN coating layer with both stainless steel and GDL resulted in greatly reduced ICR. Kraytsberg et al. Available online at www.sciencedirect.com ScienceDirect Materials Today: Proceedings 4 (2017) 5336â€“5343 www.materialstoday.com/proceedings 6th International Conference of Materials Processing and Characterization (ICMPC 2016) Mechanical Behaviour Of Friction Stir Welding On Aluminium Based Composite Material G. Hemath Kumar1, Babu Vishwanath1, Rajesh Purohit2, R. S. Rana and rotating tool â€œstirsâ€� the material, softened by the frictional heat generated, and consolidates the stirred material behind the tool. This process has several advantages when compared to conventional fusion welding process. The present paper introduces the welding process and the welding of metal matrix composites. The welding was carried out on a CNC milling machine that was adopted for this work. Under Experimental condition of the study, mechanical strength, maximum temperature between the edge of the stir zone and the top surface, and effect of force against the tools are investigated. The micro hardness was also found to slightly increase with increased feed rate of the tool. Â© 2017 Published by Elsevier Ltd. Selection and/or Peer-review under responsibility of 6th International Conference of Materials Processing and Characterization (ICMPC 2016). Keywords: Friction Stir Welding, Heat Affected Zone, Mechanical Properties Saurabh Singh Rajpurohitc 1Professor, Department of Mechanical Engineering, Meenakshi College of Engineering, Chennai, India. 2Student, Saveetha Engineering College, Chennai, India. 3Associate Professor, Mechanical Engineering Department, MANIT Bhopal, India cMechanical Engineering Department, Marudhar Engineering College, Raiser, Bikaner, India. Abstract Friction-stir welding (FSW) is a solid-state joining process (meaning the metal is not melted during the process) and is used for applications where the original metal characteristics must remain unchanged as far as possible. This process is primarily used on aluminium and most often on large pieces which cannot be easily heat treated post weld to recover temper characteristics. The 2214-7853 Â© 2017 Published by Elsevier Ltd. Selection and/or Peer-review under responsibility of 6th International Conference of Materials Processing and Characterization (ICMPC 2016). Email ID : [email protected] G. Hemath Kumar / Materials Today: Proceedings 4 (2017) 5336â€“5343 5337 1. Introduction Friction Stir Welding is a type of metal joining processes which was introduced by The Welding Institute about two decades ago during (1991). It is abbreviated as FSW. It became a topic of great interest to the engineers and researchers since its discovery. FSW can be defined as a solid-state metal joining process. It utilizes a non- consumable tool, which is rotated and traversed along the weld-path. Due to the interference of the tool and workpiece, frictional heat is generated which increases the temperature of the workpiece. Care is taken that the frictional heat is just sufficient to raise the temperature to plastic state. Since 1991, FSW is subjected to intensive research and development activity. This has lead to many new parameters included and excluded to make this process one of the widely accepted welding process. FSW has been risen to global acceptance within a few years and is still continuing to achieve new level of dominance. Importance of Tiâ€“6Alâ€“4V alloy has been stated from the fact that presently it is most broadly used alloy, accounting for more than 50% of all titanium tonnage in the world [3]. Tiâ€“6Alâ€“4V alloys exhibit a unique combination of mechanical and physical properties. Precisely, its high specific strength (strength/density) at low to moderate elevated temperature makes this alloy as a desirable candidate for selection of aerospace engines, airframe structures and components [4]. Its admirable corrosion/erosion resistance provides the prime motivation for chemical process, marine, energy and bio-medical industrial service [5]. (A) Two discrete metal work pieces butted together, (B) The progress of the tool through the joint, also along with the tool (with a probe). showing the weld zone and the region affected by the tool shoulder. Fig.1 Schematic diagram of the FSW process [4] FSW can be opted to weld any type of metals provided the tool can withstand the extreme heat developed during the process. The many research and development activities carried out during the past 20 years in FSW have given rise to many different tools with different pin profiles and different grades. The current scenario of FSW is the process can be used to join any metal or combination of metals to get good joint strength and joint efficiency. The FSW does not give raise to any weld related problems since the weld material is heated using frictional heat till plastic stage as shown in the above Fig 1 (a), Fig (b). Aluminium is one of the metals that can be welded with ease using FSW. Pure aluminium have a melting point of 660oC, it is the lowest among metals. Hence it can be welded using any commercial welding processes. The man practical difficulty to weld aluminium is its alloys represented in terms of grades such as 1XXX, 2XXX, â€¦., upto 7XXX. By mixing different proportions of metals to aluminium, we get aluminium alloys. Each aluminium alloys have its own strengths and weaknesses and hence suited for specific needs. 5338 G. Hemath Kumar / Materials Today: Proceedings 4 (2017) 5336â€“5343 Experimental Procedure In this paper the aluminium alloy 6061 is mixed with (80 ï�m) silicon carbide particulates (SiCp) to get metal matrix composites (MMCs). Different specimen of MMC having varying percentage by weight composition of SiCp (5%, 10%, 15%, 20%, 25% and 30%) were made. The mixture of SiCp in aluminium tends to improve its mechanical behaviour and have advantages over conventional 6061 aluminium. The present paper brings light on the ability of FSW to weld MMC. An experiment was conducted to analyze the feasibility of FSW on MMC, in which aluminium 6061 is the matrix while silicon carbide particulates of size 80 Âµm act as the reinforcement. Even after several years after introducing FSW, little is known about the possibility to weld composites using FSW. The MMC welded using FSW is subjected to different analysis such as micro-hardness, joint strength, temperature distribution and maximum force during weld. The MMC was produced by die casting using induction furnace and extruded into as required dimension (5 x 100 x 300 mm from 6 x 100 x 250 mm) with heat treated to T6 temper condition. The chemical composition of the aluminium alloy can be seen in Table 1. Table 1: Chemical compositions of the aluminum alloy AA 6061 (%weight) [9] The FSW machine used for the experimental studies in this paper was manufactured by HMT technologies. The machine has three axes, which are denoted x (perpendicular to the tool axis in the direction of welding), y (perpendicular to the tool axis in the direction of welding and perpendicular to x axis) and z (Parallel to the tool axis and in the plunge direction), It is controlled by the CNC displacement control milling machine with a maximum continuous power of 15 kW, Table size: 305 mm X 1250 mm, and maximum speed is 1500 rpm. The total weld length was around 150 mm from pin entry to pin exit, with pin inserted at 25 mm from the leading plate edge and extracted at 200 mm. The FSW tool material is EN18. The tool pin profile is square with rounded edges and having depth of 5 mm. The geometrical characteristics of the pin are as shown in Fig 2. The square butt joint has been prepared to fabricate FSW joints, this configuration as shown in Fig 3. Fig.2 Configuration of Tools Alloy Si Fe Cu Mn Mg Cr Zn Ti Al 6061 0.4- 0.8 0.7 0.15- 0.4 0.15 0.08- 0.12 0.04- 0.35 0.25 0.15 Remainder G. Hemath Kumar / Materials Today: Proceedings 4 (2017) 5336â€“5343 5339 Fig.3 Configuration of the weld join specimen Results and Discussions In the current investigation, an attempt has been made to study the effect of tool pin profile and welding speed on the formation of friction stir welding. The micro hardness and microstructure of FSP reigns produced by square pin profile tool was better than other profile as they exhibited maximum tensile strength, higher hardness and fine grains in the FSP reign [1]. The tool used for the experiments conducted was essentially a two-step tool designed so as to provide appropriate material movement. The weld parameter and designations are given below for this experiment. Constant parameter: Shoulder diameter â€“ 25 mm Pin diameter (square) â€“ 12 mm Tool speed â€“ 400 rpm, 600 rpm and 800 rpm When the tool is made to rotate and traverse along the weld direction (x direction), the temperature at the tool and weld metal interface tends to increase. By properly controlling the rate of tool rotation and tool traverse, the temperature is made to increase to the extent that the weld material just gets to the plasticised material. There are three regions in the weld depending upon the extent of heat distributed to the weld material. The three regions are explained below: Weld nugget: This region is very close to the tool surface, and is the main part of the weld. Thermo Mechanical Affected Zone: This zone occupies larger volume when compared to weld nugget. Intense stirring is experienced in this region because of the tool rotation and traverse. Heat Affected Zone: This region act as the transition between the weld and the base material. As the name implies this region indirectly has become the part of weld because of the heat due to the weld. The three regions of the weld are shown below in Fig. 4. Fig. 4 A Schematic Diagram of Different Regions of FSW [3] 5340 G. Hemath Kumar / Materials Today: Proceedings 4 (2017) 5336â€“5343 Effect of Micro-Hardness: Vickers micro hardness determination was carried out with a 100 N load and 15s dwell time. Three rows of indents at 0.5, 2.5 and 4.5 mm from the top surface made along the cross section of the weld, using a semi-automatic micro-hardness tester. The Vickers indents were made with a spacing of 0.3 mm and were used to quantify the effect of heat input during the process. The measures were made in accordance to the ASTM E384 standard [1]. There was no appreciable change in the micro hardness readings along the weld. The Fig. 5, Fig 6 and Fig.7 shows that there is no adverse effect of the welding process on the hardness and it remains nearly constant throughout. From the Fig. 5, Fig 6 and Fig.7 it can be observed that the micro hardness increases with increase in feed rate of the tool. Fig.5 Effect of Micro hardness at tool speed 400 rpm Fig.6 Effect of Micro hardness at tool speed 600 rpm M ic ro ha rd ne ss H V Position At 400 rpm 50 mm/min 80 mm/min 100 mm/min M ic ro ha rd ne ss H V Position At 600 rpm 50 mm/min 80 mm/min 100 mm/min G. Hemath Kumar / Materials Today: Proceedings 4 (2017) 5336â€“5343 5341 Fig.7 Effect of Micro hardness at tool speed 800 rpm Effect of Tensile test To determine mechanical properties of obtained weld joint, the tensile tests has been performed according to EN 895 by preparing three test specimens [1]. The details are given in Fig. 8. Fig. 8 Dimension of the tensile test specimen Average tensile strength is given in Fig. 9 which is matched with strength properties of base metal. It has been observed that weld joint strength improves and its appearance gets better if welds speed is being raised upto 100 mm/min and tool speed to 800 rpm. The weld joint breakage occurs either in stirred welding or heat affect zone. It has been determined that weld joint tensile properties are satisfactory even through not comparable with base materials Fig. 9 Effect of tensile strength of Al-SiCp at diferent welding speed with the tool rotation speed M ic ro ha rd ne ss H V Position At 800 rpm 50 mm/min 80 mm/min 100 mm/min Jo in t S tr en gt h M Pa Tool Speed (rpm) 50 mm/min 80 mm/min 100 mm/min 5342 G. Hemath Kumar / Materials Today: Proceedings 4 (2017) 5336â€“5343 Temperature Distribution FSW results in intense plastic deformation around rotating tool and friction between tool and work pieces. Both these factors contribute to the temperature increase within and around the stirred zone. The temperature measurements within the stirred zone are very difficult due to the intense plastic deformation produced by the rotation and translation of tool. Therefore, the maximum temperatures within the stirred zone during FSW has been either estimated from recorded by embedding thermocouple in the regions adjacent to the rotating pin. The Fig. 10 shown the peak temperature distribution adjacent to the stirred zone and edge of the stirred zone and the temperature decreased with increasing distance from the stirred zone. The temperature at the edge of the stirred zone increased from the bottom surface of the plate to the top surface. The maximum temperature was recorded near the corner between the edge of the stirred zone and the top surface. Fig.10. Effect of tool feed rate on peak temperature as a function of distance from weld centre line for constant speed at 600 rpm Effect of Forces against the tool When pin rotate at speed 600 rpm at different weld speeds of 50, 80, 100 mm/min, the force act on the pin due to normal force acting on tool. It significantly affects the motor as well as bed of milling machine. In this experiment the co-axial force acting in X axis is perpendicular toward tools and y axis force is perpendicular to and forward to the tools. The special attachment has been design and developed for finding the force acting against tools for this experiment [2]. It is shown in Fig. 11. Friction stir welds were made by joining two welded part. Welding was performed perpendicular to the rolling direction with a backward tool. AA6061 plates along with a steel backing plate were clamped firmly onto the load measuring device as shown in Fig. 12 in order to prevent the abutting faces from being forced apart. The device in turn was placed on machine bed with stainless steel bright rods in between with its movement restricted in three planar directions whereas the unrestrained positive X direction movement allowed the measurement of the X- direction force. Lab VIEW (Laboratory Virtual Instrumentation Engineering Workbench), a visual programming language from National Instruments, was used to write a program to interface the load measuring device via a PCL 818HG data acquisition card. This paper mentions the results of experiments conducted with the variation of welding speed while other parameters, namely tool RPM, shoulder diameter and pin diameter & profile being constant. Three runs were carried for each parameter combination. The total weld length was around 150 mm from pin entry to pin exit. FSW tool was machined from square tool with a measured hardness value of 55 HRC. A two-step pin was used; the geometrical characteristics of the pin are as shown in Fig. 4. X axis force was increased and that is acceptable, as more material is to be plasticized. Y axis force was also increased which is acceptable as time per unit length decreases therefore heat input per unit length decreases. Te m pe ra tu re C Distance from weld centre, mm 50 mm/min 80 mm/min 100 mm/min G. Hemath Kumar / Materials Today: Proceedings 4 (2017) 5336â€“5343 5343 Fig. 11 Laboratory Virtual Instrumentation Engineering Workbench (Lab VIEW) Fig.12 Effect of force acting on the tools Conclusions A FSW process was performed on Al-SiCp composites. The feasibility of the weld was analysed using various techniques to check the nature of the weld. It was found out that the hardness of the weld increases with an increase in tool rotation rate and tool traverse rate. However, the increase in hardness was compromised by a decrease in ductility. It has also been found out that the temperature is maximum at the region very nearest to the tool and with an increase in distance from the tool the temperature drops considerably. The majority of the temperature of the weld was backed by the frictional heat generated due to force by the tool along the x direction. References 1. Murr L E, Liu G, McClure J C (1997). Dynamic recrystallization in the friction-stir welding of aluminium alloy 1100, Journal of Materials Science Letters 16 (22), 1801â€“1803, 10.1023/A, 1018556332357. 2. Cemal Meran (2006). The joint properties of brass plates by friction stir welding, Material and design, 27, 719-726. 3. Sutton M A, Yang B, Reynolds A P, and Taylor R (2002). Microstructure studies of friction stir welds in 2024-T3 aluminium, Materials Science and Engineering, A323, 160-166. 4. Yang B, Yan J, Sutton M A and Reynolds A P (2004). Banded microstructure in AA2024-T351 and AA2524-T351 aluminium friction stir welds, Part I. Metallurgical studies, Material Science and Engineering, A364, 55-56. M ax . F or ce (N ) Tool Traverse mm/mm X direction (N) Z direction (N) corner between the edge of the stirred zone and the top surface. Fig.10. Effect of tool feed rate on peak temperature as a function of distance from weld centre line for constant speed at 600 rpm Effect of Forces against the tool When pin rotate at speed 600 rpm at different weld speeds of 50, 80, 100 mm/min, the force act on the pin due to normal force acting on tool. It significantly affects the motor as well as bed of milling machine. In this experiment the co-axial force acting in X axis is perpendicular toward tools and y axis force is perpendicular to and forward to the tools. The special attachment has been design and developed for finding the force acting against tools for this experiment [2]. It is shown in Fig. 11. Friction stir welds were made by joining two welded part. Welding was performed perpendicular to the rolling direction with a backward tool. AA6061 plates along with a steel backing plate were clamped firmly onto the load measuring device as shown in Fig. 12 in order to prevent the abutting faces from being forced apart. The device in turn was placed on machine bed with stainless steel bright rods in between with its movement restricted in three planar directions whereas the unrestrained positive X direction movement allowed the measurement of the X- direction force. Lab VIEW (Laboratory Virtual Instrumentation Engineering Workbench), a visual programming language from National Instruments, was used to write a program to interface the load measuring device via a PCL 818HG data acquisition card. This paper mentions the results of experiments conducted with the variation of welding speed while other parameters, namely tool RPM, shoulder diameter and pin diameter & profile being constant. Three runs were carried for each parameter combination. The total weld length was around 150 mm from pin entry to pin exit. FSW tool was machined from square tool with a measured hardness value of 55 HRC. A two-step pin was used; the geometrical characteristics of the pin are as shown in Fig. 4. X axis force was increased and that is acceptable, as more material is to be plasticized. Y axis force was also increased which is acceptable as time per unit length decreases therefore heat input per unit length decreases. Te m pe ra tu re C Distance from weld centre, mm 50 mm/min 80 mm/min 100 mm/min G. Hemath Kumar / Materials Today: Proceedings 4 (2017) 5336â€“5343 5343 Fig. 11 Laboratory Virtual Instrumentation Engineering Workbench (Lab VIEW) Fig.12 Effect of force acting on the tools Conclusions A FSW process was performed on Al-SiCp composites. The feasibility of the weld was analysed using various techniques to check the nature of the weld. It was found out that the hardness of the weld increases with an increase in tool rotation rate and tool traverse rate. However, the increase in hardness was compromised by a decrease in ductility. It has also been found out that the temperature is maximum at the region very nearest to the tool and with an increMechanical Behaviour Of Friction Stir Welding On Aluminium Based Composite MaterialFriction-stir welding (FSW) is a solid-state joining process (meaning the metal is not melted during the process) and is used for applications where the original metal characteristics must remain unchanged as far as possible. This process is primarily used on aluminium and most often on large pieces which cannot be easily heat treated post weld to recover temper characteristics. The rotating tool “stirs” the material, softened by the frictional heat generated, and consolidates the stirred material behind the tool. This process has several advantages when compared to conventional fusion welding process. The present paper introduces the welding process and the welding of metal matrix composites. The welding was carried out on a CNC milling machine that was adopted for this work. Under Experimental condition of the study, mechanical strength, maximum temperature between the edge of the stir zone and the top surface, and effect of force against the tools are investigated. The micro hardness was also found to slightly increase with increased feed rate of the tool.Deformation-mediated superstructures and cavitation of poly (-lactide): In-situ small-angle X-ray scattering studyCavitation and superstructure evolution of polymers during stretching play crucial roles to influence the mechanical properties of materials. In this study, we investigated deformation-mediated superstructures and cavitation of poly (-lactide) (PLA) as well as their dependence on stretching temperatures by in-situ small-angle X-ray (SAXS) analysis coupled with mechanical testing. It is found that the cavitation and crystalline deformation are strongly influenced by stretching stress during deformation, which significantly depends on the stretching temperature. At lower stretching temperature (70 °C), the cavitation is initiated before the yielding and then stimulates the crystallite shearing. At higher stretching temperature (90 °C), however, the crystallites shear firstly and then crystalline deformation promotes the formation of cavities orientated along the stretching direction. High stretching temperature benefits the formation of relatively perfect crystals with high orientation. The results provide the basic knowledge of how to adjust the mechanical properties of polymer materials by controlling their superstructure in the deformation process.Deformation processing of semi-crystalline polymers is generally used to modulate their mechanical properties for fabricating final products, which directly depends on the formation of superstructures. During the stretching deformation of semi-crystalline polymers, the superstructure evolution involves the variation of crystalline and amorphous phases, including orientation-induced crystallization, crystal transition, chain orientation, fibrillar formation and cavitation, etc -lactide) (PLA) is a biodegradable and biocompatible polymer, which can be used in biomedical fields. Its proper mechanical properties and environmental friendliness make it a promising material to replace the petroleum-based traditional thermo-plastics for different industrial application The in-situ small-angle X-ray scattering (SAXS) measurement coupled with mechanical testing is one of the most powerful tools to investigate the structural information on a scale, including lamella stacking, slip and fragmentation of crystallites, fibril structures and cavitation, etc -lactide) (PLA) (2002D, Natureworks, USA) containing 4.6 wt% of D-isomer units was used in the present work. Its number-average and weight-average molecular weights are Mn = 1.5 × 105 g/mol and Mw = 2.0 × 105 g/mol, respectively. The material has a melt flow index of 4.5 g/10 min (190 °C/2.16 Kg), a glass transition temperature of about 63 °C and a melting temperature of 150 °C (10 °C/min, DSC).The PLA plates with a size of 125 × 12.5 × 1.6 mm3 were prepared by injection molding using an Ergotech 100/420–310 (Demag) machine at the temperature of 200 °C. The injection-molded plates were rapidly cooled to room temperature. For tensile stretching, the injection-molded plates were first annealed for 5 h at 120 °C to form the stable α crystals, and then waisted specimens were cut from the annealed injection-molded plates (with the size of 1.5 mm thickness, 20 mm length and 3 mm width) To characterize the structure variation during the stretching, mostly step-loading experiments were performed, namely, stretching the sample to a certain strain and then recording the patterns at this constant strain. The force (F) and displacement (L) of PLA samples were also recorded. The specimens are assumed to be incompressible, so the true stress σ can be calculated from the measured force F, initial cross section A, and tensile true strain ε as σ = F (1+ ε)/A. Engineering stress was defined conventionally as force per initial cross-sectional area.X-ray measurements were performed at the synchrotron beamline BW4 at HASYLAB (Hamburg, Germany). The wavelength of the X-ray beam was 1.3808 Å, and the beam diameter was about 400 μm. The SAXS images were collected by a two-dimensional MarCCD-detector (2048 × 2048 pixels of 79.1 × 79.1 μm2). The sample-to-detector distance was set to 4114 mm. Exposure times were chosen in the range of 30–60 s per pattern. The frame rate, determined by exposure and data storage, was 40–70 s per pattern. All of the SAXS data were corrected for the background scattering, X-ray absorption, and sample thickness.The radially integrated intensities I(q) (q = 4πsin θ/λ) were obtained for integration in the azimuthal angular range of 0° ≤ Φ ≤ 360°. The long period (L) was calculated with the Bragg equation:in which qmax corresponds to the peak position in the scattering curves (i.e., I(q) vs q).The equatorial intensities were obtained by integration in the azimuthal angular range of −10° ≤ Φ ≤ 10°, while the meridional intensities were obtained by integration in the azimuthal angular range of 80° ≤ Φ ≤ 100° (meridional direction is along stretching direction) According to Guinier approximation, if N groups of voids with different sizes exist in material, the intensity of scattering may be described by the equation where K is a constant, υi the volume of voids in the ith group, Ri the radius of gyration, and h the scattering vector. For rod-like scatterers，the radius of gyration Rg of the microvoids is obtained according to the following relationship If the function ln(I) = f (q2) was not linear for the deformed PLA, it was divided into 2 or 3 linear parts, each of them representing another group of cavities and Rg was then calculated.Wide angle X-ray diffraction measurements were carried out by using Cu Kα radiation (λ = 1.54 Å) with an X-ray 4-circle diffractometer P4 (Siemens, Germany) equipped with area detector system Histar/GADDS (Siemens Analytical, Madison/WI). The two-dimensional (2D) diffraction patterns were investigated for both the undeformed and deformed samples at room temperature with the exposure time of 300 s. Background scattering was recorded and subtracted from the sample patterns. The one-dimensional diffraction intensity for each 2θ has been obtained by integration over the azimuthal range (0–360°) of the 2D-diffraction images and was corrected for sample thickness.The WAXS intensity profiles were further treated using the PeakFit software, assuming Gaussian profiles for all scattering peaks and the amorphous halo. The amorphous scattering curves were acquired from the amorphous PLA sample and used in all further treatments of WAXS intensity profiles and calculations of crystallinity. The degree of crystallinity was computed from the ratio of Bragg scattering contribution of the crystalline phase to the total scattering intensity The orientation of the lattice plane (200/110) were calculated by the Hermans’ orientation equation where Ф is the angle between the normal direction of the crystal plane and the reference axis, and cos2Ф is defined as:where I(Ф) is the scattering intensity along the angle Ф.The crystal size was calculated from the full width at half-maximum (FWHM) of the fitted crystalline peaks using the Debye–Scherrer equation expressed as Here Dhkl represents the mean crystallite size in the normal direction of the (hkl) reflection plane and β1/2 is the FWHM of the diffraction peak (hkl) in radians. The shape factor K is 0.9 for polymer systems and the resolution of the diffractometer is neglected.The morphology of cavities in the cryogenic fractured surface along stretching direction of deformed PLA was observed on a JSM-6700F JEOL scanning electron microscope (SEM). All SEM specimens were coated with gold/palladium of approximately 5 nm thick to improve image quality.Under all the three stretching temperatures (70, 80 and 90 °C), the engineering stress-strain curves of PLA show the same trend, and can be divided into three zones (, left), i.e., pre-yielding region at low strain (O–Y), plastic-deformation region including the development of necking (Y–S), and strain-hardening up to fracture (S–F). The true stress-strain curves, which reflect the true stress and true strain values at the measured position during deformation, were calculated, and the true stress shows the same increasing tendency with true strain for all the three temperatures (, right). It is found that at the initial elastic region (O–Y), the true strain of deformed PLA is slightly lower than engineering strain. Stress relaxation is observed due to the chain rearrangements in the amorphous phase during the step-loading experiments. After the yield point, a local neck is formed, which propagates along the whole specimen (Y-S). The local strain rate is larger than the engineering strain rate, resulting in the larger true strain compared with engineering strain. In the necking region, the engineering stress decreases, while the true stress changes slightly due to the variation of cross-sectional area. Further stretching to fracture (S–F), the true stress gradually increases with the true strain and strain-hardening occurs.On the other hand, the stresses of deformed PLA at the equivalent strain and yield points show strong dependence on stretching temperature. The lower stretching temperature (70 °C) leads to the higher yield strain and the higher stretching stress as well as the lower strain at break (, right). Increasing the stretching temperature from 70 to 90 °C decreases the true yield stress from 27 to 16 MPa. Similar mechanical behavior was observed in the PP stretched at different stretching temperatures In-situ SAXS analysis is a powerful tool to characterize the evolution of cavitation and lamellar structures of semi-crystalline polymers during stretching. The scattering intensity in SAXS patterns is determined by the difference of the electron densities, including the scattering of microvoids and cavities in the low q range as well as the lamellar structure between crystalline and amorphous phases. The scattering of cavities is much more intense than that of lamellar structure due to the strongly different electron densities. 2D-SAXS patterns for deformed PLA samples at different strains and different temperatures are given in . For the undeformed PLA samples, a slight scattering near the center is observed, which is due to preexisting cavities or heterogeneities. An isotropic scattering ring is consistent with the scattering from randomly oriented lamellar stacks (see the arrow in In the O–Y pre-yielding zone, the scattering intensity in the low q range (q < 0.3 nm−1) increases quickly at the strain of 0.13 when the stretching temperature is 70 °C, which is due to the formation of cavities. Furthermore, the intensity scattered from the cavities is not uniform, which is elongated in the meridional direction (see the arrow in , strain: 0.13). With the increase of stretching temperature, there is no obvious variation in scattering intensity from cavities and voids in this zone (), there may exist crystal deformation (crystallite shearing, slips and fragmentation, etc). The scattering intensity from the lamellar structure of PLA decreases () and disappears at the stretching strain higher than 50% at 70 °C. On the other hand, the elongation of scattering patterns at low q range varies from meridional to equatorial direction, which is attributed to the orientation variation of cavities from perpendicular to parallel to stretching direction ) suggests that the crystalline lamellae are sheared and tilted to a preferential orientation. In S–F strain-hardening zone (), the intensity from cavities is further increased with stretching strains at 70 °C. The orientated cavities along stretching direction appear at the local strain higher than 200% for PLA stretched at 80 °C and the scattering from the lamellar structure disappears. When the stretching temperature is 90 °C, the 2-bar scattering pattern shows the persistence of a highly oriented crystal lamellar structure at high local strain (see the arrow in ). A large amount of scattering intensity from cavities only appears near the breaking strain of PLA.From the above results, it is obvious that the stretching temperature and strains are two important factors to influence the evolution of cavitation and lamellar structure. The quantitative analysis of the variation of cavities and lamellae structure during stretching was further studied and discussed as following. shows the integrated scattering intensity from voids and cavities at different strains for the PLA stretched at different temperatures. When the stretching temperature is 70 °C, it is found that the intensity increases with the stretching stain and shows a strong increase at the stretching strain of 200%, suggesting the formation of a large number of cavities. At 80 °C and 90 °C stretching, PLA is deformed without cavitation at the yield point. So, the higher stretching temperature leads to larger critical strain in which the cavities of PLA can be initiated. The increase of stretching temperature from 80 to 90 °C results in the increase of critical strain from about 200 to 600%. Furthermore, the numbers of cavities at the comparable strains decrease at higher stretching temperatures. The radius of gyration of cavities (Rg) was calculated by Guinier approximation (See the Supporting Information, . It shows that the size and groups of cavities increase with stretching strain. At the comparable stretching strains, the size of cavities decreases with increasing stretching temperature. SEM analysis further confirms that the size of cavities decreases with increasing stretching temperature ( shows the variation of the ratio of meridional to equatorial intensities with strains. The change of the ratio is an important evidence to indicate the shape and orientation of the cavities during deformation Besides the cavitation, superstructure is the other factor influenced by stretching temperature and strain. The scattering from the lamellar structure disappears quickly with the initiation and development of cavitation () since the initiation of cavities favors to destroy the ordered lamellar structure. At 90 °C stretching, the lamellar structure evolution of PLA was caused by the deformation without the influence of cavitation at relatively large strains (). For initial PLA sample, the isotropic scattering ring suggests that the lamellar structure arranges randomly. Before the yielding point, the intensity in meridional direction slightly increases and the scattering ring from the lamellar structure still exists ( (II)). In this region, the lamellae show no significant variation and the amorphous phase between crystalline lamellae is stretched first. Therefore, the increase of intensity in meridional direction is due to the deformation of amorphous phase along stretching direction, which increases the difference of the electron densities between crystalline and amorphous phases. In addition, the long period in the pre-yielding zone increases slightly with stretching due to the extension of amorphous phase (). After the yielding point, crystallite shearing, slip as well as preferential orientation along stretching direction happen in the necking course, which results in formation of the 4-bar scattering pattern (, II). Further increasing stretching strain to strain-hardening zone, the 2-bar scattering pattern indicates the persistence of the well-oriented and correlated layered-like lamellae with folded chains (, IV), and the long period in this zone decreases (, III). It is suggested that the increased stress promotes the fragmentation and rearrangement of crystallites followed the formation of thinner lamellae with their normal parallel to stretching direction. Combining the SAXS results with SEM micrographs (), it is found that the deformed PLA forms a ﬁbrillar structure with embedded cavities.The variation of lamellar structure and cavitation of deformed PLA during stretching accompanies with the change of crystallinity, crystal orientation and the size of crystals. The 2D-WAXS images for the PLA specimens before deformation and after extension to break and the corresponding azimuth-integrated intensity curves are shown in , respectively. It can be seen that the intensities are isotropically distributed for initial PLA samples. After extension to break, the crystalline rings change into short arcs, suggesting that the PLA crystals are oriented preferentially along the tensile direction. The diffraction peaks of 2θ = 16.3° and 18.7° are assigned to the crystal planes (200)/(110) and (203) of α crystal form of PLA, respectively. This indicates that the deformed PLA forms the orientated α crystal form. However, the diffraction arcs of different crystalline plane for deformed PLA samples mutually overlap, indicating the fragmentation of crystals and recrystallization (). After separating the intensity from crystalline diffractions and the amorphous component with a Peakfit software (See the Supporting Information, ). The crystallinity decreases after stretching to break compared to the initial PLA samples. The lower stretching temperature leads to the decrease of crystallinity and crystal size. In addition, the true stress-true strain curves show that the strain at break of PLA increases with increasing stretching temperature (), which favors the orientation of crystals (During the stretching of semi-crystalline polymers, two main variations with respect to the crystalline and amorphous phases have been found. In the crystalline region, deformation can induce the crystallite shearing, the lamellae slip and fragmentation of crystallites as well as the melting-recrystallization Based on the above discussion, we propose the following mechanism for the structure evolution of deformed PLA with strains at different stretching temperatures (). At lower stretching temperature, the cavities appear and extend perpendicular to the stretching direction before yielding ((a)) and the amorphous phase is stretched slightly. Further increasing the stretching strain, the numbers of cavities increase, and the orientation of cavities turns from perpendicular to parallel to the stretching direction. The lamella fracture to small blocks and some crystals are destroyed ( (b and C)), resulting in the disappearance of the ordered lamellar structure. On the other hand, high stretching temperature stimulates the slip of lamella without cavitation ((d and e)). In the strain-hardening zone, the orientated cavities along stretching direction appear and some lamella break to small blocks ((f)), while the number and size of cavities and the imperfection of lamella are all lower than that of deformed PLA at low stretching temperature.This work reveals the deformation mechanism of PLA under uniaxial stretching at different temperatures. It is found that stretching temperature plays an important role to influence the cavitation and superstructure of PLA as well as its deformation mechanism. The lower stretching temperature promotes the initiation of cavitation before the yielding and favors the destruction of the ordered lamellar structure with the increase of stretching strain, while high stretching temperature stimulates the crystallite deformation without cavitation and formation of well-oriented and correlated layered-like lamellae with folded chains. The mechanism of deformation-mediated superstructure and cavitation of PLA under different stretching temperature brings new knowledge to control the mechanical behavior of semi-crystalline polymer materials.Supplementary data associated with this article can be found, in the online version, at Dynamic precipitation during cyclic deformation of an underaged Al–Cu alloy► Pronounced cyclic hardening is observed in an under aged Al–4Cu–0.5Sn (wt.%). ► The origin of the hardening is room temperature dynamic precipitation of GP zones. ► The GP zone formation has a positive effect on the low cyclic fatigue performance. ► The precipitation process is controlled by deformation induced vacancy production.The cyclic deformation behavior of Al–4Cu alloy containing shear-resistant particles was investigated systematically as a function of precipitate state. Pronounced cyclic hardening was observed in the under aged Al–4Cu–0.05Sn (wt.%) alloy strained under various imposed plastic strain amplitudes at room temperature. Such cyclic hardening is absent from the longer aging treatments. Microstructural characterization reveals that the pronounced cyclic hardening of the under aged alloy is due to the dynamic precipitation of GP zones. The dynamic precipitation occurs during all the cyclic loading process and only at the peak stress, where the hardening increment from dynamic precipitation saturates, does strain localization occur which is soon followed by failure of the material. The dynamic precipitation of GP zones has a positive effect on the low cycle fatigue performance of this alloy, and can significantly elevate the strength of this alloy without loss in ductility. Experiments performed to test the dependence of the cyclic hardening on plastic strain amplitude and strain-rate illustrate a relatively strain-rate independent and strain amplitude dependent behavior. Such kinetic behavior is approximately consistent with that expected if the GP zone formation is controlled by the vacancies production process during plastic deformation.Precipitation hardened Al alloys are attractive engineering materials because of their good combinations of specific strength, formability, environmental resistance and cost. For these reasons they find widespread use in the transportation industries (e.g. automotive, maritime, and aerospace). In particular, the high-strength alloys are used extensively by the aerospace industry and in these applications the fatigue properties of the alloys are critical. Engineering alloys generally exhibit a fatigue ratio (fatigue strength/ultimate tensile strength) of ∼0.5 for 108 cycles of deformation. Unfortunately the fatigue properties of precipitation hardened Al alloys are quite poor compared with other ductile alloys and exhibit ratio's closer to ∼0.3 This comparatively poor fatigue performance of precipitation hardened Al alloys has long been known and Orowan appears to have been the first to offer an explanation Indeed, it is known that the rich variety of hardening and softening that accompanies cyclic deformation of precipitation hardenable Al alloys is closely related to the stability of the precipitate structure. Alloys containing a distribution of relatively stable shear-resistant particles tend to show very stable cyclic deformation behavior and this has been reported many times, for example in Al–Cu alloys containing θ’ (Al2Cu) precipitates Observations of room temperature coarsening of a precipitate microstructure during fatigue deformation raise the question of what mechanism facilitates the accelerated mass transport. It cannot occur with the equilibrium vacancy concentration in substitutional alloys like Aluminium. Broom et al. An alloy of composition Al–4Cu–0.05Sn (wt.%) was cast in a steel mold from high-purity elemental components and, after homogenization at 500 °C for several days, the ingot was cut into several plates that were then hot-rolled to 4 mm thick sheet from which fatigue samples (16 mm gauge length and 4 mm × 5 mm cross section area) were sparked machined. All samples were solution treated at 520 °C in a salt bath for 1 h, water quenched to room temperature and then isothermally aged at 200 °C for various times, ranging from 10 min to 30 days, to obtain different states of precipitation. Sn is added to the alloy as a microalloying addition because of its desirable effects in catalyzing the nucleation of exclusively shear resistant θ’ precipitates (Al2Cu) with a reasonably narrow size distribution. For an aging temperature of 200 °C, only plate-shaped θ’ are formed for times of at least 30 days The monotonic mechanical properties were characterized using tensile tests and are summarized in The cyclic deformation microstructures formed in the Al–4Cu–0.05Sn alloy were investigated by conventional transmission electron microscopy (TEM) and high-angle annular detector dark-field (HAADF) imaging using JEOL-2011 and JEOL-2100F microscopes, respectively, both operating at 200 kV. TEM foils were prepared using standard electro-polishing techniques for Al alloys. The surface deformation features of the fatigued samples were examined using optical microscopy.During the constant plastic strain amplitude fatigue tests, the underaged Al–4Cu–0.05Sn–10 min alloy demonstrates a pronounced cyclic hardening that is absent from the other aging states as shown in The pronounced cyclic hardening in the underaged 10 min condition was observed for all the imposed plastic strain amplitudes studied (b). In general, the larger the imposed plastic strain amplitude, the higher the peak stress obtained. The peak stress of the 10 min alloy after cyclic deformation can reach 330 MPa, which is higher than the peak strength of this alloy when aged at 200 °C b. Cyclic hardening also occurs in the 30 min alloy, but the amount of cyclic hardening is much smaller; only ∼10 to 20 MPa.In order to help identify the mechanism of cyclic hardening in the under aged alloy, the microstructures of samples before and after fatigue deformation were examined using TEM (The observations reveal that there are no obvious differences in the length, thickness and the number density of the θ’ precipitates before and after fatigue deformation, as shown in . The most obvious feature is that Orowan loops are formed on some of the θ’ precipitates after cyclic deformation, as shown in b. Some very small features can be seen between the θ’ precipitates in b and these circled regions are enlarged in c. The higher magnification image shows that these features are a second phase with the scale of 2–5 nm and a high number density. These features are absent from the starting material before cyclic deformation as can be seen from a. The sample from which the TEM foil for a was prepared was held at room temperature for the same duration as the fatigue sample from which the images in b and c were obtained. This comparison suggests that the features observed in b and c form during the cyclic deformation process and not as a result of natural aging at room temperature.Investigation using HAADF imaging techniques reveals that these features are GP zones consisting of one atomic layer of Cu atoms, as shown in . There is no obvious preference for the variants of the GP zones that form with respect to the loading direction. GP zone formation on each of the two {1 0 0}α planes perpendicular to the electron beam is observed. It appears evident that room temperature, fatigue induced precipitation of GP zones is the origin of the pronounced cyclic hardening observed in the under aged alloy. It would seem reasonable that such precipitation is not observed in the other aging states because there is insufficient solute Cu remaining in solution.In order to examine in more detail the dynamic precipitation process, the derivative of the cyclic curves were calculated and plotted and these are shown in . The 10 min underaged sample exhibits two hardening stages during cyclic deformation: a fast hardening during the initial few 10's of cycles and a second stage with almost constant hardening rate (b). The second hardening stage begins at ∼70 cycles.In order to examine the microstructural changes during dynamic precipitation, the fatigue tests were interrupted at 70 cycles, 300 cycles and the peak stress (∼1000 cycles), and the corresponding deformation structures were characterized using TEM and optical microscopy. a, c and e are conventional TEM micrographs showing the progression of dynamic precipitation during cyclic deformation. It is difficult to be quantitative about the sizes and number densities of the GP zones based on conventional TEM but there is some indication that the sizes do increase with cumulative plastic strain. During this process, the surface morphology of the polished fatigue samples was also monitored and optical micrographs illustrating this evolution are shown in b, d and f. It is clear that significant strain localization in the form of slip bands start to form only at the peak stress. Whilst dynamic precipitation is contributing to the hardening, strain localization appears to be resisted even though shearable precipitates are being added to the microstructure. It is only after reaching the peak stress level when the hardening rate decreases to almost zero, that slip localization and the formation of slip bands is observed.The GP zones formed during cyclic deformation appear essentially identical to the GP zones formed during artificial aging (e.g. after aging at 65 °C . It can be seen that the Coffin–Manson plot for most of the aging states exhibits a bilinear behavior, which can be divided into two parts at Δɛpl/2 = 1 × 10−3. This behavior has been observed a number of times. However, the performance of the underaged 10 min alloy tends to exhibit a much more linear behavior. At low imposed plastic strain, the slopes of the fitting line for all the aging states are similar, however, at larger imposed plastic strain amplitudes, the underaged alloy has larger slope that corresponds to better fatigue performance at higher imposed plastic strain amplitudes. The relevant fitting parameters according to the Coffin–Manson equation are listed in . The dynamic precipitation of GP zones appears to benefit the low cycle fatigue performance of this alloy, especially at higher imposed plastic strain amplitudes. Lumley and co-workers have reported that an enhancement in high cycle fatigue performance is also observed in the underaged alloys based on Al–Cu compared with other tempers To examine the magnitude of the strengthening from the dynamically formed GP zones, a sample was fatigued to the peak stress at Δɛpl/2 = 1 × 10−3 and then unloaded. This sample was then deformed under monotonic loading and the stress strain response was compared with the as-aged 10 min sample (i.e. containing shear-resistant θ’ precipitates and no GP zones). The comparison of the tensile curves is shown in . The comparison shows that the dynamically formed GP zones increase the yield stress of the alloy from 210 MPa to over 300 MPa. The uniform elongation of this material is ∼8%, and is ∼1% less than the as aged material. It is suggested that the bimodal structures formed through dynamic precipitation can significantly improve the monotonic mechanical properties of this alloy system and similar observations have been made in thermally produced bimodal precipitate containing alloys GP zone formation requires mass transfer and this depends on the presence of vacancies. It can be readily shown that room temperature precipitation of GP zones to the extent observed in this study requires a large excess vacancy concentration. It is well known that the plastic deformation can produce a large number of vacancies. Hence the required excess vacancy concentration for diffusion likely is a result of the cyclic plastic deformation. In general the production rate of deformation-induced vacancies is expected to be proportional to the applied strain-rate a. Even though the strain-rates differ by approximately two orders of magnitude (therefore also the test durations), the cyclic hardening behavior as a function of cumulative plastic strain of the three tests is very similar.Although the production rate of vacancies (and therefore the effective Cu solute diffusion coefficient) increases with increasing strain-rate, the time to reach a given cumulative plastic strain (and therefore the time for Cu diffusion to make GP zones) decreases with increasing strain-rate. It appears from a that, to a first approximation, these competing effects cancel each other, and give rise to a relatively strain-rate independent cyclic hardening behavior. This observation would be consistent with the formation of growth and GP zones being controlled simply by diffusion, with little effect from ballistic mass transfer or forced chemical mixing. Under other conditions of deformation and strain-rate it is known that strain-induced dissolution of GP zones can occur in this system The production rate of vacancies during plastic deformation should not only depend on strain-rate but also on the number of jogs on dislocations. It would be reasonable to expect that the number of jogs formed during plastic deformation is proportional to the amount of imposed plastic strain, since this partially determines the mean dislocation slip distance and the chances of intersecting with other dislocations and forming jogs. In order to study the effect of applied plastic strain amplitude, fatigue tests were conducted at various imposed plastic strain amplitudes but at constant strain-rate. b displays the cyclic deformation curves of the underaged 10 min alloy tested at the same strain-rate but different plastic strain amplitudes. The cyclic hardening process appears to exhibit a dependence on the plastic strain amplitude, as expected. In general, the higher the imposed plastic strain amplitude, the higher the peak stresses.The results obtained so far suggest that the strain-rate and strain amplitude dependence of the cyclic hardening is consistent with that expected from the diffusional formation of GP zones facilitated by the deformation-induced vacancies. However, it is also necessary to show that the magnitude of the hardening is consistent as well as the detailed kinetics. Efforts in this direction require detailed quantitative characterization of the kinetics of GP zone formation, as well as the evolution in their density. Efforts in this direction are currently underway.Pronounced cyclic hardening is observed in an under aged Al–4Cu–0.05Sn (wt.%) alloy strained under various imposed plastic strain amplitudes. Microstructural characterization reveals that the origin of the cyclic hardening is the room temperature dynamic precipitation of GP zones. The dynamic precipitation occurs during all the cyclic loading process and strain localization does not occur until the increment in strengthening from dynamic precipitation approaches zero. The dynamic precipitation of GP zones has a positive effect on the low cyclic fatigue performance of this alloy, especially at the larger strain amplitudes, and can significantly elevate the strength of this alloy without significant loss of ductility. The dynamic precipitation process is, to a first approximation, strain-rate independent and strain amplitude dependent and controlled by the deformation induced vacancy production.Minor Cr alloyed Fe–Co–Ni–P–B high entropy bulk metallic glass with excellent mechanical propertiesIn this study, we propose a new strategy for designing ductile Fe-based bulk metallic glasses by minor substitution, which strengthens the local solute-centered atomic clusters and increases the concentration of free volume. The locally modified structure results in a stronger barrier to the formation and propagation of shear bands, which appears to be decisive for enhancing both yielding strength and plasticity. Accordingly, (Fe1/3Co1/3Ni1/3)77.5Cr2.5(P1/2B1/2)20 high entropy bulk metallic glass has been developed by minor substitution of (Fe–Co–Ni) in (Fe1/3Co1/3Ni1/3)80 (P1/2B1/2)20 by Cr. The compressive yielding strength increased by approximately 200 MPa and plasticity was enhanced from 4.4% to 11.2%. We believe that the proposed design strategy will provide a new method for improving the plasticity of Fe-based bulk metallic glass, and therefore, expand its applications in engineering.Bulk metallic glasses (BMGs) are considered as the potential candidates for engineering structural materials owing to their unique properties []. However, their room-temperature brittleness significantly limits their applications. In particular, Fe-based BMGs, which show an attractive utilization as magnetic materials usually ruptures with nearly no plasticity []. Over the last few decades, several strategies have been proposed to improve the plasticity of BMGs [], however, most of them have focused on typical ductile BMGs. Therefore, it is crucial to obtain an effective method that enhances the room-temperature plasticity of Fe-based BMGs.The intrinsic plasticity or brittleness of a BMG is determined by its internal structure, i.e., the way various atoms in the BMG are mixed, bonded, and packed []. In this case, micro-alloying may be a useful strategy for modifying the structure of BMGs, thereby enhancing their mechanical properties. Generally, introducing hard particles into crystalline alloys improves their strength. However, whether their plasticity or ductility can be enhanced depends on the dislocation movement, during which the interface between hard particles and soft matrix plays an important role. Due to the absence of dislocations, the plasticity of BMGs is usually carried by shear band, which is a result of the combination of activated shear transformation zones (STZs) []. Therefore, it can be speculated that the plasticity can be enhanced by introducing hard particles through external addition or in situ formation, which will influence the formation and propagation of the shear bands. In this study, Cr in minor amounts was substituted for the (Fe–Co–Ni) in (Fe1/3Co1/3Ni1/3)80 (P1/2B1/2)20 high entropy bulk metallic glass (HE-BMG) [] due to the most negative mixing enthalpy of Cr–B and Cr–P among the metal–nonmetal atomic pairs in this alloy. It is observed that the minor addition of Cr resulted in a significant improvement in the plasticity of (Fe1/3Co1/3Ni1/3)80 (P1/2B1/2)20 HE-BMG accompanied by a slight increase in yielding strength. The underlying mechanism is ascribed to the harder solute-centered atomic clusters and the larger amount of free volume caused by the addition of Cr.(Fe1/3Co1/3Ni1/3)80 (P1/2B1/2)20 (Cr0) and (Fe1/3Co1/3Ni1/3)77.5Cr2.5(P1/2B1/2)20 (Cr2.5) alloys were prepared by torch-melting and then purified by fluxing treatment. Cylindrical specimens for compressive tests were cut from the as-cast cylindrical rods with a diameter of 1 mm, which were obtained by J-quenching technique. Details of the fluxing and J-quenching techniques have been reported previously []. To rule out the influence of sample size, all the samples for compressive tests had the same aspect ratio of 2:1. Furthermore, it was ensured that the two surfaces of the compression samples were parallel and orthogonal to the loading axis. The amorphous states of the all specimens were confirmed by X-ray diffraction (XRD) and high-resolution transmission electron microscopy (HRTEM, JEOL JEM-2100F). The thermal behaviors of glassy samples were characterized by differential scanning calorimetry (DSC, TA Q2000) with a heating rate of 20 K/min under the flow of Ar. Quasi-static compressive experiments were conducted on a computer-controlled WANCE ETM 105D material testing machine with a nominal strain rates of 2.0 × 10−4 s−1 at room temperature. To ensure the reliability of the experimental results, at least five samples were tested at each case. After tests, the side surfaces of the ruptured samples were investigated by high-resolution scanning electron microscopy (HRSEM, SU6600).a shows the XRD patterns of Cr2.5 and Cr0 HE-BMGs rods with diameters of 2 and 2.2 mm, respectively. No crystal signals were found in the XRD patterns, which indicates that the specimens are in a fully glassy state. When alloy rods for both Cr0 and Cr2.5 with larger diameters were fabricated, the corresponding XRD patterns indicated signals representing crystal phases. In other words, the results demonstrated in a are the critical size of the two HE-BMGs. Consequently, it can be concluded that the addition of Cr leads to a slight enhancement in the glass formation ability (GFA) of Cr0 alloy. The DSC curves are illustrated in b, where the inset is the magnification of the area marked by the rectangle. Accordingly, the glass transition temperature (Tg) and the onset crystallization temperature (Tx) of the two alloys were determined and summarized in . Obviously, both the glass transition temperature and the width of the super-cooled liquid region (ΔTx=Tx−Tg) of Cr2.5 HE-BMG are larger than those of Cr0 HE-BMG, which corresponds to a higher yielding strength [], respectively. In addition, as shown in b (inset), the Cr2.5 HE-BMG has a larger heat release (ΔHrel) prior to the Tg, which is an indicator of the excess free volume (vf) in metallic glasses, with an empirical equation of ΔHrel=β′vf [], where β′ is material constant. Therefore, the minor addition of Cr results in an increase of the yielding strength, the GFA and the free volume content.The HRTEM images and the corresponding selected area electron diffraction (SAED) patterns are shown in a–b, respectively. The maze-like distribution of the atoms and the halo ring in the SAED patterns further confirm the amorphous structure of the samples. Moreover, by a quantitative analysis on the SAED patterns, the diffraction intensity profiles Ired(Q) can be obtained []. After a further Fourier transform of the Ired(Q), the atomic radial distribution function (RDF) in real space is demonstrated in c. For clarity, the marked portion of the peak for the two samples is enlarged and presented in the inset. Accordingly, a larger first peak position is found for Cr2.5 HE-BMG, which corresponds to an increase in average interatomic spacing caused by Cr addition []. This means a more loosely packed structure, and therefore, a larger content of free volume in Cr2.5 HE-BMG than that in Cr0 HE-BMG, which is in line with the larger ΔHrel observed in a illustrates the typical engineering stress–strain curves of the two HE-BMGs. All of them exhibit a linear elastic deformation followed by a distinctly yielding behavior. Compared with Cr0 HE-BMG, a synchronous enhancement in yielding strength and plastic strain is observed for Cr2.5 HE-BMG. Furthermore, lateral surfaces of the ruptured samples were investigated using SEM. As presented in b and c, the two HE-BMGs fractured in a typical shear mode with a shear angle of approximately 42°, which falls in the general range for BMGs in uniaxial compression []. Moreover, multiple shear bands can be observed on the side surfaces of the two specimens, and the shear band density is larger in Cr2.5 than that in Cr0. Considering that the plasticity of BMGs is mainly sustained by shear band, a larger shear band density of Cr2.5 HE-BMG implies a better plastic deformation, which is consistent with the result of the compressive tests as shown in To obtain a direct comparison between the developed Cr2.5 HE-BMG with other typical Fe-based HE-BMG and BMG systems, comparative data for yielding strength and plastic strain are summarized in ]. Strikingly, the newly explored HE-BMG exhibits a breakthrough in the common trade-off between strength and plasticity in the Fe-based HE-BMG and BMG families. Therefore, it is reasonable to conclude that the current minor addition of Cr is an effective strategy for improving the plasticity of Fe-based BMGs.In multi-component alloys, the phase competition between amorphous phases and solid solution phases can be evaluated by ΔHmix, ΔSmix and δ, which corresponds to the mixing enthalpy, the mixing entropy and the atomic size difference, respectively [The detailed definitions or values of all the parameters can be found in Ref. []. Accordingly, the values of ΔHmix, ΔSmix and δ for Cr0 and Cr2.5 HE-BMGs were calculated and are listed in ], when the alloy satisfies the conditions −49≤ΔHmix≤-5.5 kJ/mol, 7≤ΔSmix≤16 J/(K·mol) and δ≥9, it will form BMGs. Obviously, the calculated values of the three parameters fall in the proposed glass formation range, which indicates an amorphous phase for the Cr2.5 alloy. Moreover, the values of all three parameters for the Cr2.5 alloy are slightly higher than those for Cr0 alloy. It is accepted that a more negative ΔHmix and a larger δ usually correspond to a more efficient arrangement of the local atoms, thereby suppressing the long-range diffusion []. Furthermore, a higher value of ΔSmix means a higher degree of randomness, thereby hindering crystallization process, which is beneficial to the GFA of the alloy. The Cr2.5 alloy shows a higher ΔSmix than Cr0 alloy, i.e., Cr2.5 alloy possesses a larger GFA. This is consistent with the lager critical diameter and the wider super-cooled liquid region for the Cr2.5 HE-BMG mentioned above.The structure of BMG can be treated as a composite consisting of elastic backbone and liquid-like regions containing high density of free volume []. When the BMG experiences an external stress lower than the yielding strength, it will shear elastically. However, the local liquid-like regions will sustain an inelastic deformation due to its low shear resistance. This corresponds to the activation of the STZs, which is the elementary carrier of the stress relaxation processes in BMGs []. Because of the random distribution of the liquid-like regions, the activated STZs are scattered and embedded in the elastic backbone. If the solitary STZs do not penetrate a sizable length-scale, they can be reverted upon unloading with the help of the back-stress from the backbone []. As the external stress increases continuously, more and more STZs will be activated and the atoms in the surrounding zones will be absorbed into the STZs. This corresponds to the early embryos of shear band. When the external stress increases to a critical value, the embryos of shear band will connect with each other and percolate the elastic backbone, which in turn results in the formation of one mature shear band and the irreversible macroscopic yielding []. During this process, the strength of the elastic backbone will play a key role in the combination of the embryos of shear band. The stiffer the elastic backbone, the harder the connection of the embryos of shear band. In the Cr2.5 alloy, as listed in , the mixing heat of Cr–B is −31 kJ/mol, which is larger than that of Fe–B, Co–B, and Ni–B. Meanwhile, the mixing enthalpy of Cr–P is −49.5 kJ/mol, which is also the most negative value among all Metal-P atomic pairs []. This implies that the minor addition of Cr will make the local solute-centered atomic clusters of Cr2.5 alloy stiffer than those of Cr0. Therefore, a stronger resistance to the combination of the embryos of shear band is expected in Cr2.5, which finally enhances the yielding strength of the newly developed HE-BMGs. This is in line with the results observed in As mentioned above, the elementary carrier of plasticity in BMGs is the STZs. Upon loading, the activation of STZs will take place firstly, and then plasticity grows, resulting in a creation of free volume []. By incorporating the interaction of shear transformations and free volume dynamics, Jiang et al. [] proposed a constitutive model to describe the homogeneous elastoplastic deformation of BMGs:ε˙pl=exp(−1/ξ)exp[EA(1−1/T)][Λsinh(σ/T)−Δcosh(σ/T)]where ε˙pl is the plastic strain rate. ξ is the average free-volume concentration. EA=ΔG/kBTg, where ΔG and kB correspond to the STZ activation energy and Boltzmann constant, respectively. Δ and Λ represent, respectively, the bias and summation of normalized populations of two STZ states. σ is the shear stress and μ is the shear modulus. T is the ambient temperature and ε˙ is the overall shear-strain rate. ϕ=σ0ε0ϕ‾ is the proportional coefficient between plastic work rate and STZ-creation/annihilation rate. Dia=D‾iaσ0ε0/P∗ is a dilatancy factor, where P∗ is a characteristic pressure. φ=φ‾/χ is the ratio of the coefficient φ‾ and the geometrical factor χ. As for Cr2.5 and Cr0 alloys, it is reasonable to adopt the same value of the above parameters except for the initial free volume content, ξ0, which shows an apparent difference as demonstrated in b. Based on the measured ΔHrel, the ξ0 is fitted as 0.03 and 0.05, respectively, which has the same ratio to the value of ΔHrel for the two alloys. Then, a quantitative dependence of σ/σ0 on ε/ε0 can be plotted in under a fixed strain rate of 2.0 × 10−4 s−1 and an initial system (Δ0=0, Λ0 = 0.5 and Dia = 0.01) at 298 K. Apparently, a smaller stress overshoot (σpeak) can be found in Cr2.5, while the flow stress (σ∞) of the two alloys is nearly the same. As mentioned above, there are elastic backbone and liquid-like regions in BMGs. Upon loading, the liquid-like regions will act as the potential sites of STZs []. As the external stress keeps increasing, a larger number of STZs can be activated due to the higher probability of finding the potential STZ sites results from the higher free volume content. This leads to a more homogeneous distribution of the strain, i.e., a higher degree of mechanical homogeneity. As the embryos of SBs are the results of expansion and combination of the activated STZs [], the larger number of activated STZs corresponds to a higher nucleation rate of the SBs. When the external stress increases to a critical value, the embryos of SBs will connect with each other and percolate the elastic backbone, which leads to the formation of mature SBs []. During this process, the more embryos of SBs, the less elastic backbone needed to be percolated, and hence a lower stress overshoot. This is consistent with the smaller stress overshoot in Cr2.5 alloy presented in . On the contrary, the strain will concentrate in a small number of already-activated STZs due to the less potential STZ sites, i.e., a higher degree of strain localization, results in the lower degree of mechanical homogeneity. The formation of mature SBs needs to percolate more elastic backbone and therefore leads to a higher stress overshoot. This is in line with the larger stress overshoot in Cr0 alloy presented in . During the propagation of SBs, a stiffer local solute-centered atomic clusters will create a more serious obstacle in the expansion of the SBs, leading to the bifurcation and proliferation of SBs and finally results in the larger density of SBs. This agrees well with the results observed on the lateral surface of Cr2.5 as shown in c. In BMGs, the plastic strain is usually carried by shear band, a higher density of shear band means a larger plastic strain, which is consistent with the results demonstrated in In summary, (Fe1/3Co1/3Ni1/3)77.5Cr2.5(P1/2B1/2)20 HE-BMG with a critical diameter of 2.2 mm has been developed by the minor substitution of Cr for (Fe–Co–Ni) in (Fe1/3Co1/3Ni1/3)80(P1/2B1/2)20 HE-BMG. The newly developed HE-BMG exhibits an enhanced plastic strain of 11.2% and a higher yielding strength of approximately 3050 MPa compared with 4.4% and 2860 MPa for the (Fe1/3Co1/3Ni1/3)80(P1/2B1/2)20 HE-BMG. The minor addition of Cr strengthens the local solute-centered atomic clusters and increases the free volume content, which contributes to the improvement of yielding strength and plasticity. This study provides a new strategy for designing new Fe-based HE-BMGs with excellent mechanical properties.We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, “Minor Cr alloyed Fe–Co–Ni–P–B high entropy bulk metallic glass with excellent mechanical properties”.The raw/processed data required to reproduce these findings cannot be shared at this time due to time limitations.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Effect of heat treatment and chemical composition on the corrosion behavior of FeAl intermetallics in molten (Li + K)carbonateThe corrosion performance of various Fe–Al alloys in 62 mol. %Li2CO3-38 mol.%K2CO3 at 650 °C has been studied using the weight loss technique. Alloys included FeAl with additions of 1, 3 and 5 at.% of either Ni or Li with or without a heat treatment at 400 °C during 144 h. For comparison, 316L type stainless steel was also studied. The tests were complemented by X-ray diffraction (XRD), scanning electronic microscopy and microchemical studies. Results showed that FeAl base alloy without heat treatment had the highest corrosion rate but by either heat treating it or by adding either Ni or Li the mass gain was decreased. When the FeAl base alloy was heat treated and alloyed with either 5Ni or 1Li the degradation rate reached as low values as those found for 316L stainless steel which had the lowest degradation rate. Both Ni and Li improved the adhesion of external protective layer either by avoiding the formation of voids or by lowering the number of precipitates and making them more homogenously distributed.Conventional molten carbonate fuel cells (MCFC) operate at 650 °C and consist of several cells made of a porous, lithiated NiO cathode, a molten (Li,K)2CO3 electrolyte in a LiAlO2 ceramic matrix and a porous Ni anode FeAl type intermetallics are widely used for their high temperature oxidation resistance due to their ability to develop an Al2O3 protective layer, which also provides corrosion resistance in molten salts Intermetallic Fe50Al50 alloy were melted in an induction furnace using silicon carbide crucibles. Pure Li and Ni elements with 1, 3 and 5 at.%, respectively were added to the AlFe intermetallic compound. All elements were 99.9% of purity. In order to avoid the specimens machining procedure the ingots were obtained with ending dimensions according to the E800b ASTM standard. Cylindrical specimens dimensions were 0.5 in. diameter × 2 in. length in the test section and 2.5 in. for the final section. The ingots were homogenized to minimize the thermal vacancy effects by heat treating them (HT) at 400 °C during 120 h under an argon atmosphere. The corrosive agent used in the tests was synthetic potassium carbonate (K2CO3) and pure lithium carbonate (Li2CO3) with the composition 62 mol. %Li2CO3-38 mol.%K2CO3 at 650 °C. All the reagents were analytical grade. Before corrosion tests the specimens (30 mm × 20 mm × 1 mm) were cleaned with acetone and dried and then packed in the mixture of salts in porcelain crucibles with 500 mg cm−2 of the synthetic salt. Coupons were completely immersed in the carbonate salt. The corrosion tests were carried out in electric furnaces in a static air during 100 h. After the corrosion tests, the corrosion rate was measured as weight loss. Three specimens of each condition test were decaled and chemically cleaned according to ASTM G1 81 standard. One of each heat was mounted in bakelite in cross section and polished to analyze the subsurface corrosive attack using a scanning electron microscopy (SEM) aided with energy dispersive spectroscopy (EDX) to carry out micro chemical analysis. Finally, the corrosion products of some specimens were analyzed in a Phillips X-ray diffractometer. shows the mass loss of the different materials after exposure beneath a molten (Li,K)2CO3 deposit during 100 h at 650 °C. It can be seen that the FeAl base alloy without heat treatment suffers the greatest mass loss, whereas 316L stainless steel and the heat treated alloy containing 5Ni had the lowest. By heat treating the FeAl base alloy decreased the mass gain for more than 50%, but it was still higher than 316L stainless steel. If the FeAl alloy without heat treatment was alloyed with either Ni or Li in any quantity, the corrosion rate was decreased, especially with 3%, where the improvement in the corrosion rate was the highest, i.e. 10 times. Heat treated FeAl with either 1Li or 5Ni had low corrosion rates too, very similar to the316L stainless steel. It can be said that for unalloyed FeAl intermetallic, a decrease in the mass loss was obtained either by heat treating it or by additions of less than 5% of Ni or 1Li, but additions of 5% of this element increased the mass loss.An SEM micrograph of the 3Li containing alloy without heat treatment is given in , showing the corrosion products layer. An EDX spot analysis done in point (a) and shown in revealed that this point consisted of C, O Fe and some Al. XRD of the corrosion products showed the presence of the FeAl aluminide phase together with LiFeO2, Fe2O3 and LiAlO2 oxides, . LiAlO2 has been reported to give some corrosion protection in molten carbonate mixtures An SEM of the corroded surface of the heat treated alloy containing 3Li is shown in . A spot EDX analysis to the interface metal/deposit, point (c), revealed that it is rich in C, O and Al with some traces of Fe, . On the other hand, punctual EDX analysis in the middle of the deposit and in the outer part of the deposit showed that the content of C and O is similar to that found at the metal/deposit interface but the content of Al is much lower, which may indicate that at this interface there is some Al2O3 which has not been dissolved by the (Li,K)2CO3 deposit, although the XRD analysis did not reveal its presence, maybe because it was localized at this point only. The corrosion products consisted, again, of LiFeO2, Fe2O3 and LiAlO2 oxides and the FeAl phase, as shown in A cross section of the corroded surface for heat treated alloy containing 3Ni is shown in . This figure shows the presence of some pits, whereas a punctual EDX analysis done in points 1 and 2 revealed that they consisted of C, O and some Al, as shown in . The XRD analysis of the corrosion products consisted of the same phases found in the other specimens, i.e. LiFeO2, Fe2O3 and LiAlO2 oxides and the FeAl phase, as can be seen in Finally, a cross section of corroded 5Ni containing FeA alloy with X-ray mappings of C, Al, K, and O is shown in . It can be seen that the presence of aluminum together with oxygen outside the alloy suggests the formation of the protective alumina, Al2O3 layer. Also, we can see that elements of the molten salt, such as C and K, are not only outside the alloy, but they have penetrated and dissolved the Al2O3 layer, being present inside the alloy, which is evidence of the dissolution of the underlying alloy once the protective oxide, e.g. Al2O3 layer has been dissolved by the melt.These reactions are governed by the acidity of the melt and, in the less acidic melts which correspond to our conditions, the reaction in Eq. prevails, including a more important CO2 formation in the melt. In the case of immersion of Al-rich alloys in molten carbonate, the following electrochemical reactions would take place:Al → Al3+
+ 3e−
to form Al2O3
and LiAlO2Fe → Fe3+
+ 3e−
to form Fe2O3
and LiFeO2O22−
+ 2e−
→ 2O2−
to form reactions (2)–(4)but, since the amount of Ni present in the alloy is little, lower than 5 at.%, corrosion products given by reaction were not detected neither by EDX nor by XRD analysis. The corrosion protection of an alloy against salt melt attack depends on the chemical stability of both the kind of metal and their compounds such as oxides, carbonates, etc …. In fact, a breakdown of the protective oxide readily occurs by dissolution into the melt, and the degradation rate can be specially fast if the oxide has a high solubility. With the establishment of the Al2O3 layer, the corrosion rate decreases. The predominant surface product that forms between 600 and 800 °C has been reported to be α-Al2O3). On the other hand, the formation of Al2O3 consumes certain quantity of Al, reducing its activity and partial pressure of the oxygen. This causes a relative increase in the activities of the Fe driving it to react with the molten mixture and to obtain compound such as LiFeO2.The scale cracking, spaling or dissolution in a melt, gives as a result that the film becomes less protective and, thus, the corrosion rate is increased. Additionally to the dissolution of the protective scales, the dissociation of the (Li,K)CO3 allowed the diffusion of Li and K, and an increase of these elements in the metal/scale interface. This caused the detachment and cracking of the protective scale, allowing the corrosion of the material. Incorporation of ions such as Ni2+ and Li+ into the scale could improve the resistance of the oxide layer to the dissolution by the melt, and, thus, decrease the corrosion rate, as evidenced by This explains the values of the corrosion rates that were observed in for the FeAl + Li and FeAl + Ni alloys.A study on the effect of heat treatment and additions of 1, 3 or 5 at.% of either Ni or Li on the corrosion performance of FeAl intermetallic alloy in molten 62 mol. %Li2CO3-38 mol.%K2CO3 at 650 °C has been carried out using the weight loss technique. Results showed that the FeAl base alloy showed the highest degradation rate whereas 316L type stainless steel had the lowest one. When the FeAl intermetallic alloy was heat treated at 400 °C during 144 h the corrosion rate was decreased by more than 50% but it was still much higher than the corrosion rate exhibited by the stainless steel. If the base alloy without heat treatment was alloyed with either Li or Ni the weight loss was decreased up to 10 times, reaching values close to those for 316L type stainless steel, especially with 3%. Finally, when the base alloy was heat treated and alloyed either with 5Ni or 1Li, the degradation rate reached the lowest values, similar to those for 316L type stainless steel. This was because by adding Ni, the adhesion of external protective layer was improved by avoiding the formation of voids on the surface. Addition of Li, on the other hand, decreased the corrosion rate because it reduced the amount of particles precipitated and they were more homogenously distributed, thus, a better anchoring of the external protective layer was promoted. Thermal annealing helped to reduce the corrosion rate by minimizing thermal vacancies and reducing the number of voids.Shearing effects on the breathing mechanism of a cracked beam section in bi-axial flexureThe main purpose of this paper is to complete the works presented by Andrieux and Varé (2002) and El Arem et al. (2003) by taking into account the effects of shearing in the constitutive equations of a beam cracked section in bi-axial flexure. The paper describes the derivation of a lumped cracked beam model from the three-dimensional formulation of the general problem of elasticity with unilateral contact conditions on the crack lips. Properties of the potential energy and convex analysis are used to reduce the three-dimensional computations needed for the model identification, and to derive the final form of the elastic energy that determines the nonlinear constitutive equations of the cracked transverse section. We aim to establish a relation of behavior between the applied forces and the resulting displacements field vectors, which is compatible with the beams theory in order to allow the model exploitation for shafts dynamics analysis. The approach has been applied to the case of a cracked beam with a single crack covering the half of its circular cross section.Since the early 1970s when investigations on the vibrational behavior of cracked rotors began, numerous papers on this subject have been published, as a literature survey by shows. The analysis of the behavior of cracked rotating machinery shafts is a complex structural problem. It requires, for a relevant description, a fine and precise modeling of the shaft and cracks in order to allow the identification and calculation of the parameters characterizing their presence.Researchers dealing with the problem of rotating cracked beams recognize its two main features, namely:the determination of the local flexibility of the beam cracked section;the consideration of the opening – closing phenomenon of the crack during the shaft rotation, commonly called breathing mechanism of the crack, and responsible of the system nonlinear behavior: when the shaft is rotating, then the crack opens and closes according to the stresses developed in the cracked surface. If these stresses are extensive, then the crack opens, resulting in a reduced shaft stiffness. When the stresses are compressive, then the crack remains closed and the shaft has the same stiffness as the non-cracked shaft. Thus, the system stiffness is depending on the cracked section position (This breathing mechanism depends on the shaft rotation in the case when the static deflection dominates the vibration of the rotating shaft. This is a very common situation in large turbine-generator rotors.During the last three decades, great attention has been paid by several research scientists to the analysis and diagnosis of cracks in rotating machinery. The excellent review papers by cover many aspects of this area and summarize the most relevant analytical, experimental and numerical works conducted in the last three decades and related to the cracked structures modeling.There have been different attempts to quantify local effect introduced by cracks. The analysis of the local flexibility of a cracked region of structural element was quantified in the 1950s by by relating it to the Stress Intensity Factors (SIF). Afterwards, the efforts to calculate the SIF for different cracked structures with simple geometry and loading was duplicated (Most researchers agree with the application of the linear fracture mechanics theory to evaluate the local flexibility introduced by the crack (). Obviously, the first work was done in the early 1970s by at the General Electric Company. The energy release rate approach combines the linear fracture mechanics to rotordynamics theory in order to calculate the compliance caused by a transverse surface crack affecting a rotating shaft. A good review on this method is presented by For an elastic structure, the additional displacement u due to the presence of a straight crack of depth a under the generalized loading P is given by the Castigliano theoremG is the energy release rate related to the SIF by the Irwin formula (). Then, the local flexibility matrix coefficients are obtained byExtra diagonal terms of this matrix are responsible for longitudinal and lateral vibrations coupling that could be with great interest when dealing with cracks detection.) computed the local flexibility corresponding to tension and bending including their coupling terms. This coupling effect was observed by in their study of cracked elastic plates for stress analysis. introduced the full (6 × 6) flexibility matrix of a cracked section. They noted the presence of extra diagonal terms which indicate the coupling between the longitudinal and lateral vibrations. computed all the (6 × 6) flexibility matrix of a Timoshenko beam cracked section for any loading case.However, there are no results for the SIF for cracks on a cylindrical shaft. Thus, have developed a procedure which is commonly used in FEM software: the shaft was considered as an assembly of elementary rectangular strips where approximation of the SIF using fracture mechanics results remains possible (). The SIF are obtained by integration of the energy release rate on the crack tip byAlthough it offers the advantage of being easy to insert in a numerical algorithm, this method has some limitations. In fact, some numerical problems were reported by when the depth of the crack a exceeds the section radius R. , in his reply, stated that this divergence does not reflect reality; it is due to the assumption of a 2D stress distribution which is not valid near the ends of the crack tip.when the crack depth a exceeds the shaft radius R. explored the dynamics of a cracked, distributed parameter rotor component. The proposed model is a rotating Timoshenko shaft which is also flexible in extension and torsion. The stiffness matrix is constructed using the energy release rate approach as described in papers by . The geometric discontinuity due to the crack is replaced by a load discontinuity. The procedure reduces the problem to equations for one uniform beam with a modified load distribution. The proposed approach is a powerful instrument to obtain approximate results by a relatively small calculation expense. Although the shearing is considered in this approach, the author did not discuss the importance of its effects on the crack breathing mechanism.An original method for deriving a lumped model for a cracked beam section was proposed by . Based on three-dimensional computations, the procedure incorporates more realistic behavior of the cracks than the previous models, namely the unilateral contact conditions on the crack lips and their breathing mechanism under variable loading. The method was derived from three-dimensional formulation of the general problem of elasticity with unilateral contact conditions on the crack lips. The authors established properties of the potential energy of this problem to reduce the amount of computation required for its determination in the case of a beam containing cracks of any shape and number. Convex analysis was also used to derive the final form of the energy that determines the nonlinear constitutive equations of the section of the beam which was incorporated in a FE analysis code. Great attention is paid to the capability of such a model to take into account the real 3D geometry of a crack and to represent, as general as possible, the effects of different load components on its nonlinear behavior.The experimental validation of the approach is presented by . The authors reported that the model reproduces with good accuracy the overall behavior of the shaft line in presence of cracks. The experimental validation allows the use of the model, with confidence and reliability, for the determination of the dynamics of supposed cracked rotors. presented a method of construction of a cracked beam finite element which they used afterwards for the stability analysis of cracked shafts. The authors distributed the additional energy due to the cracked section on the entire length of the cracked beam finite element. Considerable gain in computing efforts was reached compared to the nodal representation of the cracked section when dealing with the numerical integration of differential equations in structural dynamics. is subjected to an end moment M2L=(Mx(2L),My(2L)) at z
= 2L. has demonstrated certain properties of the problem elastic energy, W∗, leading to a considerable gain in the three-dimensional calculus required for the identification of the constitutive equations. In particular, for a linear elastic material, under the small displacements and small deformations assumptions, and in the absence of friction on the crack lips, the energy function could be written by distinguishing the contribution of the cracked section from that of the non-cracked elements, in the form:W∗(M2L)=W∗(M)=Ws∗(M)+w∗(M)=LEI\|\|M\|\|2(1+s(Φ))where M
= (Mx, My) is the resulting couple of flexural moments at the cracked section, Ws∗ the total elastic energy of non-cracked structure subjected to the flexural moment M and w∗ the additional elastic energy due to the presence of the cracked section. In order to simulate a rotating load on a fixed beam, the bending load is applied in several aperture angles Φ=atan(My/Mx), with Φ varying over [0, 2π [. E is the Young modulus and I quadratic moment of inertia.In this framework, the nonlinear constitutive equations of the discrete element modeling the cracked section are obtained by differentiating w∗ with respect to M. We obtain[θ]=([θx][θy])=2LEI(s(Φ)−12s′(Φ)12s′(Φ)s(Φ))(MxMy)withs′(Φ)=ⅆs(Φ)ⅆΦHowever, for finite element computational codes in rotordynamics, a nonlinear relation of the form [θ] =
f(M) is to be identified. Thus, introduced some properties of the additional deformation energy due to the cracked section, w([θ]). Thus, w could be written as a quadratic function of the rotations jumps as:w([θx],[θy])=EI4Lk(φ)\|\|[θ]\|\|2withφ=atan([θy][θx])The Légendre–Fenchel transform is used to establish the relation between the two energy functions w∗ and w, then the stiffness function k is obtained from the compliance function s identified from three-dimensional calculus., the constitutive equations are finally obtained by differentiating w with respect to [θ] as(MxMy)=EI2L(k(φ)−12k′(φ)12k′(φ)k(φ))([θx][θy])withk′(φ)=ⅆk(φ)ⅆφThe purpose of this paper is to complete the models suggested by by considering the shearing effects in the constitutive equations of a cracked beam section in bi-axial flexure. Our main purpose is to establish constitutive relations (nonlinear) between the applied forces and the resulting displacements field, which is compatible with the beams theory in order to allow the model exploitation for shafts dynamics analysis using a beam model.The study of the in-plane flexural behavior of a cracked beam by showed that for straight line tip cracks the shearing and flexure effects could be separated when aiming to identify the constitutive equations of a cracked transverse section. In fact, the bending moments are only responsible for the rotations discontinuities, and the shear forces for the displacements discontinuities (slips). In this paper, we present the case of the bi-axial flexural behavior.Our objective is to identify the characteristics of a one-dimensional model () from accurate three-dimensional FE model ((b)) is replaced by two lumped nonlinear flexural and shearing springs ((d)) for which we aim to establish the constitutive equations.The three-dimensional FE model considered is that of a cylinder of axis (oz), diameter D
= 1m, cross section S, length 2L
= 4D, containing, at midspan, a cracked section, cf. . The structural element, clamped at its end z
= 0, is subjected at z
= 2L to a couple of shear forces and a couple of flexural moments: (Tx(2L), Ty(2L), Mx(2L), My(2L)). In the one-dimensional (beam) model, the non-cracked parts of the structures are represented by Timoshenko beam elements, and the cracked section by a nodal element (zero length) allowing discontinuities of displacements and rotations. Indeed, this nodal element is composed of two uncoupled nonlinear springs modeling the cracked section flexural and shearing stiffnesses, cf. . The unilateral contact between the crack lips is considered.The following assumptions are considered for the modeling of the structure:assumption of small displacements and small deformations,transverse cracks of any shape and in any number,unilateral contact without friction between the crack lips,the crack is completely closed in the unstressed configuration.Let W∗ be the total elastic energy of the system. According to what precedes, W∗ can be put in the formwhere W∗s denotes the total elastic energy of the non-cracked structure under the loading F(2L), and w∗(F) the elastic energy due to the presence of the crack. The study of the in-plane flexural behavior showed that the bending and shearing effects can be dissociated. Based on this result, w∗ is divided into:wf∗(F)=wf∗(M) denotes the part of w∗(F) due to the resulting couple of flexural moments M
= (Mx(L), My(L)) at the cracked section, andwc∗(F)=wc∗(T) the part due to the couple of shear forces T
= (Tx(L), Ty(L))., w∗ is strictly convex and positively homogeneous of degree 2, from which rise the following properties:Property 1 Functions wc∗ and wf∗ are strictly convex.Property 2 Functions wc∗ and wf∗ are positively homogeneous of degree 2:∀λ≥0we have:{wf∗(λM)=λ2wf∗(M)wc∗(λT)=λ2wc∗(T)It should be noticed that an essential hypothesis for obtaining properties 1 and 2 is that the gap between the lips of the crack is zero in the unstressed configuration. For the contribution of the bending moments, the quadratic form of w∗f used in the study presented by With Φ=atan(My(L)/Mx(L)) and s(Φ) the additional flexibility due to the presence of the crack and related to the effects of flexural moments at the cracked section of the beam. Energy due to the shearing effects at the cracked section is also quadratic and can be put in the form:wc∗(T)=LμκS‖T‖2sc(Φc),withΦc=atan(Ty(L)Tx(L))μ is the shear modulus and κ the shear correction factor of Timoshenko. Due to property 2, the problem of identification of the function wc∗ on R2 is reduced to the identification of the flexibility function sc(Φc) on the interval [0, 2π] by considering the particular case of ‖T‖=1. This additional flexibility is identified from three-dimensional finite element calculus using Code_Aster©. presented a simpler form of wc∗. They brought the problem back, for certain shapes of cracks, to the identification of three constants by writing:wc∗(T)=12Tx2(L)sx+12Ty2(L)sy+sxyTx(L)Ty(L)sx, sy and sxy depend only on the geometry of the crack, they are independent of the parameters of loading and identified using the three following three-dimensional finite element calculations cases:wc∗(Tx=1,Ty=0),wc∗(Tx=0,Ty=1)andwc∗(Tx=1,Ty=1)This model allowed the obtaining, for certain cracks geometries, of results in excellent agreement with the three-dimensional FE calculations. However, it cannot be applied to any geometry of crack affecting beams or shafts with various cross section forms. Indeed, the shearing forces at the cracked section lead to the opening and closure of the crack according to mode II and/or mode III (modes of fracture). This depends on the orientation of the shearing force defined here by angle Φc. The contact area between the lips of the crack, and consequently the additional flexibility due to its presence, depends on the direction of the applied shear force.The present method, based on energy properties, could, without the use of additional simplifying assumptions, be applied to cracks of any shape and number affecting the same beam transverse section.The required relation describing the nodal element ([u]={[ux][uy]}={ux(L+)−ux(L−)uy(L+)−uy(L−)}[θ]={[θx][θy]}={θx(L+)−θx(L−)θy(L+)−θy(L−)}Consequently, it is necessary to identify the stiffness matrix of the nodal element. Thus, we need to exploit the properties of the additional elastic deformation energy w due to the presence of the cracked section for the displacements discontinuities [u] and the rotations discontinuities [θ].Given the assumption of separating the shearing and flexure effects at the cracked section, w could be written in the form:wf and wc are the elastic deformation energies associated with flexure and shearing, respectively. According to the work by , wf and wc have the following properties:Property 3 Functions wc and wf are strictly convex.Property 4 Functions wc and wf are positively homogeneous of degree 2:∀λ≥0we have:{wf(λ[θ])=λ2wf(λ[θ])wc(λ[u])=λ2wc([u])With φ=atan([θy]/[θx]) and k the flexural stiffness function of the nodal element. Function k is deduced from s by using the Légendre–Fenchel transform relating wf to wf∗.Following the development steps described in (With φc=atan([uy]/[ux]) and kc the shearing stiffness function of the nodal element to be identified. Using the Légendre–Fenchel transform we establish the relation between wc to wc∗ by writing:wc([u])=supT(T·[u]−wc∗(T))=sup\|\|T\|\|=1λ≥0(λT·[u]−wc∗(λT))=sup\|\|T\|\|=1λ≥0(λT·[u]−λ2LμκS‖T‖2sc(Φc))Contrary to the flexural flexibility function s of the nodal element which vanishes for certain couples of flexural moments leading to a total closing of the crack, the linearity noted with respect to the shearing action shows that the flexibility function sc due to shearing is never zero:Thus, for [u]={cosφcsinφc}andT={cosΦcsinΦc}, we obtain:kc(φc)=supcos(Φc−φc)≥0(cos2(Φc−φc)sc(Φc))The condition cos(ϕc−φc)≥0 implies, for a given φc, that:kc(φc)=supΦc∈[φc−π2,φc+π2](cos2(Φc−φc)sc(Φc))The constitutive equations of the cracked section is obtained by differentiating w([u], [θ]) as follows:{Tx=∂w([u],[θ])∂[ux]=∂wc([u])∂[ux],Ty=∂w([u],[θ])∂[uy]=∂wc([u])∂[uy]Mx=∂w([u],[θ])∂[θx]=∂wf([θ])∂[θx],My=∂w([u],[θ])∂[θy]=∂wf([θ])∂[θy]Finally, the required relation is given by:(TxTyMxMy)=(μκS2Lkc(φc)−μκS4Lkc′(φc)00μκS4Lkc′(φc)μκS2Lkc(φc)0000EI2Lk(φ)−EI4Lk′(φ)00EI4Lk′(φ)EI2Lk(φ))([ux][uy][θx][θy])Three-dimensional finite element calculations were carried out under the Code_aster© to identify sc. The cracked structure, cf. F=(Tx(2L)=cos(Φc),Ty(2L)=sin(Φc),Mx(2L)=LTy(2L),My(2L)=−LTx(2L))which leads, at the cracked section (z
=
L), to:(T,M)=(Tx(L),Ty(L),Mx(L),My(L))=(Tx(2L),Ty(2L),0,0)Thus, the additional deformation energy due to the cracked section w∗ is reduced to wc∗. The angle Φc varies in [0°, 360°[ at a rate of a loading case every 5° and, thus, a total of 72 loading cases where carried out. The identification of function sc also requires the realization of the same three-dimensional calculations on the non-cracked structure (of the same geometry). The formula of Clapeyron makes it possible to calculate, for each loading case, the elastic energies Ws∗ and W∗ of the non-cracked and the cracked structures, respectively. Consequently, wc∗ is given by, the additional shearing flexibility function is obtained, for all loading cases, by: shows the evolution of sc for a straight line front crack with a relative depth a/D
= 50%. It is noticed in particular that sc does not vanish on [0, 2π[. Also, the strong dependency of sc on the loading direction Φc is clearly visible. Moreover, we show that the model presented by corresponds to particular loading cases sincesx=2LμκSsc(Φc=0),sy=2LμκSsc(Φc=π2)andsxy=2LμκSsc(Φc=π4)The stiffness function kc is then calculated by using the formula . Finally, its derivative kc′ is calculated using the centered differences method, cf. Now that we have identified the constitutive equations of the nodal element that represents the cracked transverse section, it is the objective of this section to introduce it in a one-dimensional FE code and see if we get sufficient agreement with three-dimensional representation. For a better validation of the approach, it is certainly more adequate to consider a cracked structure different from the one used in the identification procedure of the nodal element.Let consider a cylinder of axis (oz), diameter D
= 0.5m, quadratic moment of inertia I
= πD4/64, total length 3m, clamped in z
= 0 and subjected at the other end to a couple of forcesThe cylinder contains, at z
= 1m, a straight line front crack with a relative depth a/D
= 50%. Three-dimensional calculations accounting for the unilateral contact without friction between the lips of the crack are carried using the Code_aster©. The one-dimensional model of the same structure is made of two non-cracked elements of Timoshenko beam type and respective lengths 1m and 2m connected at z
= 1m by a nodal element that represents the cracked section (node 2), cf. in the first, the effects of shearing at the cracked section are neglected. Only discontinuities of rotations are then allowed at node 2 ([ux] = [uy] = 0). In this case we consider the model presented by in the second, the nodal element behavior is described by relation : shearing effects are considered in this case. shows an excellent agreement between the beam and the three-dimensional models. It appears that the effects of shearing on the crack breathing mechanism are negligible since the model (with no consideration of the shearing effects) and the current model (taking into account the shearing effects) give the same results. The breathing mechanism is, thus, governed by the normal stresses on the crack lips.The present approach consists in introducing the effects of shearing in the constitutive equations of a beam cracked transverse section. Three-dimensional calculations were carried out in order to identify the required nonlinear relations. In particular, the 3D nonlinear finite element calculations allowed the breathing mechanism of the crack to be predicted accurately. Based on the properties of the problem energy, the procedure presented in this paper could be applied to cracks of any shape and, moreover, to the case of multiple cracks affecting the same section. The approach was applied to the case of a single straight line front crack covering the half of a cylindrical beam cross section (a/D = 50%). For this form of crack, as illustrated in the , the shearing effects on the breathing mechanism of the crack are negligible when compared to those of the flexural moments. The opening and closure of the crack are governed by the normal stresses on the crack lips. The relative slip between the crack lips associated with shear forces remains very small compared to the rotations jumps due to the flexural moments at the cracked section (Pre- and post-TLP bond solution treatments: Effects on the microstructure and mechanical properties of GTD-111 superalloyThis paper addresses the effects of bonding time and standard solution treatment on the microstructure and mechanical properties of GTD-111 superalloy bonded by transient liquid phase (TLP) using a Ni-7.58Cr-3.42Fe-3.6Si-2.95B amorphous interlayer. In this regard, three different heat treatment cycles namely HT were applied to separate TLP joints. In the HT-A cycle, full-solution annealing (1200 °C/4 h) of the base metal was first carried out followed by TLP bonding at 1120 °C/105 min, partial solution annealing (1120 °C/2 h) and finally aging treatment (845 °C/24 h). In the HTB cycle, the first step was TLP bonding for 105 min at 1120 °C followed by full-solution, partial solution and aging heat treatments. Finally, the HTB cycle except for the TLP bonding process which was performed at 1120 °C/15 min. The results indicated that HTB treatment leads to a more uniform microstructure in the bond area and base metal compared to the microstructure obtained from HT samples. Mechanical testing results indicated that a completely uniform hardness profile, similar to the base metal, was perceived in the bond region in the HTB sample. The highest joint shear strength among all of the samples was obtained for the HTGTD-111 is a cast nickel-based superalloy which has a multi-phase microstructure consisting of gamma matrix (γ), gamma prime precipitates (γʹ), carbides, gamma-gamma prime eutectic (γ/γʹ) and minor amounts of detrimental phases such as: δ, σ, ɳ and Laves [] have explained that there are two major strengthening mechanisms in GTD-111: 1) solid solution strengthening, 2) second-phase strengthening (i.e. precipitation hardening). The presence of elements such as W, Cr, Ti, Ta and Mo in the nickel matrix leads to solid solution strengthening. Sajjadi et al. [] have reported that the formation of gamma prime precipitates with considerable amounts of Ni, Al, Mo and W in GTD-111 superalloy improves the strength of the alloy via precipitation hardening. The gamma prime precipitate is a superlattice phase with a general composition of Ni3(Al,Ti). There are two distinguishable structures of gamma prime phase in GTD-111 superalloy. The primary gamma prime with a cubic shape which is formed during solidification below 1200 °C and the secondary gamma prime with a spherical shape which nucleates and grows during the aging process after partial-solution treatment. Typical mechanical properties of GTD-111 include an ultimate tensile strength of 1011 MPa, hardness of 580 HV, shear strength of 750 MPa and high temperature strength of 854 MPa at 816 °C [] have pointed out that GTD-111 is susceptible to erosion, corrosion, oxidation, thermal fatigue cracking and foreign object damage caused by drastic service conditions, which can lead to premature failure of the alloy, in spite of its remarkable properties. Huang and Miglietti [] have reported that due to the high cost of turbine components manufactured with superalloys, it is economically favorable to repair the damaged components using techniques such as fusion welding, traditional brazing and diffusion brazing instead of manufacturing new components. Athiroj and Wangyao [] have shown that fusion weld repaired GTD-111 and similar superalloy components are more vulnerable to mechanical property degradation due to heat affected zone (HAZ) cracking during the welding and post-weld heat treatments (PWHT). Moreover, in high temperature brazing, melting point depressants (MPDs) namely phosphorus, silicon and boron are added to the braze alloy in order to increase its fluidity. Philips et al. [] have found that nevertheless the presence of these elements leads to the production of detrimental phases (e.g. borides, silicides and phosphides) during non-equilibrium solidification of the remaining liquid phase in the cooling stage. Adebajo [] has claimed that the existence of intermetallic phases in the centerline of joints can have adverse effects on the overall performance of the component such as significant reduction in the mechanical properties, re-melting temperature and also corrosion and oxidation resistance.Diffusion brazing (DB) also recognized as transient liquid phase (TLP) bonding is a superior technique in order to produce strong joints while overcoming the aforementioned limitations of prevalent joining methods [] have described that diffusion brazing process is carried out in four stages: (i) heating the bond setup to the bonding temperature and melting of the braze metal; (ii) dissolution of the substrate material after melting of the braze metal; (iii) isothermal solidification of the liquid phase in the joint when the liquid composition reaches the liquidus temperature; (iv) fulfillment of the isothermal solidification with diffusion of the MPD elements in to the substrate.Heat treatment is carried out on bonded components for commercial applications to create a microstructure and elemental distribution in the bonding area similar to the base metal. The common heat treatment procedure for bonded superalloys consists of a heat treatment cycle for the TLP bond followed by a standard heat treatment for the base metal []. There is no doubt that it is economically preferable to be able to simultaneously carry out the TLP bonding heat treatment and standard heat treatment cycles to save time and resources.There are many reports on the effects of joining parameters on the microstructure and mechanical properties of the bond. Arhami et al. [] have reported that increasing bonding time results in the growth of a solid solution phase (e.g. γ in superalloys) and also avoids the formation of adverse brittle intermetallic phases in the bond area in a superalloy system. Baharzadeh et al. [] have investigated dissimilar joining of IN X-750 to SAF 2205 by TLP process with BNi-2 interlayer foil. They have reported that raising of bonding temperature will increase the isothermal solidification rate and reduce the bonding time. According to the results of Hadibeyk et al. [], the width of the diffusion affected zone (DAZ) and the athermally solidified zone (ASZ) are raised by increasing the thickness of the filler metal. However, little research can be found on the application of standard heat treatment cycles on the TLP bonded joints, or on the combination of TLP bonding and standard heat treatment. Pouranvari et al. [] have reported that using the standard heat treatment on the TLP joint can eliminate the boride precipitates in the DAZ and increase the amount of dissolved Nb + Al + Ti in the isothermally solidified zone (ISZ) leading to the improvement of overall mechanical properties. Shakerin et al. [] have illustrated that applying standard heat treatment on TLP bonded IN-738 leads to increased Ti and Al content, as the base alloying elements, in the ISZ region and enhances the overall mechanical properties. However, there is no research about the effect of full solution annealing after diffusion brazing on the microstructure and mechanical properties of the bond.In this paper, the effects of standard solution annealing (partial and full-solution) and aging heat treatment of GTD-111 superalloy, before and after TLP bonding, on the microstructure and mechanical properties are investigated. In addition, the effect of a simultaneous post-TLP bonding and base metal heat treatment process on the microstructure and mechanical properties is also studied for the first time.As-cast GTD-111 was used as the base metal in this research. Amorphous Ni-Si-B-Fe-Cr interlayer (AWS BNi-2) with a thickness of 25 μm was applied as the filler metal. The chemical composition of the substrate and filler material are listed in . Specimens with dimensions of 10 × 10 × 5 mm were sectioned from the base metal using electro-discharge machining (EDM). All surfaces of the test coupons were polished by means of silicon carbide grinding papers (from 100 to 800 grit) and subsequently the samples were ultrasonically cleaned for 15 min in an acetone bath.The interlayer foil was embedded between two pieces of the base metal to be joined. Samples were fixed using a Cr-Mo steel fixture to prevent the movement of the whole assembly during the process. The joining process was carried out at the bonding temperature of 1120 °C for different time periods of 15 and 105 min in a vacuum furnace under the pressure of 3.5 × 10−5 torr. After bonding, specimens were furnace cooled to room temperature.In order to investigate the effects of standard heat treatment of the base metal on isothermally solidified and non-isothermally solidified samples, three different samples with specific conditions were prepared. The standard heat treatment consists of three distinct and consecutive steps namely full-solution (FS), partial-solution (PS) and aging treatment (AT). They were performed according to Ref. []: full-solution at 1200 °C/4 h followed by air cooling, partial solution at 1120 °C/2 h followed by air cooling, and aging treatment at 845 °C/24 h followed by air cooling. Moreover, the influence of full-solution annealing before or after TLP bonding in the isothermal solidification condition was investigated. In this regard, schematically depicts the three different heat treatment cycles (namely HT). In the HT-A cycle, full-solution annealing of the base metal was first carried out followed by TLP bonding at 1120 °C for 105 min, partial solution annealing and aging treatments. In the HTB cycle, the first step was TLP bonding at 1120 °C for 105 min followed by the three sequential heat treatment steps. Therefore, the sole difference between HT is the changing of the sequence of the full-solution annealing. Finally, the HTC cycle consisted of TLP bonding at 1120 °C for 15 min followed by full-solution annealing, partial solution annealing and aging heat treatments. It should be mentioned that no full solution annealing was done for HT samples before joining. Moreover, to study the effect of post heat treatment on microstructure and mechanical behavior of the produced joints, a joint produced at 1120 °C for 105 min without any pre- or post-heat treatment (NHT) was examined.For microstructure observations the bonded coupons were sectioned, polished, cleaned and etched using Marble solution (50 mL HCl, 50 mL H2O, 10 g CuSO4). The prepared samples were evaluated using optical microscopy (OM), scanning electron microscopy (SEM) and field emission scanning electron microscopy (FESEM) with an ultra-thin window energy disperse X-ray spectrometer (EDS) for semi-quantitative analysis.The hardness profile of the bonded region and base metal for all the samples before (NHT) and after heat treatment (HT) as well as the base alloy (GTD-111) were obtained using a Buehler microhardness machine with a 25 g load as per ASTM:E384. Shear strength tests were carried out according to ASTM:D1002 at room temperature with a constant cross-head speed of 1 mm/min using a Zwick Z250 tensile machine. shows the custom-made fixture utilized for shear testing. Shear tests for each bond and heat treatment conditions were performed on three 10 × 10 × 10 mm specimens and the mean value has been reported here. shows the most common phases present in the microstructure of GTD-111 superalloy in the as-cast or pre-standard heat treatment condition. As shown in , the GTD-111 includes different phases such as γ matrix, γˊ precipitates, γ - γˊ eutectic islands, carbides and topologically closed packed (TCP) phases. The mole fraction of equilibrium phases formed in the base metal were calculated using Thermo-Calc Software TTNI7 database and are presented in . According to this figure, during solidification and cooling from 1400 °C, the γ matrix is initially formed with a FCC structure. Afterwards, the γˊ particles are precipitated in the matrix at temperatures lower than 1200 °C. As the temperature is further decreased, carbides, detrimental TCP phases and very small amounts of boride phases are also formed in the structure.The shape and volume fraction of γˊ precipitates before and after solution annealing and also after the aging of the base metal are presented and compared in . As can be observed from this figure, γˊ precipitates are tightly packed and close to each other, nonhomogeneous and shapeless before heat treatment (a). The reason for this can be attributed to the formation of non-equilibrium casting micro-constituents resulting in an uneven distribution of base metal elements in the microstructure. As a result, in some areas with accumulation of base metal alloying elements (specifically Ti and Al) near the initial γˊ precipitates, new γˊ precipitates form and adhere to the previous γˊ particles and cause their elongation in that region. Whereas in the adjacent regions of the precipitates, the growth of these particles is impeded due to the reduction in the amount of composing elements. Therefore, the shape of precipitates appear irregular and non-geometric.The shape of the precipitates in the solution annealed condition changes to spherical (b). This can be attributed to the equilibrium between the elastic strain energy and the interface energy in order to minimize the total free energy. Berahmand and Sajjadi [] have stated that the interface energy is the dominant factor for stability of the spherical shape when the precipitates are small. However, elastic strain energy dominates to form cube-shaped precipitates as the particles become larger.The γˊ precipitates are almost completely block-shaped, separate and have a regular structure after performing the standard heat treatment (] have reported that almost all of the γ' precipitates are dissolved after full-solution annealing and subsequently precipitate with morphologies depending on the cooling rate. The density of γ' precipitates after solution annealing is lower in comparison to the aged samples which indicates the partial solution of the particles during solution annealing treatment (] has explained that the increased density of γˊ particles results in an increase in the dissolution temperature of γˊ particles which in turn, increases the service temperature. In addition, very small and spherical secondary γˊ particles are observed only in the aged sample (] have expressed that the presence of the precipitates in the γ matrix is necessary to enhance the strength of the superalloy GTD-111 in service conditions.(a) shows the SEM image of the sample TLP-bonded at 1120 °C for 15 min. (b) presents the mole fractions of equilibrium phases formed in the BNi-2 interlayer calculated using Thermo-Calc Software with TTNI7 database. The microstructure of the bond region shown in 1- Isothermal solidification zone (ISZ): This area includes the nickel solid solution phase (γ) formed by diffusion of alloying elements from the filler metal (e.g. B and Si) into the base metal which is solidified isothermally.2- Athermal solidification zone (ASZ): Nickel and chromium rich borides and also Ni-Si-B intermetallic compound with eutectic gamma are observed in the ASZ region of the bond. The presence of these phases is also predicted using the calculated diagram shown in ] have explained that the reason for the formation of the boride and silicide phases can be ascribed to the segregation of base metal and interlayer alloying elements such as Ti, B and Si into the remaining liquid phase and reduction of the liquidus temperature. Malekan et al. [] have studied the TLP bonding of Hastelloy X and have reported that insufficient time for bonding leads to the conversion of the remaining liquid to intermetallic and eutectic phases near the center of the joint (ASZ).3- Boride precipitation zone (BPZ): Nickel rich boride phases are observed within the bonding area and adjacent to the bond/base metal interface.4- Diffusion affected zone (DAZ): Block and needle-shape boride precipitates in the base metal near the bond/base metal interface are formed through a solid-state diffusion reaction. Liu et al. [] have stated that the existence of boride forming elements such as Cr, W and Mo in this region and also low solubility and high diffusion coefficient of boron relative to silicon [] are the reasons for the formation of these precipitates. Pouranvari et al. [] have reported that the precipitates impede the growth of grains by pinning the boundaries in the base metal.Detailed information and discussions about the microstructure of the bond region have been presented elsewhere [ shows FESEM images and EDS line scan analysis of the joint after full-isothermal solidification in the sample joined at 1120 °C for 105 min and before performing any heat treatment (NHT sample). As can be seen, the bonding zone has a single-phase structure, without any intermetallic and eutectic phases (a). The reason for this can be attributed to the increased diffusion of MPD elements and lower concentrations of these elements in the base metal and in the interlayer, respectively. Cook and Sorensen [] have explained that the uniform distribution of alloying elements at the solid/liquid interface leads to the absence of harmful intermetallic compounds and to a single-phase structure during isothermal solidification. As seen in b, the density of secondary phases in the microstructure of the DAZ zone is greatly reduced due to the long bonding time, but not completely removed. Pouranvari et al. [] have reported that the precipitates in DAZ are formed during the boron solid state diffusion into the base metal prior to the completion of base metal dissolution and also during isothermal solidification. These precipitates are enriched with elements such as Mo and Cr leading to the depletion of the γ matrix of these elements [As can be observed by the EDS line scan analysis across the joint (d), a non-uniformity of the concentration of alloying elements is observed in this region as compared to the base metal. The increased concentration of some elements such as Ni, Fe, and Si in the ISZ can be associated to the higher amounts of these elements in the initial interlayer relative to the base metal. Also, Cr, Co and Ti contents in the ISZ are less than the base metal. This observed non-uniformity in elemental concentrations can be attributed to the minor dissolution of the base metal during the bonding process and also insufficient opportunity for interdiffusion at the joining time and temperature conditions.c), primary γˊ precipitates are formed during 105 min at the bonding temperature of 1120 °C. The presence of γˊ precipitates in the bonding zone after complete isothermal solidification has been less reported []. The increased concentration of Ti and Al (the constituent elements of γ') due to boosted diffusion of these elements from the base metal to the bond region during long bonding times, is the reason for the formation of these precipitates. However, these precipitates are much smaller than those in the base metal because of inadequate time and temperature for complete diffusion of alloying elements from the base metal into the bonding area and also lack of subsequent heat treatment (] have declared that the absence of small and spherical particles of secondary γ' in the bonding zone can be attributed to the lack of aging treatment.TLP joint microstructures of specimens HTa, in HT-A sample, the interface between the interlayer and base metal is still detectable after partial solution and aging treatment. However, in HTc and d), the interface between the interlayer and base metal has disappeared and the bond region and base metal are indistinguishable. The indistinct boundary formed in this area is the only sign of the bonding region (the black arrows shown in c and d). The uniformity observed at the interface between the joint region and base metal can be attributed to a rise in the dissolution of the base metal, the enhanced diffusion of alloying elements into the bonding zone from the base metal and vice versa (due to the high temperature and sufficient time of full-solution annealing treatment). However, the liquid phase which solidifies at the final stage of the TLP process appears at the boundary of the bonding region in the form of discontinuities in the HTC sample (the area indicated by arrows in d). Block and needle-shape phases (DAZ zone) are observed at the bonding/base metal interface in HTA sample. The cause of this can be the lack of full-solution treatment after the bonding and also the low temperature of partial solution and aging treatment in this sample (a). This suggests that the precipitates in the DAZ are more sensitive to temperature than time. The block and needle-shape boride precipitates (DAZ zone) in the bonding region are not observed in HTc and d). Dissolution of these precipitates can be associated with the high temperature of the full-solution annealing along with non-equilibrium formation of precipitates, leading to instability, dissolution and also gradual removal of boron from these precipitates.(a–c) depict the microstructure of the bond region of HTA sample. As can be observed from this figure, the bond/base metal interface has not been completely removed. In addition, the boride phases in the DAZ zone are still found at the bond/base metal interface (b). This can be attributed to the inadequate diffusion of base metal alloying elements into the joint region. The EDS analysis from the bond region of HTA sample confirms the non-uniformity of the alloying elements in the joint district and the base metal (d). This is because of the low temperature of the heat treatment after the TLP process. The FESEM image of the bond region of HTA sample shows that the morphology and size of γ' phases differ from the precipitates formed after the standard heat treatment of the base metal (c). This is because of the inadequate driving force for diffusion of constituent elements of γ' (Ti and Al) into the bond region during the processes of post-bond heat treatment and aging. These precipitates are much smaller than those found in the base metal because of inadequate time and temperature for the diffusion of alloying elements from the base metal into the bond area and also lack of subsequent full solution heat treatment (The microstructure of the bond region of HT (a–c). As can be observed from these images, the microstructure of the region is completely integrated with the base metal after standard heat treatment. The EDS line scan (B specimen demonstrates the uniformity of the composition across the joint region and into the base metal. The reasons for this uniformity are full diffusion of alloying elements into the joint region and the complete removal of boride phases in the DAZ during full-solution treatment. Comparing (b and c), it can be seen that the primary γ' phase is similar to the base metal in terms of density, shape and size. The reason for this is the full-solution of the base metal γ' phase at 1200 °C and sufficient diffusion of its constituent elements namely Ti and Al into the bond region. In other words, diffusion of Al and Ti in HTB sample occurs in the liquid state while this diffusion takes place in the solid state in the ISZ in HTA and NHT samples. This will have a kinetic effect on the amount of Ti and Al in the isothermal solidification zone. Generally speaking, performing the standard heat treatment on the HTB sample results in the development of primary and secondary γ' in the bonding region with morphology, volume fraction and dimensions similar to those in the base metal (] have stated that this could significantly increase the bond strength (especially high temperature strength) to values close to the strength of the base metal. displays the FESEM image and the EDS line scan from the joint area after standard heat treatment for HT, full-solution annealing treatment on HTC sample has led to the formation of a liquid phase in small areas at the centerline of the bond region. This can be attributed to the dissolution and melting of boride phases (formed in the ASZ) during solution annealing and diffusion of boron into the liquid phase. As stated by the Ni-B phase diagram [], heat treatment at temperatures greater than the Ni-B eutectic, leads to a decrease in the solubility of B in Ni, reduction in the diffusion of B into the base metal and therefore, accumulation of B in the remaining liquid phase. Whereas, segregation of the base metal alloying elements into the remaining liquid phase results in its enrichment of these elements. Linear scan analysis from this region also shows a non-uniformity in the distribution of alloying elements caused by the solidified liquid phase (d). As stated by the Ni-B and Ni-Si phase diagrams [b, silicide and boride compounds (observed in the ASZ in a) are dissolved and/or melted in the bonding zone at the solution annealing temperature. The chromium boride phase does not disappear due to its stability at the full-solution temperature (b). However, due to the fact that the temperature of the full-solution annealing is close to the dissolution temperature of this phase (∼1250 °C), local dissolution is expected to occur at this temperature. During solution annealing, the fraction of the formed liquid phase is gradually reduced because of the high diffusion rate of B into the γ matrix. The products are solidified from the remaining liquid during cooling from the solution annealing temperature ( displays the chemical analysis of the phases indicated in . The phases are formed during the solidification of the remaining liquid phase and the standard heat treatment and consist of γ matrix, γˊ precipitates, γ - γˊ eutectic, sheet of η phase, chromium rich boride, MC carbide and M6C carbo-boride.) confirms the existence of the nickel rich γ solid solution. The presence of high amounts of chromium in this region verifies the separation of this element into the remnant liquid during re-solidification.A thick continuous film of the γ' precipitates is formed in region B in b along the liquid/solid boundary because of the enrichment of the remnant liquid from γ' constituting elements such as Ti and Al. It has been confirmed by Thermo-Calc that this film is formed from full-solution temperature during solidification. Smashey [] has reported that the presence of coarse γ' particles, such as those present in the continuous film, will lead to a brittle structure and a decrease in mechanical properties.γ - γˊ eutectic islands are shown in region C in ] have stated that the size and amount of these islands depend on the solidification time and the composition of the remaining liquid phase. It has been reported that these islands significantly affect the overall mechanical properties of joint using creation of a preferred area for crack progression and failure [b shows the η phase with a sheet structure. Generally, γˊ precipitates in nickel-based superalloys have Ti and Al elements in addition to Ni and for this reason, these precipitates are pseudo-stable. As a result, the cube-shaped γˊ phase (with a FCC crystal structure) in reaction with the matrix alloying elements transforms into a sheet-shaped η phase (with a HCP crystal structure), at high temperatures. According to Bouse [], this phase is very brittle and weak and does not have any coherency with the γ matrix. Generally, the η phase (Ni3Ti) will precipitate when the Ti content exceeds its solubility limit in Ni (2.7 at.%) [, the η phase present in the HT-C TLP joint is rich in Ti. It has been reported elsewhere that the η phase is a stable component and it can also be generated directly from the liquid phase [] have reported that when the η phase is deposited at the grain boundaries in the form of layers, it leads to a decrease in mechanical properties.The chromium rich boride phase in region E in b has not completely disappeared during the heat treatment and has only locally dissolved. This is because of the high dissolution temperature (greater than the full-solution temperature) of the chromium boride phase formed during the TLP bonding.A very high Ta concentration and also high Ti concentration in region F in ) proves the presence of MC carbides. Sajjadi et al. [] believe that these carbides are formed during solidification and their solution into the γ matrix during the heat treatment is with great difficulty. For this reason, these carbides prevent grain growth during long holding times at higher temperatures. In fact it has been stated that these carbides are the main source of formation of other carbides such as M23C6 and M6C in Ni-based superalloys [The presence of Cr-, Mo- and W-rich carboboride phases in region G in c is confirmed considering the composition of this area presented in ] have proved the presence of this phase in the form of a complex FCC structured Cr-Mo-W-rich carboboride. They have stated that the reason for the formation of these phases was the solid-state diffusion of boron into the γ matrix and also the reduction of the carbon solubility potential in the presence of strong boride and carbide forming elements. Lvov et al. [] have claimed that the tendency to form these phases with slow decomposition of MC carbides can be increased by heat treatment. As can be observed in c, the formation of carboboride phases adjacent to the MC carbides, confirms this theory. According to the EDS analysis from the matrix surrounding this phase (region H from ], the formation of this phase leads to a sharp reduction in the local concentration of chromium and other refractory elements such as W and Mo in the matrix. This could have harmful effects on the corrosion properties at high temperatures.The hardness profile throughout the joint is a qualitative measurement of the mechanical properties of various bonding regions. It is also an appropriate index for the degree of homogenization of the joint microstructure. indicates a comparison of the hardness profile throughout the bond region and the base metal for NHT, HT bonded samples. In the NHT sample, the ISZ hardness is less than that of the BM. This can be attributed to the inadequate diffusion of alloying elements between the base metal and the bonding zone [A sample increases by about 13 % relative to NHT sample. This can be explained by partial solution of γ' precipitates in the base metal and the diffusion of Ti and Al elements from the dissolved precipitates into the bonded area. The hardness peak seen in the DAZ region of NHT sample, in relation to the hardness of the BM, can be linked to the existence of Cr- and Mo-rich boride precipitates in this zone., the DAZ hardness in HT-A sample, despite the reduction in the density of the boride phase as shown in b, is not significantly altered compared to NHT sample. The hardness of the DAZ is affected by two factors:The hardness of the matrix: the heat treatment applied and also the presence of γ' precipitates will increase the hardness of the matrix in this region.The hardness of boride phases: some of the boride phases are dissolved in the alloy matrix during partial solution annealing resulting in a reduction in hardness.The combined effect of these two factors leads to no significant changes in hardness of the DAZ region in HT-A sample.B sample, an increase in the hardness accompanying a complete uniform hardness profile similar to the base metal is observed in the bond region. This is due to full-solution annealing at 1200 °C which leads to the complete dissolution of gamma prime precipitates in the base metal and the complete diffusion of alloying elements, namely Ti and Al, into the bond region. Ghasemi and Pouranvari [] have stated that the increased Ti and Al amounts in the matrix have led to the solid solution strengthening and the formation of γ' strengthening precipitates with a morphology and volume fraction similar to the base metal. Moreover, the hardness peak previously observed in the DAZ has been eliminated in HTB sample and the hardness profile is quite analogous to that of the base metal. The reason for this is the high full-solution temperature and the instability of the boride precipitates at this temperature, which has led to their complete solution.C sample, a hardness peak is seen in the center of the bond region. The existence of various brittle phases, such as carbide, carboboride, boride and sheets of η phase discussed in the previous section is the root cause of this detrimental increase in the hardness in this area. Other regions in this sample have similar hardness values as the base metal.Shear test was performed by exerting a shear stress to the bonding zone in order to investigate the mechanical properties of the TLP joints. shows the stress-strain curve, toughness and maximum displacement obtained from shear strength tests of the joints before and after various heat treatment cycles (i.e. NHT, HT samples). Generally, the influence of heat treatment on shear strength of the specimens can be examined separately in three ways:The partial solution annealing and aging heat treatment performed on HTA sample led to an improvement in the shear strength of about 21 % compared to the NHT sample (-a). Additionally, the toughness and displacement values have increased in the HT-b). The reason can be associated with the increase in the diffusion of Al and Ti into the bond area because of the partial dissolution of gamma prime precipitates which in turn, results in an increased contribution of solid solution strengthening to the overall strength of the joint. Moreover, in HT-A sample, the amount and density of the boride phases in the DAZ have been significantly reduced which in turn, increases the joint strength.Application of full-solution annealing to the sample in which isothermal solidification has been completed (HTB), resulted in the highest joint shear strength, toughness and displacement among all the samples. The reason can be associated to the amplified interdiffusion of alloying elements between the bonded district and base metal due to the complete dissolution of gamma prime precipitates and also the complete elimination of boride phases from the DAZ. In addition, the subsequent partial solution annealing and aging treatment led to the highest solid solution strengthening contribution and the formation of γ' precipitates in the joint zone.C sample in which the standard heat treatment has been applied, however the isothermal solidification has not been completed, has decreased compared to the other heat-treated samples. This is because of the formation of intermetallic and brittle phases in the final liquid phase prior to solidification in the bond region (explained in the previous section). However, the shear strength of the joint in this sample is still greater than that of the NHT sample despite the formation of these harmful phases. This can be attributed to the fact that these detrimental phases are sparsely distributed along the centerline of the bond region in HT shows the relationship between the average hardness of the ISZ and the shear strength of the joints for all of the specimens investigated in this study. As can be seen, for NHT, HT samples, the ISZ hardness has a direct relationship with shear strength of the joint. However, the HTC sample does not follow this rule because of the formation of intermetallic phases in the bond region. In other words, the shear strength of the joint is improved as the average hardness value of the ISZ approaches the hardness value of the heat treated base metal (). As a result, it can be stated that the shear strength of the joint is largely dependent on the hardness of the ISZ.As the results show, the application of the HTA heat treatment results in eliminating the necessity of standard heat treatment on base metal before TLP bonding. Moreover, an ideal joint similar to the base metal has been obtained without any extra treatment. Therefore, they can lead to reducing of time and cost in the industrial applications.TLP bonding of GTD-111 was carried out at 1120 °C for two different times, according to incomplete and complete isothermal solidification. Standard solution annealing was performed as pre- or post-TLP bond treatment. The microstructural and mechanical study illustrated the following results:γ' precipitates were observed before and after solution annealing and also after aging in the form of non-geometric, spherical, blocky structure, respectively. Very small and spherical secondary γˊ particles were observed only in the aged sample.A non-uniformity in the concentration of alloying elements during the joining procedure for 105 min at 1120 °C was observed in the bonding region.The increased concentration of Ti and Al led to the formation of γˊ precipitates after complete isothermal solidification (105 min at 1120 °C). However, the size of these precipitates was much smaller than those in the base metal.In the condition of incomplete isothermal solidification (15 min at 1120 °C), during cooling from the solution annealing temperature, segregation of alloying elements into the remnant liquid phase resulted in the formation of MC and M6C carbo-boride, η phase, γ - γˊ eutectic leading to reduction of mechanical properties.Lack of full solution annealing after TLP bonding, led to the stability of boride phases in the DAZ and also non-uniformity of the alloying elements even after partial solution annealing and aging treatment.The standard heat treatment led to a uniform composition and the development of primary and secondary γ' in the bonding district identical to the base metal.In the sample with complete isothermal solidification, performing full-solution, partial solution and aging treatment led to a completely uniform hardness profile in the bonding region and the base metal. Moreover, this specimen presented the highest joint shear strength and toughness.The shear strength of the joint is improved as the average hardness value of the ISZ approaches the hardness value of the heat treated base metal.Brittle fracture in glass materials has been explained by linear elastic fracture mechanics (LEFM) on atomic bonds rupture with surface energy. However, this explanation became controversial as the nucleation, growth, and coalescence of nanosize cavities were detected in glasses at the crack front during its propagation in double cleavage drilled compression experiments by atomic force microscopy (AFM) In general, two kinds of plastic deformation in glass materials are possible. (i) shear flow, which represents a plastic flow generating a variation in the body shape but no volume change, and (ii) densification, which is based upon the compaction of material structure and produces a volume reduction. The occurrence of the former is usually referred to as normal behavior, and the latter is termed as anomalous The concept of competition between brittle fracture and ductile deformation have been exclusively used in metallic materials with constant yield and fracture strength ), mode I stress intensity factor is given as KI=σπa should be modified considering competition between brittle fracture and ductile deformation.In contrast to metallic materials, yield strength of brittle material depends on both shear stress and hydrostatic pressure where s is the deviatoric stress tensor, σ is the stress tensor, p is the hydrostatic pressure, σo is the zero-pressure yield strength (cohesion of materials), and β is the friction angle. The σo is related to uniaxial compression yield strength σyc, if hardening is defined by the σyc, as There have been several attempts to shed light on the mechanism of spherical indentation Besides, brittle materials show different deformation behavior depending on the indenter radius. In brittle materials, Mouginot ). According to competition model and general state of stress in micro and macro scale, brittle fracture occurs at points F, yielding occurs at points A, and neither yielding nor brittle fracture happens at points D and E. In case of points B and C, plastic deformation/ductile fracture and brittle fracture occurs, respectively, based upon nano/micro scratch test experimental results in our previous works An axisymmetric two-dimensional (2D) FE model, which contains about 15,600 nodes and 15,300 elements (), is created for load control simulation of spherical indentation test () is conveniently used in the transition region where element size changes, but constrained mid-nodes of tends to give discrete stress-strain values. Thus, we choose trapezoidal elements in the transition region near the contact surface and apply in only the transition region far from the contact surface The material is assumed to be isotropic and follows the linear DP model. A non-associative flow rule is used to compute the directions of plastic flow in the stress space, and rate effects are neglected. The micro-cracks result in dilation due to discontinuous gaps. Since the most pores collapse and result in permanent condensation As a material, soda-lime-silica glass is chosen. By assuming Poisson's ratio ν = 0.23 Due to severe subindenter deformation characteristics, the size of the element at the region beneath the indenter is of great importance. We examined the effect of FE mesh on the characteristics of maximum indentation depth hmax, maximum von Mises stress σvmax, maximum principal stress σpmax, and maximum radial stress σrmax (). The ratio of minimum element size to indenter diameter, e/D, are 0.5%, 0.125%, 0.0625% and 0.03125%, respectively. Since the existence of plastic deformation can affect the mesh-size-effect, both elastic (E) and elasto-plastic (EP) case are considered.We confirmed that the mesh size of subindenter surface region barely affects hmax (). On the other hand, it significantly affects σvmax, σpmax, and σrmax due to a large gradient of stress near the maximum stresses. We thus adopt the FE model with minimum element size e/D = 0.0625% for accurate data acquisition considering the computational cost.Based on the literature experimental data of critical load Pc inducing ring cracks for each r) and stress and plastic strain εp fields at certain values of r = 0.1, 0.5 mm (). In addition, to study BD transition, σv, εp, p, and σy at element ep where σpmax occurs were obtained (). Here, σy is calculated from the constitutive model, Eq. . To show the effect of plastic deformation on the stress fields, both elastic (E) and elasto-plastic (EP) case are considered.The results show that when r ≥ 32 mm, material deforms elastically as stress fields between E and EP cases are the same (). In addition, fracture strength (σpmax ≈ 0.1 GPa) does not change and thus it is not volume-dependent in this r. When 1 ≤ r ≤ 16 mm, a material also deform elastically but fracture strength increases as specimen get smaller (). Therefore, the fracture strength is volume dependent within this r. When r = 0.5 mm, plastic deformation occurs under the indenter (a and b). The σv (EP) field is different from σv (E) field due to the plastic deformation and hence it changes σp field and thus σpmax (EP) is different from σpmax (E) (), even though the plastic deformation does not reach the outside of contact area where cracking occurs (b and c). On the other hand, when r = 0.1 mm, experimental data reports that plastic deformation occurs instead of brittle fracture ) and thus plastic deformation can occur (d–f). The reason σv<σy at ep is because it is a centroid value. At the ep located at the surface of specimen (f), yielding occurs at the two integration points on surface of specimen, σv = σy = 1.67 GPa, but yielding does not occur at the two integration points of ep located inside the specimen, 1.6 GPa = σv<σy = 1.67 GPa (). The pressure dependence of σy in Eq. is precisely reflected in the results (). If the material has a strain-hardening characteristic, the value of σy changes depending on plastic strain εp. Thus, σy should be a function of p and εp, hence expressed as σy (p, εp) in In spherical indentation, as the state of stress is not uniaxial but general state, σpmax and σv at ep are different (). Thus, both criteria, the failure strength of the material (maximum principal stress fracture criterion) and yield strength of the material (von Mises yield criterion), have to be considered and thereby CTC model is needed (To clarify size effect and BD transition, the plot of r versus maximum principal and von Mises stresses is subdivided as described in the following stages (Stage I: Regardless of the value of r, σpmax is constant. Thus, in this region, the size effect derived from the volume dependence of fracture strength is not significant.Stage II: σpmax increases as r decreases. However, as plastic deformation does not occur, it is only due to volume dependence of fracture strength.Stage III: As in stage II, volume dependence of fracture strength increases σpmax as r decreases. Moreover, plastic deformation occurs under the indenter. Even though it does not reach the contact boundary where cracking occurs (a–c), it also increases σpmax. The difference of σpmax between E and EP model proves this (). Values of σpmax thus cannot be accurately calculated from the theoretical solution in Eq. , which assumes an elastic body of specimen.Stage IV: At this stage, plastic deformation occurs in advance before the occurrence of brittle fracture. Specifically, yielding starts to occur at ep when r = rt = 0.1 mm since σv reaches σy at that location (d–f). Consequently, stress–strain relation follows plastic yield criterion, linear DP model, at ep instead of fully elastic behavior. Since cracking does not occur regardless of indentation depth in this case, we deduce that a<at (It is possible to apply the competition model where either brittle or ductile works in XFE model. In XFE model, if centroid of the element reaches damage initiation strength (maximum principal stress) before the integration points in the corresponding element reach yield strength, brittle fracture occurs based on the cohesive zone model. In the converse case, plastic deformation occurs. As extended finite element analysis is based on LEFM, integration points, where cracking already occurs in the corresponding element, does not undergo yielding and vice versa.Here, the same XFE model in our previous work ). However, plastic properties of linear DP yield criterion are additionally implemented to consider plastic deformation underneath indenter and the occurrence of cracking behind scratch tip at the same time.The results show that plastic deformation occurs at first. It starts inside the specimen (a), not peripheral contact point between the indenter and specimen since high von Mises stress occurs inside the specimen (b). It seems that plastic deformation occurs even at the contact area (a), but εp = 0 at the integration points at the contact area and thus yielding does not occur. Secondly, before plastic deformation occurs at the contact area, brittle fracture starts to occur behind the scratch tip (d), and plastic deformation occurs continuously inside the specimen (c). Lastly, at the surface, both brittle and ductile criteria are satisfied. Then brittle fracture disappears, and only plastic deformation occurs (e). It does not reflect on real experimental results in which brittle fracture occurs continuously. It is because XFEM is based on LEFM. The integration points check plasticity in advance, then once plasticity occurs at the integration points, a fracture cannot occur at the centroid of the corresponding element in extended finite element analysis (XFEA). On the other hand, the total coefficient of friction μt of FEA results agrees with experimental results () and therby it successfully describes plastic deformation of the micro scratch test experiment.In both nano/micro scratch test experimental results from the literature ), on the other hand, brittle behavior occurs in materials for a>at which corresponds point C (). If stress at point B increases, then ductile fracture would occur as in the tensile test experiments of small nano-fiber for a > at where the point is above yield criterion and under fracture criterion, like point A for a < at. However, this case cannot be schematically described in , thus should be evaluated based upon competition between σf and σy additionally.We confirmed that both brittle fracture and ductile deformation during the scratch test can be implemented by XFEM simultaneously. However, it has a limitation that brittle fracture does not occur when the integration points reach yield strength before it satisfies the fracture criterion on the centroid of the element. In other words, the integration points and centroid of an element which satisfies both yield and fracture criterion for a>at cannot be described through XFEM and thereby, user materials subroutine of the CTC model should be developed in the future to describe the material behavior with respect to size effect and BD transition.The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.Kwangmin Lee: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing - original draft, Visualization, Funding acquisition. Karuppasamy Pandian Marimuthu: Validation, Investigation, Writing - review & editing, Funding acquisition. Hyungyil Lee: Resources, Writing - review & editing, Supervision, Project administration, Funding acquisition.where ν is Poisson’s ratio of the indenter, E is Young’s modulus of the indenter, H is Vickers hardness, pm is mean pressure beneath the indenter, κ is a dimensionless factor, and J2 is the second invariant of the deviatoric stress tensor. Through Eqs. , Θ is analytically obtained by using Hertz’s equation where P is applied normal load on the indenter. Since Hertz’s relation assumes elasticity of the material, it is not accurate when plastic deformation occurs under the indenter. Thus, when r is as small as just before BD transition occurs, Pc in Eq. is not accurate. In addition, Py in Eq. is also not an accurate value. It assumes that yield strength of materials is related to with hardness H aswhere ζ is a dimensionless factor. Above relation is derived with the assumption that material is perfectly plastic as the indenter is pushed into the material; the yield strength does not change Optimization and application of a crashworthy device for the monopile offshore wind turbine against ship impactThe risk of offshore wind turbines collision with ships is on the rise during the service period with the increase of offshore wind farms and ship routings. In order to minimize the damage of offshore wind turbines caused by ship impact, a crashworthy device, which contains a rubber blanket and outer steel shell, is proposed. The rubber hardness and the rubber and steel shell thicknesses of the crashworthy device are optimized by comparing the collision-force and nacelle acceleration using LS-DYNA explicit code. The main reason for lessening the maximum collision-force and nacelle acceleration is that the rubber blanket could absorb a portion of ship energy by using its own structure deformation. Therefore, an optimal crashworthy device for the monopile offshore wind turbine, meeting the weight constraint, is suggested and implemented in various impact scenarios. The obvious effects of crashworthy devices are a decrease of the maximum collision-force and nacelle acceleration, especially for ships with smaller initial kinetic energy. The damage area of plastic strain for foundations is reduced to zero when crashworthy devices are used in the analysis scenarios. This paper may be useful in anti-impact design of offshore wind turbines.constant characterizing strain rate effectconstant characterizing strain rate effectfirst deviatoric strain invariants of right Cauchy–Green tensorsecond deviatoric strain invariants of right Cauchy–Green tensorthird deviatoric strain invariants of right Cauchy–Green tensorabsolute value of the relative velocity between two nodes of springstrain occurred at one-half of the maximum stress in undrained compression testOffshore wind farms, whose wind power is much stronger than that of onshore wind farms, are the main source of renewable energy. Nowadays, offshore wind turbines (OWTs) have been built in many countries, especially in Europe, and the installed capacity is still increasing. By the end of 2012, the global installed capacity of existing OWTs has reached 5117 MW, and the top three countries, Britain, Denmark and China, own 2948 MW, 921 MW and 389.6 MW respectively The type of OWT foundations is a monopile sized 5.0–6.7 m in diameter, 55–70 mm in wall-thickness and 86.5 m in average length, whose top elevation is 14.0 m, and -1 soil layer acts as bearing stratum for the monopile. The OWT, SWT4.0-130 model (. The maximum allowable acceleration of nacelle is 6 m/s2 according to SIMENS, what means that the risk of failure is considered to get strong beyond this value. The plastic strain is not allowed to appear in serviceability limit state for marine structures. Hence, it is of practical significance to find a crashworthy device guaranteeing the normal operation of OWTs with no maintenance or a light maintenance after a ship impact.Compared with static loads, plastic deformation of the steel subjected to impact loads will occur more rapidly, and the strain rate will increase significantly at the same time. Dynamic test of steel materials shows that a series of physical and chemical changes will happen with the increase of strain rate, leading to change in stress–strain relation and basic parameters, including yield limit, transient stress and ductility damping, which will have an effect on dynamic response of the structure. Taking account of the strain rate-dependent plastic behavior of the steel, an elastic–plastic model by LS-DYNA based on the Cowper and Symonds formula, which scales the yield stress by a strain rate dependent factor:where q and F are constants characterizing strain rate effect and ε˙ is the strain rate defined as:The current radius of the yield surface σy is the sum of the initial yield strength σ0, plus the growth βEpεeffp, where β is strain hardening parameter varied from 0 to 1, representing isotropic hardening, kinematic hardening, or a combination of isotropic and kinematic hardening, as shown in , σr is the unloading point. Ep is the plastic hardening modulus:where E and Et are elastic modulus and tangent modulus respectively. And εeffp is the effective plastic strain:where ε˙ijp is the plastic strain rate, ε˙ijp equals the difference between the total and elastic strain rates:The materials of the OWT tower and bow are Q235B, and steel-pipe pile uses a high strength steel of Q345. The properties of Q235B and Q345 are listed in , ρ is the density, ν is the Poisson's ratio, σ0 is the initial yield stress, ɛf is the failure strain.Rubber is a kind of material with remarkable viscoelasticity and high elasticity, which is widely used as energy dissipation device for offshore and building structures. As a kind of hyperelastic material, the rubber has the constitutive properties of a relatively low elastic modulus and high bulk modulus, and can experience large strain and deformation. If a material is hyperelastic, there must exist a strain energy density function W that is a scalar function of the strain tensor components, whose derivative with respect to a strain component determines the corresponding stress component. The strain of the Mooney–Rivlin model with two coefficients from the LS-DYNA theoretical manual can be up to 200%. The model is suitable for practical calculates of the response of crashworthy devices with rubber material. The Mooney–Rivlin material model, provided by LS-DYNA, is based on a strain energy density function, W, as follows:W=C10(I1−3)+C01(I2−3)+C(I3−2−1)+D(I3−1)2where C10 and C01 are Mooney–Rivlin coefficients which can be obtained from the stress–strain curves or the hardness of rubber; I1, I2, I3 are the first, second, third deviatoric strain invariants of right Cauchy–Green tensor, C and D are related to C10 and C01 as Eqs. where ν
= 0.499 is the Poisson's ratio, the initial shear modulus G and the Young's modulus E are defined as Eqs. , and the initial bulk modulus K and the incompressibility parameter d can be calculated from Eqs. , is theoretically driven based on Eqs. . It can be reduced to a more simple equation, as Eq. , by assuming that the rubber is incompressible. The relation of Mooney–Rivlin coefficients can be set as C10
= 4C01There are several quick ways to obtain Mooney–Rivlin coefficients without conducting expensive tests or curve-fitting the data. A good method where HA is the Shore A ranged from 10° to 90° normally.Six types of natural rubber with different Shore A are used as cushioning material of OWT crashworthy devices, and the Mooney–Rivlin coefficients of the natural rubber are listed in It is the dominant factor of ship–OWT collision that boundary conditions of the monopile are able to reflect the conditions of the seabed where the OWT stands, and boundary conditions can be reflected by the pile–soil interaction model. Currently, the pile–soil interaction is modeled prevailingly through the p–y curves method The pile–soil interaction is mainly in horizontal direction for ship–OWT collision, and axial resistance from the soil has little effect on the foundation which can be ignored. Spring elements (x and y directions) are adopted to simulate the pile–soil horizontal interaction at different depths below the seabed, one node of springs is linked to pile and another node is fixed as shown in , and the bottom of pile is fixed in z direction. The pile–soil spring has different stiffness at different depths, the horizontal equivalent stiffness of springs at −1 m below the seabed can be calculated, as shown in , by the p–y curves parameter values listed in (ɛ50 is the strain which occurs at one-half of the maximum stress in laboratory undrained compression tests of undisturbed soil samples). The spring damping where Dpile is the pile diameter; ρ is the soil density; Vs is the soil shear wave velocity.To account for “strain rate” effects, LS-DYNA provides a simple method of scaling the forces based to the relative velocities that applies to springs. The forces computed from the spring elements are assumed to be the static values Fs and are scaled by an amplification factor to obtain the dynamic value Fd:where kd
= 0.5 is an amplification factor, V is the absolute value of the relative velocity between two nodes of spring, V0 is the dynamic test velocity, which can be assumed as vessel speed.According to the design code of DNV-OS-A101 . The FE model of the vessel mainly consists of the bow and the remaining parts. The bow, including main deck, bulkhead, tank top and bottom plating, etc., is simulated by shell elements of which thickness is assumed to be 20 mm and size is 0.5 m, while the remaining parts are simulated by rigid solid elements with size of more than 1.0 m in order to improve the computation efficiency. The method of changing remaining parts’ density can control the ship's center of gravity and weight. The FE model of the bow and its internal structure is shown in . To consider the effect of water surrounding the vessel, the added mass factor of vessel is assumed as 0.1 A new anti-impact device, a natural rubber annulated column surrounded by Q235 steel shell, is proposed to be set up at the OWT's impacted part to protect the whole OWT structure from vessels impact. The thickness of annulated column and steel shell are 1.0–1.5 m and 5–20 mm respectively. The FE model of the crashworthy device, shown in , adopts solid elements for rubber cushion and shell elements for steel shell, and the elements’ size is 0.25 m (from a convergence study).The contact condition between ships and OWTs (or crashworthy devices) is set to be automatic surface-to-surface, of which coefficient of kinetic and static friction is 0.2 because the contact materials are all steel. In addition, a single surface contact is used for the self-contact of the bow. In order to ensure no initial contact, a certain distance between two contact structures must be kept. shows the FE model of the collision system.The equations of motion are solved in time with the central finite difference method. The stability of this method is ensured provided the time step is lower than a critical time step. In practice, the time step is about 50 ms. The total time calculated was 5 s.The energy changes of the collision system are analyzed firstly to guarantee the accuracy of numerical simulation results. Generally, the initial kinetic energy of the ship gradually transforms into structural internal energy, remaining kinetic energy, damping energy, sliding energy and hourglass energy during the collision process. The OWT will free vibrate with damping after collision, and only the structural damping C =
a0M (a0
= 2ξω) is considered (C is the damping matrix and M is the mass matrix), ξ
= 0.02 . The kinetic energy falls rapidly at the beginning of the collision stage, and reaches the minimum at 1.225 s. Rebound of the kinetic energy after 1.225 s means that the ship leaves in the opposite direction after collision, and the kinetic energy oscillation after 2.335 s implies that the OWT is damped free vibrating. Damping energy, sliding energy and hourglass energy are on the rise, but the maximum value is much smaller compared to the total energy. The ratio of hourglass energy to total energy is 0.48% which is less than 5%. Therefore, the numerical simulation results are satisfactory.The monopile weights about 900 tons. In order to ensure that the crashworthy device can be fixed on the monopile and will not fall down when collision occurred, the weight of crashworthy devices must be constrained within 135 tons (about 15% of 900 tons). Considering the rubber hardness, rubber thickness and steel shell thickness of crashworthy devices, optimized analyses are made. The tower top acceleration and collision-force are crucial for nacelle's normal operation and foundation safe, hence the performance of crashworthy devices are compared through the maximum acceleration of tower top and collision-force.The effects of impact are investigated in terms of the maximum tower top acceleration and collision-force of the OWT collided with 2000 tons ship at speed of 2.0 m/s, and the collision angle α is 90°. Crashworthy devices with rubber of Shore A 60°–10° are equipped with 1.5 m thick rubber and 10 mm thick steel shell, and their weights are all 130.9 tons meeting the requirements. The OWT structure with different fenders is checked for the maximum tower top acceleration and collision-force after collision, and all the analysis results are summarized in . The results demonstrate that crashworthy devices can effectively protect OWT against accidental ship impact. The lower hardness of the rubber, the higher anti-impact property of the crashworthy device. The optimal rubber hardness (shore A 10°) for crashworthy device could have 20.4% reduction for maximum collision-force and 30.5% reduction for the maximum tower top acceleration relative to no crashworthy device.For crashworthy devices with rubber of Shore A 10° and 10 mm thick steel shell, analyses are conducted with 1.0 m, 1.25 m and 1.5 m thick rubber to see their effects on the maximum acceleration and collision-force of the OWT. The results are listed in . It can be seen that the crashworthy device with 1.5 m thick rubber is better than that with 1.0 m and 1.25 m thick rubber in crashworthiness performance, especially in reducing collision-force. The three crashworthy devices weigh 83.2 tons, 106.3 tons and 130.9 tons respectively, which is less than 135 tons.Three kinds of crashworthy devices with 5 mm, 10 mm and 20 mm steel shell thickness (126.7 tons, 130.9 tons, 139.3 tons) are compared with that without crashworthy device in . The thickness of rubber for these crashworthy devices is 1.5 m and the hardness is shore A 10°. Crashworthy devices with 10 mm steel shell thickness has the biggest drop about 20.4% to the maximum collision-force, but it is not superior in lessening nacelle acceleration to the crashworthy device with 5 mm steel shell thickness. Taking fully into account the effects of steel shell thickness to prevent environment eroding rubber and the close effects about 34.6% and 30.5% in reducing the maximum acceleration, combined with overweight of that with 20 mm steel shell, the steel shell thickness of 10 mm is firmly confirmed to the most ideal for crashworthy devices.By comparison and optimization, we can get the most superior crashworthy device with the rubber hardness of shore A 10°, rubber thickness of 1.5 m and steel shell thickness of 10 mm. The impacted substructure without crashworthy device absorbed all the ship collision energy alone, but the impacted substructure with crashworthy devices absorbed a very small proportion of the ship collision energy. That is because the rubber blanket in crashworthy devices played a role in helping the substructure to absorb the ship kinetic energy by using its own structure deformation.The cases of 5000 tons ship–OWT head-on collision at 2 m/s are conducted while the OWT is equipped with crashworthy device or not respectively. The collision-force curves of two cases are shown in . For the OWT with crashworthy device, the maximum collision-force is decreased by 8.0%. The curve with device is smooth obviously, which indicates that damages of foundation are alleviated. The collision duration is 1.495 s and 3.050 s respectively in . Therefore, the crashworthy device can effectively protect the foundation and the key electric control equipment located the impact area through decreasing the maximum collision-force and increasing the collision duration.Different impact scenarios are analyzed to assess the effects of crashworthy devices through comparing the maximum value of collision-force. The results are listed in . It is clear that the effects of crashworthy devices in lessening collision-force are declined with the increase of ship displacement, velocity and collision angle. In other words, the level of reduced collision-force has an inverse relationship with the initial kinetic energy of ships. shows the time–history curves of nacelle acceleration of the OWT with or without crashworthy device subjected to a 5000 tons ship (v
= 2 m/s) impact. The maximum value of nacelle acceleration is decreased from 10.1 m/s2 to 8.0 m/s2 when the OWT has a fender. The curve with device is smoother which implies that the frequency spectrum of the nacelle acceleration is narrower and concentrated in the lower frequency domain.The nacelle acceleration results of each scenario are given in that the drop of maximum acceleration is very significant for OWTs installed crashworthy devices. There will be a high drop of 54.1% when the initial kinetic energy of ship is 2.5 MJ.In order to describe the extent of damage of the monopile foundation for OWTs, the damage area of plastic strain, A, is defined as follows:where ɛ and ɛ0 are equivalent plastic strain and yield strain respectively, tstart and tend are start time and end time of collision. shows the plastic strain contour image of the foundation collision with 5000 tons ship (v
= 2 m/s) at 0.9 s, and the damage area of plastic strain A is 15.2740 m2. But the damage area of plastic strain A will became 0 m2 if foundation is equipped with the crashworthy device. Since the crashworthy device absorbs a great part of ship impact energy through its own plastic deformation, as illustrated in , the OWT is effectively protected. For others scenarios (refer to ), the damage area of plastic strain still keeps 0 m2 with installed crashworthy devices.A dynamic collision analysis between ships and monopile of OWTs was carried out in this paper with LS-DYNA, a commercial finite element package. A crashworthy device for the monopile foundation of OWTs is proposed and optimized to prevent the impact damage of foundation and tower top structure. By comparing the rubber hardness, rubber thickness, as well as steel shell thickness, an anti-impact equipment with optimal crashworthiness performance in reducing the maximum collision-force and nacelle acceleration is found, and it meets the constraint requirements. The main reason is that the rubber blanket absorbs a portion of ship energy by using its own structure deformation.The optimal crashworthy devices are implemented in the different impact scenarios, including the change of ship displacement, velocity and collision angle. The obvious effects of crashworthy devices are a decrease of the maximum collision-force and nacelle acceleration, especially for ships with smaller initial kinetic energy. The smoother time histories of collision-force and acceleration illustrate better protection of OWTs through reducing structural vibrations frequency. With the crashworthy device, there are no plastic strain (A
= 0 m2) for OWTs in any impact scenario. A further analysis is planned to find an optimized crashworthy device for jacket or tripod based structure and considering the fluid–foundation interaction.Fine grained Mg–PSZ ceramics with titania and alumina or spinel additions for near net shape steel processingMg–PSZ materials exhibit high corrosion resistance in steel/slag-systems. Through special additions of TiO2 and Al2O3 or MgAl2O4 special microstructures have been obtained by slip casting with improved thermal shock performance and corrosion resistance for applications in near net shape steel processing. The thermomechanical properties have been measured at room and at elevated temperatures up to 1450°C and the corrosion rates have been investigated in a specially designed device simulating real operating conditions of thin slab casting of steel. The thermal shock behaviour has been evaluated due to water quenching tests and measuring of the remaining four point bending strengths. In addition disc shapes have been shocked by the aid of an arc torch.The phase equilibrium of zirconia with other oxide systems is fundamental to the application of zirconia as an advanced refractory ceramic. Of greatest interest are the oxides such as MgO or Y2O3 with similar atomic radii, which dissolve to a significant extent in zirconia and tend to stabilise, full or partially, the cubic fluorite phase.In the case of hot steel applications, such as the near net shape steel processing with its basic versions of thin slab casting and strip casting, low porous MgO partially stabilised ZrO2 (Mg–PSZ) shows the highest corrosion resistance at the interphase steel/slag/ceramic, at the interphase slag/ceramic/ air and against steel and its alloys in comparison to all conventional oxide and non-oxide refractory materials. As a competitor BN also appears with very good properties against corrosion attack at the above mentioned interphases, but unfortunately it partially dissolves in steel. Further, the manufacturing costs for a monolithic component (submerged nozzle or slide gate) are much higher in comparison to densed zirconia components.In spite of this excellent performance in aggressive corrosive environments, zirconia suffers under thermal shock attack. Especially in the secondary metallurgy, critical casting components such as nozzles have to survive the thermal shock attack in the beginning of casting when the molten steel of the tundish (1580°C) contacts the preheated ceramic. Due to insufficient preheating control during operation, a temperature difference up to 500°C has to be bridged. Hasselman has established the thermal stress resistance parameters related to the thermal expansion coefficient, the Young's modulus of elasticity, the fracture tensile stress and the thermal conductivity. He has illustrated the effect of thermal shock on the strength of ceramics and the regions of applicability (resistance to fracture, loss in strength due to fracture and crack stability followed by further weakening) of the various thermal stress fracture parameters.In order to control the microstructure for superior thermomechanical and corrosion resistance properties several scientists have worked with different stabilising agents and additives for zirconia based materials. This paper concentrates on the influence of Al2O3, TiO2 and MgAl2O4 additives in Mg–PSZ materials because of their contribution to thermal shock behaviour.In particular, the fracture toughness and fracture behaviour of ZrO2–Al2O3-ceramics are influenced strongly by the size, size distribution and location of the particles. Small additions of TiO2 (0.5 mol%) are suggested as a sintering aid. In the case of Y2O3 stabilised zirconia, additions of Al2O3 and TiO2 have been induced due to a plasma powder preparing technique, where structures are consistent with co-condensation of the liquid phase to form ultrafine droplets and a variety of metastable phases during solidification. Further, an increased TiO2-content in Y2O3 stabilised ZrO2 increases the grain size of zirconia and destabilises the cubic phase. In the case of the cubic phase destabilisation the c-axis of the tetragonal structure increases while the a-axis decreases. This is quite interesting because the ionic radius of Ti4+ is smaller than that of Zr4+. The destabilisation of the cubic phase is attributed to the reduced coordination number. Besides this explanation an additional reason for this expansion of the c-axis and contraction of the a-axis with increasing TiO2 content is believed to be due to the preferred repulsion between Ti4+ cations and the effective double positive charged oxygen vacancies in [001] direction. The length change in both directions suggests that the Ti4+ cations are not incorporated randomly in the lattice (up to 6.71 wt% TiO2 a solid solution in zirconia is expected, ZrTiO4 does not exist) but in preferred energetically favourable sites which cause a repulsion between the dopant cations and the vacancies. Furthermore there is a progressive decrease in the temperature of inversion (tetragonal to monoclinic) as the amount of TiO2 is increased, lowering the point of the polymorphic change from about 980°C for pure ZrO2 to about 340°C for specimens containing 40 mol% TiO2.In general ZrO2 with Ti (metal) additions exceeding the solubility limit (>4 mol%) showed better sintering due to liquid–phase sintering and had better strength and thermal shock resistance than ZrO2 with less or no Ti. The improved thermal shock resistance could be attributed to the better thermal conductivity and plasticity of metallic Ti. The presence of Ti in ZrO2 during sintering inhibits the grain growth and the smaller grain size of ZrO2 leads also to a better thermal shock performance.Another work describes fine grained Mg–PSZ-type that has been produced by adding MgAl2O4 spinel to a ternary Y2O3–MgO–ZrO2 system. A mean cubic grain size below 10 μm has been achieved and through special aging treatment the toughness has been improved through the formation of transformable tetragonal precipitates.In many cases of partial MgO stabilised zirconias the tetragonal phase can be recognised as spheroids or lenses of approximately 50–500 nm in big cubic grains or at their grain boundaries, whereby the tetragonal “lenses” are aligned at right angles. During thermal, chemical, mechanical or kinetical (particle size) destabilisation a martensitic phase transformation takes place (tetragonal to monoclinic). Martensitic monoclinic twins appear in the cubic crystal (or at the grain boundaries) in the magnitude of 0.5–3 μm.At high temperatures, although amphoteric and comparatively stable to both acid and basic slags and glasses, stabilised zirconia can be destabilised on prolonged contact with siliceous and alumino silicate compounds. The destabilisation of MgO partial stabilised zirconia is by the presence of SiO2, TiO2, Fe2O3 and Al2O3 enhanced, whereby SiO2 dominates by removing the MgO of the zirconia crystal and producing magnesium silicates at the grain boundaries.In a previous work the corrosion mechanisms of low porous Mg–PSZ materials in steel/slag- systems have been extensively described by the aid of a corrosion testing device simulating operating conditions of submerged nozzles including the oscillation of the mould and the relative movement of the steel and the slag against the ceramic component. The same device has been used for the corrosion evaluation of the present materials. The main task of this work is to improve the thermal shock behaviour of zirconia based materials by keeping the corrosion resistance at least at the same level as in pure zirconia.The slip casting technique has been selected as the most suitable processing to disperse and incorporate homogeneously in the MgO partial stabilised zirconia matrix additional phases. Furthermore this forming process enables the manufacturing of thin wall components that are needed for near net shape casting technologies.A partial stabilised ZrO2 (3.5 wt% MgO)-powder (Unitec, M3.5) with a grain size distribution of 0–12 μm and d50=7.6 μm has been used as the main component. A higher densification was achieved by a zirconia powder of d50=2–3.5 μm. The grain size distribution of 0–12 μm has remained.There have been mixed different zirconia based slips of 70 wt% solids with 0.3 wt% electrolyte (related to solids); TiO2 (Bayer, Bayertitan-T) of d50=0.2 μm, Al2O3 (Martinswerk, CS400) of d50=2 μm and MgAl2O4 (Alcoa, AR78) of d50=3–4 μm have been homogeneously dispersed in different compositions as listed in Discs of 100×4 mm have been slip casted and sintered at 1600°C in an electrical furnace by sintering curves obtained due to dilatometer curves. The obtained microstructures have been characterised by scanning electron microscope (SEM) and electron dispersive X-ray (EDX) analysis. Due to X-ray diffraction (XRD) the zirconia phase composition (monoclinic, tetragonal and cubic) of the different materials has been measured. Further the monoclinic and tetragonal phase have been identified by transmission electron microscope (TEM) X-ray diffraction patterns.The characterisation has been completed through corrosion tests that have taken place in the special designed device as mentioned before. Specimens of 90×25×4 mm have been cut out of discs and placed in ceramic dyes based on MgO partial stabilised dense zirconia with 600 g steel St37 and 300 g slag (30 wt% SiO2, 30 wt% CaO, 10 wt% Al2O3, 5 wt% F−, 6–8 wt% Na2O–K2O, 10–12 wt% Ctotal) at 1550°C. The rotation (60 rotations through 90°/min) and the oscillation (lift10 mm, 60 oscillations/min) of the testing device have been tuned according to the conditions observed for conventional submerged nozzles during operation in steel plants. the materials III and IV achieved less open pores than the pure zirconia material II. the results of the XRD measurements are listed. Both pure materials I and II exhibit approximately the same amount of monoclinic, tetragonal and cubic phase. Through the addition of TiO2 and Al2O3 (material III) approximately the whole amount of the tetragonal phase has been transformed and the monoclinic phase has increased tremendously. The XRD analysis identified spinel (MgAl2O4) and no free Al2O3 or TiO2. It is assumed that TiO2 has been incorporated in the zirconia lattice and a part of the MgO stabilising agent has been removed from the zirconia cell and has reacted with the Al2O3 to give MgAl2O4. Through the loss of the stabilising agent martensitic phase transformation occurred. The Ti4+ cations, as mentioned in the introduction, were not randomly incorporated in the lattice but in preferred energetic sites which caused a repulsion between the dopant cations and the vacancies. The removal of the Mg2+ out of the lattice was followed by the energetically suitable formation of spinel with the free alumina. The Ti4+ cations did not stabilise the zirconia.Through the addition of MgAl2O4 instead of Al2O3 (material IV) no significant change of the monoclinic phase amount was observed. In this case no free MgO could be identified at the grain boundaries through EDX and XRD analysis and also the primary spinel has remained with the same amount of MgO (78 wt% Al2O3 and 22 wt% MgO). Further the material IV exhibit an increased amount of tetragonal precipitates. It is assumed that mechanical stress transformation of the cubic to the tetragonal phase occurred due to the spinel dispersed phase (lower thermal expansion coefficient than the cubic zirconia). a surface (not polished) of material I is presented. Tetragonal precipitates of 1 μm and microporosity of 2–5 μm appear in 5–15 μm cubic grains and at their grain boundaries. In a higher magnification () a nanoporous microstructure of the cubic phase can be observed. Similar tetragonal precipitates can be identified on the surface of material II but the micropores reach higher values, up to 10 μm. Material III is shown in . The tetragonal phase disappears and long sharp monoclinic twins are recognised and identified also by TEM X-ray diffraction patterns. During TEM sample preparation, in some crystals, tetragonal to monoclinic phase transformation occurred due to stresses resulting from ion thinning and electron beam heating. Further spinel phase is identified and the micropores of 10 μm disappear. In microcracks are recognised, starting in the region of the spinel phase and diverting at the monoclinic grains. When free alumina and magnesia are present together in a mix and heated, spinel formation occurs, causing a 5% volume expansion. This reaction starts approximately at 1000°C and is responsible for the microcrack formation of the material properties. Especially the thermal expansion coefficient and the young modulus are influenced strongly as it will be shown later.As discussed before no significant change of the monoclinic phase has been identified in material IV in comparison to I and II, . Tetragonal precipitates and spinel phase are observed in the cubic grains or at their boundaries. Apart from some individual tetragonal grains, the tetragonal phase appears more concentrated in groups of 20–40 precipitates in the cubic grains, ) material III reaches, at 1450°C, a thermal expansion coefficient of 5.5 10−6 K−1, approximately 50% reduced compared to the pure zirconia materials. Considering the remaining strengths of the thermal shocked specimens materials III and IV exhibit a very good thermal shock performance at a ΔT of 600°C in comparison to the pure materials I and II. In addition the fracture toughness of materials III and IV consisting of zirconia and spinel has been enhanced.In spite the fact, that with material III the lowest thermal expansion coefficient and young modulus of elasticity and in addition the highest remaining strengths were obtained, only material IV has survived a thermal shock attack due to an arc torch. In discs of material III and IV are presented after such a thermal shock attack. Material III failed after 90 s when a ΔT of 800°C (measured by thermocouples placed in the body of the discs) between the hot centre (spot of arc torch) and the outer area was achieved. In material IV microcracks are identified after the thermal shock attack, . These microcracks are observed at the spinel regions and are diverted at the tetragonal precipitates. This diversion caused martensitic phase transformation and the formation of monoclinic twins. A theory for stress induced tetragonal to monoclinic transformation of constrained zirconia is based on the assumption that when forcibly strained to a regime of absolute instability where the free energy density of the tetragonal phase has a negative curvature, the constrained tetragonal zirconia becomes unstable with respect to the development of a modulated strain pattern that will evolve into a band of twinned monoclinic domains.Both materials contain spinel as secondary phase, probably also as a diversion phase. The energy of the thermal shock cracks is muffled in material IV due to the martensitic phase transformation of tetragonal to monoclinic and in material III due to the existing microcracks (caused by the spinel formation and by the martensitic phase transformation) and the diversion at the monoclinic grains. At temperatures above the transformation temperature tetragonal to monoclinic the thermal shock resistance of material IV is impaired. The microcracks of material III caused by the martensitic phase transformation are cured partially but the microcracks caused by the spinel reaction remain and contribute to the thermal shock resistance at high temperatures (>1200°C).The thermal shock test of the remaining strengths exercised on four point bending strength specimens and the calculation of R1 or R2 thermal shock parameters as they are described by Hasselman, do not completely cover the thermal shock attack by an arc torch. In the case of the thermal shocked four point bending strength specimens a homogeneous heating and cooling over the surface is applied and thermal gradients are observed only across the depth. On the other hand the thermal shocked disc shapes by an arc torch present strong thermal gradients over the surface during heating and cooling down. Further, in case of the calculation of R1 and R2 parameters, the thermal expansion coefficient and the Young's modulus are considered as individual values measured at a specific temperature and no gradients are included. The thermal conductivity λ describes in R2 how “easily” heat can be transferred, but again no gradients are enclosed.The thermomechanical behaviour of the microstructure at elevated temperatures depends on the matrix material, secondary phases, pores with different sizes and distributions, inclusions, phase transformations, heat treatments etc. and is registered mainly due to the thermal hysteresis. In the thermal expansions during heating up and cooling down are listed. Material III exhibits a remarkable thermal hysteresis. At 900°C a thermal expansion coefficient of 5×10−6 K−1 is observed during heating up and at the same temperature during cooling down only a value 0.7×10−6 K−1 is measured. This difference is responsible for the failure of the disc based on material III. In spite of the higher values of the thermal expansion of material IV, the more linear behaviour of the thermal expansion accompanied by a higher amount of tetragonal metastable phase has led to a better thermal shock behaviour of the disc components. the results of the corrosion tests are listed. The corrosion mechanisms have been already illustrated in another work. Chemical destabilisation of the cubic and tetragonal grains occurs due to the diffusion of the Si and Na slag elements in the ZrO2 cell. Si removes the MgO stabilising agent and settles at the grain boundaries as magnesium silicate. Due to the removal of the stabilising agent, martensitic phase transformation takes place followed by volume expansion and microcracks. The microstructure loses its integrity and new paths for slag penetration are created. Material III presents the highest corrosion resistance at the interfaces ceramic/steel/slag and ceramic/air/slag in comparison to materials II and IV with approximately the same porosity. This improvement deals with the higher monoclinic amount of material III that cannot be destabilised.By the slip casting technique, zirconia dispersed materials have been developed with improved thermal shock and corrosion resistance performance.In spite the fact, that in both materials III and IV only zirconia and spinel can be identified due to XRD and EDX quantitative analysis, their thermomechanical properties are different. Material III consists of secondary spinel, formed during sintering of the reaction between free alumina and the removed (from the zirconia lattice) magnesia. This reaction is followed by a 5% volume expansion and the formation of microcracks. In addition, due to the loss of the stabilising agent, martensitic phase transformation occurs followed again by microcrack formation. The sum of the microcracks is responsible for the reduction of the thermal expansion coefficient in comparison to pure materials (approximately 50%).Material IV contains primary spinel and a much higher amount of tetragonal phase because of the fact that no stabilising agent has been removed from the zirconia cell. Further, the amount of the cubic phase has been decreased, probably due to mechanical stress transformation because of the spinel inclusions. Material III exhibits a very good thermal shock performance according to the water quenching tests because of the lowest thermal expansion coefficient and Young's modulus of elasticity. Further its microstructure consists of microcracks due to the spinel formation that remain also at high temperatures above 1200°C. On the other hand material IV with the modified thermal expansion coefficient (higher than that of material III) presents the best results of thermal shocked disc shapes by an arc torch. Material III has failed because of the highest thermal hysteresis. The thermal shock conditions of the application have to be studied very carefully before choosing the best available modification or a combination of both of them. In the literature, in order to achieve a zirconia based material with a good thermal shock performance at least an amount of 30 vol% monoclinic phase has been suggested. This composition offers a low thermal shock coefficient accompanied by an acceptable thermal hysteresis.Zirconia materials with high amounts of monoclinic phase (above 50 vol%) present high porosity levels followed by worse corrosion resistance and pour mechanical strengths. In this matter material III is produced due to an in situ phase transformation with approximately 55% monoclinic phase, porosity less than 18%, a very good corrosion resistance against steel/slag-systems and four point bending strengths at RT above 120 MPa. The microcracks that are caused due to the zirconia destabilisation are muffled by the microcracks out of the spinel formation. Both microcrack patterns are overlapped and lead to sufficient mechanical strengths at RT.The thermal hysteresis registers the influence of pores, inclusions, secondary phases, heat treatments etc. The R1 and R2 thermal shock parameters have to be modified and include also this information (of the hysteresis curve) due to a definition of a linearity factor related to the maximum difference of the thermal expansion at the same temperature during heating up and cooling down.The MgO–Al2O3 binary system opens for the Mg–PSZ based materials the horizon of tailoring their thermomechanical properties for applications in near net shape steel processings through toughening mechanisms, whereby the amount of TiO2 addition can control the rate of the formation of MgAl2O4 and the stabilising level.Last but not least the ionic and electronic conductivity of materials III and IV have to be studied according to the contribution of MgAl2O4 defect structures and the TiO2 semiconductor properties to new oxygen sensor approaches.A tool to predict the evolution of phase and Young’s modulus in high entropy alloys using artificial neural networkWe report an artificial neural network (ANN) based tool to predict the evolution of phase(s) in high entropy alloys (HEAs) and their Young’s modulus. Two independent networks as single channel output and four channel binary output methods have been adopted for testing as well as for predicting the evolution of either single-phase BCC, FCC solid solution (SS) phase, or a mixture of SS phase(s) and intermetallic compound (IM). The data of as-solidified HEAs were collected from the literature, and various thermo-physical as well as electronic parameters, such as mixing entropy (ΔSmix), mixing enthalpy (ΔHmix), atomic size difference (δr), Allen electronegativity ΔχA, Pauling electronegativity (ΔχP), and valence electron concentration (VEC) were calculated for each alloy composition, which was used as input features. The Bayesian regularization backpropagation has been adopted as the learning algorithm. Furthermore, the model has been trained and validated by developing eutectic CoCrFeNiNbx (x = 0.45, 0.5, 0.55 and 0.65) and CoCrFeNiTay (y = 0.2, 0.4, 0.455 and 0.5) HEAs experimentally. The single channel output approach and four channel binary output approach generate the matching accuracy of 85.95% and 92.97% for the main dataset, where the same is 70.83% and 91.67% for the deployment dataset, respectively for phase prediction. The predicted values of Young’s modulus have achieved the relative accuracy of 94.96% and 96.44% for the main and deployment dataset, respectively. The ANN suggests that VEC
becomes the dominant factor for phase stability when δr < 3%, whereas the higher value of δr promotes the evolution of two phases in HEAs.High entropy alloys (HEAs) or multi-principal element alloys have gained a deep interest among material engineers due to their exceptional ability to retain a combination of different mechanical properties at room temperature and at elevated temperatures Several efforts have been made earlier to predict the evolution of a single SS phase or a mixture of phases in HEAs Artificial intelligence with ANN base methods are powerful tools for predicting and exploring the refined relationships between the composition and engineering properties of materials. In past years, the ANN based machine learning tools have been extensively used in materials research due to computer-aided design and the backpropagation artificial neural network (BP-ANN) technology In this work, ANN based models have been developed to predict the evolution of phases and E values of HEAs. The machine learning based ANN method can summarize the hidden rules from the prevailing experimental data by simulating neurological interconnections of neurons in the brain to learn the external environment and deal with a complex non-linear relationship between inputs and outputs. The major objectives include developing artificial neural network models that can mimic the real-world non-linear relationship between thermodynamic, physical, and electronic features with the microstructure and mechanical performance of the as-cast HEAs.Nominal compositions of CoCrFeNiNbx (x = 0.45, 0.5, 0.55 and 0.65) and CoCrFeNiTay (y = 0.2, 0.4, 0.455 and 0.5) were prepared by arc melting of Co, Cr, Fe, Ni, Ta and Nb purity above 99.99 wt% in a Ti-gettered high purity argon atmosphere. The as- solidified ingot was obtained by cooling the melt into the shape of a button in a water-cooled Cu hearth. The ingots were remelted three times to maintain the chemical homogeneity. Phase identification of the samples was done by Philips PANalytical X-ray diffraction (XRD) unit (PW3373, Netherlands) having Cu-Kα radiation. Microstructural characterization was performed by ZEISS EVO60 scanning electron microscope (SEM, Germany) at 20 kV. The composition of the alloy phases was analyzed using an Oxford ISIS300 energy dispersive spectrometry (EDS).The neural network modeling and simulation procedures were implemented through the following steps: (i) data collection and pre-processing of the collected dataset, (ii) neural network architecture, (iii) neural network training and testing, and (iv) predictive simulations using the trained neural network models.Artificial intelligence (AI) is an expert system, which simulates human intelligence-like processes by machines or computer systems shows the artificial neural cell model comprised of the weight of input features, addition and activation function, and output. The value of the input (xi) features is collected from literature, and the weight (wij) establishes the effect of these input features in an ANN. The net input in a neural network was evaluated from an addition function (netj) as per Eq. where xi is the ith input feature, wij is the connection weight from jth element to ith element,
θj is the “-ve” threshold polarization value, and n is the highest input features sent to the previous layer. Generally, a sigmoidal function is commonly used as an activation function in ANN, combines all the behavior, including linear, curvilinear, and near constant behaviors The artificial neuron output (yj) value relies on the designated activation function, which employs a sigmoid function. The ANN output sends via the network connections as follows In case of multiple parallel processing artificial neuron cells, a feed-forward multi-layer perceptron may be used for engineering applications.Two different sets of data with 209 and 140 numbers of HEAs were collected for phase prediction and determination of E value, respectively. The data of the chosen HEA compositions ranging between quaternary and nonary were collected from the literature, and experimental data were generated to create and to train the multilayer feed-forward networks for prediction of the evolved phase(s) and E, respectively. The limited information of E has restricted the selection of 140 numbers of HEA compositions. shows the classification of collected data sets into the main dataset and the deployment dataset. The majority of the data were used in the main dataset than that of the deployed dataset. The main dataset is further classified into the training set, the validation set, and the testing set as 70%, 15%, and 15% of the total, respectively, in our ANN model. In the present study, the chosen HEAs were synthesized by arc-melting and exhibited either FCC, BCC, FCC + BCC, FCC + IM, or BCC + IM phases, assuming that the obtained data from the literature are correct and reliable. The precision of the input data does not change the methodology of the ANN analysis, but it may affect the results, as the ANN would learn the incorrect details due to incorporate noise and its learned weights. Therefore, the collected dataset was first sorted and then checked so that neither any HEA composition is repeated nor any data is duplicated, which, if present, may risk overfitting, as the network would observe repetitive samples in the same epoch.Various thermo-physical and electronic features such as, ΔSmix, ΔHmix, δr, Ω, ΔχA, ΔχP and VEC were calculated for the collected alloy dataset (). The influence of the following parameters was grouped for training and testing data considering for the prediction and simulation using ANNs forecast models as in Eq. (3)-(9) where ci and cj are the molar fraction of the ith and jth element, respectively, n is the number of elements in an alloy system. ri is the atomic radius of the ith element, Ωij=4ΔHmixij, where ΔHmixij is the mixing enthalpy of the binary alloys, and r-=∑i=1nciri is the average atomic radius. VECi is the valence electron concentration of ith element. Tm is the melting temperature of the alloy. The Tm value can be calculated by taking the weighted average of the melting temperature of individual elements. Although, the differential thermal analysis (DTA) is a widely used technique to measure Tm; but very limited experimental values of the melting temperature have been reported for HEAs. The χiP and χiA are Pauling and Allen electronegativity of ith element, respectively. χ-=∑ciχiPand χa=∑ciχiA are the average Pauling and Allen electronegativity, respectively. The authors have built functions for each feature (ΔSmix, ΔHmix, δr, Ω, ΔχA, ΔχP, and VEC) using Matlab 2020b for user simplicity that returns the respective values of the features The predicted phase(s) were classified into 5 types, such as, BCC, FCC, FCC + BCC, BCC + IM and FCC + IM. Among 209 numbers of HEAs, 24 were kept completely separated for later testing once the network was deployed in the field and henceforth will be termed as deployment dataset. The remaining 185 samples were used to train the neurons to understand the correlation of the multivariate data samples. (a) shows the classified grouped sample distribution as a two-dimensional scatter matrix plot. The relative correlation between the features can be observed along with a few outliers, which may appear as noise. The diagonal entries of the matrix plots show the histogram of the grouped classes among the data samples.Furthermore, 12 out of 140 numbers of all HEA sample data were kept apart as deployment datasets for testing later once the ANN deployed in the field to predict the E values. Therefore, a total of 128 samples were used for the training, validation, and testing of the neurons. The data analysis begins by calculating the Pearson correlation coefficient P(b). Here, the reflectional symmetry is shown along the main diagonal in the matrix. The P ranges between −1 and 1, where “1” denotes the strong positive correlation and P = “−1” denotes a strong negative correlation and 0, denoting no correlation. The absence of any significant correlation amid any pair of features indicates that all metrics should be taken in the ANN model.ANNs are described as a wide variety of models with interlaced structures of computational neurons. In the present study, a network model has been developed by using BP ANN, that primarily composed of (i) identification of suitable input features as an important hyperparameter, (ii) determination of the number of neurons and the hidden layers, (iii) choice of the proper cost function, and (iv) choice of efficient BP algorithm (a) and 4(b). The input features, such as ΔSmix, ΔHmix, δr, ΔχA, ΔχP, and VEC were chosen out of the plethora of thermodynamic, physical, and electronic parameters, as shown in (a) and 4(b). The hidden layer size is one of the crucial hyperparameters for the network performance, which was fine-tuned iteratively, taking various combinations of neurons and their numbers to assess the potency of the overall network. The selection of the proper number of hidden layers and the neurons are equally important for obtaining a good fit for the network. Furthermore, the mean squared error (MSE) has been chosen as the cost function.Two different approaches were considered for the choice of the output as (i) single channel output approach (SCOA) having values mapped with each of the five combinations of phases, i.e., single-phase BCC, single-phase FCC, FCC + BCC, BCC + IM and FCC + IM. (ii) The second approach involves four channel binary output approach (FCBOA), i.e., a combination of the classified phase distributions. (a) shows the ANN model for single channel phase prediction and prediction of the E values. The second approach involves the binary output channel, as illustrated in (b). In the present study, the number of channels optimized by the output value, as the number of output channels increases with the number of possible states, i.e., 2x number of possible states can be considered for x number of binary output channels, which increases the chances of scattered values in the final result.The output layer depends on the respective output parameters. In the case of Young’s modulus, the output parameter returns a single value. Whereas, numerical values were assigned to represent individual cases of phase prediction to train the network. Initially, a single channel output was selected, which returns −2, −1, 0, 1, or 2 representing BCC + IM, single-phase BCC, FCC + BCC, single-phase FCC, and FCC + IM, respectively, as shown in . The second ANN model was designed to return the binary values, which is less prone to shift the prediction. As discussed above, 4 numbers of binary channel output were selected and were mapped the 5 different cases with 4-bit combination, as shown in . The Bayesian regularization BP algorithm has been selected for the present study by comparing the general performance of standard Gradient Descent (GD), Scaled Conjugate Gradient Descent (SCG), Levenberg- Marquardt (LM), and Bayesian regularization (BR) on the deployment dataset, as BR shows the least amount of overfitting. Furthermore, BR also adjusts the weights and bias of the ANN considering the relevance of the input features for the prediction The multilayer feed-forward neural-network was used for the training and prediction using MATLAB 2020b software package (a) and 5(c) show the plots exhibiting the MSE variation of the ANN throughout the learning process for phase prediction using SCOA and FCBOA, respectively. At the beginning of the learning process, there is a sharp decline in the MSE for all the training, validation, and testing datasets, indicating the effectiveness of the training process. Subsequently, the MSE for validation and testing datasets ceases its steady decline and then becomes relatively constant, whereas the MSE for the training set keeps on declining. Such feature indicates that the best fit for the ANN model is in close proximity. After a few epochs, it has been observed that the MSE for validation and testing datasets rises, whereas, for the training set, it continues its decline. As the validation and testing datasets are not involved in the learning process, they can be taken as a substitute for a real-world unknown data, and their performance indicates the generalization of the ANN model. Hence, such rise in the MSE for validation and testing set can be understood as the model being overfitted. Thus, the training process is pushed to an early stop. The point where the MSE value for the validation dataset reaches to minimum, i.e., prior to the early-stop (epoch = 76), which is considered the best fit for the model.The final training state plots for the SCOA and FCBOA are shown in (b) and 5(d), respectively. The training state plots show the variation of the parameter gradient, mu, gamk, ssX, and val fail. The gradient parameter represents the backpropagation performance gradient of the model. Mu/Momentum is the control parameter for the training algorithm and is dependent on the maximum Eigenvalue of the input correlation matrix, which approximates the inverse of the Hessian matrix. gamk denotes the effective number of coefficients. Sum squared error of the model is represented by the parameter ssX. Vail fails parameters show the total validation fails incurred in the learning process and are reset every time the validation passes after consecutive fails. The maximum number of validation failure was set to be 20, which means after 20 consecutive validation fails, early-stop conditions will be imposed over the model. Similar considerations were adopted in the ANN for the prediction of the E value, as depicted in (a) and 6(b). Here, the maximum number of the validation failure was set to be 15 to stop the iteration.The SEM back scattered electron (BSE) image of CoCrFeNiNbx (x = 0.45, 0.5) and CoCrFeNiTay (y = 0.4, 0.5) are shown through (a)-(d), correspondingly. The XRD pattern of CoCrFeNiTa0.5 is shown in inset of pointing the presence of the FCC and C14 [JCPDS #00–015-0039, Pearson symbol: hP12] Laves phase. The SEM and EDS analysis confirm the presence of FCC SS and intermetallic C14-type Laves phase in all the alloys irrespective of addition of Nb or Ta. The microstructure varies from hypo-eutectic (x = 0.45 and y = 0.2), fully eutectic (x = 0.5 and y = 0.4) to hyper-eutectic (x = 0.65 and y = 0.5) microstructure The various thermo-physical and electronic features such as, ΔSmix, ΔHmix, δr, Ω, ΔχAVEC and ΔχP are proposed to predict the evolution of a single SS or two phases in HEAs where x‾i and σ(xi) are the mean deviation and standard deviation of the input feature xi. The min–max normalization technique can preserve the exact relationship of the feature data. The Z-score normalization technique can reduce the effect of outliers significantly (a) and 8(b) show the regression plot for the main and deployment datasets, respectively, using the SCOA. Similarly, (c) and 8(d) show the regression plot for the main and deployment datasets using the FCBOA, respectively. The regression plots represent the linear fit between the target and output values and also show the scattered output values for a specific target. The main dataset and deployment dataset’s output was fitted as 0.94 × Target+(−0.027) and 0.95 × Target + 0.17, respectively, for the SCOA, as shown in (a) and 8(b). The output in the main dataset and deployment dataset were fitted as 0.92 × Target + 0.047 and 0.94 × Target + 0.021, respectively, in case of FCBOA, as in (c) and 8(d). The trained network was then used to generate the output for each HEAs, as available in the main dataset and deployment dataset by adopting both approaches., to classify the unassigned integers into the relevant phase classes. Similar improvisation has been adopted for the FCBOA, and the improvised mapping table is shown in The phases are predicted by considering the rounded-off output values for both the trained networks using these improvised mapping tables. shows the experimentally observed phases and the predicted phases for both the methods for each alloy, as available in the deployment set only. shows the predicted phases for all the alloys, as available in the main and deployment dataset. In the main dataset, 159 out of 185 predictions match using SCOA, whereas 172 out of 185 predictions match using FCBOA, pointing an accuracy of 85.95% and 92.97%, respectively. On the other hand, in the deployment dataset, 17 out of 24 predictions using SCOA and 22 out of 24 predictions using FCBOA match, pointing the prediction accuracy of 70.83% and 91.67%, respectively. The obtained results show a higher prediction efficiency and generalization of the FCBOA than that of SCOA. Additionally, two statistical identifiers were used to analyze the network performance as follows r=∑i=1nyt-y‾tyt'-y‾t′∑i=1nyt-y‾t2∑i=1nyt'-y‾t′2where yt and y't are the experimentally observed target and ANN output values, respectively. The parameter r is the correlation coefficient, which shows the correlation between yt and y't, whereas R2 represents the quality of the fit. The value of both the parameters r and R2 lies within the range of 0 and 1. The value of r and R2 are 0.9317, 0.8655 for the main dataset, and 0.8883, 0.7803 for the deployment dataset, respectively, for SCOA. Whereas, the value of r and R2 as 0.9147 and 0.9051 for the main dataset and 0.9416, 0.9327 for the deployment dataset, respectively, in the case of FCBOA. Therefore, FCBOA provides a better fit for the deployment dataset whereas, both the ANNs provide a good fit for the main dataset.The relevance of the individual thermo-physical and electronic features with the phase prediction is assessed by matching the predictions with the targets while sequentially dropping one input feature once at a time. Such a drop in the feature leads to the corresponding drop in prediction accuracy, which indicates the importance of the respective input feature. The importance of the input features is shown in (c) and (d) for SCOA and FCBOA, respectively. The three rows in both the plots indicate the feature importance for the main dataset, total dataset, and deployment dataset. In the case of SCOA, the most important and the least important input features are VEC and Ω, respectively, as depicted in (c). Whereas, δr and Ω are the most important and least important input features for FCBOA, respectively, as depicted in (d). The developed ANN shows the importance of VEC
and δr on the evolution of phase stability, which was also studied by the authors earlier Initially, both the normalization techniques were used iteratively for training the network to predict the E values. Since the min–max normalization has demonstrated the best accuracy, the same was finally adopted for the prediction. All the real E values are distributed over a wide range; thus, these values were also normalized using the min–max technique. The normalized values of the E were stored in the main dataset, which was used later to normalize the input features of the deployment dataset and recalculate the E values for both the datasets. The regression plot for the main and deployment dataset are shown in (a) and 10(b) pointing to a good linear fit for both the datasets. The output for the main dataset and deployment dataset were fitted as 0.9 × Target + 18 and 1 × Target+(-0.19), respectively, as shown in (a) and 10(b). The trained network is then used to predict the E values for both datasets. The normalized output was then transformed back into the real value using previously-stored E values in the main dataset. The experimental and predicted E values are shown in (c) and 10(d) for the main and the deployment dataset, respectively, along with the relative error percentage for individual alloy as bar plots. The predicted values (EANN) were close to the experimentally measured values (Eexp), as shown in . Relevant E prediction data for both datasets are provided in . An additional statistical identifier, i.e., mean average relative error (MAPE), is used along with r and R2 to assess the training efficiency for the prediction as follows where MAPE equals to 0 in an ideal case. In practice, the lowest value of MAPE indicates the goodness of the fit. The value of r and R2 are 0.9424 and 0.9934 for the main dataset and r = 0.9825 and R2 = 0.9986 for the deployment datasets, respectively. Whereas, the MAPE value is 5.54% for the main dataset and 3.56% for the deployment dataset showing an average relative accuracy (100-MAPE(%)) of 94.46% and 96.44% for the respective datasets. Therefore, the value of r, R2 and MAPE parameters indicate an exceptionally good fit, good performance of the network prediction and generalization of the trained network.The relative importance of the individual input feature has been assessed by dropping them individually and by retraining the network. The effect of the drop of each input feature on the output value is represented in error percentage, as is shown in (e). It has been noticed that VEC and Ω are the most and the least important input features for the prediction of the E values, as shown in (e). Besides using the Pearson correlation and sequential feature selection, Penalized Linear Regression (both L1 and L2, which are also known as Lasso and Ridge regression, respectively) has been analysed. It has been observed that the feature importance is in good resemblance with our sequential approach as shown in ANN based tools have been developed to predict the phase evolution in HEAs and explore a refined relationship between the composition, thermo-physical parameters, and electronic parameters, microstructure, and Young’s modulus. The following conclusions have been drawn from the present study:The two independent ANN tools based on SCOA and FCBOA have been developed for training, testing, and prediction of the evolution of single-phase BCC, single-phase FCC, FCC + BCC, BCC + IM, or FCC + IM phases. The matching accuracy using SCOA and FCBOA are 85.95% and 92.97% for the main dataset and 70.83% and 91.67% for the deployment dataset, respectively. The FCBOA shows better accuracy and generalization than that of SCOA for phase prediction.A SCOA base ANN tool has been developed for network training and predicting the E values of HEAs. A high relative accuracy of 94.46% and 96.44% was achieved for the main and deployment datasets, respectively.Assessment on the importance of the input features, i.e., ΔSmix, ΔHmix, δr, Ω, ΔχA, ΔχP, and VEC have been performed by dropping them individually for re-training the model and re-evaluation of the performance. The VEC and Ω were identified as the most and the least important features, respectively, during phase prediction using SCOA. Whereas, δr and Ω were identified as the most and least important features, respectively, during phase prediction using FCBOA. In the case of prediction of Young’s modulus, VEC and Ω were identified as the most and least important features, respectively.The ANN tools were validated experimentally by developing CoCrFeNi(Nbx/Tay) HEAs, and their data have been incorporated in both the main dataset for network training as well as in the deployment dataset for network testing. The ANN has predicted the evolution phase(s) in experimented HEAs to be FCC + IM as output. In addition, Young’s modulus values of developed HEAs have been predicted with good accuracy with minimal error (%) in the range of 2.32–2.87%.Barnasree Chanda: Investigation, Methodology, Data curation, Formal analysis, Writing - original draft. Parijat P. Jana: Investigation, Data curation. Jayanta Das: Conceptualization, Methodology, Funding acquisition, Supervision.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Supplementary data to this article can be found online at The following are the Supplementary data to this article:Effects of constrained groove pressing, severe shot peening and ultrasonic nanocrystal surface modification on microstructure and mechanical behavior of S500MC high strength low alloy automotive steelS500MC high strength low alloy automotive steel is exposed to bulk severe plastic deformation (SPD) via constrained groove pressing (CGP) and surface severe plastic deformation (S2PD) via severe shot peening (SSP) and ultrasonic nanocrystal surface modification (UNSM). SSP and UNSM could create a nanocrystallization layer till 50–100 µm away from outmost surface. EBSD investigations showed average nano-grain size obtained via SSP and UNSM was found to be below 100 nm regime. The strength was improved via 1st to 4th pass of CGP, but elongation percentage decreased abruptly. UNSM achieves both strength-ductility improvement with gradient structure. SSP improves the total elongation however a slight decrease on strength is observed. SSP and UNSM showed better wear and friction resistance particularly at lower loads compared to CGP and untreated specimens. Nevertheless, wear and friction behavior at higher loads showed better responses for Bulk-SPD applications regardless of pass numbers. The frictional load increase played a detrimental role in removing a nanocrystallization surface layer and diminishing the positive influence of SSP and UNSM.S500MC high strength low alloy (HSLA) steels are selected for automotive, transport and offshore applications for high strength, effective weldability and limited carbon content Grain size is a crucial microstructural factor for determining physical and mechanical properties of metallic materials The literature studies presented the tensile and yield strength of the treated materials up to two times has been accomplished within the nano-regime grain size. CGP is applied to the materials like aluminum, copper, magnesium, Al-Cu, Al-Mg and Cu-Zn alloys due to the lower strength and high ductility. Since the press forces could only be able to achieve the process effectively for these alloys. In recent years, some scientists tried to apply the bulk and S2PD processes to low carbon steel owes the lowest strength-hardness capacity among iron based structural alloys SPD processes are not only used for grain refinement in bulk materials, but also applied to the surfaces to form a nanocrystalline layer having a depth of several microns at the surface materials. The SPD for surface nanocrystallization is named as surface severe plastic deformation (S2PD) methodology. Severe shot peening (SSP) performed by enhanced shot peening parameters UNSM is a novel surface modification process for improving the wear, corrosion and fatigue resistance via deeper plastically deformed layer with precisely controlled surface roughness and integrity The goal of this study is to compare the S2PD processes SSP and UNSM with one another CGP of bulk SPD process in terms of the mechanical and tribological properties of HSLA S500MC steel. To this end S500MC sheet metal specimens were subjected to UNSM, SSP and CGP processes. Tensile, micro-hardness and wear tests were performed on the untreated and treated specimens. For microstructural investigations optical microscopy (OM), scanning electron microscopy with electron back scatter diffraction (SEM-EBSD) and X-ray diffraction analysis (XRD) were carried out. Grain refinement and distributions based on bulk and S2PD were comparatively investigated.Material used in this work is commercial S500MC steel plate (3 mm in thickness) with the chemical composition of 0.12C, 0.50Si, 1.7 Mn, 0.025P, 0.015 S, 0.015 Al, 0.09 Nb, 0.15 Ti, 0.20 V and balance Fe (wt.%). The steel has quite fine microstructure with ultra-fine particle sized precipitations due to the stages of thermomechanical progress. The steel is used for intrinsic shapes and geometries particularly selected for automotive industries UNSM is an effective mechanical surface treatment for surface nanocrystallization with considerable surface roughness. UNSM is an economic, simple and appropriate method for producing various machine components by using ultrasonic vibrations a. The WC tip diameter is 2.38 mm and frequency of strikes is 20 kHz. The average distance of two sequential impact route is 70 µm. UNSM treatment parameters are listed in SSP is a modified version of the commercially available shot peening process that has long been used to increase fatigue life by inducing compressive residual stress on the material surface b. The SSP is performed by increased peening parameters that causes higher energy impacts and increased plastic strain could be obtained on the material surface. Repeated high energy impacts of SSP lead to reorder dislocations and twins, consequently new grain boundaries and ultrafine grains occurs from surface through a depth of several microns . Four successful CGP passes performed on S500MC steel specimens with the use of rubber pad between the samples and dies. Without using any rubber-pad, the sharp corners of groove die cause damage on specimen and only one pass could be applied. Four passes CGPed specimen is also seen in For microstructural characterization specimens were cut from each series of samples and mounted in resin. The specimens were polished with 180–2500 grid SiC sandpapers then polished with polycrystalline diamond suspensions. Polished specimens etched with 5 ml nitric acid and 100 ml ethyl alcohol solution, wiped to specimen with tissue and washed with ethyl alcohol. OM characterizations were conducted with Nikon Eclipse Ma100. EBSD analysis was carried out using an Oxford, Nordlys EBSD detector in TESCAN MAIA3 XMU SEM. XRD was performed by RIGAKU Smartlab X-ray diffractometer at a voltage of 40 kV and current of 30 mA.Micro-hardness measurements are performed on the polished specimens using a Qness Q10M hardness tester. Test condition is HV0,02 of Vickers hardness with a static load of 20 gf and a dwell time of 15 s. Indentations were conducted with 200 µm depth from surface at specimens which were surface treated and 300 µm depth at CGP treated specimen. Tensile tests were carried out using Instron Satec™ DX universal tension and compression testing machine operating at a constant test speed of 5 mm/min at room temperature. Tensile test specimens (shown in b) were manufactured with the dimensions of 110x15x3 mm according to the TS EN ISO 6892. The geometry and dimensions had been determined and the test specimens were initially manufactured to preserve the influence of the whole treatments and prevent any machining effect on the surface.Wear and frictional behavior of the treated specimens was investigated by reciprocating tribometer tester under the conditions of dry sliding with a 6 mm diameter WC ball at 5 N, 10 N and 15 N. The tests are employed with a sliding speed of 8 cm/s through a linear path of 12 mm for a total distance of 500 m sliding distance. The volume loss was approximately evaluated by the multiplication of wear probe stroke (linear path), track width and track depth. The wear stroke was constant as 12 mm for the whole specimens. The wear track width and depth were measured by optical profilometer for each 0.5 mm of throughout the path and the arithmetic mean of the width and depth were obtained.The as received state of the steel was as rolled and the initial microstructure before treatments was observed in a. The microstructure is composed of majorly ferrite involved small amount percentage of pearlite. The microstructures of 1–4 passes CGP treated S500MC steel sheet are shown in b to 4e. Although it is impossible to make exact interpretation about grain size of specimen by OM, grain size reduction is evidently seen through four passes of CGP treated samples. The microstructure observed from OM is homogenous. CGP is applied significantly to the S500MC sheets. The production of homogenous grain refinement is one of the purpose of the study since the work is led the CGP field due to the selection of a high strength low alloy S500MC steel has a very fine grained with ultrafined-nano sized precipitations . The grain boundary is hardly distinguished due to owing quite fine grained (average grain size is 3.7 µm of the untreated specimens) of structure (a). It becomes much harder when grain refinement procedure is completed (Due to ultra fine-grained structure of 1 pass, grain boundaries are almost indistinguishable (b). Distinguishing grain boundaries is getting much harder in further CGP passes (OM observations of the UNSM and SSP treated specimens are shown in a and 5b, respectively. Effects of peening treatments are clearly seen from the surface morphology of the specimens. While the UNSM treated surface has smooth surface and SSP treated one has much more deteriorated. UNSM and SSP deform certain layer on and sub-surface with the thickness of approximately 60 µm and 20 µm, respectively. The operations have distinguishable characteristics due to the operating pre-conditions. The SSP uses high velocity kinetic energy to deform the surface plastically, on the contrary, UNSM uses a high vibration energy. The SSP gathers the influence substantially on the surface, but UNSM distributes the deformation through interior. Amanov et al. emphasized the UNSM distributes the influence through the interior homogenously, therefore it could be able to prevent probable crack initiation on the sub-surface. The fatigue improvement is remarkable accordingly compared to SSP EBSD analysis of CGP, SSP and UNSM treated specimens are employed for more detailed investigations on grain size and distributions given in , grain size reduction is clearly seen between the as received (a) and one-four passes of the CGP treated specimens (b, 6c, 6d and 6e). The grain size of the as received specimen presents a homogenous distribution (a) with an average grain size of 3.7 µm (). The S500MC steel is a product of thermo-mechanical process and owes a very fine-grained structure. However, the application of 2 passes, emerges non-homogenous distribution of grains. The distribution of grains moves through left of the fraction-grain size diagrams (c, 7d). The average grain size is reduced to 1.4 µm, 1.4 µm, 1.3 µm and 1.2 µm for 1 pass, 2 passes, 3 passes and finally 4 passes, respectively (). After 4 passes, the grain refinement is dominant throughout the microstructure and densifies predominantly on the left side of distribution bar graph. Many studies have shown that fine grained materials exhibit better mechanical properties due to the increase of grain boundaries EBSD image of SSP and UNSM treated specimens are shown in a and 8b, respectively. As can be seen from the figure that the original grain boundaries could no longer be observed due to the large amount of accumulated plastic strain by plastic deformation. The alterations in the microstructure of SSP and UNSM treated specimens according to depth from surface suggest that the deformation depth is quite compatible with the OM observations. SSP and UNSM achieve an effective grain reduction on the surface. According to the , approximately 98% percent of the grains owe the size down from 500 nm. 85% of the finer grains are less than 200 nm. The average grain sizes for SSP and UNSM are 0.14 and 0.16 µm, respectively. The nanocrystallization layer could not be observed by EBSD due to the lack of the indexing Kikuchi patterns The properties of nanocrystalline materials processed by SPD methods are highly correlated with particle sizes, therefore the characterization of the microstructure of NC materials is of great importance. Transmission electron microscopy (TEM) and XRD investigations are two effective methods for determining the grain size. TEM enables to characterize the cell structure, dislocation density and low-density stacking faults. Moreover, XRD analysis could be performed in within different gradients and allows us to obtain various results for bulk material gradients shows the XRD patterns acquired from whole treated specimens. After all SPD process, remarkable changes were observed. It is obvious that remarkably decrease of diffraction peak intensity of the SSP, UNSM treated and one to four passes CGP specimens reveal full width at half maximum (FWHM) of diffraction peak broadened compared to that of as received specimen. The decrease of the diffraction peaks is attributed to the grain refinement and increased crystal lattice distortions . It is seen that one pass CGP treated specimens, FWHM distinctly increased with compared to as received one. With the increasing of CGP pass, FWHM continued to increase with small amounts. The highest FWHM belongs to SSP treated specimens with compared to all other specimens. The peak shift on (2 1 1) peak is attributed to distinctive phenomena. The most common reason is chemical change or solid solution occurrence with providing new additions. However, the methods mentioned in the study have no chemical or new additional alterations. The shift is attributed to tensile/compressive residual stress and crystallite size orientations due to plastic deformation FWHM change is attributed to crystallite size orientations, strain deformations, dislocation density increase, and grain size variance. The results by changing FWHM demonstrate the hardness, residual stress, and grain refinement alterations.Tensile test results of SSP, UNSM and CGP treated specimens are shown in . A slight decrease can be observed on the yield and tensile strength of SSP treated specimen compared to the as received one, however, increased tensile elongation obtained. UNSM treated specimens exhibited clear increase on the tensile strength and in addition significant increase acquired on elongation. Tensile and yield strength of as received and 1–4 passes CGP specimens are shown in a bar graph of . Improvement can be seen on yield and tensile strength of CGP treated specimens compared to as received one. The highest yield and tensile strength values exhibited by 3 passes CGP specimens are 677 MPa and 714 MPa, respectively. The whole CGP processes contribute the strength improvement regardless of the number of pass. Some studies reported increased yield-tensile strength The CGP process achieves the improvement of hardness particularly through interior. Since the agglomeration of plastic deformation is occurred through interior. Although the CGP process ensured the hardness improvement on the steel, hardening relaxation was observed only on the pressed surface (). The phenomena could be clarified by using a rubber between the upper die and specimens to prevent microcracks on the surface during the initial contact. After a certain point, the hardness reaches its highest value. Unique pass remains a value of 248 HV, on the contrary the hardness is raised to 265 HV for 2, 3, and 4 passes, respectively. The core hardness of all CGP specimens are shown in a. Core hardness of as received and 1–4 passes of CGP specimens are 248, 264, 263 and 263 HV, respectively. No significant change was observed on core hardness of unique pass CGP specimens compared to untreated specimen and a slight increase can be seen in 2, 3 and 4 passes. Besides, SSP and UNSM contribute the surface hardness up to 280 HV and 295 HV, respectively (b). The surface SPD shows a better response on the surface compared to CGP (b). The core hardness is reached at approximately 125 µm away from the surface for SSP specimens however, UNSM effect is substantially vanished and the core hardness is observed at a depth of 200 µm. The grain size reduction (also illustrated by FWHM analysis) reveals a positive influence on hardness change. The effective change in surface hardness (SSP) reveals the widest FWHM. The UNSM and as received hardness are compatible with their FWHM values. On the contrary, the CGP specimens’ accuracy for FWHM-hardness is lower due to the usage of rubber pad between the die and specimens (). Two mechanisms are mainly observed as “grain refinement” and “deformed zone” via surface-based deformations. Both zones ensure effective hardness and strength. UNSM enhances the surface hardness, provide nanocrystallization and leads to diffuse the plastic deformation through interior and contribute thicker deformed layer (b). However, SSP gathered the kinetic energy completely on the surface, therefore grain refinement and nanocrystallization were performed majorly on the surface. Therefore, hardening capability remains beneath UNSM through the core structure. shows the friction behavior of CGP, SSP and UNSM treated specimens as a function of sliding distance under different loads of 5 N, 10 N, and 15 N. For the loading condition of 5 N, the untreated specimen shows higher friction coefficient among all specimens with an average value of 0.46. SSP and UNSM exhibited a lower friction coefficient against untreated and CGP treated ones. The average friction coefficients of SSP and UNSM are closer to each other with the values of 0.40 and 0.42, respectively. However, SSP exhibited better response for the initial stage of the test. The EBSD investigations revealed that SSP demonstrated its whole capability on the surface. On the contrary, UNSM kept the sustainability throughout the interior. Therefore, the SSP is more effective than UNSM at the initial stage but the effect is lightly vanished after the sliding distance of 300 m. For CGP process, the average friction coefficients of all CGP specimens are lower than untreated specimen and exhibits close average friction coefficients.For the loading condition of 10 N, the behavior of the specimens against friction was changed. SSP dominates the friction and reduces the average coefficient of friction (0.39) with increasing the load. However, UNSM loses the dominant capability shown in the loading condition of 5 N. UNSM reveals inefficacious counteraction as a contrary to expectations for the initial stages of the distance (until 200 m). The unexpected phenomena could be expressed with the instantaneous and short time interaction of the micro-channels with the tip of the wear probe. Nevertheless, UNSM clears up and raises the behavior and resistance against friction after the sliding distance of 300 m. In general, the higher frictional coefficient for the entire sliding distances goes to untreated specimens. Partial raisings could also be observed for CGP treated specimens particularly at the initial stages. The exceptional situation is also supported with the microhardness results from surface through interior for CGP specimens. The hardness diminishes due to the usage of rubber as a supporter between upper die and specimen for preventing the initial contact and thus occurring micro pre-cracks. However, the average frictional coefficients of 1st, 2nd, 3rd, and 4th CGP specimens is lower throughout the entire distance compared to untreated one. The CGP behavior against friction for the initial and towards to the end sliding distance effectively raised and become comparable to SSP and UNSM with increasing the load.For the loading condition of 15 N, 2 and 4 passes of CGP and SSP presented the most penetrating reaction to friction at the first 100 m sliding distance. The load increase attributes the role of bulk severe plastic deformation against surface-based ones. However, SSP behaves quite tough for resisting friction through entire distance. The 1st pass of CGP underwent high friction due to the lack of adequate hardening densified on the surface. On the contrary, it gets better compared to untreated one through the end of the distance. The 3rd pass also achieved the lower frictional coefficient at the end., the friction coefficient reduced with increasing normal load for all the samples. In general, the coefficient of friction depends on the normal load, friction coefficient decreases with increasing of the load b show the variations of volume loss and effective wear loss coefficient graphs of polished and SPD processed specimens. It is evident from the figures that SPD processes had positive effect on wear behavior of S500MC steel. Wear volume of all samples were increased with increasing normal load. Surface treatments have been found to be more effective than bulk SPD treatment to improve wear resistance. Although there is a slight difference in wear volume between SSP and UNSM processes and SSP exhibit better wear resistance. However, the increasing of the wear load provides a crucial candidate for bulk severe plastically deformed bodies since the nanocrystallization layer after S2PD has a critical probability to be removed. The removal of the layer could convert the material to the as received. Therefore, SPD treated specimens could be preferred instead of S2PD within the condition of high contact stresses.The worn surface morphologies of untreated and SPD processed S500MC steel specimens under the load of 10 N are shown in . Two typical worn surface morphologies could be seen. The dominant wear mechanisms were oxidative wear and delamination wear which characterized with smooth and dark grey regions (tribo-oxide layer) and delaminated regions. It could be said that adhesive wear is more effective with plastic deformation and furrows. However, all specimens showed signs of both wear mechanism, involves smooth surfaces, worn particles and furrows. shows EDS analysis of the oxidative wear regions. Analysis shows the fields are radically composed of Fe-O and involves trace quantity of the other elements.In this study, bulk SPD (CGP) and S2PD (SSP and UNSM) methods are compared for S500MC automotive steels in terms of microstructural mechanical properties and, friction and wear behavior. CGP achieves volumetric grain size reduction, but reduction can be able to reach to ultrafine grain structure (around 1000 nm). S500MC steel is accomplished to the CGP process as a HSLA steel with an average grain size of approximately 3.7 µm. SSP and UNSM contribute nanocrystallization (below 100 nm) on the surface. UNSM contributes both the total elongation with the yield and ultimate tensile strength improvement. On the contrary, SSP tends to reduce the stresses slightly. Moreover, SSP is another effective way to raise the ductility. CGP is the one which can affectively increase the strength of the material regardless of the pass number. SSP and UNSM showed better wear and friction resistance particularly at lower loads compared to CGP and untreated specimens. Nevertheless, wear and friction behaviors at higher loads give better responses for bulk-SPD applications regardless of pass numbers.Ibrahim Karademir: Investigation, Data curation, Writing - original draft. Mustafa B. Celik: Supervision. Fazil Husem: Data curation, Methodology. Erfan Maleki: Data curation, Writing - review & editing. Auezhan Amanov: Supervision, Methodology. Okan Unal: Conceptualization, Supervision, Writing - review & editing.The authors declared that there is no conflict of interest.Determination of heat capacity of pure metals, compounds and alloys by analytical and numerical methodsPhase diagrams are normally calculated from a combination of physical equations and experimental parameters. Gibbs free energy of mixing; thermodynamics activity and enthalpy of mixing; transformation temperatures and the concentration range of the alloys components are calculated to permit an alloy system database to be constructed. The molar specific heat capacity (cv) is normally obtained by numerical derivative of the enthalpy equation with respect to temperature and concentration. The experimental determinations of the topological parameters as a function of concentration and temperature is an enormous task. On the other hand, physical formulations such as Einstein’s and Debye’s equations are physically consistent models for the molar specific heat capacity of the solid, and they depend only on a set of basic physical parameters. Einstein’s formulation works very well for temperatures T > 102 K, however, as it varies in the form of 1/T2, it fails to conform to lower temperature experimental data. Debye assumed only three branches of the vibrational spectrum with the same linear dispersion relation, and derived an equation also consistent for lower temperatures, and as the temperature decreases to absolute zero, it varies as a function of 1/T3 thus permitting experimental scatters to be fitted. Another way for calculating cv is by carrying out polynomial functions [], which are only recommended for temperatures above 298.15 K, because bellow this temperature, cv is strongly dependent on the quantization of thermal energy, which can be stored in different forms in the material, such as electronic, magnetic, vibrational, rotational and translational energies. In this paper corrections for Debye’s and Einstein’s equations for cv are derived to encompass its thermal history dependence, electronic and rotational energies for both lower and higher temperatures in order to permit the calculation of the molar specific heat capacity of pure metals, phases and single-phase alloys.In many areas of science and engineering, the calculation of thermophysical properties of pure elements, compounds and alloys are a need for R & D. In this sense, alternatives combining the application of analytical theoretical models, thermodynamics software and numerical models can be used to provide thermophysical properties of relevant multicomponent alloys. The use of computational thermodynamics coupled to numerical algorithms of heat transfer have been recently applied for the determination of thermophysical properties of multicomponent Al-based alloys, such as surface tension and Gibbs-Thomson coefficient []. Theoretical models from the literature, represented by analytical equations used to provide simulations of viscosity of liquid metals have been extended to encompass the important case of multicomponent alloys. The proposed approach has been validated against an existing theoretical model and experimental results of ternary and quaternary Al-based alloys [Basically, for the solid state of matter there are two main approaches for the calculation of the molar specific heat capacity: (i) for high temperatures, in which empirical formulae based on integrals and experimental coefficients are used to estimate the molar specific heat capacity as a polynomial function of temperature [], and (ii) with the use of thermodynamics software packages and databases obtained numerically for a specific class of materials. For lower temperatures, in which the quantum effects are pronounced, Einstein’s and Debye’s models can be used, besides, ab-initio models. Einstein’s [] energies contributions to the molar specific heat capacity. Nevertheless, the complex mathematics involved to derive magnetic ordering contribution energy for the molar specific heat capacity, made possible many empirical formulae to account for contributions of Curie, Neel, Schottky transition anomalies []. According to Schliesser and Woodfield [], Einstein modelled the atoms in a solid as independent harmonic oscillators vibrating at the same frequency, thereby modelling the density of state as a delta function. This simple density of state sometimes provides adequate correlation with experimental heat capacity measurements at high temperatures, failing at low temperatures. Debye otherwise, modeled the vibrations in a solid as normal modes of a continuous elastic body, which corroborates well for long wavelength vibrations that do not depend on the detailed atomic character of the solid and do conform to lower temperatures experimental scatters, but failing for many materials with a gap in density of state [In this paper, two models for pure elements, that is Einstein’s and Debye’s, are used considering the additions of electronic and rotational energies contributions to the molar specific heat capacity (cv) and its temperature corrections to the energy gap of the rotational term. Based on the Neumann-Koop principle [], two corrections for Debye and Einstein’s molar specific heat capacity for metals, alloys and compounds are proposed. The approach to be developed can be summarized in terms of addition of electronic and rotational contributions to the isochoric specific heat. The electronic contribution is based on existing solutions in the literature, but the rotational term is new and it encompasses the increase in rotational energy with temperature and its rotation retrains of atoms bond stiffness, that in this case is approximated by a relative sound speed in the lattice, which is a novel approach. But the most important contribution of this approach for both pure metals, phases and single-phase alloys, lays in important observation in the practice of Thermodynamics of phase equilibria. Physicists and materials engineers during DTA (Differential Thermal Analysis)-DSC (Differential Scanning Calorimetry) can observe that the values of cV depend on the thermal history of the sample and there is absolutely no equation conforming this observation with the cV theory. Analyzing in terms of Gibbs-Thomson coefficient, when the sample is out of equilibrium the latent heat decreases as the undercooling increases for higher solidification rates. Then, the latent heat decreases as the bulk liquidus temperature remains constant. Assuming here, as an approximation, that the solid-liquid surface energy remains constant, this means that higher solidification rates will promote a lower solidification entropy, resulting in higher Gibbs-Thomson coefficient, changing the critical radius, which, ultimately, will change the volume relation and the number of atoms in the primary critical cluster of atoms. The present approach will predict the influence of the Gibbs-Thomson coefficient on the value of cv. Models predictions are compared to Thermo-Calc simulations using the TTAL7 (Thermo-Tech Aluminum Alloys Database v. 7) and the TCMP2 (Materials Processing Database) databases for pure metals, alloys and compounds.The thermal energy of a material can be stored into several forms, such as, translational (cvTrans), vibrational (cvVib), rotational (cvRot), electronic (cve) and magnetic (cvMag) energies [In the case of solids, the translational energy cvTrans can be assumed as cvTrans≅0. In this model we will neglect the magnetic contribution, cvMag, as far as the magnetic energy contribution, such as Curie and Neel transitions have been modelled empirically in a number of previous studies [], since the theoretical formulation of magnetic order demands complex mathematical and physical formalisms. For the vibrational contribution, the approaches used by both the Einstein and Debye models will be used. The electronic cve and rotational cvRot contributions will be modelled accordingly.Einstein’s Molar Specific Heat Capacity ModelFor pure elements, the Einstein’s model for the vibrational contribution [where, R is the gas constant, i is any pure chemical element and βi is defined as,, ℏ and kB represent the constants of Planck and Boltzmann, respectively, ωi is the fundamental frequency of a harmonic oscillator of an element i, and T is the absolute temperature.The electronic contribution is written in terms of the vibrational or phonon energy contribution, that iswhere ΘD,i is the Debye’s temperature assumed to be equal to the Einstein’s temperature ΘE,i, TF,i is the melting temperature of element i, Zi is the valence of element i.As an approach for rotational energy, we regard the following basic equation,where ri is the atomic radius of element i, M¯i is the molar mass of element i.cvRot=54Rℏ3kB2ωD,iT+ΘD,i2JJ+1M¯iri2JmolK, ωD,i is the maximum admissible frequency known as Debye’s frequency, M¯i is the molar mass of element i, and J is the rotational level corresponding to integer J=0,1,2,3,…A relation between vibrational and rotational transitions are show in Then, the molar specific heat capacity regarding vibrational, electronic and rotational energies is given by the following equation,cv=(1.0+D(ω))3Rβi2eβi(βi-1)2(1+cve)+(n+1/2)[9.0⋅ERot+(1-Ei⋅ρDiaEDia⋅ρi)RT3ΘD,iTF,i2]where, n is the vibrational energy level, whose relation to the rotational energy is presented in , Ei is the Young modulus of component i and EDia the Young modulus of diamond. In the same way, ρi and ρDia represent the densities of the component i and diamond, respectively. The square root of the specific Young modulus of component i with respect to that of diamond, can be approximated by the ratio of the speed of sound of component i and the speed of sound of diamond.], ri is the atomic radius of component i,, ω is the frequency, ν is the speed of the sound in the solid, ∀ is the volume of the crystalline lattice.The Gibbs-Thomson effect lowers the melting temperature []. Considering an isolated solid particle of diameter d in its own liquid, the Gibbs-Thomson equation for the structural melting point depression can be expressed by [where, ΔS∀ and rC are the effective entropy of melting per unit volume J.m-3.K-1 and spherical grain critical radius m, respectively. σsl is the solid-liquid interface surface tension, Γ is the Gibbs-Thomson coefficient K.m, Tmbulk is the bulk melting temperature [K], ΔH∀ is the latent heat of fusion J.m-3.After the calculation of critical nucleation radius, the critical grain volume ∀ is assumed as spherical. Since the molar specific heat capacity is dependent on the Gibbs-Thomson coefficient and on the temperature drop, which is associated with the nucleation kinetics of the critical grain volume, the molar specific heat depends on the thermal history of the sample., the solid-liquid interface surface tension σsl and the melting temperature Tmbulk of the elements can be found in previous studies [Debye’s Molar Specific Heat Capacity ModelThe Einstein’s model predictions do not conform to experimental scatters for low temperatures, decreasing rapidly to the absolute zero, due to its 1/T2 dependence on temperature, while the experimental data follows an= 1/T3 dependence. Petrus Debye [] considered only three branches from all the vibrational spectra, assuming the same linear dispersion relation, and from the knowledge of existence of a maximum admissible harmonic frequency, known as Debye’s frequency [where, Na is the Avogadro number, ΘD,i is the Debye’s temperature. Concerning the definition of x, it is a function of the linear dispersion relation of three acoustic branches, ω=ck, where c is the speed of light in vacuum and k is the wave number, given as a function of the wavelength λ, providing k=2π/λ, according to the Debye’s approach to the treatment of vibrational spectra, which results in x=ℏck/kBT. A relation between the Debye’s maximum harmonic frequency ωD,i and the Debye’s temperature is given by,The Debye’s temperature for pure elements is normally found in the literature [ of the electronic and the rotational contributions to cv, it provides,cv,i=(1.0+D(ω))9NakB(TΘD,i)3∫0TΘD,ix4ex(ex-1)2dx(1+cve)+(n+1/2)[9.0⋅ERot+(1-Ei⋅ρDiaEDia⋅ρi)RT3ΘD,iTF,i2]Modified Einstein’s Model for Multicomponent AlloysThe principle behind the calculation of the molar specific heat capacity for multicomponent systems here carried out is the Neumann-Koop principle [], which states that each element in the solid state has essentially the same specific or atomic compound as it has in the free state, which involves both stoichiometric compounds and solid solutions. This rule cannot be generally considered as a simple addition scheme based on calculating a compound property as a sum of the respective properties of real elements forming the compound. The best response of application of the Neumann-Kopp rule is expected when the chemical activity of the elements or compounds forming the mixture are close to one. According to Leitner et al. [], this rule represents a combination of an additive and contribution method. Later, several empirical contribution methods have been proposed that can be applied for the estimation of the molar specific heat capacity of solids [cv,i=(1.0+DAlloy(ωAlloy))3RβAlloy2eβAlloy(βAlloy-1)2(1+cve)+(n+1/2)(9.0⋅ERot+(1-Ei⋅ρDiaEDia⋅ρi)RT3ΘD,AlloyTL2)where, DAlloyω is the density of state, ri is the atomic radius of component i,, ωAlloy is the frequency, ν is the speed of the sound in the solid, ∀ is the volume of grain regarding the critical nucleation radius.Concerning the critical grain volume ∀, the Gibbs-Thomson is now applied, providing,where, ΔS∀ is the effective entropy of melting per unit volume J.m-3.K-1, rC is the critical grain radius m, σsl is the solid-liquid interface surface tension, Γ is the Gibbs-Thomson coefficient K.m, TLbulk is the bulk liquidus temperature [K], ΔH∀ is the latent heat of fusion J.m-3. The volume of the critical grain is assumed to be spherical.ERot=54Rℏ3kB2ωD,AlloyT+ΘD,Alloy2∑i=1nxiJiJi+1M¯iri2where, βAlloy and ΘD,Alloy are: equation parameter and the Debye’s temperature for the alloy/compound, respectively, defined as,The alloy/compound fundamental frequencies are expressed as a function the linear combination of Debye’s temperatures of elements/compounds described by Eq. The element/compound electronic contribution to the molar specific heat capacity can be expressed in terms of the phonon contribution as,Then, the total electronic molar specific heat capacity provides,cve,Alloy=∑i=1nxicve,i+∑i=1n∑j>inxixjcve,icve,j+∏i=1nxicve,iModified Debye’s Model for Multicomponent AlloysThe modified Debye’s equation for alloys compounds and single-phase alloys is derived based on the same Neumann-Koop principle. Debye is important as it can handle from low temperatures, where the quantum effects on the molar specific heat capacity are very pronounced, to higher temperatures until melting. Here magnetic anomalies such as Curie, Neel and Schottky are not taken into account.cv,i=(1.0+DAlloy(ωAlloy))9NakB(TΘD,Alloy)3∫0TΘD,Alloyx4ex(ex-1)2dx(1+cve)+(n+1/2)[9.0⋅ERot+(1-EiρDiaEDiaρi)RT3ΘD,AlloyTL2] presents the molar specific heat capacity as a function of temperature for pure Al, Cu, Si and Mg according to the models of Einstein, Debye, Modified Einstein and Modified Debye compared to calculations provided by the Thermo-Calc database TCAPI 7. Clearly, aluminum, copper and silicon fitted better both modified models in the level 2 (n = 1), while for silicon both levels 1 and 2 (n = 0 and n = 1, respectively) show good agreement with Thermo-Calc results., zinc conforms better to the Thermo-Calc scatter regarding level 2 of both modified models (n = 1), while titanium and manganese (n = 4), nickel (n = 3) better agree to level 7 (n = 6). The worst case in this set was that observed for manganese. presents the molar specific heat for chromium level 1 (n = 0 and n = 1), iron both level 3 (n = 2), cobalt (n = 2) and zirconium (n = 4). All elements present better agreement with modified Debye’s models. The agreement is also good but not so good as Zr in the beginning of the curve., Pb does not agree with the predictions of the modified Einstein’s model for levels 1 and 2 (n = 0 and n = 1). Nevertheless, level 1 has the closest agreement. Sn agrees better with level 1 (n = 0). Predictions furnished by both modified models level 2 for V and C graphite are very good indeed. In the case of diamond it can be observed a deviation similar to the shape of the models. For carbon graphite and diamond, Einstein, Debye, Modified Debye and Modified Einstein models all agree, for both 1 and 2 levels.For the case of alloys, the contents of Si in were varied. Here these alloys were assumed to be single-phase alloys to avoid calculations of the phase fractions of each phase by the Thermo-Calc software. Nevertheless, in , very good agreement with both modified models for level 3 (n = 2) in all examined alloys can be observed. Exception is a, where three phases were observed for the selected range of temperatures. a very good agreement can be observed among the Thermo-Calc results for modified Einstein’s and modified Debye’s models for level 5 (n = 4). we present the Al-1 wt%Cu-1 wt%Si-XMg phase diagram and its magnification between 0 wt%Mg and 6.0 wt%Mg and the simulation for the alloys phase compounds. An excellent agreement with the modified models for level 2 (n = 1) was found for ALCUMG_S, ALCU and FCC_A1 phases. In the case of MG2SI an exact solution was found for level 1 (n = 0).] and beryllium, Debye can only reach good agreement if the Debye’s temperatures are set to ΘD,Dia≅1900 K and ΘD,Be≅981 K, respectively. These results are presented in The model for pure elements and the model for single-phase alloys/compounds was shown to agree well with Debye’s and Einstein’s models for low temperatures curves, considering the same set of additional equations for the thermal history dependence, for the electronic and for the rotational energy contributions to the molar specific heat capacity. This demonstrates the physical consistence of both basic models. In general, for pure elements, a second level of state (n = 1) was enough to conform to the Thermo-Calc calculations. In the case of graphite all models based on the Debye’s approach for the first (n = 0) and second level (n = 1) fitted well the Thermo-Calc results. For diamond, nevertheless, considering Debye’s temperature of ΘD,Dia=2250 K, the Thermo-Calc data do not conform to the fundamental Debye’s model and the current approach. The predictions only fit the Thermo-Calc scatter, in the same way graphite did, if Debye’s temperature is set to ΘD,Dia=1900 K, as far as beryllium Debye’s temperature is set to ΘD,Be=981 K. In the case of Zr and Co, the modified Einstein’s and modified Debye’s models level 6 (n = 5) fitted the data properly, and level 7 (n = 6) was necessary for Ti, Ni, Mn, Cr and Fe. For Al-(2.5–20.0)wt%Si-1 wt%Cu-0.5 wt%Mg, Al-1 wt%Si-(2.5–20.0)wt%Cu-0.5 wt%Mg and Al-1 wt%Si-1 wt%Cu-(2.5–20.0)wt%Mg alloys the level 3 (n = 2) agreed well with Thermo-Calc simulations. In the case of the Al-(5–20)wt%Ag-14 wt%Cu-2.0 wt%Si alloys level 5 (n = 4) was needed to conform to Thermo-Calc calculations. In this case, the same trends were observed for high temperatures for both Einstein’s and Debye’s based models. Concerning the compounds Al2CUMG_S and FCC_A1, a level 2 (n = 1) is enough to fit the Thermo-Calc scatter. For the intermetallic compound MG2SI, level 1 (n = 0) for both Einstein’s and Debye’s based models was enough, while for AL2CU level 5 (n = 4) was necessary for both Einstein’s and Debye’s model to conform to the Thermo-Calc scatter. Nevertheless, Debye’s based modified model fitted better the Thermo-Calc data for the entire range of the examined elements, alloys and compounds.The authors declare that this manuscript is original, has not been published before and is not currently being considered for publication elsewhere. The article has been written by the stated authors who are ALL aware of its content and approve its submission, as well as by the responsible authorities – tacitly or explicitly – at the institutes where the work has been carried out. No conflict of interest exists. If accepted, this article will not be published elsewhere in the same form, in any language, without the written consent of the publisher.A sample calculation of the molar specific heat capacity for a pure metal (Aluminum -Fig. 2a) as a function of temperature can be found in this section. The code was written in Python 3.Strength assessment of a severely corroded box girder subjected to bending momentThis work deals with the evaluation of the ultimate bending moment of a severely corroded box girder subjected to uniform vertical bending moment through a series of nonlinear finite element analysis. Two models of corrosion degradation have been adopted, one is an average general corrosion thickness reduction, and the other is the real thickness of the corroded plates. New stress–strain relations have been developed to account for the effect of corrosion on the flexural rigidity. To validate the new developed stress–strain relationships, a comparison between the finite element analysis results using the existing stress–strain models, the newly developed ones and the experimental test results of a severely corroded box girder have been conducted. The comparison showed a good agreement and supported the choice of the newly developed stress–strain relationships of corroded structures.A ship hull girder is a structure built up of unstiffened, stiffened plates, frames and other components subjected to complex loading. The ultimate hull girder strength is the maximum bending capacity that a ship hull girder can sustain under longitudinal bending.The linear elastic theory has been employed to predict the longitudinal strength of the ship hull for years. According to this theory, the maximum bending moment that the hull cross-section can withstand is equal to the bending moment corresponding to the first yield, that is, the bending moment when the maximum stress on the hull cross-section reaches the yield stress of the material. In design practise, an allowable stress is used instead of the yield stress, which corresponds to a safety factor against yielding.However, in the last decades, it has been established that ship hulls have considerable additional strength beyond the first yield and thus the ultimate strength is the appropriate criterion to determine the ship hull strength and to be used in codified design as proposed by Guedes Soares et al. To estimate the longitudinal strength of the ship hull several factors have to be accounted for: (1) various possible failure modes including buckling, (2) progressive and interactive behaviour of the failure of structural members, (3) redistribution of stresses on the hull cross-section and (4) residual strength of structural members after buckling and even after the collapse. By considering these factors, the maximum bending moment that the hull cross-section can withstand is designated by the ultimate longitudinal strength, which represents the maximum load-carrying capacity of the ship hull under longitudinal bending.The ultimate longitudinal strength assessment is a nonlinear problem in which both the nonlinearity related to material behaviour and geometry are involved Later, the method was extended by Smith Many other methods have been also proposed to simulate the progressive collapse behaviour of the hull girder. Billingsley The second method used to calculate the ultimate strength is the nonlinear finite element method (NFEM), the applications of this method to the collapse analysis of ship's hull are very few; the earlier attempt was done by Chen et al. A series of finite element analyses were conducted to simulate the behaviour of tested box girders. Hansen The third method is the idealised structural unit method (ISUM), the most obvious way to reduce modelling effort and computing time is to reduce the number of degrees of freedom, so that, the number of unknowns in the finite element stiffness equation decreases, and this concept is the base of the ISUM that has been proposed in With the existing standard ISUM elements, the main difficulty is the computation of the post-collapse behaviour in the structural elements beyond their ultimate strength as well as the flexural–torsional collapse behaviour of stiffeners is not very successful. Therefore, some research works have been carried out by many authors for example, Ueda and Rashed All of the mentioned methods were dealing with intact structures. A step forward is the study of the ultimate strength of corroded box girders performed by Saad-Eldeen et al. Another box girder test was analysed in A series of nonlinear FEA of an intact box girder have been performed in The post-buckling behaviour demonstrated a very good agreement with the experimental results. Comparisons between numerical and experimental results have been performed for the slightly corroded box showing a very good agreement.The study presented here deals with the nonlinear finite element analysis of corroded steel box girders, where the analysed box here is subjected to severe corrosion and a different slope of the moment–curvature relationship has been observed from the experimental results as given in The hull girder ultimate strength is defined as the maximum bending capacity of the hull girder beyond which the hull will collapse. Hull girder failure is controlled by the ultimate strength of structural elements accounting for buckling and yielding.The principal parameters governing the structural design of a ship's hull subjected to compressive loading and influencing the compressive strength are the plate and column slenderness, in addition to the material yield strength and the Young modulus, defined as:where tp is the plate thickness, b is the plate width between stiffeners, a is the stiffener span between frames, I is the moment of inertia, A is the cross-sectional area of the stiffener including the associated plate and r is the radii of gyration of the cross-section area of the stiffener with the associated plate calculated as:The principal characteristics of the analysed box girder are given in . A thickness measurement survey has been performed to find out the remaining thicknesses of the box girder structural elements, the measured remaining thicknesses of the box girder deck and bottom panels are plotted as shown in . A more detailed information about the severely corroded box girder are reported in It has to be pointed out that the box girder is a thin-walled structure and due to corrosion, the structural elements become much thinner, therefore, there is no significant effect of residual stresses as has been also concluded by Ueda et al. The box girder has been mounted between two stiff supporting arms, using bolt connections as shown in . The box girder was subjected to four-point vertical bending moment. The bottom part is subjected to tension and the upper part, deck, is under compression. The bending moment is kept constant along the box girder, between bolt connections.The test of ultimate strength is conducted in two loading cycles. During the second loading cycle, which is the final one, the box girder is subjected to the maximum load to which it can withstand. Through the final load step, the box girder folds up in a progressive collapse defined with a great discharge of load and a large deformation due to the formation of plastic hinges in both plating and stiffeners at the deck and at the deck/side connection as presented in Numerical analyses of the ultimate strength, for the severely corroded box girder, are performed based on general nonlinear finite element commercial code — ANSYS. The finite element analysis utilises the full Newton–Raphson equilibrium iteration scheme. The large deformation option is activated to solve the geometric and material nonlinearities and to pass through the extreme points. The automatic time stepping features are employed allowing the programme to determine appropriate load steps.The geometry of the box-girder structure is modelled in the same way as the real one used during the ultimate strength test without any simplifications, see . Shell elements are used to generate the entire FE model. The shell element, SHELL 93 is defined by eight nodes, four nodal thicknesses, with six degrees of freedom at each node: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z axes. The deformation shape functions are quadratic in both in-plane directions. The element has plasticity, stress stiffening, large deflection, and large strain capabilities.The material used to build up the model is shipbuilding low carbon steel with yield stress, σy of 235 MPa, the Young's modulus, E of 206 GPa and the Poisson's ratio, υ of 0.3.Before performing the ultimate strength test, the box girder was subjected to severe corrosion in a corrosion test, reported in . Therefore, it may be concluded that, in addition to the thickness reduction, corrosion has an additional effect on changing the mechanical properties of the material. As may be observed from , the slope of the linear stress–strain relationship, which is defined as the first tangent modulus is different for the box girder without corrosion and for the one subjected to real sea water severe corrosion.By fitting the stress–strain relationship, up to the first yield for the severely corroded box using a linear regression, it can be observed that there is a significant reduction of 54.3% in the apparent tangent (elastic) modulus (), which demonstrates that, with increasing the severity of corrosion, the mechanical properties changed.This observation also coincides with the direct tension tests on corroded steel wires after 60, 90 and 180 days of exposure to the aggressive corrosion environment that have been carried out by Vu et al. The changes in mechanical properties, due to the effect of corrosion degradation, lead to a modified stress–strain relationship, which is applicable for severely corroded structures. To analyse this effect four stress–stain models are used in the FEA to analyse the ultimate strength and the post-collapse behaviour of the box girder modelled with average and real corrosion thickness reductions.The elastic-perfectly plastic (EP) stress–strain model, shown in , is defined in the way that at stresses below the yield stress, σy the material behaviour is linear with a tangent modulus, ET0
=
σy/εy of 206 GPa. At the level of the yield stress, the material flows plastically without strain hardening. When the material is unloaded, by reducing the stress below the yield stress, it behaves elastically in a manner unaffected by the plastic flow; the parameters that define the EP model are given in The elasto-plastic modified (EPM) stress–strain model, as shown in (b), is a modification of the idealised elastic–plastic model by replacing the intact first tangent modulus by the one, which accounts for the corrosion effect as ETC0
=
σy/εy. The first tangent modulus accounting for the effect of corrosion ETC0 is experimentally defined for the severely corroded box girder as 94.16 GPa (see ). The parameters that define the EPM model are given in The elasto-plastic modified 1 (EPM1) stress–strain model in (c), is a modification of the elasto-plastic modified model by introducing a second tangent modulus, ETC1 starting from the point up to which the stress and strain are linearly proportional, σPl,1.The second tangent modulus is calculated as ETC1
=
ETC0/(1 +
kTC1), where kTC1 is a coefficient, which accounts for the effect of the existing residual stresses in the box girder. The finite element model does not account explicitly the residual stresses. The parameters defining the EPM1 model are given in The elasto-plastic modified 2 (EPM2) stress–strain model, in (d), is a modification of the elasto-plastic modified 1 model by introducing a tangent modulus, ETpl,2 related to the second proportional limit,σPl,2, which corresponds to the contribution of the stiffeners in the load carrying capacity. Due to the corrosion degradation of the plating and stiffeners, the second proportional limit is extended to twice of the first proportional limit with a tangent modulus of ETpl,2
=
ETC0/(1 +
kTpl,2) where kTpl,2 is a coefficient accounting for the contribution of the stiffeners in the buckling region. The parameters defining the EPM2 model are given in The box girder is subjected to vertical loading, producing a constant pure vertical bending moment along the box-girder length. The load is generated by imposing a vertical displacement acting on the two heavy plates that are located outside of the analysed box-girder on the supporting arm connection (see , left). The displacement load is applied by small increments to ensure that the analysis would closely follow the structural load-response curve. Both ends are simply supported, constrained from translations in the vertical and transverse direction. The translation in the longitudinal direction is only constrained at one end. No rotation is prevented.In order to obtain precise results and to find out an appropriate element size to be used for the finite element model a systematic finite element analyses have been carried out in (right) that there is an inflection point at the level of the element size of 5 cm, which refers to the change in the gradient of the ultimate bending moment behaviour.The plate initial imperfection is modelled based on real initial imperfection measurements as reported in where wi,SC is the mean value of the amplitude of the imperfections. The mean value and standard deviation for the measured imperfections are 3.919 and 2.008 mm, respectively, as can be seen in (left). These imperfections have been generated in the finite element model by changing the vertical position of element nodes without inducing any additional stresses.Two groups of nonlinear FE analyses have been conducted. The first one deals with the corrosion degradation, which is modelled as an average thickness loss and the second one, uses the real thickness measurements at the nodal location of the finite element model. A more detailed information about the corrosion measurements is reported in The box girder element surfaces have been modelled using the average corrosion thickness as given in Four different stress–strain models are given in have been used to analyse the behaviour of the severely corroded box girder subjected to a vertical bending moment.A criterion for selecting the best stress–strain model has been developed based on two considerations; the achieved ultimate bending moment and the similarity in the stress–strain curve relationship defined by the r approach, which represent the judgement of the adequacy of the FE results (moment–curvature relationship) to the experimental results as:where BMu is the ultimate bending moment.The moment–curvature relationship for each stress–strain model is plotted in (left). For the first model, which is the EP, it is noticed that the overall behaviour of the box girder is far away from the experimental results in terms of following the shape of the curve and from the point of view of the ultimate bending moment. Finite element analysis calculates a higher ultimate bending moment than the one experimentally achieved as can be seen in Following the combined criteria (see Eq. ), which result in 0.215, demonstrate that the use of the EP model, with the first tangent modulus of 206 GPa, gives a very poor agreement with the experimental results of the severely corroded box girder.Based on the experimental results, the effect of corrosion degradation has been accounted for by modifying the EP model including a new first tangent modulus. With the use of the modified model, EPM the resultant moment–curvature relationship is plotted in , the experimental results and FEA based on the EPM model coincide very well in the linear sector, which reflects the effect of corrosion not only in the thickness reduction as in the EP model but also on the changed mechanical properties of the material., the EPM registers a bending moment slightly bigger than the experimental achieved one by 4.8%. The similarity of the bending moment curvature relation based on r is about 1.12 which means that the FEA overestimated the experimental results, see (right), but the combined criteria is quite good, 0.91.From this point ahead, modifications have been performed in the EPM model to account for the contribution of the plating and stiffeners elements in the total behaviour of the severe corroded box and also for the remaining residual stresses.The first modified model, EPM1 accounts for the contribution of the plating, which is in the pre-buckling stage in which the plate's response to the applied load follows the Hooke's Law, where the load displacement relationship is linear, which has been defined based on the experimental data, see . Therefore, the first proportional limit, σPl,1 as defined in (c) equals to 50.09 MPa, and the factor, kTC1, which is adopted to account for stiffeners contribution and the residual stresses is 0.5 as given in FEA based on the EPM1 model is shown in (right). It can be observed that by defining the first proportional limit and the tangent of the buckling to collapse the region (stiffeners contribution and residual stresses), the bending moment curvature relationship behaviour becomes closer to the experimental results with a difference of the ultimate bending moment of − 2.54% and 0.943 and 0.959 for r and combined criteria, respectively, see . The second modified model, EPM2 introduces another proportional limit,σPl,2, which accounts for the stiffeners contribution and is defined as being twice of σPl,1 with kTpl,2 equal to 0.173 to define the tangent modulus,ETpl,2 in this region (see The results of FEA based on the EPM2 model are shown in (right). It can be observed that by introducing the first and second proportional limits and the tangent of the post-buckling to collapse the region (residual stresses), the moment curvature behaviour of the box girder becomes almost the same as the experimentally defined one. The difference in the ultimate bending moment is about − 0.98% and 0.989 and 0.99 for r and the combined criteria respectively (see Based on the combined criteria used here for comparing different FEA based on different stress–strain curve models it may be concluded that the EPM2 model is the best model to fit the experimental results.The box girder finite element surfaces have been modelled using the real corrosion measurements as shown in are used to analyse the bending moment curvature behaviour of the severely corroded box girder under the same conditions that are used for the analysis based on average corrosion thickness model.The moment–curvature relationship for each stress strain model is plotted in (left). For the EP model, the overall behaviour of the box girder is far away from the experimentally achieved results in terms of following the shape of the curve and the ultimate bending moment point. FEA registers a higher ultimate bending moment than the experimentally achieved one as can be seen in , the EP model demonstrates very poor results compared to the experimental results of the severely corroded box girder, 0.37. However, the difference between the ultimate bending moment based on average and real corrosion thickness is 14.4%.With the application of the modified model, EPM the resultant moment–curvature relationship is plotted in (left). As may be seen the FEA based on EPM model coincides very well with the experimental results in the linear sector, which reflects the effect of corrosion not only in the thickness reduction as in the EP model but also on the mechanical properties of the material., the EPM registers a bending moment less than the experimental one with about − 5.2% and also r is about 1.1 (see , right), but the combined criteria is quite good, 0.93.For the model EPM1, r is about 0.875, see (right) and the ultimate bending moment is lower than the experimental with − 15.7%. If the ultimate bending moment calculated based on the EPM1 and using the average corrosion thickness is compared with the one using real corrosion the difference is about 13.2% which in fact gives a clear understanding about the big difference in the modelling methodology of the corrosion degradation.The last part of the real corrosion group analysis is the application of the EPM2. The calculated moment–curvature relationship is plotted in (right) in which the behaviour of the box girder is much better than the one based on the EPM1 model, where r is 0.925. As given in , there is a small difference between the two models in the ultimate bending moment about 0.64%.From the analysis performed it may be concluded that the EPM and EPM2 models are the most suitable ones to perform the ultimate strength analysis of severely corroded structures based on real corrosion thickness.From the ultimate strength analysis of the two corrosion modelling concepts, average and real corrosion thickness, it is concluded that the EPM2 model is the best option and the stress analysis presented in this section will only consider for the EPM2 model. (left), the first observation is that the longitudinal stress distribution in the first and third bays is similar in the case of the average corrosion thickness along the deck panel, on the contrary for the same bays with real corrosion thickness the stress distribution is different and this is much more clear near the deck-side connection, see For a more detailed understanding of the effect of the average and real corrosion thickness on the stress distribution, the 1st principal stresses at the middle bay, at the point of achieving the ultimate bending moment are plotted in (right) shows that there are many locations at which the stresses are concentrated due to real corrosion thickness distribution, especially in the middle bay stiffeners, where the sharp deformation of the stiffeners (right) occurs leading to a fracture, which was confirmed by the tested box girder as can be seen in During the test it was observed that, after the first fracture appear, a simultaneous fracture of the stiffeners occurs demonstrating a brittle behaviour of the material after being subjected to severe corrosion as was reported in (left), all of the stiffeners behave in a normal way without any sharp deformations, and the stress distribution is symmetric in the middle of the box. In fact if the corrosion degradation is modelled in a real manner, the stress distribution is asymmetric as shown in A comparison between the application of one stress–strain model, EPM2, to predict the ultimate strength behaviour of the box girder and the use of two stress–strain models, one for compressive (deck) based on the EPM2 model and one for tensile loaded part (bottom), based on the EPM model of the box girder has been carried out.The moment–curvature relationship in both cases is plotted in . As can be seen, both of the cases coincide well in the linear sector, after that a deviation starts to appear due to the fact that with the application of two stress strain models (EPM + EPM2), the bottom part, which is under tension obeys more capacity. With the use of one stress strain model for the whole box, EPM2, the behaviour is closer to the experimentally achieved one with r, ultimate bending moment and combined criteria of 0.989, − 0.98% and 0.989, respectively as given in From the stress distribution point of view, in the case of one stress–strain model, EPM2, the box girder fails before reaching the plasticity in the bottom plating, (middle), which makes the ultimate bending moment less than the experimental one with − 0.98% as given in On the contrary, with the use of two stress strain models, EPM + EPM2 a higher ultimate bending moment is achieved with 1.26% than the experimental defined one. This may be explained by the fact that the bottom part is still not reaching the plasticity (see (middle), the stress distribution is the same and this is because the upper part (deck) in both cases is using the same stress strain model, (right). The stress distribution at the side shell is different and this is because the lower part (bottom) in the case of two models (EPM + EPM2), (right) is modelled by the EPM model, which enables more capacity, therefore, some of the bottom plating and some parts of the side shell reach the plasticity. Also the stress distribution around the neutral axis is different for the two cases.A series of nonlinear finite element analysis have been carried out to evaluate the ultimate strength of a box girder subjected to severe corrosion. Two groups of analyses have been conducted. The first one deals with the corrosion degradation modelled as average thickness loss based on real thickness measurements, and the second one, the box girder element thicknesses are modelled based on the real corrosion thickness measurements.New stress–strain relationships have been developed accounting for the effect of corrosion on the steel mechanical properties. A comparative finite element analyses between the results achieved using the existing and developed stress–strain models and the test results of a severely corroded box girder have been conducted.The ultimate strength analyses, based on the two corrosion modelling concepts (average and real corrosion thickness), demonstrated that the EPM2 model of the stress–strain behaviour (which includes two changes of slope of the tangent modulus) is a good option to predict the moment–curvature behaviour and the ultimate bending moment evaluated by the combined criteria for adequacy as 0.989 and 0.887 for average and real corrosion thickness respectively.From the ultimate bending moment point of view, there is a clear difference (10.0%–14.4%) between the finite element results with the thickness of the plates modelled as average corrosion thickness and real corrosion thickness, which demonstrates a difference in finite element models for deteriorated structures.Therefore this work has reinforced the previous understanding that plate corrosion changes the mechanical properties of steel and that effect needs to be accounted in calculations.Fatigue strength of small-scale type 304 stainless steel thin filmsThis paper presents an experimental study of the fatigue strength of micrometer scale 304 stainless steel (SS) thin films using dynamic bending microbeams. The stress-life data was extended from the tests with R
= 0.15 to the condition of fully reversed loading in order to compare with literature values of the bulk 304 SS. Fatigue damage process was characterized in detail. The results show that the fatigue endurance limit of the micrometer scale samples is higher than that of the bulk 304 SS. Fatigue damage was found to originate from cyclic strain localized regions within the grains. It is argued that fatigue damage behaviors in the micrometer scale 304 SS still follow that of the bulk material, but the fatigue strength has been enhanced due to the influences of both fine grain size and small geometrical dimensions.There is an increasing need to deal with design and manufacturing issues of materials at and below the micrometer level. Fatigue, as one of the most important failure modes in conventional bulk materials, is also an important issue for the long-term reliability of the microcomponents used in micro-electro-mechanical systems (MEMS) and microdevices In this paper, we present an experimental evaluation of fatigue strengths of small scale type 304 SS films with fine grains, which are a candidate material for micro-components in biomedical MEMS. A comparison of the fatigue strength data of the 304 SS thin films with literature values of the bulk 304 SS was conducted. Fatigue damage process was characterized in detail. The possible fatigue size effect in the micrometer scale metals is discussed.The material used in this study is a rolled and subsequently annealed SUS304 SS thin film with fine grains and about 25 μm thickness. The chemical composition of the material is presented in . Micro-cantilever beam type fatigue samples were fabricated by a Focused-Ion-Beam (FIB, Hitachi FB 2000A) system at the ion beam current of 13 nA. presents an SEM image of a group of the microbeams with dimensions of 25 μm × 30 μm × 60–100 μm (thickness × width × length). In order to minimize the Ga+ implantation effect, a fine ion beam current of 10 pA was selected to clean the side surfaces of the samples at a low accelerating voltage of 5 kV.Dynamic bending tests for the microbeams were carried out using a testing machine, with a displacement resolution of 5 nm and a load resolution of 10 μN shows the microstructures of the material characterized by the FIB. The direct observation of the grain distribution through the ion channel contrast of the FIB clearly indicates that the microbeam contains at least eight grains in the width direction. The distribution of the grain size is shown in (b). The average grain size is 2.87 ± 1.15 μm.Before fatigue testing, static bending tests of the microbeams were conducted to estimate the yield stress (corresponding to 0.2% plastic strain) of the thin film. Such a method has been used by Weihs et al. to get the yield stress of thin metal films shows the load-deflection curves of the microbeams with different loading distances. The yield stress as a function of the loading distance is presented in (b). In addition, the tensile yield stress of the thin 304 SS film was also measured and has been plotted as a horizontal dash line in (b). It can be seen that the average yield stress by bending microbeams (σyB=584MPa) is significantly higher than that of the tensile sample (σyT=454MPa). This tendency may be attributed to the effect of strain gradient plasticity induced by bending deformation shows microscopic observations of fatigue damage morphologies at the microbeam surface of the fixed end of the microbeam under the stress amplitude of 234 MPa after 4.5 × 105 cycles. From the left image of , one can see that the strain localization zone (SLZ) formed at the fixed end, which was subjected to the maximum tensile stress. The FIB examination of the SLZ indicates that the extrusions/intrusions-like damage formed in the fine grain, as indicated by an arrow in the upper right image of . Further characterization of the extrusion/intrusion-like damage by an atomic force microscopy (see the lower right image of ) shows that severe strain localization has developed to form extrusions/intrusions with about several hundreds of nanometers dimensions (peaks/valleys), which may become the preferential site for crack initiation. Obviously, the strain localization by forming extrusion/intrusion-like damage in the present micrometer scale sample is still preferred, and that is quite similar to that in the bulk materials . The similar damage process was demonstrated again in another sample, which shows the development of fatigue damage after crack initiation (, two cracks initiated from both sides of the microbeam and grew toward the center of the microbeam. The FIB observation shows that the crack growth path is transgranular, as shown in the right image of . Therefore, it is suggested that the fatigue damage process experienced the following stages similar to the bulk 304 SS: (1) cyclic strain localization and accumulation in the grains oriented preferentially; (2) extrusion/intrusion-induced crack nucleation and (3) crack growth from the nucleation site by the transgranular mode.The number of cycles to fatigue crack initiation at the different stress amplitudes (σa
= (σmax
−
σmin)/2) was determined from the variation of the microbeam stiffness and is plotted in as a function of the applied stress amplitude. Considering the mean stress effect due to non-fully reversed loading here (stress ratio R
= 0.15), the modified Basquin relation by Morrow yielded σf and b as 1471 MPa and −0.123, respectively. In order to compare the present data with the values of bulk 304 SS, which is obtained at the condition of σm
= 0 and R
= −1, the fatigue life of the 304 SS films was predicted based on the Morrow relation, Eq. for σm
= 0 and R
= −1 and the obtained fatigue parameters (σf and b). presents the comparison of the predicted fatigue life and the literature values for bulk 304 SS with different grain sizes shows an SEM micrograph of the fatigue fracture surface morphology. The fracture surface also shows a transgranluar cracking mode which is consistent with the surface observation of the cracking path in The present results clearly reveal that the fatigue damage process is quite similar to that of the bulk material, but the fatigue endurance limit is higher than that of the bulk 304 SS. Similar observations have been report by Allameh et al. It is well known that fatigue damage in bulk ductile metals usually originates from the strain localized region, where extrusions/intrusions form, and from which a crack will eventually nucleate. Following such a damage mechanism, it is expected that the development of strain localization would be affected by the length scale of materials, i.e. both grain size and geometrical dimensions, when they are reduced to a certain value so that dislocation motion is strongly confined. Supporting evidence can be found in fatigue damage behaviours in the thin metal films constrained by a substrate In addition, the fact that fatigue strength is still higher than that of the bulk 304 SS with fine grains (d
= 1 μm), as shown in , implies that the potential contribution of the geometrical dimensions should not be neglected in the micrometer scale material. It is supposed that these contributions of the geometrical dimensions may result from two aspects:The increase in the ratio of surface to volume may change dislocations activity near the surface of the small scale sample. Hofbeck et al. The deformation gradient induced by bending is expected to increase the dislocation interactions both between SSDs and between GNDs and SSDs. That has been manifested by the observed enhancement of the bending yield stress in (b). Therefore, it is expected that the micrometer scale 304 SS would have a higher fatigue strength if they are cyclically deformed under a non-uniform loading condition. This may be of importance for the fatigue reliability design of microbeam-type structural components in MEMS devices.Fatigue strength and damage behavior of small scale 304 SS films have been evaluated. The stress-life data was extended from tests with R
= 0.15 to the condition of fully reversed loading in order to compare with that of the bulk 304 SS. It was found that the fatigue endurance limit of the micrometer scale 304 SS films is higher than that of the bulk 304 SS and is about one-third of the tensile strength of the thin films. Fatigue damage still experienced crack initiation from the strain localized regions and subsequent crack growth by a transgranular mode. It is argued that both fine grain size and small geometrical dimensions of the materials contributed to the increase in the fatigue strength.Microstructure and mechanical properties of AZ91 magnesium alloy developed by Spark Plasma SinteringA gas atomised AZ91 powder has been consolidated by Spark Plasma Sintering (SPS) at different temperatures in the range of 310 °C–500 °C. The influence of the sintering temperature on the Al12Mg17 precipitation and the grain size was investigated through XRD, SEM and EDX analyses. The use of SPS on a metastable powder was demonstrated to be an effective processing route to control the precipitation process while keeping fine grains. Through the estimation of the Hall-Petch and Orowan strengthening, the benefit of this fine microstructure was quantified and the Hall-Petch contribution was revealed predominant. As a consequence for all sintering conditions, the values of resulting hardness (70–90 HV) and Yield Compressive Strength (YCS) (148–230 MPa) were equal or superior to those of the conventional cast AZ91 alloy in its aged T6 condition. The optimum microstructure was obtained for a sintering temperature of 380 °C, for which maximum values of Ultimate Compressive Strength (UCS) and strain at UCS were measured (327 MPa and 13.7%, respectively). These values correspond to an increase by 16% and 11% in comparison to the heat treated cast AZ91-T6 alloy. As for the hardness and YCS at this sintering temperature, they are 8% and 49% higher than those of the cast AZ91-T6 alloy. The study also highlighted that the lack of ductility under tensile testing remains an issue for Mg alloys processed by SPS.The desired reduction of the energy cost, combined with environmental issues, has led to an increased interest in structure lightweighting. This approach particularly concerns the sector of transportation for which low energy consumptions are required. In this context, magnesium appears very promising since it represents the lightest engineering metal, with a density of 1.74 g/cm3, which is 35% and 75% inferior to the main structural metals in use: aluminium and iron respectively The alloys of the AZ series are the most common magnesium alloys, thanks to their moderate cost, improved corrosion resistance and high mechanical strength Although some studies demonstrated the potential of the SPS route to produce small complex pieces The present paper is structured in 3 different sections. The experimental part will describe the techniques and methods used to characterise the microstructure of the as-atomised powder as well as the microstructure and the mechanical properties of the sintered AZ91 alloys. In the result part, the microstructure of the as-atomised AZ91 powder will be firstly depicted in order to define the starting microstructure before sintering and establish its degree of metastability. Secondly, based on a comparison of this initial powder microstructure with those of the sintered AZ91 products, the impact of the SPS process on the alloy microstructure will be evaluated in terms of grain size, fraction and size of the Al12Mg17 precipitates. Then, the mechanical properties – hardness and compressive properties - obtained for the SPS sintered AZ91 alloys will be given. The discussion will focus on the correlation between microstructure and mechanical properties by taking into account the relative contribution of the Hall-Petch and Orowan strengthening estimated for every sintering condition. The mechanical properties of the SPS sintered products will be compared with the ones obtained for cast and heat treated commercial AZ91 alloys as well as some acquired from literature data, in order to highlight the versatility and benefit of this powder metallurgy route.A gas atomised AZ91 powder, supplied by New Material Development GmbH, was used as starting material for the SPS sintering. It consists of spherical particles having a mean size of 22 μm. gives the chemical composition of the powder provided by the supplier. Cylindrical samples, having a diameter of 30 mm and a height of 7 mm, were sintered from the as-atomised AZ91 powder by SPS using a HP D 125 SPS apparatus from FCT Systeme GmbH (Rauenstein, Germany). Different sintering cycles were applied with a final sintering temperature varying from 310 °C to 500 °C. As it is established that fast heating rates may induce local melting at the powder contacts The density of the sintered cylinders was evaluated by the Archimedes' method. The microstructures were investigated by X-Ray Diffraction (XRD), Scanning Electron Microscopy (SEM) and Energy Dispersive X-Ray Spectroscopy (EDX). The XRD analyses were carried out using a D8 Advance Bruker AXS device operating with the Cu Kα radiation. To have referential diffraction peaks on the XRD patterns, small amounts of pure Si powder were added to the as-atomised AZ91 powder or deposited as a thin layer on the sintered AZ91 samples before the XRD analysis. Based on these referential peaks, a correction of the XRD profiles was done through the internal standard method. SEM and EDX investigations were done using a Zeiss Auriga 40 electron microscope and a FEI NNS 450 electron microscope fitted with a Bruker XFlash 6130 detector. To verify the microstructure homogeneity, the analyses were carried out on slices sampled from the centre to the periphery of the sintered cylinders. Mechanical polishing was preliminary carried out on these specimens and was found sufficient to observe the secondary phases, while a subsequent etching with an acetic glycol solution was required to reveal the grain boundaries.To trace the evolution of the Al12Mg17 precipitation during the thermal cycle of the SPS sintering, the size and volume fraction of the Al12Mg17 precipitates were quantitatively measured. The volume fraction of the Al12Mg17 phase in the as-atomised powder and in the sintered AZ91 samples was determined through two distinct methods. On the one hand, a semi-quantitative analysis based on the XRD patterns was performed using the Eva software Finally, the grain size was estimated from SEM images taken from etched specimens, using the linear intercept method recommended by ASTM Vickers hardness tests were done on the sintered samples under a load of 5 kg using an EMCO test M4U-025 apparatus. The hardness values obtained for each SPS treatment condition resulted from the average of 15 indentations done every 2 mm along the thickness and every 3 mm along the radius of the as-sintered samples. Besides, the mechanical properties were also assessed by quasi-static compression tests carried out on cylindrical specimens having a 6 mm diameter and a height of 6 mm, sampled from different places in the as-sintered cylinders. The tests were done at a strain rate of 1.10−3 s−1 using an Instron 5500 K9400 machine. Three specimens were tested per sintering condition. From the true stress-strain curves, three compressive properties were extracted: the Yield Compressive Strength (YCS), the Ultimate Compressive Strength (UCS) and the strain at UCS.To evaluate the strain hardening of the sintered AZ91 alloys, the hardening capacity Hc was used. It represents the capacity to which the material can be strain-hardened For comparison, the same microstructure and mechanical characterisation procedure was applied on specimens issued from sandcast AZ91 plates, supplied by Fonderie du Midi, and heat treated following the conventional T4 and T6 treatments. T4 is a solution heat treatment consisting of a dissolution stage at 400 °C during 24 h followed by a quench SEM observations and EDX analyses were carried out on cross-sectioned particles and a typical example of this characterisation is given in a reveals a quasi-continuous network of micron-sized precipitates along the grain boundaries. The higher magnification image in b highlights the presence of finer brighter precipitates at the contact with the intergranular precipitates and within the grains. The difference in contrast suggests a difference in chemical composition of these precipitates which was confirmed by EDX spot analyses carried out on polished samples. c gives an EDX map obtained on an area located in the micrograph of b. It exhibits the location of the Mg and Al elements in this area. Mg (grey contrast) is more concentrated within the grains while Al (brighter contrast) is more segregated at the grain boundaries.From EDX spot analyses, the intergranular precipitates were identified as Al12Mg17 precipitates with an Al/Mg atomic ratio about 0.6, while the finer precipitates, containing Al and Mn, are likely to correspond to the MnAl4 intermetallic compounds. According to the literature shows the X-Ray Diffraction pattern of the as-atomised powder confirming the presence of Al12Mg17 precipitates in addition to the α-Mg phase. No peak related to the MnAl4 precipitates was detected by XRD. This is due to the low manganese content in the alloy and the low amount of these precipitates in the powder particles. Besides, all the α-Mg peaks are quite large and present a kind of peak splitting on their left (dashed arrow) and a shoulder on their right (full arrow). These features are clearly visible on the zoom of the (101) α-Mg peak given in . These features reflect the metastable microstructure issued from the rapid solidification process. This metastability is characterised by a gradient in chemical composition within the magnesium matrix with some areas being oversaturated in alloying elements, especially aluminium in the case of the AZ91 alloy. Magnesium is known to have no major interstitial site For every sintering temperature condition, the sintered AZ91 samples presented a relative density close to 100%, implying that the full densification of the alloy was obtained for the whole studied temperature range. Moreover, all the processed samples were characterised by an isotropic microstructure that was homogenous at the scale of the sintered cylinder. presents a selection of SEM micrographs at two magnifications illustrating the microstructure modifications for the three examples of samples sintered at 310 °C, 360 °C and 500 °C. For every condition, the presence of Al12Mg17 precipitates can be observed at the grain boundaries together with fine MnAl4 precipitates. For the sintering conditions between 310 °C and 360 °C, an additional population of finer intragranular Al12Mg17 precipitates was observed. Maximum at 310 °C, the amount of this intragranular Al12Mg17 precipitation reduces with increasing sintering temperatures and almost vanishes at 360 °C. While the grain boundaries are highly decorated by intergranular Al12Mg17 precipitates at 310 °C, the micrographs for the sintering temperatures of 360 °C and 500 °C clearly show that this decoration becomes increasingly sparse with the elevation of the sintering temperature. illustrates the evolution of the XRD patterns of the same AZ91 samples sintered at 310 °C, 360 °C and 500 °C, and compares them with the one of the as-atomised powder. As for the atomised powder, the XRD profiles of the sintered AZ91 alloys reveal peaks corresponding to α-Mg and others attesting to the presence of the Al12Mg17 precipitates. However, the intensity of the Al12Mg17 peaks varies with the sintering temperature. Compared to the atomised powder, the intensity of the Al12Mg17 peaks significantly increases for the sample sintered at 310 °C. Then, the intensity decreases when the sintering temperature increases, until a quasi disappearance of the Al12Mg17 peaks at 500 °C. This confirms the reduction in the Al12Mg17 content observed by SEM. Moreover, the features observed on the sides of the α-Mg peaks in the XRD profile of the atomised powder evolve with the sintering temperature. This is illustrated on the right hand side of by the focus on the (101) α-Mg peak. Firstly, the α-Mg peaks become narrower for the sintered AZ91 alloys compared to the atomised powder, and this phenomena becomes more important when the sintering temperature increases. Concomitantly, the shoulder (full arrow) on the right of the (101) α-Mg peak, referring to oversaturated matrix regions, disappears while the peak splitting (dashed arrow) on its left decreases at 360 °C and finally vanishes. These observations highlight a peak sharpening which suggests the occurrence of a homogenisation process of the initial heterogeneous chemical composition during the SPS thermal cycle. In other words, the metastability initially present in the atomised powder progressively disappeared during the SPS sintering process while the alloy microstructure was recovering its equilibrium state.a shows the evolution of the volume fraction of the Al12Mg17 precipitates in the sintered AZ91 alloys estimated by SEM image analysis and by XRD profile analysis. Both quantitative analyses clearly outline the same trends. For sintering temperatures between 310 °C and 340 °C, the volume fraction of Al12Mg17 is higher in the sintered AZ91 samples than in the atomised powder. This is consistent with the Al12Mg17 precipitation observed in the SEM images in a and b. Comparatively, above 340 °C, the Al12Mg17 fraction in the sintered samples becomes inferior to the one that was retained in the atomised powder. It is also interesting to note that the progressive decrease in amount of Al12Mg17 phase reaches an asymptotic value at about 380–400 °C and then the fraction of Al12Mg17 remains rather constant. b gives the evolution of the size of the Al12Mg17 precipitates in the sintered samples estimated by SEM image analysis. For the low sintering temperature conditions (between 310 °C and 360 °C), the Al12Mg17 precipitates have a bimodal size distribution since fine intragranular precipitates formed (see b and d) in addition to the coarse intergranular ones. Comparatively, for the higher sintering temperatures, only a population of intergranular Al12Mg17 precipitates was observed (see f). Before their dissolution at high temperature, the overall size of the intragranular Al12Mg17 precipitates decreased when the sintering temperature was increased between 310 °C and 360 °C. Regarding the intergranular precipitates, the general trend is that their size decreases with an increase of the sintering temperature. The slightly higher size at 360 °C may be due to a kind of competitive Ostwald ripening mechanism between the fine intragranular and coarser intergranular populations during the dissolution process. Above 360 °C, the rate of the size decrease in b drops significantly and, in fact, the size of the intergranular precipitates remains almost constant. Between 380 °C and 500 °C, this rather constant size of the Al12Mg17 precipitates combined with their stable volume fraction (a) indicates that the phase was fully dissolved at temperatures above 380 °C and that the Al12Mg17 precipitates formed during the final cooling. The slight difference in size in this temperature range is likely to come from remnant fluctuation in chemistry and Al distribution in the Mg matrix after the Al12Mg17 dissolution. represents the evolution of the grain size versus the sintering temperature evaluated by the linear intercept method. This evolution shows a two-stage regime with a slope change around 400 °C. Below 400 °C, the slope is modest – 0.05 μm/°C – while it rises – 0.08 μm/°C – for higher sintering temperatures. This change is consistent with the behaviour of the Al12Mg17 precipitates. For the low temperature regime, the presence of Al12Mg17 precipitates and the associated Zener pinning induces a moderate grain growth while, comparatively, their full dissolution at higher temperatures eases the motion of the grain boundaries so that the grain growth proceeds faster. summarises the microstructure characteristics of the sintered AZ91 alloys. In addition to the analysis of the Al12Mg17 evolution, the fraction and size of the MnAl4 precipitates were estimated for the samples sintered at 310 °C, 360 °C and 500 °C, using SEM micrographs at higher magnifications. The MnAl4 precipitates remain fairly stable during the SPS sintering process for the range of studied temperatures. Their average measured fraction (about 0.10 vol%) and size (about 82 nm) are rather similar to the ones retained in the powder. gathers all the mechanical properties obtained for the SPS sintered AZ91 products as well as those of the reference cast and heat treated alloys. shows the evolution of the Vickers hardness of the sintered AZ91 samples as a function of their sintering temperature. The hardness decreases fairly linearly when the sintering temperature increases: from 90 HV at 310 °C to 70 HV at 500 °C. gives the results of the compression tests. a represents the Yield Compressive Strength (YCS) and the Ultimate Compressive Strength (UCS) versus the sintering temperature. Regarding YCS, the trend is similar to the one obtained for the hardness: YCS decreases linearly from 230 MPa at 310 °C to 148 MPa at 500 °C. As for UCS, its evolution should be described in relation with the one of the strain at UCS and the hardening capacity Hc, represented in b and c respectively, for which the trends in their evolution vary in similar ways. Indeed, between 310 °C and 380–400 °C, UCS, strain at UCS and Hc increase to reach their maximum values of 327 MPa, 13.7% and 0.66 respectively. Above 380–400 °C, these three characteristics decrease gradually.This section is divided into 2 parts. Firstly, the influence of the sintering temperature on the Al12Mg17 precipitation and grain size will be recalled. Then, the impact of this microstructure variation on the mechanical properties of the sintered AZ91 alloys will be discussed through the estimated Hall-Petch and Orowan strengthening. The mechanical properties obtained for the AZ91 alloys produced by SPS will be compared to the ones obtained for the cast AZ91 plates tested here and some reported in the literature.Because of the use of a metastable atomised powder having a volume fraction of Al12Mg17 phase far from equilibrium, an Al12Mg17 precipitation occurred for the low range of SPS sintering temperatures and, between 310 °C and 360 °C, this precipitation process gave rise to a fine population of intragranular Al12Mg17 precipitates in addition to the intergranular ones that were initially present in the atomised powder. At higher sintering temperatures, dissolution took place and the intragranular precipitates were gradually completely dissolved. At sintering temperatures above 380 °C, the dissolution of the Al12Mg17 phase was fully completed and the presence of some intergranular Al12Mg17 precipitates in the microstructure is due to the re-precipitation at the grain boundaries on the final cooling. As a result, all the sintered samples presented a microstructure consisting of some fine and rather stable MnAl4 precipitates (about 0.1 vol%) that were present in the as-atomised powder, together with a variable distribution, size and amount of Al12Mg17 precipitates. In the low sintering temperature regime – between 310 °C and 380 °C –, Zener pinning operated and grain growth was restricted. For the higher sintering temperatures, the dissolution of the Al12Mg17 precipitates unpinned most of the grain boundaries and, as their mobility was accelerated, the grain growth was more effective. From , it is clear that the SPS route applied on the gas atomised powder promotes finer grain sizes (3–15 μm) than in the sandcast plates (200–220 μm). These changes in grain size as well as the size and amount of the Al12Mg17 precipitates will obviously affect the mechanical properties of the SPS sintered samples.The evolution of the hardness and YCS is directly related to the capacity of the material to delay the dislocation motion. Three sources of dislocation mobility hindering are available: the grain boundaries, the presence of Al12Mg17 and MnAl4 precipitates, and the solute content in the Mg solid solution. The contribution of the grain boundary can be estimated through the Hall-Petch law Where ΔσHP, ΔσOr and ΔσSS respectively represent the strengthening associated to Hall-Petch, Orowan and the solid solution.To get a detailed insight of the impact of these mechanical contributions on YCS, an estimation of the Hall-Petch and Orowan strengthening was attempted for each sintering condition from the microstructure characteristics of the sintered AZ91 alloys in . Hall-Petch relates the yield stress enhancement to the grain size dg by Equation Where σ0 constitutes the overall resistance of the crystal lattice to the dislocation motion, and k represents the relative hardening contribution of the grain boundaries The Orowan strengthening is expressed by Equation Where M is the Taylor factor (taken as 5 for Mg), G the shear modulus of the alloy matrix (16.7 GPa for Mg), b the magnitude of the Burger vector of the slip dislocations, υ the Poisson's ratio (0.35 for Mg), r0 the core radius of the dislocations, dp the mean precipitate diameter and λ the effective inter-precipitate spacing. Assuming spherical precipitates, λ (Equation Where f is the volume fraction of the precipitates. Besides, in the Mg case, the plastic deformation predominantly occurs via the motion of the dislocations gliding on the basal plane of the α-Mg phase ΔσOr=ΔσOrinterAl12Mg17+ΔσOrintraAl12Mg17+ΔσOrMnAl4Where ΔσOrMnAl4, ΔσOrinterAl12Mg17 and ΔσOrintraAl12Mg17 respectively correspond to the Orowan strengthening induced by the MnAl4, intergranular and intragranular Al12Mg17 precipitates. Since the fraction and size of the MnAl4 precipitates were fairly constant, their mean values – 0.10 vol% and 82 nm respectively – were considered to estimate the Orowan strengthening and their mechanical contribution was found rather limited. Finally, the solid solution strengthening was deducted by subtracting the Hall-Petch and Orowan contributions to the experimental YCS. For comparison, the same approach was employed to estimate the mechanical strengthening for the tested and heat treated sandcast AZ91 alloys – T4 and T6. The resulting mechanical contributions of the SPS sintered AZ91 alloys are listed in and compared with the ones of the heat treated sandcast AZ91 plates. Based on the estimations done for the T4 and T6 conditions, the relevancy of the mathematical approach is checked. Firstly, the estimated Orowan strengthening of the T6 condition is in good agreement with the one reported in the literature (55 MPa) shows the estimation of the three mechanical strengthening – Hall-Petch, Orowan and solid solution – versus the sintering temperature: (a) cumulatively represented and (b) separately represented. The Hall-Petch contribution appears to be the predominant strengthening for every sintering temperature, even if it tends to decrease when the sintering temperature increases due to the grain growth. Regarding the Orowan strengthening, it is mainly induced by the Al12Mg17 precipitation and it is significant for the low temperatures of sintering, for which the intragranular precipitation takes place. Above 360 °C, when the Al12Mg17 dissolution occurs, its contribution becomes much less effective. Obviously, since the Al12Mg17 dissolution induces an enrichment of the Mg matrix in alloying elements, the solid solution strengthening follows an inverse trend. It is interesting to notice that, in all cases, the Hall-Petch strengthening remains the highest mechanical contribution. This can be understood by considering the fact that the hexagonal structure has a limited number of slip systems, in which most of them are difficult to activate. At room temperature, only the basal slip is generally active, since high values of stress are required to reach the significant critical resolved shear stress τc of the additional slip systems – prismatic and pyramidal a) is primarily caused by the grain size increase, which is itself influenced by the Al12Mg17 dissolution. lists the mechanical properties obtained for the sintered AZ91 products and compares them with the ones of cast AZ91 alloys tested and reported in the literature. It is interesting to note that, because of much lower grain sizes arising from the combination of the atomisation and SPS which leads to higher Hall-Petch strengthening, the cast AZ91 products generally have lower hardness and YCS. This is still true for the aged T6 condition despite its full precipitation strengthening (Orowan contribution at 51 MPa). As a consequence, the SPS sintering at 310 °C, gathering precipitation strengthening and low grain size, results in the highest hardness and YCS, respectively 18% and 68% superior to the ones of AZ91-T6.Despite the decrease in YCS, the UCS of the SPS sintered AZ91 samples increases in the range of 310 °C–380 °C due to an elevation of the hardening capacity Hc. This rise in Hc, which represents the material ability to create and retain dislocations, is also reflected by a significant increase in strain at UCS. As a result, the sintering at 380 °C leads to the highest UCS, since its microstructure gathers the optimum conditions in terms of low grain size with moderate precipitate content together with an improved material cohesion. In comparison with the mechanical properties of the aged sandcast AZ91-T6 alloy reported in , this optimum sintered AZ91 product presents higher UCS and strain at UCS (+16% and +11%, respectively). Despite these significant improvements in compressive properties and the apparent full material densification achieved for every SPS temperature, the considerably lower Hc measured for the SPS samples (see c) suggests a rather poor material cohesion when compared to the cast AZ91 product.This was confirmed by tensile tests which revealed tensile fracture strains at around 3% and 8% for the cast alloys under the T6 and T4 conditions, while all the SPS sintered products exhibited tensile ductility at 1% or below. Investigations done in the last decades , which gives a SEM image and an associated EDX map taken from a sample sintered at 360 °C, the same phenomena was observed in our SPS processed samples, where a rather continuous oxide layer has formed at the particle periphery. The consequence of this layer is illustrated in which compares typical examples of fracture surfaces after tensile testing for the cast and SPS products. The cast AZ91-T6 alloy showed a mixed fracture behaviour, with the coexistence of cleavage like domains (arrowed), together with zones containing dimples (high magnification image in inset). It is well established that microcracks can be initiated in the AZ91 alloy at the α-Mg/Al12Mg17 interfaces and along the deformation twin boundaries Thus, it is clear that further mechanical improvement requires the removal or the disruption of the fine oxide layer. This is generally done in the literature by adding a subsequent step of plastic deformation to the powder consolidation process by hot extrusion In an attempt to improve the compressive strength of the AZ91 alloy, an as-atomised powder was used to produce pieces via Spark Plasma Sintering. The metastable microstructure of the powder consisted of fine 1.5 μm grains of α-Mg phase containing about 0.1 vol% of 98 nm MnAl4 precipitates and decorated by an intergranular precipitation of about 4 vol% of Al12Mg17 precipitates (mean equivalent size of 125 nm). From this initial state of the metastable atomised powder, several microstructure modifications were encountered with different regimes depending on the sintering temperature:In addition to the already present intergranular ones, fine intragranular Al12Mg17 precipitates formed during the sintering treatment for temperatures inferior or equal to 360 °C. For higher sintering temperatures, these two populations of precipitates progressively dissolve until their complete dissolution above 380 °C. The small fraction of intergranular Al12Mg17 precipitates observed in the AZ91 sintered between 380 °C and 500 °C is attributed to a re-precipitation process occurring during the final cooling stage.The MnAl4 precipitates were hardly impacted and it could be considered that their size and fraction remained rather constant for every sintering condition.The grain size increased with the sintering temperature following a two-stage regime. In the low temperature range, below 380 °C, the presence of Al12Mg17 precipitates restricted the grain growth through Zener pinning. Above this temperature, the Al12Mg17 dissolution removed this pinning effect, leading to a more significant kinetics of grain growth.Despite a well established lack of ductility inherited from the presence of oxide at the surface of the powder particles, such microstructure evolutions generated substantial modifications of the mechanical properties – hardness and compressive properties – of the SPS sintered AZ91 alloy, which were higher than the ones of conventional cast and heat-treated products:The hardness and YCS linearly decreased with increasing sintering temperatures. Through the estimation of the Hall-Petch and Orowan mechanisms, it was established that the Orowan strengthening was the weakest strengthening mechanism and was only efficient when the intragranular precipitation of Al12Mg17 took place in the low temperature SPS sintering regime (at or below 360 °C). Comparatively, the solid solution strengthening was essentially operating in the high temperature sintering regime (at or above 380 °C). Because of the initial fine grain size of the atomised powder particles, the Hall-Petch strengthening contribution was demonstrated predominant in all the SPS sintering products, and in particular in the low sintering temperature range for which the Al12Mg17 precipitates restricted grain growth.As a consequence of the fine grain size, the hardness (70–90 HV) and Yield Compressive Strength (148–230 MPa) of the sintered SPS samples were always equal or superior to those of the conventional cast AZ91 alloy in its optimum hardening T6 condition. For the sintering temperature of 310 °C, for which the fine grain size and precipitation hardening mechanisms were the strongest, hardness (90 HV) and YCS (230 MPa) were respectively 18% and 68% higher than those of the cast AZ91-T6 alloy.Maximum UCS and strain at UCS were obtained for a SPS sintering temperature of 380 °C, a sintering temperature at which the hardening capacity of the sintered AZ91 was maximised by the combination of three factors: a moderate Al12Mg17 content, a remaining low grain size and an improved material cohesion. At this optimum SPS sintering temperature of 380 °C, the best compromise of properties was obtained: the hardness and YCS were 8% and 49% higher than those of the cast AZ91-T6 alloy while the values of Ultimate Compressive Strength and strain at UCS were respectively increased by 16% (327 MPa) and 11% (13.7%).CFD-DEM simulation of raceway formation in an ironmaking blast furnaceThis paper presents a CFD-DEM study of gas-solid flow in the raceway region in an ironmaking blast furnace (BF). In the simulation, 120,000 spherical particles are packed into a full-scale 2D slot BF geometry. Gas is injected into the geometry via tuyeres, generating raceways in different sizes and shapes under different conditions. It is observed that the raceway characteristics are much more complex under the full-scale BF than those observed under the laboratory scale in the literature. Three kinds of raceways can be identified: anti-clockwise circulating raceway, clockwise circulating raceway, and plumelike raceway. The results are analysed in terms of solid flow patterns, and flow and force structures of particles. The simulation has a good agreement with the observed in physical experiments in terms of two contrary circulating gas vortexes located upon and below tuyeres during raceway formation. Moreover, it is also indicated that operational variables have significant effect on one of the gas vortexes, which becomes the main circulating gas flow stream and determines the gas circulating direction.In an ironmaking blast furnace (BF), hot air is injected laterally from tuyeres, and a void region so called raceway is formed. The raceway plays a critical role in BF, and essential heat and reducing gases for melting and reducing reactions are provided by raceway coke combustion In the recent years, numerical modelling has been increasingly used to study this process, including continuum-based approach (e.g., two fluid model) and discrete-based approach (e.g., CFD-DEM). In the continuum approach, both fluid phase and solid phase are treated as continuous media and described by Navier-Stokes equations. For example, Mondal et al. In this work, the CFD-DEM approach is used to simulate the raceway formation under full-scale BF conditions in a 2D slot model. The key phenomena of raceway formation are predicted. The effect of some key variables on raceway formation is also examined and analysed.For DEM, soft-particle approach originally developed by Cundall and Strack where vi and ωi are the translational and angular velocities of particle i, respectively, and ki is the number of particles in contact with particle i. The forces involved are: the gravitational force mig, and inter-particle forces between particles which include elastic force fc,ij and viscous damping force fd,ij. These inter-particle forces can be resolved into the normal and tangential components at a contact point. The torque acting on particle i by particle j includes two components: Mt,ij which is generated by tangential force and causes particle i to rotate, and Mr,ij commonly known as the rolling friction torque, is generated by normal force and slows down the relative rotation between particles. The equations used to calculate the forces and torques involved in Eqs. For fluid phase, CFD is used to determine fluid flow field. The governing equations for continuity and momentum based on local-average method ∂ρfεfu∂t+∇⋅ρfεfuu=−∇p−∑i=1kcfpf,i/ΔV+∇⋅εfτ+ρfεfgwhere u, ρf and p are the fluid velocity, density, and pressure;
τ and εf are the fluid viscous stress tensor and porosity which are given as τ
=
μe[(∇

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