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= L/26.43·hR2 has been calculated from the “corrected indentation depth” hR obtained by linear extrapolation of the unloading curve to load zero This has been shown already in our paper published nine years ago example of the indentation curve for a nanocomposite coatings with hardness of about 49 GPa, which has been verified by several methods including scanning electron microscope. The reader will also find there the “as measured” curve, which represents the true relation between the applied load and measured displacement not corrected for tip rounding (called also “tip area correction”) and the compliance of the instrument. If one evaluates the “as measured” curve by the O. & P. method, a hardness of about 52.3 GPa, i.e. only 7% higher than the correct one results due to the neglect of the correction for indenter tip rounding and compliance of the instrument. shows a comparison of the different evaluation of the indentation curves for nc-TiN/a-BN superhard nanocomposite coating (sample HF160402) vs. the maximum applied load. Crosses are the values obtained from Fischerscope, and the asterisk is the hardness of 43.95 GPa reported for this coating by Fischer-Cripps at load of 100 mN (see Table I in . This is close to the “factor of two” by which, according to the claim of Fischer-Cripps et al., the hardness of our ultrahard quasi-ternary nanocomposite coatings should be lower than what reported by us. For the ultrahard reference diamond, this factor is exactly 2 The ultrahardness of the quasi-ternary nc-TiN/a-Si3N4/TiSi2 nanocomposite coatings is also supported by the SEM micrographs of the remnant indentations. a shows two examples of such SEM images and b shows the hardness obtained from 3 SEM micrographs at each load. At a load of about 100 mN the plastic deformation of the soft substrate already occurs This paper discusses finite element study of silicone rubber prosthesis for the metacarpophalangeal joint of the hand. Based on the experimental data, a material model which incorporates test data available for different stress states was chosen and calibrated. Finite element models for three commercially available silicone joint prosthesis were developed. All models incorporated the same material model and allowed for large deformations. These models were validated against the experimental data and analyzed under demanding loading conditions. Results such as highly non-linear material behavior, dependence on the loading history and large deformations near wrinkle formation in the hinge area of the joint clearly show the necessity and importance of using multi-stress- state non-linear material models and accounting for large deformations.Flexible silicone metacarpophalangeal (MCP) prostheses are one-piece devices having intramedullary stems to maintain alignment and an inter-bone spacer portion that prevents the ends of the bones from contacting each other. Separating the ends of the bones with an inter-bone silicone material is intended to eliminate bone-to-bone contact and relieve pain.Flexible silicone MCP prostheses have a demonstrated place in MCP arthroplasty and can be effective in reducing joint pain and improving cosmetic appearance (). However, flexible silicone MCP prostheses are much less effective in establishing functional motion and functional strength. They are indicated for use in advanced rheumatoid disease where the demands for strength and motion are very limited but are less suitable for use in osteoarthritic, post-traumatic arthritis or early intervention in rheumatoid arthritic joints having the potential for good strength and motion.The silicone rubber material used in the replacement of small joints is a polydimethylsiloxane of the high consistency group polymerized by a high temperature vulcanization process. This material is ideally suited to the prostheses application as it has considerable ultimate and fatigue strength, biocompatibility, stability, and flexibility. Easily manufactured using standard elastomer techniques and sterilized by conventional methods, silicone rubbers are considered one of the most versatile and important biomedical materials available.Although considered as one the most stable and safest of implantable materials, silicone elastomer medical devices have failed in vivo (see, for example, ). Failure of silicone elastomer in the use of a finger joint is related to the material's tear and fatigue strength properties. Over the history of their use, significant advances have been made in improving the material properties of silicone elastomers as a small joint replacement material since the introduction of the first Swanson small joint prosthesis in the 1970s.However, very little work has been done on mechanical behavior of silicone implant. A few computational models failed to take into account intrinsically non-linear behavior of silicone rubber or effect of large deformations. (). In the aerospace and automotive industries, where modeling of rubber behavior has been studied extensively, these effects are known to play very important role.The present paper addresses these issues for the biomechanical community. It defines the steps required to make an accurate analysis of rubber-like prosthetic device: collection of stress–strain data sets developed by stretching the elastomer in several modes of deformation, selection of material model, calibration of the model to the strain range of application, validation of the material model and modeling of the problem of interest.In order to be able to create an accurate computational model of the silicone rubber joint it is necessary to create a reliable model of the mechanical behavior of silicone rubber. Most commonly, hyperelastic material models are used to describe stress–strain behavior of rubber (Hyperelastic material models are highly capable of representing the non-linear response and nearly incompressibility of rubber, the qualities which make modeling of rubber quite non-trivial. It is beyond the scope of this article to discuss the particularities of different mathematical models of hyperelasticity. However, by mechanically testing a particular rubber and analyzing the data one can choose a material model which would be well reproducing the mechanical response and allow for convergence and stability of the solution process.Physical testing of elastomers for the purpose of fitting material models in finite element analysis (FEA) requires experiments in multiple states of strain under carefully considered loading conditions (). In general, stress and strain data sets developed by stretching the elastomer in several modes of deformation are required. The parameters of the material models are determined by fitting model to these data. Each deformation mode puts the material into a particular state of strain. One objective of testing is to achieve “pure” states of strain such that the stress–strain curve represents the elastomer behavior only in the desired state. Although the experiments are performed separately and the strain states are different, data from all of the individual experiments is used as a set. Maximum strain level experienced by an elastomer is another important parameter, since elastic response of rubber is a function of maximum strain ever achieved. This happens due to stress softening of rubber, known as Mullins effect (). Every time elastomer is stretched to a strain level higher than it has experienced before, the response curve is different from the “stabilized” ones, which reflect the elastomer response when it is repeatedly stretched a few times. shows typical first and stabilized responses for three different maximum strain levels, and for three different modes of deformation. One can see that behavior of silicone rubber is very diverse and extremely non-linear, depending on the history and loading conditions. Linear constitutive models used by lack the ability to represent non-linearity of silicone rubber.The hyperelastic model representing the mechanical behavior of silicone rubber material is usually expressed in terms of strain energy potential (). To determine the appropriate strain energy potential function to be used in the FEA models, preliminary material testing and data analysis were conducted on medical grade silicone rubber.All material test specimens were cut from a thin slab of medical grade silicone rubber in the shapes suitable for specific deformation mode tests (). The manufacturing conditions were the same as used for production of Ascension Silicone MCP implants. Validation results () confirmed that the material properties obtained can be used to accurately model non-Ascension silicon rubber implants analyzed in this study.Stabilized stress–strain response curves for material test specimens subjected to three different modes of deformation (uniaxial tension, planar tension and equal biaxial tension) and three maximum strain ranges (“small strain range” with less than 50% maximum strain in pure shear, “medium strain range” with 50–100% maximum strain in pure shear, and “large strain range” with greater than 100% maximum strain in pure shear) were obtained at a commercial physical testing facility. shows typical stress–strain curves for three different deformation modes and shows stress–strain curves for three different maximum strain ranges (for planar tension deformation mode).Testing was conducted at 23∘C (room temperature) and 37∘C (approximate body temperature) on non-sterile material and material that was subjected to three steam sterilization cycles. These testing parameters were chosen to simulate possible thermal history and working environment for silicone rubber implant.there is no difference in the mechanical behavior of silicone rubber at 23∘C as compared to 37∘C;there is no difference in the mechanical behavior of silicone rubber in the non-sterile condition as compared to the sterile condition;the elastic behavior of the silicone rubber is a function of the maximum strain range history experienced by the material; andthe strain energy potential of silicone rubber is best approximated by Yeoh's reduced polynomial hyperelastic model (the strain energy potential of silicone rubber was modeled using Yeoh's reduced polynomial hyperelastic model (the material model was calibrated using the test data from three different deformation modes; andthe material model was calibrated using the test data for the appropriate maximum strain range experienced in the problem of interest.Failure of silicone elastomer is usually a result of large static and time-varying strains over a long time. Among many factors which contribute to mechanical failure the most important one is mechanical fatigue related to nucleation and growth of cracks in rubber. During service life of a part, the micro-cracks increase in length and depth, eventually linking together and creating a larger crack. The growth of large cracks leads to failure of the part.) is very commonly used to estimate the fatigue life of rubber. It is expected that higher strain energy density usually leads to a shorter life of a part. Since most of the hinge area of implants analyzed in the present paper is in a state of plane strain, and due to the incompressibility of rubber, shear is the main mode of deformation. Therefore, areas of high values of maximum strain energy density and maximum shear strain were used as indicators of possible failure regions.FEA models were analyzed using ABAQUS software (), which is an engineering analysis software package with extended capabilities necessary to analyze the mechanical behavior of rubber materials.most of the hinge area of studied silicone MCP implants is in the state of plane strain; andthere is a good correlation between reaction moment from two-dimensional plane strain models and those from three-dimensional solid models of the hinge area.Therefore, two-dimensional plane strain models were used, since for the same computational effort they allow for higher mesh density than three-dimensional models and therefore more accurate results. As shown in , the two-dimensional models simulated only the hinge area of the silicone MCP implants; the stems of the implants were not modeled. Nominal component dimensions were utilized. Linear, 4-node, reduced integration hybrid elements were utilized throughout the models. Hybrid elements are specially designed for prediction of the response of almost incompressible materials, especially at large strains (). Reduced number of integration points per element also alleviates convergence for nearly incompressible materials. Since solution to contact problems is not smooth enough to benefit from higher accuracy of quadratic elements, linear elements, which are cheaper computationally, were used. A convergence study confirmed that the selected element type indeed performed very well for our problem.Nominal mesh size near proximal and distal collars and refined mesh size in the web area of the hinge were kept constant for all models analyzed. There were two phases of analysis:Validation phase—In this phase, experimental results from a load-deflection test conducted on silicone MCP implant hinges were compared to FEA results to validate the accuracy of the modeling technique.Design comparison phase—In this phase, FEA models simulated hinge extension and flexion of different silicone MCP implants in order to compare the maximum strain and reaction moments for various designs.The stems were cut from the hinge area and aluminum fixture adapters were bonded to the proximal and distal collars of the hinge as shown in . The proximal adapter was attached to the cross-head of a universal test machine, and the distal adaptor was placed in contact with a horizontal linear bearing to minimize extraneous lateral loading on the hinge.The cross-head was then displaced vertically in displacement control mode.For each specimen, load–displacement data were recorded.A FEA model was created for each test specimen. Specimen dimensions were measured using an optical comparator. Boundary conditions simulated the experimental set-up; that is, the proximal collar was oriented horizontally and displaced vertically while the distal collar was allowed to slide without friction along the horizontal plane simulating contact with the linear bearing. Load–displacement curves were computed for each of the models.Two different commercially available silicone MCP implants were tested:Neuflex MCP Finger Implant Size 40, made by DePuy Orthopedics, Inc.Avanta Metacarpophalangeal Implant Size 40, made by Avanta, Inc.The cross-head displacement led to rotation in the hinge area, since there is an angle of approximately 30∘ between the proximal and distal collars. shows maximum shear strain distribution after axial displacement has caused the hinge to rotate so that the proximal and distal collars are parallel. Maximum shear strain does not exceed 50%, therefore the material model calibrated to the small strain range was used. shows excellent agreement between the experimental and the FEA load–displacement curve for this model.The cross-head displacement led to compression in the hinge area, since the proximal and distal collars are parallel. shows maximum shear strain distribution for a 5 lbf axial compression load. Maximum shear strain exceeds 100%, therefore the material model calibrated to the large strain range was used. shows excellent agreement between the experimental and FEA load–displacement curve for this model.The excellent agreement between the experimental and FEA load–displacement curves for these experiments validates the FEA modeling technique—the choice of material modeling, dimensionality, mesh selection, and the application of boundary constraints and loading conditions used for other FEA models in this study.During the design comparison phase, a lab experiment was modeled using FEA. There is no information available, which would allow the definition of exact boundary and loading conditions that correspond to implant behavior in vivo. The lab experiment, on the other hand, prescribes a priori known boundary and loading conditions. The flexion test used to examine endurance of silicone implants was conducted in the lab for three different designs of silicone MCP implants. Since boundary and loading conditions for this test were well defined, the experiment was modeled using FEA. It was speculated that areas of implant with higher levels of strain energy would exhibit shorter fatigue life.During the experiment, silicone implants are installed in a wear tester () which subjects them to 90∘ of cyclic flexion in a heated saline environment for 10 million cycles. The extent of damage sustained is evaluated at specified characterization intervals and after completion of the test. The test apparatus contains electronic control units that monitor the number of flexion cycles and cyclic rate, and a test fluid supply system that supply reservoirs at given temperature. Each test specimen is mounted such that the proximal stem is inserted into a collet attached to an articulating bracket, while the distal stem is inserted into a collet attached to a support bracket (). The distance between the proximal and distal stem collets is chosen to ensure complete stem insertion into the collets. Reciprocating rotational motion of the articulation bracket simulates physiological motion of the implant from 0∘ extension to 90∘ flexion. The distal stem, the entire central flexible hinge, and a portion of the proximal stem of the test specimen are submerged in the test fluid maintained at 40∘C.Cyclic flexion of silicone implants results in creases, pits and tears in the web portion of the hinge on the dorsal and volar surfaces on a given specimen. The number of specimens that exhibited creases, pits and tears increased with increasing number of cycles. Pits form preferentially along creases, and they increase in length and depth with increasing number of cycles to form long tears spanning the width of the specimen.The flexion test was modeled using the finite element method. Small, medium and large Neuflex MCP finger implants made by DePuy Orthopedics Inc., and Ascension silicone MCP implants, made by Ascension Orthopedics Inc., were modeled. Both of these implants are 30∘ flexed when unloaded. Dimensions for models were obtained by measuring components using an optical comparator. Boundary and loading conditions were applied to the models to simulate the lab flexion test as described below.The proximal collar surface was defined as a rigid body and was held fixed. The distal collar surface was defined as a rigid body and was subjected to rotational displacements and loads as follows.Load step 1: counterclockwise rotation of 30∘ to obtain full extension;Load step 2: clockwise rotation of 30∘ to obtain 30∘ of flexion, i.e. unloaded state;Load step 3: clockwise rotation of 20∘ to obtain 50∘ of flexion;Load step 4: clockwise rotation of 25∘ to obtain 75∘ flexion. Rotation to 90∘ flexion often lead to convergence problems; 75∘ flexion appeared to be quite a demanding loading condition yet the one that allowed us to obtain consistently a converged solution.For design comparison, the maximum shear strain and maximum strain energy density distribution on the dorsal and volar surfaces of the hinge were examined and compared. In addition, the reaction moment (i.e., the resistance to distal collar rotation to a given extension or flexion position) was examined and compared for various implant designs and sizes., all reaction moment curves have a magnitude of 0 N m at 30∘ flexion because both devices have a 30∘ pre-flex neutral angle; smaller size devices produce smaller reaction moments as compared to larger size devices. Except for the loading condition of 75∘ flexion, where the differences between the two devices are negligible (1.31E-02 versus 1.30E-02Nm), the reaction moment for the Ascension implant is less than that for the Neuflex device of the corresponding size (In order to illustrate the importance of use of hyperelastic material model for the analysis of large deformations of silicone rubber a linear material model was created. Young's modulus and Poisson's ratio for this material model were computed based on the following assumptions: since rubber is almost incompressible, Young's modulus is equal to 3μ, where μ is the shear modulus; shear modulus was assumed to be the initial shear modulus μ which can be computed as 2C10, where C10 is one of the coefficients of strain energy in Yeoh's reduced polynomial hyperelastic model (): Poisson's ratio was computed based on the assumption that the bulk modulus of rubber is approximately 1000 times larger than its Young's modulus. FEA models utilizing linear material exhibited similar load–displacement curves for validation models defined in to those computed with hyperelastic material, which are shown in . This can be explained by observing that the bulk of the material in validation models undergoes small deformations and therefore the linear model based on initial shear modulus should perform well. The result suggests that the non-linear load–displacement curve is solely result of structural non-linearity.However, for the relatively large deformations of the flexion test as defined in , the linear material model significantly overestimates the reaction moment as shown in . The non-linearity of curves presented in is due to both material and structural non-linearity since even curves for linear material models shown in For all models and all sizes analyzed, shear strain distributions were very similar. The area of maximum shear strain was localized on the dorsal and volar surfaces of the web area of the hinge, and the highest maximum shear strain magnitudes were due to 75∘ flexion (Load step 4). In all models, maximum shear strain did not exceed 85%, therefore, the material model calibrated to the medium strain range was used.Maximum shear strain and maximum strain energy density values at the most demanding loading condition analyzed (75∘ flexion) are provided in The maximum shear strain/maximum strain energy areas predicted by FEA correspond very well to the areas of implants which sustained the most damage during flexion test. This observation confirms the premise that one can expect areas of elastomer with higher levels of strain energy to lead to a shorter fatigue life of the rubber.More over, FEA predicted a counterintuitive result which was later confirmed by flexion test results—crease formation on the volar surface of the hinge. During most of the flexion cycle, the volar surface of hinge experiences not tension, but compression, and therefore intuition makes one believe that there would be no cracking and surface damage. FEA results predicted high values of shear strain and strain energy density in the crease area on the volar surface of the implant during most part of the flexion cycle (), which would lead to surface damage eventually. Indeed, as shown in , cracks were observed on the volar surface of the hinge.The objective of this article was to present to the biomechanical community challenges associated with modeling of highly non-linear mechanical behavior of rubber-like material and to propose the steps necessary to accurately conduct finite element modeling of elastomeric prosthetic device: material testing in multiple states of “pure” strain, selection of material model, calibration of material model to expected strain range, selection of proper element type, validation study, and analysis of the problem of interest.The results of this particular study further confirm the hypothesis that areas with high levels of strain energy can be considered as indicators of high fatigue areas within silicone implants. Knowledge of the locations of high fatigue areas allows one to evaluate or optimize implant design from the point of durability.In addition to improvement of the endurance of device, FEA could also be used to improve functionality of the prosthesis—for example, reaction moment calculations allow one to estimate resistance of a given implant to flexion. Based on the condition of soft tissues surrounding the implant and the corresponding muscles and tendons the surgeon could estimate the strength which the patient would exercise in flexion of the implant and therefore choose an implant design best suited for this particular patient.Further finite element study of the long term mechanical behavior of silicone joint implants calls for necessity of better biomechanical models which would allow to define in vivo loading of silicone implants, and better understanding of fracture and fatigue of rubber which would allow for accurate failure prediction of silicone implants.The authors would like to thank Kurt Miller of Axel Products and Tod Darlymple of ABAQUS Great Lakes for helpful suggestions on testing and analysis of elastomers, and Joe W. and Dorothy Dorsett Brown Foundation for support of this research.Melt-spun shaped fibers with enhanced surface effects: Fiber fabrication, characterization and application to woven scaffoldsScaffolds with a high surface-area-to-volume ratio (SA:V) are advantageous with regard to the attachment and proliferation of cells in the field of tissue engineering. This paper reports on the development of novel melt-spun fibers with a high SA:V, which enhanced the surface effects of a fiber-based scaffold while maintaining its mechanical strength. The cross-section of the fibers was altered to a non-circular shape, producing a higher SA:V for a similar cross-sectional area. To obtain fibers with non-circular cross-sectional shape, or shaped fibers, three different types of metal spinnerets were fabricated for the melt-spinning process, each with circular, triangular or cruciform capillaries, using deep X-ray lithography followed by nickel electroforming. Using these spinnerets, circular and shaped fibers were manufactured with biodegradable polyester, polycaprolactone. The SA:V increase in the shaped fibers was experimentally investigated under different processing conditions. Tensile tests on the fibers and indentation tests on the woven fiber scaffolds were performed. The tested fibers and scaffolds exhibited similar mechanical characteristics, due to the similar cross-sectional area of the fibers. The degradation of the shaped fibers was notably faster than that of circular fibers, because of the enlarged surface area of the shaped fibers. The woven scaffolds composed of the shaped fibers significantly increased the proliferation of human osteosarcoma MG63 cells. This approach to increase the SA:V in shaped fibers could be useful for the fabrication of programmable, biodegradable fiber-based scaffolds in tissue engineering.Tissue engineering has attracted considerable attention as a fusion technology enabling regeneration of tissues and organs lost by disease or accidents To achieve the desired scaffold performance, its physical and mechanical properties, such as porosity, pore interconnectivity, pore size, mechanical strength and surface-area-to-volume ratio (SA:V) must be considered Biodegradable polymeric fibers have been widely used for the fabrication of fiber-based scaffolds in the field of tissue engineering A major shortcoming of textile scaffolds is the limitation of the SA:V compared with non-woven scaffolds. SA:V is defined as the ratio of the surface area to the volume of the scaffold material Three techniques are generally used in the manufacture of polymeric fibers: wet-spinning, dry-spinning and melt-spinning The objective of this study was to produce shaped polycaprolactone (PCL) melt-spun fibers with a larger SA:V for textile scaffolds to enhance the surface effects of the scaffold while maintaining its mechanical strength. The approach for achieving this objective was based on the alteration of the fiber’s cross-sectional shape, while retaining a similar cross-sectional area. It was hypothesized that cell proliferation would be improved by the increased SA:V because of the cross-sectional alteration of fibers, while the mechanical strength of fibers could be maintained through their similar cross-sectional areas. In order to verify the hypothesis, a novel melt-spinning system with replaceable spinnerets, with various capillary shapes to produce circular and shaped fibers, was developed. The increase in the SA:V for the shaped fibers was investigated under different processing temperatures and pressures. For the optimal processing conditions, tensile tests and indentation tests were performed to evaluate the mechanical strength of the fabricated fibers and scaffolds that were woven from the fibers, respectively. The influence of increased SA:V on both the degradation of the fibers and cell proliferation on woven scaffolds was investigated.Biodegradable fibers were fabricated by a melt-spinning system using biodegradable PCL pellets (Aldrich; Mn |
= 45,000). PCL has been widely used in fabrication of scaffolds for various orthopedic tissue regeneration, because its biocompatibility, biodegradability and mechanical strength are suitable and compatible for orthopedics ). The chamber, made from aluminum alloy, efficiently transferred heat from external heaters to the polymer. The interior of the chamber was tightly sealed with rubber rings and a cap, to prevent leakage of pneumatic pressure. The temperature inside the chamber was controlled by a close-looped circuit with three cartridge heaters (capacity ∼10 W cm−2) and a thermocouple. The thermocouple was positioned near the spinneret for accurate measurement of the spinning temperature. The molten PCL inside the chamber was constantly pressurized with a precision pneumatic air regulator for stable spinning. The metal spinneret was easily replaced (when needed) by simply removing four tiny bolts at the bottom of the chamber. The end of the spinneret was dipped slightly below the surface of the deionized (DI) water contained within the cooling bath. The DI water was agitated by a magnetic stirrer and maintained at a cooling temperature of 1 °C inside a jacketed beaker with a coolant circulation system.In the melt-spinning process, the PCL pellets in the chamber were heated to spinning temperatures (TS) ranging from 65 to 100 °C by external heaters to produce the polymer melt. Pneumatic pressure (PN) ranging from 300 to 700 kPa forced the polymer melt to flow to the spinneret with a circular or shaped capillary. The extruded polymer melt, transcribing the capillary shape, was directly inserted into the cooled DI water for rapid solidification of the melt. The resulting as-spun fibers were removed from the DI water after the melt-spinning process.Three different types of spinnerets, with circular, triangular and cruciform capillary shapes, were designed to have the same cross-sectional area of ∼0.04 mm2. For the circular capillary, the diameter was ∼225 μm. Negative curvatures were applied to the triangular and cruciform capillaries to compensate for extrudate swell.The spinnerets were fabricated by deep X-ray lithography (DXRL) and subsequent nickel electroforming. Through DXRL, high-aspect-ratio polymer microstructures that had the shape of the fibers’ cross sections (the capillary shapes) were created. The process using DXRL included four successive steps: (1) X-ray mask fabrication; (2) substrate preparation; (3) exposure to synchrotron X-radiation; and (4) development of the X-ray photoresist. Using the developed photoresist microstructures as a template, nickel electroforming was then carried out to produce the spinnerets with a high-aspect-ratio capillary The SA:V of the fibers melt-spun under the different conditions of TS and PN was calculated by measuring the cross section of the fibers. After the fibers had been cut, cross-sectional images were captured by an optical microscope. Using an image analysis program, the cross-sectional area and the perimeter of the fibers were measured. The extrudate swell and the surface tension of the polymer melt distorted the cross-sectional shape of the fibers. The optimal processing conditions to produce the desired fiber were determined by varying TS and PN during processing.Woven textile scaffolds were fabricated from the as-spun fibers via a plain weaving technique using a custom-built loom, as shown schematically in The tensile strength of the as-spun fibers and the stiffness of the as-fabricated woven scaffolds were measured using an in-house testing machine. The testing machine was designed to measure the forces applied to a fiber and woven scaffold using a load cell. After mounting of a test specimen of the single fiber or the woven scaffold, the applied load was measured in response to the movement of the load cell. A motorized stage moved the load cell in a vertical direction at a constant speed to deform the specimens. The maximum load of the load cell was ∼10 N, and the accuracy was within 0.003 N. To estimate the basic mechanical properties of a fiber, a simple tensile test was performed. The single fiber was stretched by motorized stage via the load cell in the direction of length. The tensile force was measured at a speed of 0.2 mm s−1 until necking of the fiber occurred. The stiffness of the woven scaffolds was measured using an indentation test. A woven scaffold was tightly fixed between two metal plates with a 4-mm-diameter hole. An indentation rod with a 3-mm-diameter hemispherical end was moved downward to the inside of the hole at a speed of 0.4 mm s−1. The indentation force was measured until fiber necking of the woven scaffold occurred.The degradation behavior of the different fibers was evaluated under an accelerated degradation environment. The loss of weight was measured during degradation inside a bath of sodium hydroxide solution (5 M NaOH) In vitro proliferation testing of MG-63 osteosarcoma cells was performed to evaluate the enhanced-surface effect induced by the high SA:V of the shaped fibers. These cells were suspended in a Dulbecco’s modified Eagle medium (DMEM; Gibco) containing 10 vol.% fetal bovine serum (Gibco) and 1 vol.% penicillin (10,000 U ml−1)/streptomycin (10,000 μg ml−1) solution (Gibco) in 5% CO2 at 37 °C. Before cell seeding, each woven scaffold was placed in a 24-well plate, containing 500 μl of medium. Cell suspensions of 200 μl were then seeded at a density of 75,000 cells ml−1 on the medium. The medium was changed every 2 days.The cell proliferation was measured using a cell-counting kit (CCK-8, Dojindo Laboratory). The CCK-8 solution was dissolved in α-MEM with a ratio of 10. To observe the cell proliferation only on the scaffolds, the cultured scaffolds were moved to a new 24-well plate, and the prepared CCK-8 was added. Cell proliferation was estimated by measurement of the absorbance at 450 nm after 3 h. The absorbance was normalized to the weight of each scaffold to compensate for variations in the scaffold size. shows the nickel spinnerets successfully fabricated by DXRL followed by nickel electroforming, at the center of which circular, triangular and cruciform capillaries were realized. The cross-sectional areas of the capillaries were slightly larger than their original designs (PCL fibers with different cross-sectional shapes were fabricated by a melt-spinning system, using the manufactured spinnerets (). The increase in the SA:V of the different fibers was evaluated under different processing conditions of TS (80 and 100 °C) and PN (300, 500 and 700 kPa), as shown in . The fibers spun under the lowest TS (80 °C) and highest PN (700 kPa) conditions exhibited an enlarged cross-sectional area compared with each capillary, as shown in . Deniers of circular, triangular and cruciform fiber were calculated as ∼506, ∼452 and ∼461, respectively. Under these conditions, the measured SA:V increase of the triangular and cruciform fibers was ∼14.70 ± 0.82 and 35.69 ± 1.39%, respectively. The woven scaffolds were created from the circular, triangular and cruciform fibers produced under the conditions specified above (80 °C, 700 kPa).The mechanical characteristics of the as-spun fibers and the as-fabricated woven scaffolds were evaluated through the tensile and indentation tests. The load–elongation and the stress–strain curves of the different fibers are plotted in a and b, respectively. The values of elastic modulus (E), ultimate tensile strength (UTS) and elongation at necking were all calculated from the curves of the different fibers. Although the cruciform fiber and the triangular fiber exhibited the highest E of 346.8 ± 1.7 MPa and the lowest UTS of 12.1 ± 1.4 MPa, respectively, the elongation behaviors of the fibers in response to the applied tensile load showed similar tendencies. The elongations at necking ranged from 17% to 23%. The results of the indentation tests on different woven scaffolds exhibited a similar tendency of load–deflection curves. The average stiffness of the woven scaffolds, composed of circular, triangular and cruciform fibers, was calculated as 3.05, 2.47 and 2.59 N mm−1, respectively. The test results indicated that the different fibers had analogous mechanical properties, owing to their similar cross-sectional areas.The degradation rates increased in the following order: cruciform fiber > triangular fiber > circular fiber (a). The average degradation rates of the cruciform, triangular and circular PCL fibers were 3.75%, 2% and 1.5% day−1, respectively. The rate of degradation was revealed as almost constant for the circular fiber, while the degradation rate of the cruciform fiber was found to vary slightly with time at the accelerated degradation condition. After 20 days of degradation, the weight loss of the cruciform PCL fiber was up to 75%, whereas that of circular PCL fiber was only 20%. This difference in weight loss was caused by the SA:V difference of the fibers. In particular, significant changes in thickness were observed during PCL fiber degradation, as shown in The CCK-8 results of MG-63 osteosarcoma cells on the woven scaffolds over 7 days are plotted in a. The number of attached cells on the different woven scaffolds was similar at day 1. However, the cell proliferation on the woven scaffolds with the cruciform fibers was significantly higher than that on the scaffolds with the other fibers at day 4. Each woven scaffold showed statistical differences of cell proliferation at day 7. In particular, the cell proliferation on the scaffolds with cruciform fibers was more than twice that on the scaffold with circular fibers at day 7. As shown in the scanning electron microscopy (SEM) images in b–g, the amount of the extracellular matrix (ECM) secreted from the cells on the cruciform fibers was much greater than that from the circular fibers for day 7. Most of the ECM was secreted locally at the intersecting points of the weft fibers, along the groove of the cruciform fibers (g). DAPI and phalloidin staining of the cells were also performed to highlight cell distribution as shown in h–m. The scaffolds with the cruciform and triangular fibers exhibited slightly increased numbers of attached cells compared with the scaffold with circular fibers, even from day 1. After 7 days, the cell proliferation was improved on the scaffolds in the following order: cruciform fiber > triangular fiber > circular fiber, as shown in k–m, which was the same trend as the results obtained from CCK-8 and SEM observation. The cells proliferated extensively on the cruciform scaffold compared with the other scaffolds. It was also observed that the some gaps between the adjacent fibers were filled with the cells because of the improved proliferation on the scaffolds with the cruciform and triangular fibers, as indicated in Few studies have been performed to increase the SA:V of the textile scaffolds, although it is clear that the SA:V is one of the most important properties influencing scaffold performance. The lack of research to this point may be attributed to the difficulty in increasing the SA:V of spun fibers using other techniques. Studies have shown that LIGA (German acronym for lithographite, galvanoformung, abformung or lithography electroforming and molding) can be used to produce high-aspect-ratio capillaries During the melt-spinning process, the cross sections of the triangular and cruciform fibers became distorted. The cross-sectional areas were isotropically enlarged by the extrudate swell during spinning, and the cross-sectional shapes were changed from the original capillary shapes to a circular shape by the surface tension of the polymer melt shows that the SA:V of the shaped fibers tended to increase with the pneumatic pressure. This can be explained as follows. In the melt-spinning system depicted in , the cooled DI water near the spinneret was locally heated by conduction, thereby retarding solidification of the spun PCL melt. The highest PN of 700 kPa, which induced an increase in the spinning speed, resulted in rapid immersion of the molten PCL fiber in the lower cooled DI water zone in the cooling bath. This minimized the fiber’s exposure to locally heated zones in the DI water. Additionally, decreasing the TS also improved the SA:V of the triangular and cruciform fibers. It was found that the temperature of the PCL melt heated to the lowest TS of 80 °C was easily lowered to 60 °C (below the melting point of PCL) with the cooled DI water.The mechanical properties did not appear to be affected significantly by the differing cross-sectional shapes of the fibers, because they had similar cross-sectional areas. A little difference in the mechanical properties measured in this study may be induced by the shape effect of cross sections The results of the degradation tests revealed that the degradation rate of the PCL fiber increased significantly; this was attributed to the enhanced surface effects. The results showed that the degradation rate of the scaffold depended on the cross-sectional shape of the fibers. This suggests that shaped fibers could be used as a tool to determine the proper degradation rate for tissue regeneration. Additionally, the combination of different fibers could be applied to the design of a programmable biodegradable scaffold. This approach could also be used to improve the degradation rate of slowly degraded polymers, such as PCL and poly(lactic acid) (PLA). PCL, the biodegradable aliphatic polyester family used in this study, is degraded by two different erosion mechanisms: surface erosion and bulk erosion. According to a previous report ). Therefore, it could be said, from the present accelerated degradation tests, that the degradation rate of PCL fibers can be modulated by varying their cross-sectional shape.Generally, scaffolds with a high SA:V promote efficient cell seeding and subsequent cell proliferation. According to the present results, scaffolds with a high SA:V improved the proliferation of MG-63 cells. The proliferations on the scaffolds with cruciform fibers and triangular fibers increased up to 112% and 50% at day 7, respectively, compared with the scaffold with circular fibers (even though the increments of SA:V of cruciform and triangular fibers were only 35.69% and 14.70%, respectively). This suggests that the promoted proliferations increased because of the enhanced interaction between the cells and scaffold, and the enlargement of the accessible cell proliferation surface The shaped fibers with high SA:V first developed in this study can be effectively used as a textile scaffold with enhanced surface effects. To date, previous studies have focused on the improvement of textile technology by controlling porosity, pore interconnectivity and pore size In this study, shaped PCL melt-spun fibers with a larger SA:V were produced for textile scaffolds, to enhance the surface effects of the scaffold while maintaining its mechanical strength. The approach was based on the alteration of the fiber’s cross-sectional shape, while retaining a similar cross-sectional area. Using DXRL and subsequent nickel electroforming, the present authors developed a novel melt-spinning system with replaceable spinnerets that produced fibers with various capillary shapes, with circular as well as non-circular (shaped) cross sections. Tensile and indentation tests revealed that the mechanical properties of the fibers and the woven scaffolds were maintained, regardless of the cross-sectional shape, because of the similar cross-sectional area of the fibers. The enhanced surface effect induced by the increase in the SA:V was evaluated using degradation tests and cell proliferation tests. The results of the degradation tests revealed that the degradation rate of the PCL fiber increased significantly. Additionally, the results indicated that scaffolds with a high SA:V improved the proliferation of MG-63 cells. The results from this study allow the present authors to conclude that shaped fibers could be used in various tissue engineering fields for the fabrication of programmable, degradation-controlled woven scaffolds.Certain figures in this article, particularly Figs. 4–7, is difficult to interpret in black and white. The full colour images can be found in the on-line version, at http://dx.doi.org/10.1016/j.actbio.2013.05.001Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.actbio.2013.05.001Occurrence of the high grade Thabsila metamorphic complex within the low grade Three Pagodas shear zone, Kanchanaburi Province, western Thailand: Petrology and geochronology► Metamorphism took place at the medium amphibolite–lower granulite facies conditions. ► LA-ICPMS U-Pb zircon ages indicate an age of metamorphism of around ∼51–57 Ma. ► Rb-Sr biotite cooling ages of the basement rock are ∼32–36 Ma. ► The high grade metamorphic rocks were exhumed by sinistral strike-slip shearing.Within the NW–SE trending Three Pagodas shear zone, which is a result of the India–Eurasia collision, a narrow lenticular basement slice of high grade metamorphic rocks, called Thabsila metamorphic complex, is exposed. The Thabsila metamorphic complex is juxtaposed by fault contacts to the very low to non-metamorphic rocks of the shear zone. The high grade basement slice can be subdivided into four units based on lithology: (1) Unit A is composed of marble, mica schist and quartzite, (2) unit B comprises mylonites, (3) unit C is composed of calcsilicate, and (4) unit D comprises various varieties of gneisses. Classic geothermobarometry and pseudosection calculations reveal a P–T variation among the four units. Unit A experienced medium amphibolite facies conditions of 550–650 °C and 5–6.5 kbar while units B, C and D experienced upper amphibolite facies metamorphism, around 640–710 °C and ∼5.5–8 kbar. Age of metamorphism and the cooling history were constrained from LA–ICP–MS U–Pb zircon age and Rb–Sr biotite isochron age. Metamorphic zircon rims yield a metamorphic age of ∼51–57 Ma, while Rb–Sr biotite cooling ages are ∼32–36 Ma. These P–T–t data suggest that the Thabsila gneiss experienced peak upper amphibolite facies metamorphism around ∼51–57 Ma during the early collision between India and Eurasia. Subsequently, whilst lateral southeastward extrusion of the Indochina terrane during Oligocene, it was exhumed due to strike-slip faulting along the Three Pagodas shear zone in the transtensional regime. The observed deformation stages D1 (constriction) and D2 (sinistral shearing) postdate the peak metamorphism and can be related to the exhumation stage. Final cooling of the basement rocks down to a temperature of ∼350–300 °C is indicated by the biotite Rb–Sr ages at around 32–36 Ma.Since early Eocene, the collision between India and Eurasia not only resulted in orogens and plateaus such as the Himalayas and the Tibetean Plateau but also in the formation of large scale strike-slip faults which cut far into SE-Asia (). The Ailao Shan–Red River (ASRR) fault zone is probably the largest and thus the best investigated strike-slip zone related to the collisional event (e.g., Two parallel oriented NW–SE trending large-scale shear zones which are connected to the N–S trending Sakaing Fault in Myanmar, can also be found in the western part of Thailand (). From north to south these are the (1) Mae Ping shear zone, Tak Province and (2) the Three Pagodas shear zone, Kanchanaburi Province. Further south, the conjugated NE–SW trending shear zones, the Ranong and the Khlong Marui Shear zones can be traced within Peninsular Thailand (). All shear zones in Thailand were interpreted to be connected to the evolution of the Paleogene to Neogene basins, both on-shore and off-shore (). Based on field evidences and microstructures, the Mae Ping as well as the Three Pagodas shear zone’s main direction of movement is left-lateral (sinistral). Conversely, the conjugated Ranong and Khlong Marui Shear zones are right-lateral (dextral) ductile movement (The Three Pagodas shear zone (TPSZ) is approximately 250 km long and 25 km wide. Many authors have interpreted that the TPSZ cuts through the lower central plain of Thailand and continues southeastward into the Gulf of Thailand (). The TPSZ crosscuts mainly low to non-metamorphic units such as the Ordovician argillaceous limestones and the Permo-Carboniferous pelitic sequence. However, a slice of high grade metamorphic rocks, named the Thabsila metamorphic complex occurs within the shear zone close to the city of Kanchanaburi. The basement rock exposes as 2–5 km wide slice elongated in NW–SE direction parallel to the strike of the TPSZ. It is juxtaposed by either low grade metamorphic rocks or non-metamorphosed sedimentary rocks with fault contacts. The Thabsila metamorphic complex has been inferred as Precambrian basement rock () and its main rock types are calcsilicates and gneisses. Even though the Thabsila metamorphic complex was described as a metamorphic basement slice of the Three Pagodas shear zone (), little is known about its metamorphic evolution and exhumation history. A similar setting of a crystalline basement complex surrounded by lower grade rocks is reported from the Khlong Marui and the Ranong shear zones () but also from the the Ailao Shan–Red River shear zone. Four distinct and elongated complexes are known in the ASRR: the Xuelong Shan, Diancang Shan, Ailao Shan and the Day Nui Con Voi (). Most authors agree that the ASRR left-lateral strike-slip shearing started about 35 Ma ago and lasted until ca. 17 Ma (The main aim of this study is to characterize the metamorphic evolution of the Thabsila metamorphic complex and place it in the context of shear zone evolution. In addition we present zircon U–Pb and biotite Rb–Sr age data constraining the age of peak metamorphism as well as part of the exhumation history of the crystalline basement rocks by the TPSZ. The main metamorphic overprint can be related with the coupling of West Burma with India () and/or with the onset of the collision of India and Asia (). We will further show that the Thabsila metamorphic complex was exhumed by left-lateral transtensional shearing to the upper crust at 32–36 Ma. However, this event is earlier than the tectonic activity reported from the ASRR. Thus the Thabsila metamorphic complex and the TPSZ are crucial for the understanding of the tectonic evolution of Southeast Asia.The location of the study area is defined within a rectangle extending from longitude 90°00′00″–90°30′00″E to latitude 14°00′00″–15°00′00″N (small box in ). The study area is mainly composed of sedimentary rocks ranking from Cambrian to Jurassic ages and subordinate metamorphic and granitic bodies (). The dominant rock type is limestone which comprises both argillaceous Ordovician limestone and massive Permian limestone. Clastic sedimentary rocks which are less common crop out either as lenticular or narrow slices parallel to the shear zone. The oldest sedimentary formation is the Chao Nen Quartzite of Cambrian age. It comprises mainly massive orthoquartzite, brown to greenish bedded sandstone and calcareous shale. The next stratigraphic younger unit is the U-Thong Marble of Cambrian to Ordovician age. Ordovician limestones are common in this area and are named the Tha Manao limestone () which overlays conformably the Chao Nen Quartzite. The Tha Manao limestone is composed of mudstone at the lowermost part of the formation and grades into massive argillaceous limestone which contains chert nodules. In its upper part, there are some clastic sedimentary rocks, phyllite and quartzite intercalated with gray to dark gray bedded limestone. The Tha Manao limestone is overlain conformal by white shale of Silurian–Ordovician age which is named the Bo Phloi Formation. Conformable younger Carboniferous–Permian clastic sedimentary sequence exposed nearby the Thabsila Gneiss is the Kaeng Krachan Group which mainly comprises diamictite, mudstone and shale. Permian limestone, the Sai Yoke Formation, form a distinctive steep cliff of straight fault scarp with a NW–SE trend. This Permian limestone overlies the brown calcareous Khao Muang Khrut sandstone and is itself overlain by sandstone of the Tha Madua formation.Metamorphic rocks are exhumed along the northern strand of the TPSZ (). Most foliation planes are steeply dipping and strike NW–SE. Field evidence shows sinistral shear sense of ductile movement. Horizontal stretching lineation is typical for the basement rocks (The Thabsila metamorphic complex can be subdivided into four units () based on lithology and structural features: (1) Unit A consists of marble, intercalated mica schist and fine grained Bt-gneiss as well as some quartzite and is located in the northeastern most part of the Thabsila metamorphic complex. The outcrops show a well-developed steep dipping foliation with NW–SE strike and a pronounced stretching lineation with a subhorizontal plunge direction (a). (2) Unit B comprises mylonitic gneiss and mylonite with minor amount of intercalated calcsilicate rocks. This unit is found as a very narrow band of about 500 m across adjacent to unit A. At outcrop-scale, mylonitic gneisses display sometimes augen texture within a very strongly developed foliation. The subordinate calcsilicates occur as boudins or strongly folded slices within the mylonitic gneisses. Asymmetric diopside-rich boudins indicate a sinistral sense of ductile shearing (b). The strike of foliation is NW–SE with a steep dip angle of 70–80°. (3) Unit C is composed mainly of calcsilicate rocks and is located in the central part of the Thabsila metamorphic complex. The strike direction of the calcsilicates is parallel to the trace of the TPSZ but the dip angles show some differences. Most of them are subvertical (70–80°) with NE or SW dip direction. Horizontal stretching lineations and vertical fault planes related to the TPSZ can be observed locally in this unit. Calcsilicates usually occur as thick whitish colored stacks which contain diopside-rich layers alternating with nearly pure marble layers. Tight folds which have fold axis parallel to the stretching lineation are locally found in this unit. At the westernmost margin of this unit a transitional zone towards unit D is observed. In this transitional zone, a narrow band of garnet-free amphibolite occurs which gradually changes into a biotite gneiss. Tight folding is typically observed in this locally exposed zone (c). (4) Unit D consists mainly of biotite gneiss, orthogneiss, and sillimanite gneiss with rarely intercalated calcsilicate rocks. The strike of foliation planes is NW–SE with a steep dip angle of between 60° and 85°. The mineral stretching lineation with NW–SE orientation is consistent with the strike of foliation planes, contrasting to the plunge angles which are subhorizontal. Biotite gneiss usually contains feldspar augen surrounded by a mylonitic quartz-rich matrix.Large amounts of granitic rocks were emplaced within the the Tha Manao limestone and the Bo Phloi Formation shale during the Triassic (see the inset map in ). The intrusions belong to the Central Granite Belt of Thailand (). The granites are typically composed of Bt–Ms–Qtz–Kfs–Pl–Tur.Mineral chemistry of selected samples were measured at the Department of Earth Science, Mineralogy and Petrology, Karl-Franzens University Graz, Austria using a JEOL 6310 SEM equipped with a LINK ISIS energy dispersive system and a MICROSPEC wavelength dispersive system. Analytical conditions were set to an accelerating voltage of 15 kV and sample current of 15 nA. The Phi-Rho-Z procedure was used for matrix correction. Natural mineral standards were used for calibration: adular (Si, K and Al, EDS). Mg and Fe (EDS) were standardized on garnet, Ti and Ca (EDS) on titanite, Mn and Cl (EDS) on rhodonite and atacamite, respectively. Na and F were analyzed by WDS using albite and synthetic F-phlogopite standards. Si, Al, Mg, and Fe were standardized on garnet in case sample garnet is analyzed. Several samples were analyzed at the UZAG Eugen-Stumpfl microprobe laboratory, University of Leoben using a JEOL 8200 Superprobe, natural mineral standards and a ZAF correction method. Detection limits in these routine analyses varies from approximately 0.05 to 0.1 wt.% for the WDS and approximately 0.1 to 0.3 wt.% for the EDS. Mineral analyses of representative samples are shown in The bulk rock chemistry of selected samples was determined by a Bruker Pioneer S4 X-ray fluorescence spectrometer, Karl-Franzens University Graz, Austria. One gram of sample powder and seven gram of Li2B4O7 flux were fused to a glass bead for XRF measurement. About 60 international reference rock powders were used for standardization. Whole rock chemistry of samples are shown in Four representative metamorphic samples were selected from unit A, B and D for U–Pb zircon age dating and two samples for obtaining a biotite Rb–Sr age. Approximately 1 kg of each sample was crushed using a jaw crusher. The crushed material was sieved for a grain size between 0.072 mm. and 0.400 mm. Then, Franz magnetic separator was used to separate magnetic minerals from non-magnetic minerals. Zircons were separated by using heavy liquid and then picked by hand under binocular microscope. All representative zircon grains of each sample were categorized based on color and morphology then mounted in epoxy resin. Zircon mounts were polished until the core of most grains was exposed. JEOL 6310 scanning electron microscope at Karl-Franzens University of Graz was employed to take images of each zircon grain in both cathodoluminescence (CL) mode and back scattered electron (BSE) mode. LA-ICPMS zircon dating was carried out by the State Key Laboratory of Continental Dynamics, Department of Geology, Northwest University, Xi’an, China. The laser-ablation system is a Geolas 200 M (193 nm ArF-excimer laser) from the MicroLas Co. of Germany, and an Agilent 7500 ICP-MS. Instrumental conditions and data acquisition methods follow . All measurements were performed using zircon 91500 as an external standard for age calculation. NIST SRM 610 was used as an external standard for trace element concentration. Isotopic ratios and elemental concentrations were calculated using GLITTER 4.0 (Macquarie University), U–Pb age calculations and concordia diagrams were made using the ISOPLOT program of Two samples, KC 32 and KC44, were selected for Rb–Sr age dating of biotite. Biotite grains were extracted from the magnetic portion. Other non-magnetic minerals in this portion were reduced by repeated magnetic separation. Inclusions and impurities in biotite such as apatite were removed by grinding biotite in an agate mortar with alcohol several times and rinsing the dust particles away. Whole rock Rb–Sr isotope analysis Rb–Sr biotite dating was done at the Department of Lithospheric Research, University of Vienna, Austria. Chemical sample digestion, isotope dilution, and element separation for Rb–Sr analysis follow those given in . Total procedural blanks were <1 ng for Rb and Sr. Rb was evaporated using a Ta filament, and a Finnigan® MAT262. Sr (ID and IC) sample was analyzed using a ThermoFinnigan® Triton TI TIMS machine. A 87Sr/86Sr ratio of 0.710251 ± 0.000018 (2σ; n |
= 30) was determined for the NBS987 (Sr) international standards during the c. 1 year period of investigation. Within-run mass fractionation for Sr isotope compositions (ICs) was corrected for relative to 86Sr/88Sr = 0.1194. Uncertainties on the 87Sr/86Sr isotope ratios are quoted as 2σ. For the 87Rb/86Sr ratios, a mean error of ±1% is applied (representing maximum errors), including blank contribution, uncertainties on spike composition, and machine drift; regression calculation is based on these uncertainties and the isochron calculations follow . Age calculations are based on decay constants of 1.42 × 10−11 |
a−1 for 87Rb (); age errors are given at the 2σ level.Unit A is composed of marble, quartzite, and mica schist with some biotite gneiss. Marble is fine grained, equigranular and contains mainly calcite with some quartz, diopside and plagioclase while dolomite was not found in this marble. Gneissic samples comprise the assemblage Ms–Bt–Qtz±Grt±Kfs±Tur±Ilm±Rt (a). Garnet grains do not show zoning and most of them are almandine and spessartine rich. However composition between samples is variable. Xalm and Xsps contents of ∼0.55–0.57 and 0.32–0.35, respectively are observed in sample KC36. Grossular and pyrope contents are below 10 mol.%. Biotites have XMg contents between 0.27 and 0.30. Metapelitic samples contain the assemblage Bt–Qtz–Pl–Kfs±Grt±Ilm±Tur±Rt. Garnet grains do not show a pronounced zoning pattern () and have Xalm and Xsps contents of ∼0.73 and ∼0.15, respectively (samples K37, K38, and K122). Inclusion of quartz and ilmenite are common. Biotites have XMg contents between 0.28 and 0.40. Plagioclases are sodic rich with Xab contents of 0.74–0.77. Representative analyses of garnet, biotite, and feldspars are given in Unit B comprises mainly mylonitic gneiss with some intercalated calcsilicate. The mylonitic gneiss consists of Qtz–Kfs–Pl–Bt±Ms±Grt±Ilm±Rt±Sil. Some parts of this mylonitic unit are very fine grained and densely foliated (b) whereas most of the mylonitic gneiss is medium grained. The rocks contain porphyroclasts of feldspar and garnet with some recrystallized aggregates rich in biotite as well as quartz ribbon (c). Subgrain rotation (SGR) to grain boundary migration (GBM) recrystallization, strain shadow and bulging structure can be found in feldspar porphyroclasts. Myrmekite is also associated with some feldspar porphyroclasts. Most garnet porphyroblasts contain strain shadows which are commonly filled by biotite and quartz. Garnet crystals contain inclusions of quartz, biotite, alkali feldspar and some sillimanite (d). Garnet compositions do not show pronounced zoning (). Most garnets have high Xalm contents of 0.6–0.8 and Xsps contents about 0.02–0.3 while Xprp and Xgrs contents are less than 0.1 (). Biotites are seen within the foliation and are associated with sillimanite crystals. Its XMg contents are between 0.20 and 0.42 (). Sillimanites which were confirmed by Raman spectroscopy occur as either elongate solitary crystal or as aggregates. Plagioclases are albite rich with Xab contents of about 0.81–0.97 (Unit C, calcsilicates show fine-grained equigranular texture and are composed of Dsp–Pl–Kfs–Cal–Qtz±Tr±Bt±Spn±Scp (e). Garnet is usually absent in this metamorphic unit. Clinopyroxene has an intermediate XMg of 0.57–0.6. Amphibole occurs as 0.3–1 mm sized crystals with XMg contents of 0.7–0.9 and low contents of F and Cl. Plagioclase has anorthite contents of 0.6–0.8 and is usually rimmed by scapolite. Scapolite is not only observed as rims but also forms 0.2–0.5 mm large crystals. The mole fraction of meionite in scapolite (=Ca/(Ca + Na + K) varies slightly between calcsilicate samples and is 0.71–0.83 which corresponds to an equivalent anorthite content (=(Al − 3)/3) of 0.63–0.71. Representative analyses are given in Unit D is composed of varieties of gneisses. Orthogneiss (KC44, PM2) is medium to coarse grained and well foliated. Deformation indicators such as deformed quartz are surrounded by recrystallized grains or displays grain boundary migration. It comprises the assemblage Pl–Kfs–Qtz–Bt±Spn±Grt±Ms with some relic of amphibole. Plagioclase is albite rich with Xab contents of 0.72–0.74 (), unzoned garnets have Xalm contents of 0.55–0.57, Xsps contents of 0.30–0.32, Xprp contents ∼0.07–0.08, and Xgrs contents ∼0.04–0.05 (). Biotites occur as both euhedral crystal, with XMg contents of 0.38–0.40 (). Aluminiumsilicate minerals of this sample were identified by Raman spectroscopy as sillimanite. Mylonitic samples in this unit (TS37, KC284) are fine grained, highly deformed with porphyroclasts of feldspar and quartz and have a well developed schistosity (f). Mylonite is composed of the assemblage Qtz–Kfs–Pl–Bt±Grt±Ms±Rt±Ilm±Spn±Tur. Under polarizing microscope, strong deformation is seen in quartz ribbons and recrystallized aggregates rich in biotite (g), subgrain boundary rotation and S–C fabric. Strain shadows around feldspar porphyroclasts contain usually recrystallized quartz, muscovite and biotite. Some alkali feldspar porphyroclasts coexist with myrmekite texture. Garnets are almandine rich with Xalm contents of 0.70–0.72, while its Xsps contents are about 0.16–0.20, Xprp and Xgrs contents are 0.07–0.09 and ∼0.02, respectively. Xab contents of plagioclase are 0.79–0.81 and XMg contents of biotite are 0.30–0.32.Based on deformation grade, the investigated samples can be classified as high-grade quartzitic gneisses with L ≫ S (KC116) and L > S (KC49) tectonites as well as mylonitic orthogneisses (KC41) and some low-grade slates (KC 18). All four representative samples show coherent sense of shearing which is sinistral (). KC41 as well as KC18 show clear shear sense indicators like mica-fishes and σ-porphyroclasts, respectively (a and b). Due to the totally recrystallized quartz matrix in KC116 and KC49 shear sense has been elaborated by the aid of crystallographic preferred orientation (CPO) of quartz c-axes using the fabric analyser (FA) with the separate software program INVESTIGATOR (). KC116 consists of quartz grains with almost equal grain size and lobate grain boundaries which have been deformed due to grain boundary migration recrystallization at minimum temperatures of about 500–550 °C requiring a respective fluid content and strain rate (e.g. c). CPO indicates a great circle distribution of c-axes along the y–z plane which is indicative for constrictional geometries as result of uniaxial stretching (deformation stage D1: d). Asymmetry of the CPO shows NW-directed shearing. KC 49 contains grains with undulatory extinction and recrystallization at grain boundaries like bulging (BLG) resulting into core–mantle textures indicative for lower temperatures of about ⩽450 °C (e). Grains are larger in size and their c-axes distribution indicates recrystallization due to the dominance of prism 〈a〉 and rhomb 〈a〉 gliding (e.g. f; note that sample was slightly cut oblique to the direction of stretching). This indicates non-coaxial shearing and asymmetry suggests a shear direction to NW (deformation stage D2). Hence, two subsequent deformation stages ranging from uniaxial stretching (constriction D1) to non-coaxial shearing under plane strain conditions (D2) have been established. NW-directed shearing in samples KC41 and KC18 is attributed to D2 which occurred within the high-grade Thabsila gneiss complex as well as outside of the complex and is therefore related to the activity of the TPSZ.P–T conditions of metamorphism were determined by conventional method. Several classic calibrations of geothermobarometer were selected according to mineral assemblage of each selected sample. Moreover, thermodynamic equilibria calculations, pseudosections, were calculated to constrain a P–T path and/or to obtain additional information on peak metamorphic conditions where other methods could not be applied. Thermodynamic modeling was performed with Perplex (Fe–Mg exchange reaction between garnet and biotite was applied to all samples for temperature quantification, whereas, selected calibrated net-transfer reactions were employed in order to calculate pressure. Equations for both thermometers and barometers were calculated simultaneously via the Mathematica package PET (). All symbols for rock-forming minerals used in this study follow Unit A: Qtz–Bt–Kfs–Grt–Ilm(–Rt) metapelite, (KC37, KC38 and KC122) and Bt–Qtz–Kfs–Grt–Ilm gneiss (KC36) were selected to be representative of this unit. KC36 yields P–T conditions of 550–590 °C and 5.5–6.5 kbar based on Grt–Bt thermometer (), respectively. Because of the lack of plagioclase and sillimanite in samples KC37, KC38, and KC122, the phengite barometer (reaction 2) () was applied All samples show a similar pressure of approximately 4.7–6 kbar at temperatures derived from the Grt–Bt thermometer (Almandine+2Grossular+3Siderophyllite+6Quartz=6Anorthite+3Annite3Celadonite=Phlogopite+2K-feldspar+3Quartz+2H2OUnit B: Mylonitic gneiss samples TS11, TS55, TS56, EW34 and KC41 are representative samples of this unit. Grt–Bt thermometer, GASP (reaction 3), and GRAIL (reaction 4) barometer were applied to samples TS55 and TS56. Rutile is usually rimmed by ilmenite and pressures calculated by GRAIL are considered maximum pressures. The results are 645–670 °C, 7.5–7.9 kbar for TS55 and 660–700 °C, 8.8–9.7 kbar for TS56. The GASP barometer yields lower pressures of 6.1–7.5 kbar in sample TS55 and 6.1–8.1 kbar in TS56. The Grt–Pl–Bt barometer was additionally applied to sample TS 56 and results in 5.2–7.0 kbar. P–T conditions of sample EW34 were estimated with Grt–Bt thermometer and Grt–Pl–Bt barometer and the results are 670–705 °C and 6.9–8.2 kbar. The same thermometer and barometer were applied for samples TS11 and KC41. They yield 635–660 °C, 8.9–9.5 kbar and 580–610 °C and 6.5–7.0 kbar, respectively (Almandine+3Rutile=3Ilmenite+Al2SiO5+2QuartzUnit C: This unit consists mainly of calcsilicate and metacarbonate rocks. These rocks types are usually not suitable to gain information on the pressure. However, temperatures can be estimated from the observed fluid independent reactionActivities of anorthite and meionite were calculated according to the models from , respectively. Calcite was considered as a pure phase. Using the thermodynamic data from and assuming a pressure of 6 kbar, reaction 3 is overstepped between 640 and 710 °C, depending on the used sample. Calculated activities and obtained temperatures are summarized in Unit D: even though this unit is lithologically most diverse only few samples are suitable for P–T calculations. Sample TS37 is a representative sample of the mylonites in this unit. The Grt–Bt thermometer and GRAIL barometer were employed and yield a P–T range of 680–720 °C and 8.7–9.9 kbar. However, since the lack of rutile, these values only indicate maximum pressure. The GASP barometer and Grt–Pl–Bt barometer were applied to the same sample and the results are 5.8–7.5 kbar and 5.1–6.6 kbar, respectively. Orthogneiss, PM2 yields P–T conditions of 680–700 °C and 7.2–8.4 kbar on the basis of Grt–Bt thermometer and GASP barometer (, reaction 5) while the Grt–Pl–Bt barometer yields 5.5–6.6 kbar (Diffusional retrogression is commonly observed in upper amphibolite and granulite facies conditions (), hence, the obtained temperature by garnet–biotite Fe–Mg exchange reaction must be interpreted cautiously if a longer cooling period was likely to have taken place. In order to further constrain the P–T conditions, a different approach was employed, namely the calculation of pseudosection of selected samples. The calculated phase stability fields with corresponding mineral composition were compared to observed mineral assemblages and compositions.Three samples were chosen as representative, (1) KC36 for unit A, (2) TS56 for unit B and (3) TS37 for unit D. Whole rock compositions of these samples are given in . Pseudosections were calculated with the program Perplex () using the internally consistent thermodynamic dataset (hp04ver.dat) from and updates. The chemical system Na2O–MgO–Al2O3–SiO2–K2O–CaO–TiO2–MnO–FeO–H2O (TiMnNCKFMASH) was used for most samples. Activity solution models Bio(HP), Pheng(HP) (Its P–T pseudosection shows a series of mineral assemblages with steep boundaries (d). The stability field which contains the assemblage Bt–Ms–Pl–Kfs–Grt–Qtz–Ilm–H2O is stable over a wide P–T field. In order to restrict the P–T conditions, mineral isopleths of garnets (Xsps, Xalm and Xgrs) and plagioclase (XCa) were accounted and the P–T conditions can be constrained as ∼570–600 °C and ∼4–6 kbar. The pressure range is slightly lower compared to Grt–Bt–Pl and phengite barometry (5.5–6.5 kbar), whereas, the temperature range coincides well with results from the Grt–Bt thermometry (550–590 °C).P–T pseudosection of sample TS56 shows a stability field of the observed assemblage Bt–melt–Ms–Pl–Kfs–Grt–Qtz–Sil–Ilm (e). Pseudosection and mineral isopleths of garnet and biotite yield a P–T range of ∼660–720 °C and 4.5–7.0 kbar. This temperature range is consistent with Grt–Bt thermometry (660–700 °C). Pressure range is comparable with the pressure ranges obtained from the GASP and Grt–Pl–Bt barometers.This sample was chosen for pseudosection construction (f). The stability field of the observed mineral assemblage covers a large area in P–T space. Mineral isopleths of garnet (Xprp and Xsps), plagioclase (Xca) and phengite (Si content, apfu) indicate a P–T range of ∼630–660 °C and ∼7.0–8.5 kbar. The temperature is slightly lower than the range estimated by Grt–Bt thermometer (680–720 °C), while pressure is slightly higher than the pressure ranges obtained from the GASP barometer (5.8–7.5 kbar) and the Grt–Pl–Bt barometer (5.1–6.6 kbar).Besides the four samples from the Thabsila metamorphic complex, two additional samples from the nearby granitic bodies (sample KC80 and KC111, see inset map of ) which intruded approximately 15 km further NE of the shear zone were selected for U–Pb zircon ages in order to examine the spatial and temporal relationship between metamorphism and magmatic activities. Cathodoluminescence (CL) images of selected analyzed zircon grains are shown in . On some grains, several spots were analyzed based on its zonation pattern. The U–Pb–Th isotopic ratios, apparent ages, as well as concentrations for U, Th, and Pb are shown in From the muscovite–biotite gneiss sample KC32, only a few zircon grains could be obtained. The U–Pb age of this sample is therefore not well constrained. It shows inherited cores which yield some discordant ages around 400 and 800 Ma (a) and the younger discordant ages obtained from outer rims and elongated crystals yield a mean 206Pb/238U age of 194 ± 19 Ma. Some grains of this younger group show a narrow outer rim further outside of their spots but such zones are not wide enough for LA-ICP MS analysis. Almost all spots show a Th/U ratio <0.3, except the spot from inherited cores (∼760 Ma) which is 0.77. However, most spots show a discordant age which might be a result of lead loss.Orthogneiss sample KC44 gives a mean 206Pb/238U age of 57 ± 1 Ma with a Th/U ratio of 0.7–1.1. Some older ages from inherited cores yield slightly discordant ages around 350–500 Ma and 900 Ma (b). Most of them show Th/U ratio (0.36–0.58).Biotite–sillimanite gneiss (KC279) yields scattered discordant ages which can be roughly grouped into two main age groups (c). The first group obtained from the spots of either typical rounded zircon grains or inherited cores give mostly scattered discordant ages ranging from ∼400 Ma to >1100 Ma. The second age group is younger and is obtained from rims which yield discordant ages around 200 Ma. Some zircons display an outermost rim which is too narrow for LA-ICP MS technique. Most analyses show a Th/U ratio ranging from 0.01 to 0.68.Mylonite sample TS55 contains zircon grains which display some sector zoning, convolute zoning and spongy texture (). The mean 206Pb/238U ages of this sample show highly scattered discordant ages which fall into three groups (d). The oldest group is obtained from inherited cores ranging from around 300 to 1100 Ma. The second group gives discordant ages which scatter around 200 Ma. The third group yields a slightly discordant mean 206Pb/238U age of 51 ± 7 Ma. These spots have an extremely low Th/U ratio of ∼0.003.Summarizing the obtained LA-ICPMS U–Pb zircon ages of the Thabsila metamorphic complex, the following age domains can be approximately recognized: (1) zircon rims and elongated zircons give an age of ∼51–57 Ma, while (2) many zircons, partly cores, yielded an age of ∼200 Ma. (3) Some zircon cores could be dated with ∼400–1450 Ma, most likely being inherited zircons. However, most of them are discordant which can probably best be explained by Pb loss due to a metamorphic overprint.Two samples of the nearby S-type granitoids (e and f). Both granitic samples, KC80 and KC111, show a cluster of slightly discordant ages at 204 ± 3 and 206 ± 2 Ma, respectively, with some spots giving a slightly older age which is a common pattern in granitic plutons that have experienced a slow cooling stage. These spots show diverse Th/U ratio from 0.02 to 1.07. Most zircon grains show a clear oscillatory zoning and some grains show distinct inherited core. The age of some inherited zircon cores is mostly Proterozoic.Information on the cooling history of the Thabsila metamorphic complex was obtained by Rb–Sr biotite isochron ages from samples KC32 and KC44. The muscovite–biotite gneiss KC32 yields an isochron age of 31.8 ± 0.32 Ma with a Sri |
= 0.832029 ± 0.000012 while the orthogneiss KC44 yields 36.1 ± 0.2 Ma with Sri |
= 0.7131840 ± 0.0000048 (). The Rb–Sr isotopic data and calculated isochron ages are shown in In order to constrain the P–T evolution of the Thabsila metamorphic complex, both, conventional geothermobarometric methods (The Gt–Bt thermometer was applied to all samples using the calibration of , Most of the samples result in temperatures around 600–650 °C regardless of the lithological unit. However, lower temperatures of c. 550 °C are found in one sample from the northernmost unit A, while higher temperatures of up to c. 700 °C are recorded in individual samples of units B, C, and D.For the determination of pressure 4 different, mainly pressure dependent net-transfer reactions, the GASP () barometers could be used depending on the mineral assemblage. In samples like TS37, TS55 and TS56 the GRAIL, GASP and Grt–Bt–Pl barometers could be used. In some samples the GRAIL barometer was used although the full mineral assemblage, namely the absence of rutile, was not found or rutile was not in equilibrium with ilmenite. Thus the pressure represents a maximum value. In our calculations results based on GRAIL are usually 1–2 kbar higher than compared to the other three barometers. Additional information about the pressure conditions is given by the aluminium–silicate phase sillimanite, which is found in some samples in garnet as inclusion as well as within the matrix. During garnet growth and during the main deformation event the rocks stayed in the stability field of sillimanite. The Gt–Bt–Pl barometer usually gives a larger variation in pressure which indicates that either the mineral phases are not completely in equilibrium or the calibration is less suitable for our assemblages.The stable mineral assemblage field obtained by the calculated pseudosections typically cover a large area in P–T space and cannot be used alone to estimate the metamorphic peak. By combining the isopleths of garnet and plagioclase end members as well as phengite component a relatively narrow P–T field is given (d–f). From unit A sample KC36 was selected for pseudosection calculation in order to get additional information on especially pressure due to the larger uncertainties in P from the Grt–Bt–Pl and phengite barometer results. The T from the pseudosection is about 570–600 °C which is consistent with the values from the Grt–Bt thermometer. Pressure is in the same range than the values from the Grt–Bt–Pl and phengite reaction. From unit B sample TS56 was chosen for pseudosection modeling. Because of the Grt–Bt results of 660–700 °C as well as the observation of myrmekites indicating melting, a melt phase was included in the calculations. The result gives nearly identical temperatures of 680–720 °C. Except GRAIL, the pressure obtained from both GASP and Grt–Pl–Bt barometers fits well with the range of pressures of 4.5–7.0 kbar obtained from pseudosection calculation. Sample TS37 from unit D yields lower temperatures compared to the Grt–Bt thermometer, but pressure results are consistent. The differences in all used methods, however, are typically within errors which arise from errors in databases and mixing models and probably by Fe3+ content. Fe3+ was omitted in all calculations since no Fe3+ phases as well as calculated Fe3+ end members were observed.Combining the P–T results obtained from both methods we conclude the following P–T conditions for each metamorphic unit are: Unit A yields average temperatures of 550–630 °C and pressures from 5 to 6 kbar. Unit B yields average P–T conditions of 650–700 °C and 5.5–7 kbar. Unit C displays similar temperatures of around 650 °C. Unit D yields average P–T conditions of 640–710 °C and 6–8 kbar.Some zircon ages >600 Ma were obtained from cores of zircon. These zircons or zircon cores are considered to be xenocrysts and thus will be neglected for discussion. Samples KC32, KC44, KC279 and TS55 show a cluster of Devonian ages of ∼400 Ma. Most of these ages were obtained by zircon cores indicating the inherited nature of the zircons. Although similar ages are commonly found in many metamorphic complexes as well as magmatic intrusive rocks in southern and central China and Vietnam. i.e. Yunkhai Massife (), the few samples and unclear relationship to the Thabsila metamorphic complex does not allow any further interpretation.Most metamorphic samples and two granitic samples (KC80 and KC111), except orthogneiss KC44, yield an U–Pb age group of approximately 200 Ma which coincides with the timing of collision between Shan-Thai and Indochina blocks (). Some other authors relate the same event to the collision of the Shan-Thai with the Sukhothai block which is supposed to be a western continental arc of Indochina (). This collision called ‘Indosinian orogeny’ (), resulted in amphibolite to granulite facies metamorphism throughout Shan-Thai and Indochina (). In northern Thailand, Chiangmai and Tak Provinces, high temperature metamorphic events have been interpreted to be related with this orogenic phase as well (). Thus, it is possible that the Thabsila metamorphic complex also experienced metamorphism during the Indosinian orogeny. However, no clear evidences such as two phase garnet growth or mineral relics could be identified. The only hint that these rocks show some influence from this event are the U–Pb ages of around 200 Ma in samples from the Thabsila metamorphic complex.Related to the Indosinian orogeny are numerous granitic intrusion of S-type affinity extending from the north of Thailand southward through western Thailand, peninsular of Thailand, western Malaysia and to Sumatra Island (). Geochronological data of this Sn–W associated granitic belt show late Triassic to early Jurassic age (). Therefore the occurrence of the 200 Ma ages in the Thabsila gneiss can be explained by two possibilities: (1) the Thabsila metamorphic complex was affected by the metamorphic event and these ages resemble the metamorphic overprint, or (2) the Thabsila metamorphic complex consists of metasediments with sedimentation ages younger than 200 Ma and the zircons which give this age group are of detrital origin. The lack of any textural evidence for polymetamorphism and the texture of the zircons favor the second explanation.Only two samples (KC44 and TS55) show a third age group obtained from zircon rims or elongated zircons with very low Th/U ratios. The clear textural association and very low Th/U ratio in zircons from sample TS55 clearly marks them of metamorphic origin with an age of 51 ± 7 Ma. The zircons from the orthogneiss sample KC44 give a within error similar age of 57 ± 1 Ma but display a Th/U ratio of 0.7–1.1, typical for igneous zircons. Thus we conclude that this sample represents a pre- to syndeformative small magmatic intrusion. Similar U–Pb ages have been reported in other metamorphic complexes in the north and south of Thailand as well. Calcsilicates and paragneisses from the Doi Inthanon metamorphic core complex, northern Thailand, yield a poor lower intercept titanite U–Pb age at 47 ± 28 Ma ( reported an U–Pb age from monazite in orthogneisses with 72 and 84 Ma. These ages were interpreted as thermal overprint of the former Late Triassic–Early Jurassic metamorphism. However, without more age data, compilation of metamorphic events between the Thabsila metamorphic complex and those metamorphic core complexes in the north of Thailand is difficult to be succeeded. reported zircon U–Pb ages of metamorphic rocks in the Khlong Marui shear zone. Metamorphic rims of zircons yield similar U–Pb ages compared to our study, e.g. a orthogneiss sample yields 46 Ma, mylonitic granitic gneisses yield 70 ± 2 Ma, 62 ± 1 Ma, 55 ± 3 Ma and 51 ± 0.6 Ma. The author interpreted these zircon U–Pb ages as the onset of exhumation of the metamorphic rocks in the Khlong Marui shear zone prior to the collision between India and Eurasia. report U–Pb zircon ages and muscovite, biotite, and amphibole Ar–Ar ages from the Ranong and Khlong Marui shear zones. They conclude that these shear zones initiated before ∼80 Ma. Both were reactivated and are considered as conjugate shear zones to the Mae Ping and Three Pagodas shear zones between 48 Ma and 40 Ma. During late Eocene (∼37–30 Ma) these shear zones were again reactivated as upper crustal sinistral strands of the Three Pagodas shear zone. The authors attribute the older ages of ∼80 Ma to a Late Cretaceous phase of metamorphism which is also observed in Myanmar and western Thailand (). The Eocene ages (∼48 Ma) correlate to ductile shearing, comparable to the event in the TPSZ, and are interpreted to be related most likely to coupling of India to West Burma.A similar tectonic scenario where a high grade crystalline basement was exhumed within a shear zone is found in the farther north lying Ailao Shan–Red River (ASRR) shear zone. U–Pb zircon age data from the Diancang Shan massif and the Ailao Shan massif which are found within the ASRR shear zone give ages of 26 and 34 Ma (). Such ages were interpreted as magmatic intrusion age and/or metamorphic overprint connected to the activity of the shear zone during the Oligocene. also reported U–Pb zircon ages of intrusive rocks in the Diancang Shan massif with 24–31 Ma. These intrusions are spatially and temporally related to the left-lateral shearing and thus the age of ∼30 Ma was interpreted to date the initiation of the left-lateral shearing along the ASRR shear zone.Our zircon ages are significantly older than the zircon ages of metamorphic and related intrusive rocks in the ASRR shear zone. We conclude that the Thabsila metamorphic complex experienced peak metamorphism at the same time as the metamorphic rocks in the shear zone from southern Thailand and the crystalline rocks from the Doi Inthanon metamorphic core complex. However, this metamorphic event predates the metamorphism which affected the basement rocks from the Ailao Shan–Red River shear zone. This conclusion agrees well with the diachronic strike-slip movement hypothesis in Southeast Asia and China due to the indentation of India which was proposed by U–Pb zircon ages and thermobarometric estimates of this study suggest that the Thabsila metamorphic complex experienced peak metamorphism at amphibolite–lower granulite facies conditions around 51–57 Ma which coincides with the onset of collision between the Indian and Eurasian plates at around 50–65 Ma (). Conversely, this collision is related to the onset of development of the TPSZ and Mae Ping shear zone as proposed by Based on the P–T conditions obtained in this study, the Thabsila metamorphic complex was metamorphosed at mid-crustal depths of approximately 20–30 km. Consequently, the metamorphic complex was exhumed continuously to shallow depths by sinistral shearing of the TPSZ within a transtentional regime and reached 300 °C (closure temperature of biotite) at 32–36 Ma. This Rb–Sr isochron ages fit nicely with the K–Ar biotite ages of 33 and 36 Ma () which were interpreted as the cessation of left-lateral shearing within the Three Pagodas shear zone. Our interpretation is consistent with who suggested that the transtensional regime of the TPSZ was initiated during Late Cretaceous to Early Tertiary prior to the collision between India and western Burma.The observed deformation stages D1 (constriction) and D2 (sinistral shearing) can be related to the advanced exhumation stage of the Thabsila metamorphic complex postdating peak metamorphism at 51–57 Ma. Tight folds within the gneisses and calcsilicates result from D1 which produced fold axes parallel to the direction of stretching, typically for constriction () which were later overprinted by shearing (D2).Finally, these basement rocks were probably further exhumed during the reversal from left-lateral to right-lateral movement at around 24 Ma () which accompanied the east–west extension throughout Thailand and Southeast Asia. Such reversal resulted in many strands of right-lateral oblique faults within the TPSZ. Some vertical displacement evidences were found near the Khao Laem Reservoir, farther to the northwest of the Thabsila metamorphic complex (). These right-lateral faults which are still active () might also have played an important role in the exhumation of the Thabsila metamorphic complex. Concluding the exhumation history of the Thabsila metamorphic complex, we argue that this metamorphic slice was brought up from mid crustal depth to the near surface by sinistral ductile shearing and finally exposed by right-lateral oblique movements accompanied with weathering and erosion of the cover rocks.A comparable exhumation of metamorphic complexes is reported in the Red River shear zone which took also place within a transtensional regime, e.g. the Ailao Shan and Day Nui Con Voi metamorphic massifs () and the Diangcang Shan metamorphic complex in southern China (). However these shear zone related basement rocks were exhumed much later (∼10 Ma) compared to the Thabsila metamorphic complex (32–36 Ma).The Thabsila metamorphic complex comprises a variety of rocks including schists, marbles, quartzites, orthogneisses, mylonites, and calcsilicates which were metamorphosed during the Eocene and are not, as previously thought, a Precambrian basement. The four different lithological units have experienced about similar P–T conditions ranging from upper amphibolite to lower granulite facies metamorphism. Petrography and mineral chemistry suggest a single metamorphic event in the Thabsila metamorphic complex. The timing of the metamorphic overprint could be obtained by U–Pb zircon age dating with 51–57 Ma, which can be related to coupling of India and West Burma and/or the onset of the collision between India and Eurasia. The Thabsila metamorphic complex was exhumed to shallower depths at around 32–36 Ma by early constriction D1 followed by sinistral shearing D2. Both deformation phases are related to the Three Pagodas shear zone which was active in a transtensional tectonic regime. Finally, the basement rocks were exposed to the surface by right-lateral oblique faults accompanied by denudation processes.Preparation of a novel flow improver and its viscosity-reducing effect on bitumenA novel flow improver, the copolymer of octadecyl acrylate, styrene, and maleic anhydride (OASA), was prepared by copolymerization and esterification reaction to study its viscosity-reducing effect on bitumen based its existing application on crude oil. In this paper, chemical compositions, thermal stability, and viscosity were characterized by infrared spectra (IR), differential scanning calorimetry (DSC), and Brookfield Viscometer, respectively. Besides, conventional properties of modified bitumen were investigated to study the effect of modifier. Results shown that OASA modification was physical and its mechanism was the combination effect of polar moiety and long alkyl chain of OASA copolymer; thermal stability of modifier was good enough to capable for asphalt mixing and compaction; viscosity-reducing effect of OASA was proved with a considerable range and the effect was negative to temperature increasing; as for bitumen conventional properties, penetration and ductility got increased while the softening point got decreased under the OASA modifying effect.Recently, warm mix asphalt (WMA) technologies got largely developed due to the benefits such as reducing fuel usage, emissions, and worker exposure As the residuum of oil fraction distillation, the bitumen is similar with crude oil in component fractions while the contents of asphaltene and resin are higher, which appears the higher viscosity than crude oil On the basis of previous preliminary work, in this paper, copolymer of octadecyl acrylate, styrene, and maleic anhydride (OASA) was chosen as flow improver. Preparation of OASA comprised the esterification and copolymerization reactions Raw materials included octadecanol, acrylic acid, p-toluene sulfonic acid (PTSA), toluene, hydroquinone, Benzoyl peroxide (BPO), maleic anhydride (MA), and styrene (ST) were purchased as analytical grade. Virgin bitumen was produced from Karamay (Xinjiang, China) and basic properties were listed in The mono-esters, octadecyl acrylate (OA), was individually prepared via esterification reaction between octadecanol and acrylic acid. Molar feed ratio of octadecanol and acrylic acid was 1.2:1, reaction time was controlled as 6 h, and reaction temperature was set as 120 °C. PTSA served as catalyst and its dosage was 1.0 wt%. Hydroquinone was applied as inhibitor with the dosage as 0.6 wt%. Besides, toluene served as water-carrying agent and its dosage was determined as 40 ml. OASA was prepared by copolymerizing octadecyl acrylate, styrene, and maleic anhydride. Molar feed ratio of OA:ST:MA varied from 5:1:3 to 5:3:5. Reaction time was controlled as 6 h and reaction temperature was fixed as 80 °C. BPO served as initiator with the dosage as 1.0 wt%. The details of esterification and polymerization were referenced to the procedures described by Song and Guan While preparing OASA-modified bitumen, virgin bitumen was firstly heated above 130 °C and then blended with the OASA addition. Molar feed ratio of OA:ST:MA varied from 5:1:3 to 5:3:5. The dosage of modifier was varied from 3% to 7%. Process of adding OASA should be slowly and kept uniformed. The blending was committed by electric blender. Mixing velocity ranged from 450 r/min to 600 r/min and stirring time was determined as 15 min.The compositions of virgin bitumen, OASA-modified bitumen, and the OASA additives were investigated by IR spectra test. Specimens for IR test included virgin bitumen, copolymer OASA with four different molar feed ratios (OA:ST:MA were 5:1:5, 5:2:5, 5:3:3, and 5:3:4), and OASA-modified bitumen whose molar feed ratios were mentioned above. IR spectra test were conducted on each specimen with the dosage as 5%, respectively. The test method was KBr pellet technique and acetone was solvent.The thermal analysis of OASA was conducted by DSC test. Specimen for DSC test were two different copolymers which were designated as OASA1 and OASA2 for OA:ST:MA molar feed ratios were 5:2:5 and 5:3:4, respectively. The amount of OASA1 and OASA2 specimen were taken as 11.33 mg and 11.03 mg. For experimental settings, heating rate was fixed as 10 °C/min, velocity of Nitrogen flow was set as 30 ml/min, initial measuring temperature was −40 °C, and ending measuring temperature was 200 °C.Brookfield DV-II+ viscometer was utilized to measure apparent viscosity of virgin bitumen and OASA-modified bitumen with the dosage of modifier addition as 3%, 4%, 5%, 6% and 7%. With consideration viscosity reduction effect of OASA additives, both virgin bitumen and OASA-modified bitumen were adopted as S21# rotor. Reaction temperature ranged from 110 °C to 160 °C.Technical properties included penetration, softening point, and ductility was evaluated for both virgin bitumen and OASA-modified bitumen. Dosages of modifier addition were 3%, 4%, 5%, 6% and 7%, respectively. The detailed processes were performed according to Chinese specification JTJ052-2000 (in detail, T0624-2000, T0606-2000, and T0605-1993) The IR spectra of octadecyl acrylate, OASA copolymer, virgin bitumen, and OASA-modified bitumen were illustrated as that there was vibration absorption peak of (CH2)n (n |
⩾ 4) appeared at 717 cm−1, characteristic vibration peaks of hydrogen atom within carbon–carbon double bond appeared at 987 cm−1 and 1636 cm−1, vibration absorption peak of carbon–oxygen bond (O) appeared at 1188 cm−1, vibration absorption peak of ether bond (CC) appeared at 1268 cm−1, and stretching vibration peak of carbonyl group within α, β-unsaturated ester appeared at 1727 cm−1. Besides, there was a strong absorption peak located at 3460 cm−1 caused by the carboxyl group. Above all, the esterification between octadecanol and acrylic acid proceed completely and the product was proved to be octadecyl acrylate., it can be observed that there was symmetric vibration appeared at 2850 cm−1 and antisymmetric stretching vibration peak appeared at 2925 cm−1 of methylene (CH2) within long fatty alkyl chain. As there were characteristic absorption peaks of maleic anhydride appeared at 1842 cm−1 and 1781 cm−1 and the lower wavenumber peak was stronger than larger wavenumber peak, hence, we can presumably say that MA was involved in copolymerization reaction. Similarly, as there were characteristic vibration peaks of esters located at 1734 cm−1 and 1173 cm−1, from which we can analyzed that there were ester groups from octadecyl acrylate among the copolymer. Therefore, OA can also be proved as participated into the copolymerization reaction. In addition, as the benzene skeleton vibration absorption peak can be observed at 1647 cm−1 and 1467 cm−1 and combing with the disappearance of the absorption peak of carbon–carbon double bond around 1525 cm−1, it implied that ST got involved in the copolymerization reaction. Overall, the result of analysis indicated that the components OA, ST, and MA all got involved in the copolymerization reaction and the product was proved to be OASA copolymer. showed the IR spectra comparison of OASA with different molar feed ratios of each component. From , it can be found that the IR spectra of copolymers with different proportion were largely similar. The location and number of absorption peaks were accorded while the sizes were slightly varied. As component proportion of OA:ST:MA varied from 5:1:5 to 5:3:4, it should be noted that the stretching vibration peak appeared at 3432 cm−1 of hydroxyl groups were gradually got narrowed and even diminished with decrease of ST. It can be attributed to the connection of hydrogen bonds and formation of carbonyl compound, which enlarged absorption peak strength and moved peaks into the lower frequency band. In brief, infrared spectra of OASA copolymer among different proportions were similar but just differed in functional group concentrations. presented IR spectra of virgin bitumen. It can be noticed that there was a wide absorption band appeared from 3200 cm−1 to 3600 cm−1 due to the existence of NH band. As for the absorption peak located at 2970 cm−1 and 2840 cm−1, it can be accounted for stretching vibration of CH band within cycloalkane and alkane. Absorption peak appeared at 1600 cm−1 was corresponded to the stretching vibration of carbon–carbon double bond and carbon–oxygen double bond. Absorption peaks appeared at 1360 cm−1 and 1480 cm−1 were attributed to deformation vibration of alkane. Absorption peaks appeared at 1456 cm−1 was resulted from anti-symmetric deformation vibration of methyl and scissor vibration of methylene. Absorption band appeared at 1375 cm−1 was attributed to symmetric deformation vibration of methyl, which indicated the existence of saturated hydrocarbon within virgin bitumen. Absorption peak around 1078 cm−1 was in-plane bending vibration of hydrogen atom on benzene ring and absorption band around 721 cm−1 was due to out of plane bending vibration of hydrogen atom on benzene ring, which indicated the existence of aromatic compound within virgin bitumen. In short, chemical composition of virgin bitumen comprised of saturated hydrocarbon, aromatic compound and hetero atom derivatives.In order to compare clearly, IR spectra of virgin bitumen and OASA-modified bitumen were illustrated together in . It can be observed that functional region of virgin bitumen and OASA-modified bitumen was basically similar with each other. For modified bitumen, the absorption bands around 2800–3000 cm−1 were obviously stronger and wider than virgin bitumen, which can be explained as the stretching vibration of saturated hydrocarbon among copolymer molecule. For instance, on modified bitumen IR spectra, absorption peaks at 2910 cm−1 and 2840 cm−1 were attributed to stretching vibration of methylene. In comparison, on virgin bitumen IR spectra, there was a much smaller absorption peak at 2350 cm−1 which may be caused by accidentally mix of CO2. Moreover, on modified bitumen IR spectra, there were absorption peaks characterized anhydride and esters at 1750 cm−1 and 1130 cm−1 while there were no distinct absorption peaks around corresponding area on virgin bitumen IR spectra, which indicated that it was the OASA addition that introduced anhydride and ester into bitumen. Since there were no obvious reactions after introducing new groups and there were no functional groups in OASA which could react with bitumen, the mechanism of OASA addition were validated as physical modification.With the combination of IR spectra results and viscosity reduction mechanism of crude oil, the modification mechanism of OASA copolymer can be summarized as: On the one side, the polar moiety of OASA copolymer such as anhydride can form the stronger hydrogen bonds with polar groups of asphaltene and resin molecules by breaking the original hydrogen-bonding. On the other side, it is the long alkyl chain that stretch and form solvable layer which inhibit re-aggregation of asphaltene and resin molecules. With the combination effect, the structure of asphaltene-resin aggregation was changed from original planar stacking condition to looser structure with lower degree of space extension, and lower degree of order, which attribute to the significant decrease in viscosity of bitumen. demonstrated DSC curves of addition samples, OASA1 and OASA2. Obviously, endothermic peak appeared from 40 °C to 60 °C was sharp, which meant that OASA started to melt out during temperature range of 40–60 °C. It should be noted that there was a rather wide endothermic peak from 125 °C to 200 °C, which might be mixed with small molecules.Overall, with the temperature increasing, there were no other obvious endothermic peaks, which indicated that the thermal stability of OASA addition was good enough to capable for asphalt mixing and compaction (a), as the addition content was controlled as 5%, it is obviously that the viscosity of OASA-modified bitumen was additionally reduced on the basis of increasing temperature with the comparison of virgin bitumen, which validated the viscosity-reducing effect of OASA addition. However, it should also be noted the viscosity differences between virgin bitumen and modified bitumen were gradually decreased as temperature increasing, which indicated the viscosity-reducing effect was temperature-dependent.(b), the relation between temperature and viscosity-reducing percentage was illustrated, where the viscosity-reducing percentage was defined as the viscosity reduction of 5% OASA modified bitumen divided by viscosity of virgin bitumen. Obviously, viscosity-reducing percentage got decreased as time increased. However, the overall viscosity reduction percentages (As addition contents was 5% and temperature was 135 °C) were retained around 25%. Even taking the portion with the least viscosity-reducing effect (OA:ST:MA = 5:1:3) as example, the viscosity-reducing percentage in 160 °C still reached 15%, which can be regarded as a considerable reduction. Besides, it should be noted that the viscosity reduction percentages were largely varied with different portions of OASA copolymer. reflected viscosity-reducing effects of OASA addition from another perspective. The temperature was fixed at 135 °C while the addition contents were variable. As shown, the overall trend of viscosity-reducing percentage is increasing as well as the adding of OASA addition. For any OASA additions with given portion, the viscosity-reducing effect was positively-correlated with addition contents. It is rationally to supposed the copolymer would have better application effect under higher addition contents. On the whole, as the temperature set as 135 °C and the addition dosages ranged from 3% to 7%, the overall viscosity reduction percentages were varied between 10% and 12.5%. Similarly, the viscosity reduction percentage was also related to the composite portion of OASA addition. In brief, the OASA addition did reduced bitumen viscosity at a considerable range and the viscosity-reducing effect was positive to the addition contents and negative to temperature increasing, which was the basis for developing a novel warm-mix additive. However, the effect analysis on reducing viscosity was rather preliminary. Further researches about mixing temperature reduction and the effects on other modified bitumen such SBS modified bitumen were needed for more practical application on WMA technology.In this paper, the bitumen conventional properties tested comprised penetration, softening point, and ductility. illustrated the results of OASA-modified bitumen penetration at 25 °C. demonstrates the result of softening point and , for all the OASA-modified bitumen with different component proportions of OA:ST:MA, the penetration at 25 °C was increasing with adding contents. Furtherly, as the penetration value of virgin bitumen was 69 (0.1 mm) and the penetration results corresponding to 5% content were intensively varied from 86 (0.1 mm) to 104 (0.1 mm), hence, it can be preliminarily concluded that the OASA addition has a quite significant stimulation effect on bitumen penetration, which indicated that the bitumen viscosity in lower temperature was affected by copolymer addition. Besides, the effect of different component proportions should be also taken into accounted as the differences among each lines were relatively huge enough. demonstrated the modification effect on bitumen softening point. On the whole, the softening point appeared to be negative correlated with addition contents. In addition, as the softening point of virgin bitumen was 51.4 °C and almost all the softening points with different proportions were intensively varied from 47.5 °C to 48.5 °C, it can be preliminarily supposed that the OASA copolymer has a quite obvious decreasing effect on bitumen softening point. Similarly, the effect of different component proportions should be also taken into accounted if further research needed, which proved that the component proportion of OASA copolymer do affect bitumen high-temperature performance., it is easily found that the ductility was positively correlated with addition contents on the whole. As the ductility of virgin bitumen was 7.8 cm and the ductility results corresponding to 5% content were intensively varied from 9.5 cm to 11 cm, hence, it can be preliminarily summarized that the OASA addition has a quite significant stimulation effect on bitumen ductility. In other word, the copolymer addition exerted an improving effect on low-temperature performance.In brief, the effects of OASA addition on bitumen conventional properties were proved as stated above. After the addition, for modified bitumen, the penetration got obviously increased, the softening point got obviously decreased, and the ductility also got increased, which indicated that low-temperature viscosity was reduced, high-temperature performance was affected, and low-temperature performance was improved with the OASA addition.In this paper, the conclusions can be summarized as follows:The chemical composition of OASA addition and OASA-modified bitumen were investigated by IR spectra. As the result, the modification was proved as physical modification and mechanism of OASA addition was determined as the combination effect of the polar moiety such as anhydride and long alkyl chain of OASA copolymer.The result of DSC test proved that thermal stability of OASA addition was good enough to apply in mixing and compaction. Besides, the DSC test result shown that it is better to apply OASA addition under rather high temperature.The OASA addition did reduced bitumen viscosity at a considerable range and the viscosity-reducing effect was positive to the addition contents and negative to temperature increasing, which was the basis for developing a novel warm-mix additive. However, the effect analysis on reducing viscosity in this paper was rather preliminary. Further researches about mixing temperature reduction and the effects on other modified bitumen such SBS modified bitumen were needed for more practical application on WMA technology.After the addition, for modified bitumen, the penetration got obviously increased, the softening point got obviously decreased, and the ductility also got increased, which indicated that low-temperature viscosity was reduced, high-temperature performance was affected, and low-temperature performance was improved with the OASA addition.Build direction dependence of microstructure and high-temperature tensile property of Co–Cr–Mo alloy fabricated by electron beam meltingThe microstructures and high-temperature tensile properties of a Co–28Cr–6Mo–0.23C–0.17N alloy fabricated by electron beam melting (EBM) with cylindrical axes deviating from the build direction by 0°, 45°, 55° and 90° were investigated. The preferred crystal orientations of the γ phase in the as-EBM-built samples with angles of 0°, 45°, 55° and 90° were near [0 0 1], [1 1 0], [1 1 1] and [1 0 0], respectively. M23C6 precipitates (M |
= Cr, Mo or Si) were observed to align along the build direction with intervals of around 3 μm. The phase was completely transformed into a single ε-hexagonal close-packed (hcp) phase after aging treatment at 800 °C for 24 h, when lamellar colonies of M2N precipitates and the ε-hcp phase appeared in the matrix. Among the samples, the one built with 55° deviation had the highest ultimate tensile strength of 806 MPa at 700 °C. The relationship between the microstructure and the build direction dependence of mechanical properties suggested that the conditions of heat treatment to homogenize the microstructure throughout the height of the EBM-built object should be determined by taking into account the thermal history during the post-melt period of the EBM process, especially when the solid–solid transformation is sluggish.Cobalt-based alloys have been widely used as materials for valve seats in nuclear power plants, aerospace fuel nozzles and engine vanes, as well as orthopedic and dental implant materials, because of their strength at high temperature, corrosion resistance, excellent wear resistance and biocompatibility The strengthening mechanisms of cobalt-based alloys include solid-solution strengthening, secondary-phase strengthening and grain-refinement strengthening Carbide precipitates located at both grain boundaries and within the grains are expected to increase the strengthening effect Directional solidification can create aligned grain structures, grain boundaries and even strengthening filaments. It was demonstrated that the DZ40M cobalt-based alloy with a columnar grain structure oriented to the 〈0 0 1〉 direction, which was fabricated by directional solidification, has increased rupture strength and resistance against thermal fatigue Recently, EBM has become an established process for additive manufacturing that can create three-dimensional (3-D) complex structures from precursor metal powders In this study, Co–Cr–Mo alloy rods containing high amounts of carbon and nitrogen were fabricated by EBM. The high-temperature tensile properties of the rods with various orientations were investigated, with special focus on the effects of anisotropic columnar grain structure and carbide distribution.The samples were fabricated on an Arcam A2 EBM system (Arcam AB, Mölndal, Sweden). The powder used in the experiment consisted of spherical particles and attached small satellite particles, with an average particle size of 64 μm. The chemical composition of the Co–28Cr–6Mo–0.23C–0.17N alloy powder, shown in , was within the range of ASTM F75 standards. Relatively higher carbon and nitrogen contents were selected in order to obtain a large amount of precipitates and to stabilize the γ-fcc phase, which allowed the γ-fcc crystal growth with 〈0 0 1〉 orientation. The cylindrical axes deviating from the build direction (Z axis) by 0°, 45°, 55° and 90°, shown in , were chosen to orient the cylindrical axes to the [0 0 1], [1 1 0], [1 1 1] and [1 0 0] directions, respectively. Hereafter, the Co–28Cr–6Mo–0.23C–0.17N alloy rods fabricated in the directions of 0°, 45°, 55° and 90° from the Z axis are designated as the 0°-sample, 45°-sample, etc. The rods were 15 mm in diameter and 85 mm in height. The samples were held at 800 °C for 24 h to transform them all into the ε-hcp phase. The tensile samples were taken from the top part of the as-EBM-built samples and cut so that the tensile direction was parallel to the cylinder axis. The gauge part was rectangular, measuring 11 mm in length and 2 mm in width, with a thickness of 1 mm. Tensile tests were conducted at 700 °C with a strain rate of 1.5 × 10−4 |
s−1 on an Instron 8562 testing machine. In order to examine the effect of the matrix phase on the high-temperature tensile properties, the tensile test was conducted on the single-γ-phased 90°-sample. This sample was formed by skipping the post-EBM aging heat treatment because it required a relatively low build height of 15 mm, which allowed us to avoid the γ-to-ε transition during the EBM process. The microstructures were investigated by scanning electron microscopy (SEM), electron backscatter diffraction (EBSD) and X-ray diffraction (XRD) on the vertical cross-section consisting of the cylinder and z axes. The fracture surfaces and neighboring microstructures were also observed by SEM and EBSD, respectively, to determine the fracture mode and the effect of high-temperature tensile deformation on the microstructure.The microstructures of the as-EBM-built EBM samples and age-treated ones are shown in . Precipitates aligned along the build direction were observed in all of the as-EBM-built samples. The average interval between the arrays of precipitates was approximately 3 μm. The lamellar precipitate colonies, indicated by a black ellipse with arrows in , dissolved into the matrix after aging treatment. The XRD profiles () and the phase diagram calculated by Thermocalc software () suggested that the main precipitate was M23C6, and that the elongated precipitates in the lamellar colonies formed after aging treatment were predominately M2N in equilibrium with the ε-hcp phase , M was identified as Cr, Mo or Si in both M23C6 and M2N. The elemental content distribution clearly indicated that the plate precipitates in the lamellar colonies formed after aging treatment were predominately M2N. Because the wavelength of the X-ray reflected from N was very similar to that from Co, its distribution could not be distinguished. Therefore, the nitrogen distribution is not included in . The array of M23C6 along the build direction was attributed to the unidirectional heat extraction in the build direction. The lamellar structure of the M2N precipitates and the ε-hcp phase originated from the eutectoid transformation (γ |
→ |
ε |
+ |
M2N) The EBSD analysis results of as-EBM-built samples are shown in . The measurements were conducted at the top of the rods. The high- and low-angle grain boundaries are indicated by black and light blue lines, respectively, on the inverse pole figure (IPF) maps and phase maps. The boundaries were mostly seen to be aligned along the Z axis. The IPF maps showed the orientations in the direction of the cylindrical axis, and indicated that the preferential orientations of the γ phase in the as-EBM-built samples along the cylindrical axial directions were near [0 0 1], [1 1 0], [1 1 1] and [1 0 0] in the 0°-, 45°-, 55°- and 90°-samples, respectively. These orientations are believed to be a result of oriented crystal growth of the γ-fcc phase along the 〈0 0 1〉 direction.The EBSD results of samples after aging treatment are shown in . All of the samples were transformed into the single ε phase by the aging treatment, as seen in the phase maps. Compared with the grains of as-EBM-built samples, the grains tended to be equiaxed, especially in the 0°-sample. The IPF maps showed the orientations in the direction of the cylindrical axis. No significant preferential orientation was recognized in the ε grains of the aged samples, indicating that the Shoji–Nishiyama (S–N) orientation relationship ((1 1 1)γ//(00 0 1)ε; [101¯]γ//[112¯0]ε) was not fully established during phase transformation. This suggests that diffusive phase transformation occurred during the aging treatment at 800 °C. The average grain sizes of the 0°-, 45°-, 55°- and 90°-samples in the gauge area after aging treatment were 45, 32, 25 and 47 μm, respectively, as calculated from the intercept length perpendicular to the grain boundaries’ elongated direction (the cylinder axis).The stress–strain curves of the samples after aging treatment are shown in . In order to examine the effect of phase constitution on the tensile properties, the tensile result of the 90°-sample with the γ phase is also shown in . Higher UTSs of the aged specimens were obtained in the order of 55°-, 45°-, 0°- and 90°-samples. The 0.2% yield stress of the 0°-, 45°- and 55°-samples were 635 ± 13, 659 ± 30 and 684 ± 14 MPa, respectively, while that of the 90° sample was as low as 459 ± 4 MPa. The elongation of the 90°-sample was 2.5 ± 0.7%, which was comparable to those of the 0°-, 45°- and 55°-samples, at 3.1 ± 0.7, 1.7 ± 0.1 and 2.0 ± 0.5%, respectively. The mechanical properties are listed in . The differences in UTSs, 0.2% yield stresses and elongations of the samples indicated that the tensile properties strongly depended on the microstructure, including the crystal orientation, grain shape and array of precipitates. The strength of the 90°-sample with a single ε phase, represented by 0.2% yield stress and UTS, was higher than that with a single γ phase, but the elongation was as small as 2.5%, which was only about one-fifth of that with the single γ phase. This indicates that, although both of the matrices were strengthened by the carbide precipitates, the ε phase, with a small number of slip systems and higher frictional stress The EBSD results of samples after the tensile tests are shown in . Because the gauge surface is very uneven after deformation, the confidence index is very low. Therefore, the gauge surface was polished and the slip band was removed. No deformation twins were found in the samples. The average grain sizes of the 0°-, 45°-, 55°- and 90°-samples were 37, 25, 24 and 33 μm, respectively, after the tensile tests. Compared with samples before the tensile tests, the grains were almost unchanged. The kernel average misorientation (KAM), which is the average misorientation angle of all adjacent measurement points in the grain, is widely acknowledged to indicate the density of geometrically necessary dislocations (GNDs) b, d, f, h and i) indicated that the GND densities were high not only near grain boundaries, but also inside some grains. The high KAM inside some grains suggests that some grains were in easily deformed orientations, and there were many dislocation pile-ups caused by the dispersion of carbide and nitride precipitates in the grains. The misorientation in the 90°-sample with the γ phase was high throughout the entire observation area, which might be the result of dislocations piling up, caused by the precipitates and simultaneous operation of multiple slip systems in the γ-fcc phase. The ε-hcp phase was not observed in k, suggesting that strain-induced martensitic transformation (SIMT) might not occur in the Co–28Cr–6Mo–0.23C–0.17N alloy.The fracture surface morphologies of the tensile samples are shown in . All samples showed dimple-type fracture surfaces, and carbide precipitates could be seen inside the dimples, as indicated by white arrows. Necking was not observed in any of the samples. The dimple features suggested that the voids were initiated around the precipitates, and their growth and coalescence led to fracture. A large amount of long continuous precipitates or long grooves could be seen on the fracture surface of the 90°-samples (There are several possible factors which can give rise to the differences in the tensile properties of the EBM-built Co–Cr–Mo alloys with different build directions, i.e. the anisotropy of grain boundary shape, carbide arrangement and crystal orientation. Also, the operating slip system should be taken into account for understanding the roles of these factors. Here the roles of the factors are discussed.If anisotropy of the grain boundary shape was the dominant factor, the 45°-sample would exhibit the lowest strength among the samples with different build directions since the largest shear stress, which is applied on planes inclined to the loading axis by 45°, could be applied parallel to most of the grain boundaries, which were mostly inclined to the loading axis by 45°. Also, the probability of dislocations to be blocked by grain boundaries is lower in the shear parallel to the elongated grain than that in the shear perpendicular to the elongated grain. However, the 45°-sample exhibited an even higher UTS than the 0°-sample. This suggests that the effect of grain-shape anisotropy is very weak. It appears that the carbide dispersion hid the effect of grain-shape anisotropy. Grain boundary sliding was also very difficult, probably because of the relatively large grain size and the M23C6 precipitates aligned along the grain boundary. Thus, the effect of grain shape on deformation could be ignored.Here, the operating slip system is discussed. TEM bright-field images of a 0°-sample before tensile tests (after aging treatment at 800 °C) are shown in . The stacking fault (SF) fringe contrast can be seen in a. When the incident beam direction B was [21¯1¯0], the fringe contrast disappeared and the straight line contrasts parallel to the trace of basal planes in the matrix were observed. This indicates that most of the dislocations were on the basal plane, suggesting that the basal slip were ready to operate even before the deformation. Matsumoto et al. Generally, for calculating SFEs of γ-fcc alloys where ΔGγ→ε is the molar Gibbs energy change of the γ→ε phase transformation and σγ/ε is the interfacial energy between the ε and γ phases, which is generally between 2.5 and 7.5 mJ m−2where a is the lattice constant of the alloy and N is Avogadro’s number where ΔGε→γ is the molar Gibbs energy change of the ε→γ phase transformation. This value of SFE at room temperature is positive (130.4 mJ m−2), in contrast to the case in the γ-fcc phase. The value of the SFE of the Co–28Cr–6Mo–0.23C–0.17N alloy with an ε-hcp phase decreases with increasing temperature, and becomes approximately 0 mJ m−2 at 922 °C. The difference between the values of SFE of the Co–28Cr–6Mo–0.23C–0.17N alloy with an ε-hcp phase and that of the Co–27Cr–5Mo alloy with an ε-hcp phase at a given temperature is negligibly small. The value of SFE of ε-hcp Co–28Cr–6Mo–0.23C–0.17N alloys at the deformation temperature of 700 °C is 32.0 mJ m−2 and is much lower than the value at room temperature. The extremely low SFE results in a very widely dissociated Shockley partial dislocation pair, which leads to a low probability of cross slip of dislocations on the basal plane to the prism plane. The difficulty in cross slipping was probably responsible for the low ductility of the ε-hcp Co–Cr–Mo alloys at 700 °C.Here, the role of the carbide arrangement is discussed on the basis of fracture behavior. For the 90°-sample, regardless of whether the matrix phase was in the ε or γ phase, the loading axes were perpendicular to the direction of the carbide array and the longitudinal axes of the elongated precipitates. Under such loading conditions, voids were easily formed around the precipitates. Once the voids coalesced around the precipitates, long cracks could form in the transverse direction, which could easily lead to the final fracture. Therefore, it was natural that the 90°-sample had the lowest UTS value among the samples.Although the appearances of the fracture surfaces were similar to those of Co–Cr–Mo alloys deformed at room temperature with large elongations of more than 30% shows the EBSD image quality (IQ) + IPF map and KAM map of the 0°-sample near the fracture position. It can be clearly seen that the cracks propagated along the grain boundary. Therefore, the fractures of the samples appeared to be intergranular. This may seem contradictory to the dimple-type fracture surface (a), which is generally considered to be characteristic of intragranular fractures. However, it was also observed that the misorientations in the vicinity of the cracks along the grains were very high, indicating that large plastic deformation occurred locally along the fractured grain boundaries. These observations suggest that the cracks tend to initiate at or near the grain boundaries and propagate along grain boundaries decorated with precipitates on a relatively macroscopic length scale, while the fracture occurs intragranularly on the microscopic scale, associated with dimple appearances because of the large plastic deformation localized around the precipitates.k), and certainly would not propagate along the interface between the γ-fcc matrix and the SIMT ε-hcp phase on {1 1 1} to form a quasi-cleavage fracture. For the age-treated samples, the matrix phase had already transformed to a single ε-hcp phase, thus no SIMT was possible. The grain interior did not deform much because of the restriction of a limited slip system in the hcp-structure and the low value of SFE at 700 °C, as mentioned above. The limited slip system resulted in the incompatibility of plastic deformation across grain boundaries and thus the stress was highly concentrated. Also, the carbides decorating the grain boundaries increased the incompatibility of the plastic deformation across the grain boundaries. Therefore, the cracks were inclined to initiate along the grain boundaries. However, large plastic deformation could take place in the vicinity of a crack because a dislocation slip was not difficult under high stress owing to the stress concentration near crack tips. Voids could initiate around the precipitates as a result of large plastic deformation near the crack tip, and their growth and coalescence along the grain boundaries would lead to final fracture. The above should explain the apparent discrepancy between the low ductility and the ductile fracture surface of the EBM-built Co–28Cr–6Mo–0.23C–0.17N alloy with an ε-hcp phase deformed at 700 °C.The pole figure and phase map of transverse cross-section of bottom and top part of the as-EBM-built 0°-sample are shown in . The normal direction (ND) corresponds to the cylinder axis, and the reference direction and transverse direction correspond to the X- and Y-direction electron beam scanning in the EBM process, respectively. a shows that the γ-fcc phase in the bottom part, which was built in the early stage of the EBM process, was transformed into ε-hcp phase during the post-build part (i.e. the period when the upper parts are built) of the EBM process. The peak position of the (0 0 0 1) pole figure in b shows that the (0 0 0 1) plane normal (i.e. [0 0 0 1] direction) was deviated from the ND (i.e. the cylinder axis which used to be oriented to [0 0 1] of the γ phase before phase transformation) by approximately 55°.c shows that the γ-fcc single phase was maintained in the top part, which was built in the late stage of the EBM process. The pole figure of (1 1 1) plane is shown in d. We can examine whether the S–N relationship was maintained during the phase transformation by comparing the position of the {1 1 1} plane of the γ-fcc phase in the top part to that of the (00 0 1) plane of the ε-fcc phase in the bottom part. There are four distinct peaks in the {1 1 1} pole figure of the γ-phase in the top part (d are mostly included in the ring-shaped band of the (0 0 0 1) pole figure of the ε-phase in the bottom part (b). This suggests that there is a considerably high probability that the S–N relationship was maintained throughout the phase transformation during the EBM process. This is probably because isothermal martensitic transformation took place which maintained the S–N relationship The samples for the tensile test were taken from the top part of the rods, which were single γ phase, and transformed to ε-phase by aging-treatment at 800 °C. The random orientation shown in suggests that diffusion transformation occurred during the aging treatment at 800 °C (for 24 h), which was higher than the temperature of the post-melt period in the EBM building process and led to the massive transformation. The different ε-hcp transformation microstructures in the top and bottom parts infer the potential difference in mechanical properties.The phase transformation from γ-fcc to ε-hcp with the S–N orientation relationship is modeled in a in order to examine the possible orientation dependence of tensile properties for the case of phase transformation occurring by isothermal martensitic transformation while maintaining the S–N relationship, as was actually observed in the bottom part of the as-EBM-built sample. The basal plane of ε-hcp corresponds to four nonparallel {1 1 1} planes, α, β, γ and δ, of the parent γ-fcc. Hereafter, the four ε-hcp variants corresponding to α, β, γ and δ are designated as εα, εβ, εγ and εδ, respectively. M23C6 carbides were supposed to align discontinuously along the [0 0 1] direction of the parent γ-fcc, and to be distributed in the parent γ-fcc at equal intervals of 3 μm, as shown in shows the carbide array on the basal plane of εα, εβ, εγ and εδ. The arrows indicate the slip directions of perfect dislocations with the two highest Schmid factors for basal slip in the 0°-, 45°-, 55°- and 90°-samples. Arrows and corresponding build angles are shown in the same color. When two slip directions are the same for different build angles, the same color is used for the different build angles. Because the angles between the [0 0 1] direction of the carbide array and the normal of the four {1 1 1} planes (i.e. the α-, β-, γ- and δ planes) on the parent γ-fcc phase are all 54.76°, the cross-section of the carbides on the basal planes were the same. Also, based on the assumption of the regular arrangement of carbides, the carbide array on the basal planes of εα, εβ, εγ and εδ are exactly the same. This suggests that there is no difference in the effect of carbide arrangement on dislocation slip in the different ε variants. There are slight differences in the carbide intervals along the slip direction in the different variants because of the elongated cross-section shape of the carbide on the slip plane; however, these can be ignored because of the small size of the carbide compared to the carbide–carbide intervals and its fluctuation. Therefore, only the effect of the Schmid factor on the dislocation slip should be considered.Schmid factor μ for basal 〈a〉 system of εα, εβ, εγ, and εδ are shown in . The loading axis in the 0°-, 45°-, 55°- and 90°-samples are supposed to be [0 0 1], [0 1 1], [1 1 1] and [0 1 0] of the parent γ-fcc, respectively. The maximum μ was 0.408 for the 0°-, 45°- and 90°-samples, while it was 0.272 for the 55°-sample. This suggests that the dislocation in the 55°-sample was the most difficult to slip. Supposing the probabilities for εα, εβ, εγ and εδ to be the same, only 50% of the grains in the 45°-samples will deform according to the Schmid factor, as opposed to 33.3% of grains in the 55°-sample and 100% of grains in the 0°- and 90°-samples. Therefore, the 45°-samples would be much more difficult to deform than the 0°- and 90°-samples, though their maximum Schmid factors are the same. Based on the discussion above, the strength is expected to be high in the order of 55°-, 45°- and 0°- or 90°-samples.When the grain orientation of ε-hcp was random as a result of the diffusion transformation, such an orientation dependence of strength would diminish. However, the order of the strength of the samples was similar to those expected for the case of S–N relationship. This suggests that some portions of the ε-phase grains formed by the aging treatment are formed by isothermal martensitic transformation, which maintains the S–N relationship.It is also suggested that the conditions of heat treatment to homogenize the microstructure throughout the height of the EBM-built object should be determined by taking into account the thermal history during the post-melt period of the EBM process, especially when the solid–solid transformation is sluggish.The preferential crystal orientations of the γ phase in the as-EBM-built 0°-, 45°-, 55°- and 90°-samples along the cylindrical axial directions were near [0 0 1], [1 1 0], [1 1 1] and [1 0 0], respectively. M23C6 precipitates were observed to align along the build direction with intervals of around 3 μm in all of the samples.The γ-fcc matrix phase could be wholly transformed into ε-hcp phase after aging treatment at 800 °C for 24 h. No significant preferential orientation was recognized in the ε grains of the aged samples. Also, lamellar colonies composed of M2N precipitates and the ε-hcp phase appeared in the matrix after aging treatment. M was determined to be Cr, Mo or Si in both M23C6 carbide and M2N nitride.An SF existed on the basal plane of age-treated ε-hcp samples, and the basal slip might be the only deformation mode during high-temperature tensile deformation. Grain boundary slip did not occur at 700 °C. The extremely low SFE and carbide array are possible reasons for the poor ductility.All of the aged samples exhibited intergranular fracture. Voids were initiated around the precipitates, and their growth and coalescence along grain boundaries led to final cracks.The sample built with 55° deviation from the Z axis had the highest UTS of 806 MPa at 700 °C with a strain rate of 1.5 × 10−4 |
s−1. The diffusional phase transformation does not weaken the anisotropic mechanical properties notably.It is suggested that the conditions of heat treatment to homogenize the microstructure throughout the height of the EBM-built object should be determined by taking into account the thermal history during the post-melt period of the EBM process, especially when the solid–solid transformation is sluggish.Rheology investigations on the influence of addition sodium polyacrylate to calcium carbonate suspensions▶ By combining rheological tests, TD-NMR relaxation and particle size distribution measurements, we were able to obtain a clear picture on the effect of sodium polyacrylate on the stability of CaCO3 suspensions. ▶ Flocculation effects were reduced by increasing NaPAA concentration on CaCO3 suspensions. ▶ Selective Adsorption of Polyacrylic acid fraction with low molar mass on CaCO3 and consequentelly better suspension stability.The stability of concentrated CaCO3 suspensions (40 wt%) on addition of sodium polyacrylate (NaPAA, PA20, with molar mass of 2100) has been investigated using rheological measurements. On addition of NaPAA to the suspension, there is a selective adsorption of PA fraction with molar mass of 2000–5000. This selective adsorption is due to entropic effects and heterogeneous charge distribution. The smaller sized polyelectrolyte chains can more easily find local patches at the interface, devoted of previously adsorbed molecules, which are characterized by more favourable interaction profile. Steady-state shear stress-shear rate curves were obtained as a function of PA20 concentration (0–0.7 wt%). All suspensions showed pseudoplastic flow curves (shear thinning behavior) with some thixotropy. In the absence of PA20, and in the presence of 0.1% PA20 the flow curves show significant hysteresis indicating weak flocculation. This was confirmed by measuring the particle size of the suspension on dilution of system. On further addition of PA20 (0.2–0.7 wt%), the suspensions showed much less thixotropy and the weak flocs produced were broken down on dilution giving a mean diameter of about 1 μm. The flow curves could be fitted to the Herschel Bulkley model and values of the yield value σβ, consistency index k and shear thinning index n were obtained as a function of PA20 concentration. Initial addition of PA20 (0.1 wt%) caused an increase in σβ and k indicating more flocculation at this PA20 concentration. The data showed a reduction in σβ from 7.6 Pa at 0.1 wt% PA20 to 1.7 Pa at 0.7% PA20. The rheological results also showed a continuous reduction in k and increase in the value n (less shear thinning behavior). However, all suspensions showed weak flocculation at such high CaCO3 concentrations (40 wt%). Further insights into the flocculation behavior of CaCO3 suspensions with added NaPAA were gained in proton TD-NMR studies of the water phase of the suspension and sediment phases. This weak flocculation could be significantly reduced on dilution of the suspension from 40 to 20 wt%. A plot of σβ versus ζ2 showed non-linear behavior and this clearly indicated that the stability of CaCO3 suspensions in the presence of NaPAA could not be accounted for in terms of the DLVO theory. The presence of adsorbed loops and tails of NaPAA molecules on CaCO3 suspensions could play a major role in the stability of the suspensions.High solid content formulations such as ground calcium carbonate aqueous suspensions have a wide range of applications in the paper industry To produce a low viscosity, colloidally stable calcium carbonate aqueous suspensions with high solid content (higher than 40 wt%), it's essential to add a dispersant, usually, sodium polyacrylate. The latter is commercially available with various molecular weight ranges. The polyelectrolyte is effectively adsorbed on the calcium carbonate particle surface, providing a high negative charge which provides effective electrostatic repulsion between the particles. In addition, these molecules can also extend from the surface forming loops and tails which can provide an extra steric repulsion The adsorption of polymers and polyelectrolyte such as sodium polyacrylate is more complex One of the most powerful techniques for studying the colloid stability of concentrated suspensions is rheology Calcium carbonate powder was supplied by Imery Performance Mineral (Cornwal, UK). The particles are rhombohedral with aspect ratio of 3:1 and density of 2.7 g cm−3. A 40 wt% suspension was prepared by ball milling in aqueous solution using zirconium dioxide balls (diameter = 1 mm) to break up the aggregates. Milling was carried out in a nitrogen atmosphere. After shaking for 2 hours by SCANDEX® shaker(Fast & Fluid, The Tinting Company, Northbrook, USA), the suspension was separated from the beads by ultrafiltration.Two types of sodium polyacrylate (NaPAA) were used as dispersants and these were supplied by BASF (Ludwigshafen am Rhein, Germany). They were PA20 (Molecular weight Mw = 2500 g/mol and polydispersity index PDI = 2.1) and PA40 (Mw = 15000 g/mol and PDI = 5.9). To 100 g calcium carbonate suspension, different amounts of 5% NaPAA solution were added to cover the concentration range from 0.1 to 0.7% NaPAA. The suspension was stirred for 10 mins after NaPAA addition. The particle size distribution of each suspension was measured using static light scattering technique (Microtrac Inc. Montgomeryville, USA) with wavelength red 780 nm and blue 405 nm. The calculation was based on the modified Mie-theory for non-spherical materials. For the determination of the selective adsorption of NaPAA, the molecular weight distribution of NaPAA was determined before and after addition of 0.4, 0.7 and 1% NaPAA to a CaCO3 slurry, (using size exclusion chromatography, SEC) of the supernatant liquid after centrifugation.Steady-state rheological measurements were carried out using a Bohlin CVO rheometer (Malvern Instruments Ltd, Malvern, United Kingdom), fitted with concentric cylinder platens. The outer cylinder has a diameter of 26.5 mm and inner cylinder has a diameter of 25 mm. This means that the gap width is 1.5 mm (1500 μm) which is sufficiently larger than 10 times particle size. All measurements were carried out at 25 °c. The suspension was left for 10 mins in the concentric cylinder to reach a constant temperature. Thereafter, the shear rate was increased from 0 to 500 s−1 over a period of 1000 s and then decreased again from 500 s−1 to 0 over a period of 1000 s.Zeta potential measurement was carried out using AcoustoSizer IIs™ (Colloidal Dynamics, LLC, North Attleboro, USA) after each addition of NaPAA to the CaCO3 slurry without dilution.TD-NMR: (proton) TD-NMR experiments were carried out on a Bruker minispec mq20 spectrometer with a 1 cm diameter variable temperature probe head. In order to be compatible with earlier NMR experiments on a Bruker NMR 120 spectrometer with a constant measuring temperature of 40 °C, the experiments were conducted at the same temperature. The internal diameter of the glass sample tubes was 8 mm, and the filling height was 10 mm. Transverse relaxation of the water phase inside the sedimentation suspension samples was studied using a Carr–Purcell–Meiboom–Gill (GPMG) train of echoes with an 8-fold phase cycle. The pulse spacing between the echoes was 0.36 ms and 8000 echoes M(t)=Msedimentexp−tT2sediment+Mwaterexp−tT2waterwith two signal components corresponding to contributions from water in the sediment phase and the overstanding free water phase. shows the molecular weight distribution of PA20 before (Solid line) and after adsorption (dashed lines) from three different concentrations (0.4, 0.7 and 1 wt%) on CaCO3. It can be seen that after adsorption, there is a significant shift in the molecular weight distribution to lower molecular weight values. This clearly indicates selective adsorption of 2000 to 5000 molecular weight fractions. shows the corresponding results for PA40 at different concentrations. Again the shift in the distribution indicates the selective adsorption of 2000 to 5000 molecular weight fractions. These results are comparable to those obtained by Geffroy et al. shows the particle size distribution of CaCO3 suspensions in the presence and absence of PA20, the measurement was carried out after considerable dilution of concentrated CaCO3 suspension (which is necessary for static light scattering technique). In all cases a wide size distribution is obtained and in a summary of mean volume diameter and standard deviation is given in . Apart from the result obtained at 0.1% PA20, all other samples should roughly the same mean volume diameter and standard deviation. It seems from this result, the additional of 0.1% PA20 causes more extensive flocculation of CaCO3 suspensions and even after dilution the flocs persisted. All other suspensions are probably only weakly flocculated and on dilution the flocs are dispersed into single particles. The most surprising result is that obtained in the absence of PA20 which shows dispersion on dilution. It's likely that CaCO3 suspensions in water have some electrostatic repulsion as a result of significant positive charge on the particles as will be shown from the zeta potential results. shows the variation of shear stress and viscosity with shear rate for 40% CaCO3 suspension without adding polymer and in the presence of 0.1% PA20. In both cases, pseudoplastic(shear thinning) curves are obtained, which also show time dependent thixotropy as indicated by the hysteresis loop between the up and down curves. A very interesting feature is the higher value obtained on addition of 0.1% PA20 which indicates more extensive flocculation of the suspension at this polymer concentration. This extensive flocculation is due to the heterogeneous charge distribution in the presence of partial coverage of the surface by the polyelectrolyte chains.The rheological data could be fitted to Herschel Bulkley model Where σβ is the yield value, k is the consistency index and n is the shear thinning index. that addition of 0.1% PA20 causes an increase in σβ and consistency index which indicate more extensive flocculation of CaCO3 suspension at this polymer concentration as discuss above. However, the shear thinning index n does not change significantly on addition of 0.1% PA20. In the presence and absence of PA20, the CaCO3 suspensions are thixotropic as illustrated in . The hysteresis loop doesn’t change significantly on addition of 0.1% PA20 and it seems that in both cases, the suspension is weakly flocculated. However, the flocs produced on addition 0.1% PA20 appear to be stronger and on dilution they don not break up into single particles as is illustrated from particles size distribution shown in shows the variation of shear stress and viscosity as a function as shear rate at 4 concentrations of PA20. At 0.2% PA20, the suspension is still thixotropic, but the yield value and k deceases significantly when compared with the results obtained at 0.1% PA20 and the system shows weak flocculation with a significant hysteresis loop. In addition, the value of n is similar to that obtained at 0 and 0.1% PA20. On further increasing the PA20 concentration to 0.4%, there is a significant reduction in σβ and k, the value of n increases to 0.51 and hysteresis loop becomes much smaller. It seems that at such PA20 concentration, stabilization of suspension occurs with only very weak flocculation. Further increase of PA20 to 0.5 and 0.7% does not show any significant reduction in σβ, k and n, and the hysteresis loop also is very small. It seems from the above rheological results, that the CaCO3 suspension becomes reasonably stable when PA20 concentration is ≥0.4%. However, in all cases, the suspensions show weak flocculation resulting in shear thinning behavior. This weak flocculation can be understood from consideration of energy-distance curve as discussed quantitatively by the DLVO theory ΔHflocs is enthalpy of flocculation whose value is determined by the depth of the minimum (Gmin), ΔSflocs is entropy loss on flocculation. For a concentrated suspension such as 40% CaCO3, the entropy loss on flocculation is quite small, and hence the free energy of flocculation is determined by Gmin. In this case, a small value of Gmin is sufficient to cause weak flocculation as is illustrated in this study.On decreasing the concentration suspension, the entropy loss on flocculation is significant and hence a large value of Gmin is necessary to induce flocculation. To prove this hypothesis, we reduced the concentration of CaCO3 from 40% to 20% while keeping the PA20 concentration the same as 0.4%. The results for the shear stress and viscosity versus shear rate are shown in , which also shows the results for the 40% suspension for comparison. It can be seen from that the stress and viscosity versus shear rate are dramatically reduced, the values of σβ is also significantly reduced from 2.03 to 0.4 Pa as concentration of CaCO3 is reduced from 40% to 20%. In addition, the k value decreases significantly from 0.49 to ∼0, indicating the dramatic reduction in viscosity. The n value increases from 0.51 to 0.80 which indicate that 20% suspension is much less shear thinning and almost approaching a Newtonian's behavior. These results clearly indicate that weak flocculation almost disappears as the particle number concentration is reduced. shows the variation of zeta potential with PA20 concentration; the pH value of each sample is also shown on the same Figure In the absence of PA20, the CaCO3 particles have a positive zeta potential of about 25 mV; this positive zeta potential may be due to this specific adsorption of Ca2+ on the surface of CaCO3 particles. This value of zeta potential should be sufficient for stabilization of CaCO3 suspensions but the system shows flocculation (possibility weak and reversible) as illustrated in the shear stress -shear rate curve () and the high yield value of 6.6 Pa, the high k value of 16.3 and the low n value of 0.34. On addition of 0.1% PA20 reversal of charge occurs and the surface become negatively charged as a result of absorption of PAA−. In this case, the negative zeta potential (−19 mV)exhibits a smaller absolute value than the positive zeta potential obtained in the absence of PA20, but this value should be sufficient for electrosatic stabilization Thus, the enhanced enhanced flocculation as indicated by the higher σβ (7.6 Pa), the higher k value (30.0) cannot be accounted for by the DLVO theory. In this case, the system is still shear thinning (n |
= 0.27) and it also shows thixotropy (see ). By increasing PA20 concentration to 0.2%, the zeta potential becomes more negative (−30 mV) as a result of the increased adsorption PAA− molecules. However, the suspension is still weakly flocculated; it shows thixotropy (see ) and the yield value decreases to 2.8 Pa, the k value decreases to 8.2 and n value remains the same. On further increase of PA20 concentration, the negative zeta potential continues to increase reaching about −45 mV (at ≥0.4%). Under these conditions, the suspension becomes more and more stable showing lower σβ values, lower k values, and higher n values. In this case, the hysteresis becomes less significant but all suspensions show some weak flocculation as discussed above. This weak flocculation can only be significantly reduced by decreasing the CaCO3 concentration as illustrated in where the first term is the Van der Waals force and the second term the electrostatic force. A121 is the effective Hamaker constant of particle in water, C = 2πɛ |
ln [1–exp (–κDo)], κ is the Debye–Hückel or the inverse of the double layer thickness, ɛ is the electrical permittivity of water, ϕ is the solid volume fraction of the dispersion, Do is the minimum surface separation distance, a is the particle size and ζ is the zeta potential which is proportional to the surface potential. The term ϕ2/a2 is the number of particles per unit area and is related to ϕ2/a in Eq. after the dependence on a for both the attractive and repulsive forces has been taken into account. Essentially the yield stress is the product of the number of particle bonds per unit area and the DLVO force interacting between a particle pair.Equation 3 is only valid for zeta potential less than 25.6 mV. However, we plotted the yield stress versus zeta square and the results are shown in . It can be clearly shown that the yield value does not give a linear decrease with increase of the zeta potential square. This result is consistent with those obtained by Ong et al , the signal fraction of overstanding water and the reciprocal value of the relaxation time inside the sediment phase are plotted for three 40% CaCO3 suspensions with different amounts of added PA40. The large variations of the fraction of overstanding water for the high-polymer samples at longer sedimentation times are due to problems with evaporation and condensation of water outside the sensitive volume of the NMR system. This problem can be corrected on the basis of overall signal amplitude values. After this correction, the water content inside the sediment phase can be determined from an overall water balance. This quantity should be related with the relaxation time of the solution phase.In a concentrated suspension of mineral particles surface relaxation of water molecules is the main mechanism both for longitudinal and transverse relaxation. Due to the short distances between the particles (well below 1 μm), we can safely assume that the water inside the system undergoes fast exchange. In this case, the relaxation rate of the water can be expected to be proportional to the surface/volume ratio with T2 denoting the transverse relaxation time inside the pore system ρ the surface relaxivity of the suspended particles and T2,bulk the transverse relaxation time of bulk water. Local variations in the surface/volume ratio of the sample may be averaged out by diffusion effects on the NMR time scale , the relaxation rate and the reciprocal water fraction in the sediment phase are correlated with each other. In the high-polymer-sample, the linear relationship expected in absence of flocculation is found. For the lower polymer contents, increasingly strong devations from the linear behaviour are found.In absence of flocculation, a linear relationship between both quantities is expected. In the case of the suspension with 1% PA40 this is observed indeed.(strait line showed in ). For the lower polymer contents, relaxivity increases due to the immobilization of the individual CaCO3 particles are obvious.Using rheological measurements, we could prepare stable CaCO3 suspensions (40 wt%) by addition of sodium polyacrylate (NaPAA, PA20). In the absence of PA20, the suspension is flocculated even though the positively charge particles have a sufficient zeta potential (+25 mV) to ensure electrostatic stabilization. The same applies at 0.1% NaPAA which shows extensive flocculation. It seems that the instability of these suspensions cannot be accounted for in terms of the classical DLVO theory. At PA20 concentration ≥0.4 wt%, the zeta potential reached much higher negative value (−45 mV) which is more than sufficient for electrostatic stabilization. However, plots of the yield value versus square of zeta potential gave a non-linear curve thus confirming the inadequacy of the DLVO theory in explaining the stability of CaCO3 suspensions in the presence of NaPAAAnalysis of microcrack growth in a 1015 SAE steel subjected to uniaxial and multiaxial loadingThe influence of different types of cyclic loading on the microstructural damage of a case-hardening steel is investigated in strain-controlled fatigue tests within the LCF (low cycle fatigue) range. For the investigations, fine polished tubular specimens were applied which were analysed for microcracks on the specimen's surface after a defined number of cycles. The development of microcrack density and length was evaluated with respect to the applied load level and the number of cycles. Connecting these results with frequency distributions of the grain size it was concluded that the growth of microcracks stagnates at the grain boundaries. At the same time the number of newly developed short cracks rises.The lifetime during cyclic loading can be distinguished in (a) the formation of microcracks, (b) microcrack growth and (c) macroscopic crack propagation; the portion of microcrack growth can consume a substantial portion of the total lifetime. This is very often dependent on the surface quality of the material and/or the material condition. Very often the growth of one and/or a few cracks is examined to get the experimental data for lifetime calculations indicates the chemical composition of the case hardening steel in weight percentage as determined by means of spectrographic analysis.The pearlitic-ferritic case hardening steel exhibits a equiaxed crystal grain structure. The pearlite occurs in lines of longitudinal direction.The determination of the grain size and phase shares takes place on the basis of microscopic pictures (enlargement:100×1). The share of the pearlite phase amounts to 23.6%. The average grain diameter was found to be 23.6 μm in transverse direction and/or 18.0 μm in longitudinal direction. The particle size distribution reveals that the case hardening steel has a microcristalline structure, A cross-sectional core sample and a sample from the edge of the specimen were taken from the cylindrical investigation material with an initial diameter of 40 mm. The position of the edge sample is selected in a way that it lies within the range of the external diameter of the hollow cylinders, which are to be examined. While the core sample has a rotation-symmetrical texture, a and therefore does not have a preferential orientation of the crystallites, the edge sample shows a split ‘butterfly-texture’, b in which 80% of the crystallites in the (001)-plane are tilted at about 15°.The tensile tests were conducted according to DIN EN 10002. The results are given in . The determination of the hardness was carried out according to DIN 50145. A average hardness by 127 HV 10 could be determined.For the investigations of the microstructural damage tubular specimens with a wall thickness of 1.5 mm are used The microstructural damage on the surface of the specimen after cyclic loading is documented after completion of each load interval by means of light microscopic pictures, a and b. In order to determine the growth rate and the number of microcracks as well as their length and orientation these microscopic pictures were taken of every specimen along four characteristic lines across the surface of the specimen. The length, number and orientation of the microcracks is determined as a function of the respective number of completed cycles. The microcracks found on the specimen surface after a defined number of loading cycles are classified according to their orientation—with respect to the specimen axis—in steps of 5° in between −90° and +90°. The number of cracks in each category is plotted in a diagram as a function of their orientation. As a result of the microcrack evaluation, the frequency distribution, the average crack density and crack length can be determined for each load interval The evaluation of the microcrack propagation occurring from tension/compression loading shows that the maximum percentage of microcracks are found at an orientation of 60°. A deviation of +/−15° related to the maximum of the respective shear stress could be observed, a. It is shown that existing microcracks propagate, and in addition, new microcracks develop, b. The peaks of the distribution (M1, M2) shift to categories of increased length as the number of cycles increases. Additionally the frequency distribution become wider in shape. Similar frequency distributions result for M1 (N=400) and M2 (N=200) with 156 (M1) and/or 173 (M2) microcracks in the 3 μm length class. The evaluated number of microcracks under M2 is twice as high after N=600 cycles as under M1 after N=1200 cycles. The macroscopic failure of the samples finally takes place perpendicularly to the maximum of the normal stresses.Through the influence of torsion loading microcracks develop with an orientation of 0 and 90° following the direction of the maximum shear stress which is effective in these orientations, a. An increase of the number of microcracks and a shift of the maximum of the frequency distributions to larger length categories occurs at M1 and M2. Compared with the microstructural damage caused by tension/compression loading the detected number of microcracks and the respective crack length develop at a higher number of cycles (N=9000). The lower maximum of microcracks shifts from the 4 μm- to the 5 μm-length class after N=12,000 cycles which can be attributed to a widening of the frequency distribution and the increasing number of longer microcracks (>45 μm) at the same time, Considering multiaxial proportional loading the maximum of the shear stress is found at −67.5° and +22.5°. The maximum of the microcrack distribution occurs at −35.0° and +75.0°, a. The distribution of the number of cracks according to their length shows that a shift of the distribution maximum towards categories of larger cracks takes place at both load levels M1 and M2. This is connected with a general increase of the number of cracks (especially long cracks) which leads to a continuous widening of the distribution curve, b. After N=400 cycles (load level M1) a maximum of 912 cracks of the 4 μm length class could be detected whereas 786 microcracks of the 5 μm length class (load level M2) could be observed after the same number of cycles. In the latter case the frequency distribution had wider scatter revealing that a higher number of longer cracks had formed. Comparable frequency distributions were analysed after N=800 cycles (load level M1) and N=600 cycles (load level M2).A comparable mean microcrack density and a mean microcrack length adjusts according to the number of cycles which range between those for the tension–compression and those for the torsion loading experiments.During phase-shifted loading microcracks can develop in any direction from −90° to +90°. The evaluation of the microcracks from the experimental fatigue testing with phase-shifted loading shows that the frequency distribution has a peak at +/−90°, a. The frequency distributions of the quantity of microcracks (length category 4 μm) as a function of the microcrack length show that a similar degree of microstructural damage has already developed after N=100 and N=200 cycles without a shift of the curve's maximum as compared to proportional loading, b. Consequently the phase shifted loading has considerably stronger effect on the formation of microcracks and thus on the microstructural damage in comparison to proportional loading. Both the mean microcrack density of 1762/mm2 after N=400 cycles of M1-loading and 1854/mm2 after N=200 cycles of M2-loading as well as the mean crack length of 4.7 and 5.2 μm after N=200 cycles of M1- and M2-loading, respectively, show that in the case of phase-shifted loading the relatively highest degree of damage can be expected. Due to a strong deformation of the specimens a microcrack evaluation could only be performed for two cycle intervals in both loading cases (M1 and M2 loading).In all cases investigated in the experimental program it was found that an increase of the microstructural damage occurs as the number of load cycles increases, but no shift of the maximum of the crack orientation could be found in any of the frequency distributions. display the development of the mean microcrack density—and length—related to the examined intervals and loadings. Also in these diagrams the number of cycles to failure Nf is given.In the case of torsion loading more cycles are necessary to create the same amount of microstructural damage compared to tension/compression loading. During torsion loading more cycles are required to achieve a comparable crack density and mean crack length. A phase-shifted loading only requires a relatively low number of cycles to achieve a high crack density and longer cracks leading to a substantial microstructural damage.The experimentally determined results of the microcrack evaluation show that the characteristic material properties on the one hand and the type of loading and its magnitude on the other hand have an essential influence on the development and growth of microcracks. All investigated test series of the case hardening steel show that the microcrack density increases with the number of load cycles. It is shown by means of the frequency distributions that new microcracks develop during a long period of the total lifetime. The development of microcracks takes place inside the grain whereas the cracks propagate until they reach a grain boundary where the crack is stopped, a and b. This effect shows that a grain boundary is a strong microstructural barrier. The pearlite which occurs in longitudinal lines can also be considered as a main barrier for microcracks. The formation and propagation of a macroscopic crack takes place only within a small number of cycles provided that a high density of microcracks already prevails (microcrack coalescence).Phase stability, mechanical property, and electronic structure of Mg–Li systemFirst principle calculation reveals that the HCP, BCC, and FCC Mg100−xLix phases are energetically favorable with negative heats of formation, and are predicted to be the most stable structures at 0 K when 0 ≤ |
x |
< 18, 18 ≤ |
x |
< 73, and 73 ≤ |
x |
≤ 100, respectively. Calculation also shows that for Mg–Li phases there is an almost linear variation of bulk moduli with composition, and crystal structure has only a little effect on bulk moduli. In addition, it is found that Mg3Li and MgLi have phase sequences of BCC → HCP → FCC and BCC → FCC under high pressure, respectively, and that the anomalous mechanical instability of the HCP MgLi phase would be attributed to its weak bonding and step-like electronic structure of valence bands.During the past decades, the binary alloy system of Mg–Li has raised great research interests due to its unique structural, mechanical, electrical and thermal properties, etc. It is well known that the simple metals of Li and Mg are regarded as alkali and alkaline-earth metals with only one and two conduction s-electrons, respectively. The phase transitions of the Mg–Li system at low temperature, however, have been found to be complicated and attractive for many years among scientists. For instance, in 1947, Barrett Another interesting aspect of the Mg–Li system is that it could be regarded as a kind of ultralight materials with high specific strength, and is a promising candidate for commercial transport, aerospace and high-performance applications To understand the intrinsic mechanism of various properties of Mg–Li phases, it is of importance to investigate the Mg–Li system at an electronic scale theoretically. Regarding this respect, however, there are only several theoretical calculations of the Mg–Li system in the literature The first principles calculation is based on the well-established Vienna ab initio simulation package (VASP) within the density functional theory At the very beginning, we did a series of test calculations, such as the k-point convergence test. As a result, the k-mesh of 13 × 13 × 13 was adopted for all calculations. For k space integration, the temperature smearing method of Methfessel–Paxton In order to find out the ground-state crystal structure of the Mg–Li system, five compositions, i.e., Mg3Li, MgLi, MgLi3, pure Mg and Li, with several possible ordered structures are selected for total energy calculations. As a typical example, shows the correlation between the total energy and the ratio of volume (V/V0) for these MgLi phases. One sees from the figure that the MgLi phase with a B2 (BCC lattice) structure has the lowest total energy and is therefore predicted to be the most stable structure corresponding to the ground state. Similarly, the A3 (HCP lattice), A1 (FCC lattice), D03 (BCC lattice), and L12 (FCC lattice) are predicted to be the ground-state structures of Mg, Li, Mg3Li, and MgLi3 phases, respectively (figures not shown). For convenience, the Bravais lattice symbols (FCC, BCC and HCP), instead of the Strukturbericht types, are adopted in the following text, tables, and figures. Accordingly, lists the calculated physical properties of these Mg–Li phases with three common structures (BCC, FCC and HCP) as well as relevant experimental data . It is of interest to see that the ΔE in the Mg-rich region is bigger than those in the Li-rich region.To further reveal the structural stability of the Mg–Li system, the above five Mg–Li phases are expressed as the form of Mg100−xLix (x is the atomic composition of Li), and the total energy differences of the FCC and HCP Mg100−xLix phases with respect to the BCC structures are calculated and are shown in . It can be observed from this figure that the HCP structure has lower total energy than the BCC and FCC structures when 0 ≤ |
x |
< 18, the BCC structure is more stable than the other two structures when 18 ≤ |
x |
< 73, while the FCC structure is energetically more favorable when 73 ≤ |
x |
≤ 100. It is of interest to compare the above results with similar experimental and theoretical observations in the literature The heat of formation, ΔHf, is derived according to the following formula:where EMgmLin, EMg and ELi are the total energies of MgmLin, pure HCP Mg and BCC Li, respectively. After the calculation, the derived values of ΔHf for various Mg–Li phases are all listed in . It can be seen from this table that the values of ΔHf are all negative, and the most stable structure has the lowest ΔHf. Such negative values of ΔHf imply that all the three common structures of Mg–Li phases would be energetically favorable from the point of view of thermodynamics, and the most stable structure with the lowest ΔHf would be the most likely to be formed during experiments, which match well with experimental observations in the literature for the sake of comparison. It is of interest to see that the ΔHf of the FCC Mg3Li and HCP MgLi phases from the present study are −2.43 and −3.28 kJ/mol, respectively, which are very close to the experimental values of −2.50 and −3.20 kJ/mol of the corresponding liquid phases To find out the intrinsic mechanism of the Mg–Li interaction, the electronic structures of all Mg–Li phases are also calculated. As a typical example, shows the total densities of states (DOSs) of the BCC MgLi as well as the mechanical mixture of 50 at.% Mg and 50 at.% Li bulks (without any Mg–Li interaction). Several characteristics can be seen from this figure. First, compared with the mechanical mixture, the DOSs of the BCC MgLi become more localized with a bandwidth reduction of about 2 eV, signifying that a strong chemical bonding is formed between Mg and Li atoms. Second, due to the Mg–Li interaction, two peaks of DOSs of the BCC MgLi phase appear at the points of about 1 and 3 eV below the Fermi level (Ef), and the maximum peak of DOSs above the Ef is split into several peaks. Third, there is a negligible difference between these two DOSs at the Ef.The theoretical elastic constants of Mg–Li phases are calculated according to the method adopted by Wang and Ye lists the derived elastic constants of several ground-state and room-temperature structures, as well as available experimental results regarding the elastic constants of Mg–Li phases in the literature It is of interest to investigate the mechanical stability of various Mg–Li phases. According to the strain energy theory, for a mechanically stable phase the strain energy should be positive, and the matrix of elastic constants should be positive, definite, and symmetric that the elastic constants of various Mg–Li phases, except HCP MgLi, all follow the above strain energy theory, suggesting that these phases should be all mechanically stable. Such a mechanically stable feature seems consistent with the thermodynamic stability of various Mg–Li phases with negative heats of formation shown in . It should be pointed out that the HCP MgLi phase listed in possesses an anomalous mechanical instability, which will be discussed in Section . In addition, it is also of interest to find out the values of the shear coefficients (C11–C12)/2 for the BCC Mg–Li phases, as proposed by Zener It is of engineering importance to derive the elastic moduli of polycrystalline materials, which could be approximately estimated from elastic constants of the single crystals through Voigt's and Reuss's approximations for maximum and minimum values of the moduli as well as Hill's approximation for the average value of maximum and minimum values The Voigt's (GV), Reuss's (GR), and Hill's (G) approximations are given as follows:GV=115(C11+C22+C33)−115(C12+C13+C23)+15(C44+C55+C66)GR=154(S11+S22+S33)−1−154(S12+S13+S23)−1+5(S44+S55+S66)−1where Sij is the compliance matrix obtained by Sij=Cij−1.The Young's modulus (E) and Poisson's ratio (v) are expressed according to the following formulas:As a result, the calculated B, G, E, and v of the Mg–Li phases with various polycrystalline structures are displayed in shows various bulk moduli of polycrystalline Mg–Li phases from the present study as well as experimental and theoretical data in the literature High pressure is known to influence electronic structure and crystal packing, and plays an important role in materials properties, such as phase transition, superconducting phenomenon, etc. For instance, Li, as the simplest metal, has received considerable attention in terms of high-pressure behavior In the present study, the Mg3Li, MgLi, and MgLi3 phases are selected to find out phase transitions under hydrostatic pressure between the common BCC, FCC, and HCP structures. The total energy is calculated as a function of the ratio of the volume (V/V0) which ranges from 1.55 to 0.2 with an interval of 0.04. The derived total energies of the three phases with various structures are then fitted through the Vinet's equation of state (EOS) After the calculation, it is found that for the MgLi3 phase there is no any high-pressure phase transitions between FCC (ground-state structure), BCC and HCP structures (figures no shown). For the Mg3Li and MgLi phases, the energy differences (ΔE) of the FCC and HCP structures with respect to the BCC structure are derived and the results are shown in . It can be seen from this figure that the ΔE curves as well as the line of zero intersect with each other, and that these intersections could be regarded as the critical points corresponding to the phase transitions under pressure. By means of fitting, the Vinet's EOS is then used to derive the critical pressures corresponding to the above points of phase transitions, and the calculated results are all listed in . Several characteristics can be observed from (a) that Mg3Li has a phase sequence of BCC → HCP → FCC under pressure. In other words, the BCC structure, i.e., the most stable structure of Mg3Li under normal conditions, is first transformed to the HCP structure, and then to the FCC structure with the increase of pressure. Second, it is of interest to see that for the transition of BCC to HCP in the Mg3Li phase, the critical volume is almost coincident with the equilibrium volume and the corresponding pressure is very close to zero. Such a feature suggests that the transition from BCC to HCP would be very easily achieved for the Mg3Li phase, which is in excellent agreement with the coexistence of these two structures from the experimentally observed phase diagram of Mg–Li that the critical ratios of volume corresponding to the phase transitions of the MgLi phase are much lower, and the critical pressures are significantly higher than those of the Mg3Li phase, implying that the high-pressure phase transitions of the MgLi phase would be much more difficult to happen than those of the Mg3Li phase. Forth, it could be seen from (b) that MgLi has a phase sequence of BCC → FCC under pressure, which is quite different from that of Mg3Li. It should be pointed out that although there is an intersection between the HCP and BCC curves in (b), the transition from BCC to HCP for the MgLi phase could not actually happen under pressure as the transition from BCC to FCC would happen first within the entire range of V/V0, and there is no any intersection between the HCP and FCC curves. In other words, neither BCC nor FCC MgLi could be transformed to the HCP structure, suggesting that the HCP MgLi could not be obtained even under high pressure.It is of interest to find out the anomaly of the HCP MgLi phase. From , it can be seen that the heat of formation of the HCP MgLi is calculated to be −3.28 kJ/mol, suggesting that the HCP MgLi phase should be thermodynamically favorable. As related in Section that the HCP MgLi is mechanically unstable as it disobeys the strain energy theory of C112 |
> |
C122(b) as well as the above analyses of high-pressure behavior, the HCP MgLi is identified to be unstable even under high pressure. It should be noted that such an anomalous behavior regarding the stability of the HCP MgLi phase is quite different from those of other MgLi phases. To get a better understanding of the HCP MgLi phase, the electronic structure of the HCP MgLi is calculated, and shows the comparison of the total densities of states (DOSs) of the HCP MgLi as well as the mechanical mixture of 50 at.% Mg and 50 at.% Li bulks (without any Mg–Li interaction). One sees from this figure that the DOSs of the HCP MgLi are similar to those of its mechanical mixture in terms of the bandwidth, shape, and the peaks of the DOSs, etc., implying that the HCP structure of MgLi should have a weak bonding. Interestingly, the DOSs of the HCP structure have a remarkable step-like feature near the bottom of the valence band and it remains almost constant within the energy range of −5.5 to −3 eV. Such an unusual electronic structure of the HCP MgLi phase would be probably due to large size differences between the ionic cores of Li and Mg, i.e., as the density increases under pressure, the Li cores start to overlap and thereby expel valence electrons into delocalized free-particle-like states in the vicinity of Mg ions In the present study, first principle calculation has been conducted to investigate the structural stabilities, mechanical properties, and high-pressure phase transitions of the Mg–Li system. It is demonstrated that first principle calculation is able to reveal various physical properties of MgLi phases, such as the lattice constants, heats of formation, total energy differences, elastic constants, bulk moduli, mechanical stabilities, phase transitions under high pressure, etc. It is also shown that the electronic structures of the MgLi phases from the present first principle calculation would give a deeper understanding of various properties of the MgLi phases. In addition, the calculated results are compared with experimental evidences in the literature, and the agreements between them are fairly good.Probabilistic effective characteristics of polymers containing rubber particles of Gaussian random diameterThis study is focused on the problem of statistical distribution of the size of rubber particles as fillers in elastomeric composites. This distribution (average diameter of the injected particles) is assumed to be Gaussian and uniquely defined by its mean value as well as standard deviation. The basic probabilistic parameters of the effective elasticity tensor of the entire elastomer are under consideration by using of the homogenization method. The basic computational ideology is based on strain deformation of the Representative Volume Element under uniaxial and biaxial loads. This deterministic method is enriched with the generalized stochastic perturbation technique and also by semi-analytical strategy, which are used together with the system ABAQUS® as the Stochastic Finite Element Method (SFEM) serving for a solution of the homogenization problem for such a composite. The basic stochastic characteristics of the homogenized elasticity tensor and its deterministic sensitivity coefficients are verified with such coming from analytical deterministic homogenization method extended towards random case in the computer algebra system MAPLE®. The computational study contains additionally computational error analysis as the homogenization problem is solved here with tetrahedral and hexahedral 3D solid finite elements with linear as well as with parabolic shape functions and their meshes with different densities.Sensitivity analysis and uncertainty modeling of composite materials has been an attractive and interesting area of investigations since many years This work addresses the determination of the first four probabilistic moments of the effective elasticity tensor components of elastomers filled with rubber particles of Gaussian random diameter. Homogenization method is based upon the deformation energy of the Representative Volume Element (RVE) under uniaxial and biaxial stretches Let us consider a statistically heterogeneous and bounded continuum Ω⊂R3 with no initial stresses and strains consisting of spherical rubber particles statistically uniformly distributed into the homogeneous polymeric matrix (). We assume a perfect contact in-between these two constituents throughout all the interfaces and also a lack of any contact of any two neighboring particles. The rubber and polymer phases work both in the linear elastic regime and their material characteristics are uniquely defined by their Young’s moduli and Poisson’s ratios and they are given in a deterministic manner. We assume that the filler particles have random Gaussian size distribution defined by the expectation and standard deviation of their radii, namely E[R] and σ(R). These operators are traditionally defined as where pR(x) is the probability density function assumed to have the formWe use further also skewness and kurtosis classically introduced in probability theory in the following form (Monte-Carlo simulation explores a variety of estimators, whose accuracy depends on the few parameters):which equal both to 0 for Gaussian variables and wheredenotes the mth central probabilistic moments of the variable R for any natural number m. The main goal of further considerations is to determine the basic probabilistic material characteristics of the equivalent homogenized medium and we introduce for this purpose the Representative Volume Element () consisting of a single rubber particle within the surrounding polymeric matrix in the form of a cube (due to the same importance of all directions related to Cartesian coordinates which is affected by statistical isotropy of the matrix and the whole composite themselves). We determine numerically for this purpose the random displacement fields uix1,uix2,uix12 and random stress tensors σijx1,σijx2,σijx12 satisfying three specific linear elasticity elliptic boundary–value problems – of uniaxial horizontal extension of the RVE (x1), of uniaxial vertical extension (x2) and also of the biaxial extension of the RVE (x12). Assume for the needs of numerical analysis that there are non-empty subsets of external boundaries of the domain Ω (with the dimensions 2δ |
× 2δ |
× 2δ), namely ∂Ωσ and ∂Ωu, where the stress and displacement boundary conditions are defined.According to the main idea of the generalized stochastic perturbation technique εkl(ζ)(x;ω)=12∂uk(ζ)(x;ω)∂xl+∂ul(ζ)(x;ω)∂xk,Then we follow the finite set of integral variational equations to get an appropriate numerical solution for the strain energy in the context of the Finite Element Method. It yields∫ΩCijklεij(ζ)δεkl(ζ)dΩ=∫∂Ωσt̃iδui(ζ)d(∂Ω), corresponds to elastic behavior of the structure and the R.H.S. is equivalent to the stress boundary conditions applied. It needs to be mentioned that indexing with respect to the RFM should be added to the computational domain Ω as far as stochastic shape sensitivity is to be modeled; the corresponding extension to ∂Ωu,∂Ωσ and additional conditions may reflect an uncertainty at the structure external boundary. Final determination of the effective material tensor needs the strain energy of the original heterogeneous mediumThe homogenized medium is a linear and isotropic one, which accumulates the same amount of energy having effective elastic characteristics’ series Cijkl(eff)(ζ), so that we compare this against the energy stored in the homogenized mediumU(α)=12∫ΩCijklεij(ζ)εkl(ζ)dΩ=Uhom(ζ)=12∫ΩCijkl(eff)(ζ)εijh(ζ)εklh(ζ)dΩ.where εijh(α) denotes the strain tensor adjacent to the homogenized equivalent medium.We apply for this purpose specific boundary conditions at the RVE, which correspond to the uniform expansion of this cube at its outer surfaces, i.e.The remaining components of the displacement fields on these surfaces and the displacements of the other RVE surfaces equal to 0. So that, one writesTherefore, we obtain the following system of linear algebraic equations for effective characteristics:12C1111(eff)(ζ)(ε11x1)2=U1(ζ)12C2222(eff)(ζ)(ε22x2)2=U2(ζ)12{C1111(eff)(ζ)(ε11x1)2+2C1122(eff)(ζ)ε11x1ε22x2+C2222(eff)(ζ)(ε22x2)2}=U12(ζ)U12=U1+U2+12∫Ωσijx1εijx2dΩ+12∫Ωσijx2εijx1dΩin case of any combination of the aforementioned boundary conditions imposed. It needs to be mentioned that a full continuity of displacements and no additional boundary tractions are assumed on the particle–matrix interface. The resulting effective medium would be also isotropic according to the adopted geometry of the RVE, so that an analogous solution for x3 it is not mandatory here. It should be recalled that the analytical solution of the fully deterministic problem exists (originally no randomness in the particles’ radius) k(eff)=k(m)+fpk(p)-k(m)1+k(p)-k(m)k(m)+43μ(m)μ(eff)=μ(m)-μ(m)15(1-ν(m))(1-μ(p)μ(m))fp7-5ν(m)+2(4-5ν(m))μ(p)μ(m),where fp is the volume fraction of the rubber particles, index p stands for the particle characteristics and m – for the matrix elastic parameters. They are both classically combined into the effective tensor asCijkl(eff)=δijδklk(eff)+(δikδjl+δilδjk)μ(eff).So that we are going to compare the expected values, coefficients of variation, skewness and kurtosis computed for the SFEM-based homogenized tensor with the corresponding probabilistic characteristics derived analytically from the set of equations recalled above for the effective moduli k(eff) and μ(eff). Using the basic properties of the linear transform of the Gaussian variable there holds in our caseEk(eff)=k(m)+k(p)-k(m)1+k(p)-k(m)k(m)+43μ(m)Efp,Eμ(eff)=μ(m)-μ(m)15(1-ν(m))1-μ(p)μ(m)7-5ν(m)+2(4-5ν(m))μ(p)μ(m)EfpVar(k(eff))=(k(p)-k(m))21+k(p)-k(m)k(m)+43μ(m)2Var(fp),Var(μ(eff))=μ(m)151-ν(m)1-μ(p)μ(m)7-5ν(m)+24-5ν(m)μ(p)μ(m)2Var(fp),where the first two moments of the variable fp are derived in further analysis. These expressions are of course combined into the corresponding effective tensor’s probabilistic moments asECijkl(eff)=δijδklEk(eff)+δikδjl+δilδjkEμ(eff),VarCijkl(eff)=δijδklVark(eff)+δikδjl+δilδjk2Varμ(eff).It is necessary to mention that this short derivation is valid for all continuous probability functions and follows from the nature of a linear transform in-between particle’s volumetric ratio fp and these moduli. Somewhat different situation takes place when we discuss the transition in-between particles radius R and this ratio fp. The radius has Gaussian distribution, while the variable fp – definitely not, which may be deduced from the higher order statistics (skewness and kurtosis) derived below together with the first two basic moments. If we assume thatVar(fp)=112σ2(R)π2(3E4[R]+12E2[R]σ2(R)+5σ4(R))δ6,β(fp)=63E[R]σ(R)(3E4[R]+16E2[R]σ2(R)+15σ4(R))δ93E4[R]+12E2[R]σ2(R)+5σ4(R)δ632,κ(fp)=3(9E8[R]+240E6[R]σ2(R)+1326E4[R]σ4(R)+1920E2[R]σ6(R)+385σ8(R))(3E4[R]+12E2[R]σ2(R)+5σ4(R))2-3Interestingly, both skewness and kurtosis are independent of the RVE external edges expressed by δ here, skewness remains always positive except the trivial case of 0 for deterministic analysis (when input standard deviation simply vanishes). The very important aspect of these equations is that they do not demand perturbation approach (released with the use of series expansions) and in this context they are exact (and also completely free from probabilistic modeling error). Looking for Eq. one may notice that the volume fraction of the matrix in the RVE is equal to 1 − |
fp, which means that its expectation is different than E[fp] (and usually much bigger) but both fp and 1 − |
fp have the same variance. Therefore, the coefficient of variation (uncertainty) of the parameter fp itself becomes also much bigger than for 1 − |
fp relevant to the matrix, so that the randomness in particle radius plays crucial role in micro-geometry uncertainty in the RVE considered. A combination of Eqs. enables to adopt the third order polynomial basis of the resulting homogenized elasticity tensor in addition to the particle radius with no further statistical numerical optimization inherent in the Least Squares Method applied here in the SFEM analysis.The first part of computational analysis is of a pure deterministic character and concerns the relative error of the deformation energy accumulated in the RVE during all the homogenization tests. This is provided for varying total number of the finite elements in the RVE mesh (from about 50.000 up to 1.500.000) and also for 4-noded and 10-noded tetrahedral as well as for 8-noded and 20-noded hexahedra. The most detailed meshed created with the used of these finite elements are presented in . Elastic parameters of the rubber particle are: Young’s modulus E(p)=1.0MPa and Poisson’s ratio equal to ν(p)=0.489, while for the polymer matrix the same parameters equal to E(m)=4.0GPa and ν(m)=0.34, correspondingly. The expected value of the particle radius equals to E[R] = 0.25 μm (effectively a particle volume fraction is 6.5%), while its coefficient of variation varies in the interval α(R)∈[0.00,0.15]. Eleven series of the homogenization problems have been solved to create the response functions in-between the effective tensor components and the particle radius – all with deterministically modified particle radius (plus additional automatic re-meshing with the same parameters), whose values are taken from the following set R |
∊ {0.2375, 0.24, 0.2425, 0.245, 0.2475, 0.25, 0.2525, 0.255, 0.2575, 0.26, 0.2625} μm. The results of relative numerical error analysis are contained in – for uniaxial horizontal extension of the RVE, in – for the uniaxial vertical extension of the RVE. The functions in do not need to be exactly the same, because spatial distribution of the finite elements in both directions is not exactly the same, so that deformation energies may differ. This error is calculated aswhere the quantity U¯ stands for the deformation energy computed for 107 finite elements in the RVE. We compare the numerical error associated with this energy because it is decisive (and equivalent through Eqs. ) to the overall error of determination of the effective elasticity tensor in our method.It is worth mentioning that even in the case of a mesh with the smallest density the relative error under consideration is smaller than a half percent. As we could suppose, the largest error is obtained for the most primitive mesh and for tetrahedral linear finite elements because this model contains the smallest number of degrees of freedom for the same number of finite elements as the remaining models. The alternative mesh consisting of hexahedra with 20 nodes shows almost no error (equal to 0% with satisfactory accuracy – even with the mesh of an initial density. This one is taken for further SFEM experiments, because as was mentioned above, the mesh is successively modified during different homogenization tests to recover the response functions. Nevertheless, the energy relative error approaches zero very fast for any type of the finite element included in this study and we can reach almost 0% error level for about a million of the elements in the RVE. Finally, one may conclude that the results included in allow to predict a complete lack of difference in-between probabilistic moments computed via the SFEM homogenization with hexahedral finite elements and these obtained by using tetrahedral mesh. Further computational advances of this methodology should include initial mesh adaptation process to shorten the overall time and computer power consumption of numerical homogenization with the same final accuracy.Further numerical results include the sensitivity coefficients of all components of the homogenized tensor in addition to the particle radius R. These are the first order partial derivatives of C1111(eff), C1122(eff) and C1212(eff) (given in turn in ) scaled with a ratio of the mean radius with respect to the mean value of the particular component of Cijkl(eff) under consideration. This is applied to detect the most and the least sensitive elasticity tensor component to possible fluctuations of the filler particle radius. Additionally, we contrast here the FEM and analytical homogenization results in this context to have a more detailed comparison than just traditional verification of the effective tensor mean values (the left versus the right series, correspondingly). This analysis is done in each case for five different Least Squares Method polynomial basis to check possible differences in-between approximating polynomials of the first, the second and further up to the fifth degree. This is also provided to verify (confirm) further a choice of the third order polynomials in probabilistic analysis. It needs to be mentioned that both FEM and analytical method sensitivities are calculated with the use of series of deterministic computations with the additionally modified R and further – by using of the Least Squares Method; this was invented to avoid any methodological differences for these two approaches. Despite of the homogenization method and even of the particular component of the effective tensor all the sensitivity coefficients become negative. This result is rather expected because Young modulus of the rubber particle is more than thousand times smaller than the modulus of a polymeric matrix, so that increasing of the particle size must result in a decreasing of the overall elastic characteristics. This effect should increase together with the mean size of the radius R and this is also remarkable in . The next important observation is that the first order polynomial basis brings for all the components of the tensor Cijkl(eff) significant numerical discrepancies out of the mean value of the particle radius. All the remaining polynomial basis orders result in exactly the same sensitivities (for C1111(eff) and C1122(eff)) or at least very similar (in case of C1212(eff)). Generally, analytical homogenization method results in the effective tensor, which is more sensitive to the particle radius than it is observed for the FEM-based simulation. Both homogenization methods indicate here that C1122(eff) is the most sensitive to the filler radius variations, while C1111(eff) and C1212(eff) are less sensitive.The final and the most important part of these computations concerns determination of the expected values of the effective elasticity tensor components E(Cijkl(eff)) – given in as well as kurtosis of the homogenized tensor shown in . This is all computed for the input coefficient of variation (uncertainty level) of the filler radius varying in the interval α(R)∈[0.00,0.15] and by using of the two alternative probabilistic numerical strategies – Stochastic Semi-Analytical Finite Element Method (SSAFEM) and Stochastic Perturbation-based Finite Element Method (SPFEM). They are both based on the third order polynomial basis of random R recovered numerically with the same LSM strategy, but SSAFEM employs symbolic integration according to the probability theory definitions (similar to Eqs. ), while SPFEM includes partial derivatives of up to the tenth order in the additional Taylor expansions (and also their integration over probabilistic space). All these aforementioned probabilistic characteristics are also calculated concurrently twice – via the FEM experiments (left series in all graphs) and from probabilistic extension of the analytical solution (right column of the results), where instead of the abbreviations SSAFEM and SPFEM one may find similarly SSAM and SPM correspondingly (Stochastic Semi-Analytical Method and also stochastic perturbation method). enables to conclude that both probabilistic methods give exactly the same results for any value of the input coefficient α(R). The expectations all remarkably decrease together with an increase of the particle radius uncertainty level unlike during homogenization of the same material with randomized material characteristics, where Poisson’s ratio uncertainty (close to the physical incompressibility limit) brought similar expectation variations The coefficients of variation of the effective tensor components are also exactly the same in semi-analytical and for the stochastic perturbation method, for the entire variability range of the coefficient α(R). The resulting values of α(Cijkl(eff)) increase all together with this α(R) from trivial 0 for a deterministic case at the beginning of each curve, but unlike in most of the previous studies Contrary to the first two probabilistic characteristics, skewness () computed by using of the stochastic semi-analytical approaches (SSAFEM and SSAM) and of the stochastic perturbation method (SPFEM and SPM) diverge from each other. This divergence remarkably increases in case of the skewness for all the effective tensor components, while kurtosis divergence is less regular and may exhibit some local variations (see , right diagrams, while α(R)→0.15). These discrepancies concern analytical homogenization method only, the SFEM results diverge in a quite predictable way. Despite of the calculation method both skewness and kurtosis significantly differ from zero for all the components of Cijkl(eff), so that the resulting distribution cannot be Gaussian except for the trivial case of no randomness in composite, i.e. α(R)=0; this result was indeed expected after Eqs. . Skewness is negative for all components of the effective tensor and this is obtained according to all numerical methods, which means that the left part (below the expectation) of the probability density function is longer than the right one (left side asymmetry). It is interesting that the skewness of C1111(eff), C1122(eff) and C1212(eff) are almost equal to each other while computed by the SFEM, and independently, by the analytical formulas (these adjacent to analytics are a little bit larger). Mathematical function describing β(Cijkl(eff)) versus α(R) is in most cases linear or quasi linear. Kurtosis of all the components of the homogenized tensor Cijkl(eff) is positive independently of the homogenization method and of the probabilistic technique applied, so that the resulting probability distributions are more concentrated about their expected values than the Gaussian one; the only exception from this rule is κ(C1212(eff)) obtained for an analytical homogenization. Now the SFEM-based and the analytical calculus return each time completely different values, while semi-analytical and stochastic perturbation methodology keep close for this first group only. The most apparent differences are noticed here for the kurtosis of C1212(eff), where the FEM-based approach returns extreme value more than ten times larger than during analytical predictions. All the results grouped in the left column show monotonous increase of kurtosis of Cijkl(eff) together with an input coefficient α(R), so that this concentration increases together with an initial uncertainty in the particle radius R.Summing up all the computations presented above it is documented that the dual approach proposed results in continuous distributions of all the probabilistic characteristics in addition to the input uncertainty level with neither singularities nor discontinuities, which enable quite reliable discussion of the basic statistics of the effective elasticity tensor of the polymer with rubber filler.Computational deterministic error analysis provided in this work shows that the deformation energy of the RVE is less dependent upon the finite element type, on the elemental shape functions type as well as upon the mesh density than upon material properties of the elastomer constituents. This observation should not be common for all the particle composites, because elastomer contains two materials with extremely large contrast in-between elastic moduli affecting significantly this energy. It shows that the Stochastic Finite Element Method shows a very similar insensitivity to the mesh type and mesh size as its deterministic counterpart. Analytical homogenization method significantly overestimates the sensitivity gradients for the effective tensor components, so that seems to be unavailable for this specific purpose.Probabilistic analysis of the effective elasticity tensor for the uncertainty in particle radius has been done in a dual way and it shows that the two stochastic numerical methods employed result in the same first two probabilistic characteristics. Higher order statistics are similar but diverge together with an increasing value of the input coefficient of variation α(R). The expectations of the tensor Cijkl(eff) are also sensitive to this parameter and decrease with α(R) quite contrary to α(Cijkl(eff)), whose values additionally never exceed the input random dispersion. Higher order statistics – skewness and kurtosis – show with no doubt that the resulting random effective tensor cannot have the component distributed according to the Gaussian distribution. The probabilistic methods implemented with the FEM-based homogenization bring the very similar probabilistic characteristics as the analytical approach with the only exception (kurtosis), however this discrepancy is mainly affected by the differences in deterministic homogenization procedures applied here.The next step in further probabilistic analysis of the homogenized behavior computational modeling for polymers containing rubber particles would be a development of the multi-particle RVE of an elastomer (and its numerical homogenization), a verification of possible lognormal distribution of the particle radius as well as successive randomization of the hyper-elastic response of such a composite during tension–compression uploading and unloading cycles (to document effective material hysteresis). Prior to such an extension one needs to justify possible and the most convenient random 3D distribution of the particles, computational strategy relevant to lognormal variables (out of the Monte-Carlo scheme) and, finally, efficient numerical way to recover probabilistic moments and coefficients related to this hysteretic behavior A conceptual model for the process variables related to heat generation in friction stir welding of aluminumThis paper seeks to describe relationships between the independent process variables and the dependent process outcomes related to heat generation and dissipation in friction stir welding. A conceptual model, proposed earlier, has been modified to specifically distinguish between plastic work and friction in the generation of heat. A case study is used to confirm and explore the relationships expressed in the conceptual model. Further, a method for expressing friction coefficient variation with respect to the key process variables is introduced. |
It is important for users of friction stir welding (FSW) to have a conceptual understanding of how the process works. Such an understanding is helpful in deciding how to change process conditions to achieve desired effects, such as for improving joint strength, for eliminating certain common weld defects, and for transferring a known welding procedure to new conditions. Computer-based models and empirical studies of the stir welding process have been developed by many researchers to examine heat transfer, metallurgical evolution and material flow. This work has been very useful for building an understanding of the different physical effects in FSW. A general examination of the relationships between variables can now be used to develop a conceptual model of the process. The goal of this paper is to propose a conceptual model that relates the different process variables with key process conditions in a way that will allow the practitioner of FSW to develop a general understanding of the process. In addition, the framework for coefficient of friction during the friction stir process is discussed.A conceptual model is proposed that relates the main process variables, structured around the interrelation of the main categories of physical effects that come into play in the generation and distribution of heat in FSW. A preliminary version of this model was published earlier . In this diagram the process variables are represented in boxes with solid borders, while the physical effects are represented in boxes with dashed borders. The arrows start at a process variable, pass through a physical effect, then terminate with a process variable.First, the flow stress of the workpiece at the welding tool surface is the result of the thermal history, the amount of strain and the strain rate experienced by the workpiece. Similarly, the friction force is affected by the workpiece material and the thermal history it experiences as it approaches the tool. Thermal history effects can further be subdivided into slow processes that depend on the temperature distribution in advance of the welding tool, which result in metallurgical alteration of the workpiece, and rapid, deformation heating that takes place as the material is deformed by the pin. The relatively slow metallurgical alteration of the workpiece can be thought of as preconditioning that the workpiece experiences as it heats from room temperature to the temperature just in front of the pin. This preconditioning has the effect of eliminating the effects of thermomechanical treatments in the base metal, so that alloys of identical composition behave essentially the same in welding. Softening from deformation heating occurs from plastic work and friction caused at the surface of the welding tool pin.Friction between surfaces has been extensively studied in the past and it has been shown that friction is strongly dependent on local conditions. For sliding friction between clean metallic surfaces at high temperatures, the friction coefficient has been shown generally to decrease with increasing temperature , flow stress and friction force lead to the development of spindle torque as the workpiece material resists tool rotation. When torque is applied through rotation at a given speed, heat is generated in the workpiece. The torque can be used to calculate the power (energy per unit time) delivered to the workpiece simply by multiplying the torque by the spindle speed, and can be used to calculate the specific energy (energy per unit weld length) by dividing the power by the travel speed. In this model the specific energy is related to the temperature distribution within the workpiece, as justified earlier , the temperature distribution is the result of the balance between heat generation and heat loss to the environment. Important variables in the determination of the temperature distribution are the thermal diffusivity of the workpiece and anvil (how easily the heat dissipates), the size of the workpiece and anvil, and the workpiece surface convection characteristics. The maximum temperature is not linked to the flow stress in , since this effect is already captured in the deformation heating effect, discussed above.Conceptual modeling of the relationships between the variables can be further enhanced by showing whether the relationship is a direct relationship or an inverse relationship, as shown in . In this diagram the relationship is coded as a ‘+’ sign for a direct relationship and a ‘−’ sign for an inverse relationship. As will be seen in the case study below, the relationships between variables can be used to help understand how changing welding conditions will influence the key features of flow stress and friction, torque, heat generation and workpiece temperature.In this case study, an experiment was performed to explore the effect of spindle speed on welding conditions. A fixed-geometry bobbin tool was used to weld 11.9 mm 2195 Al–Li alloy plate. The fixed-geometry, bobbin-style FSW tool is a variation of FSW that employs two shoulders connected by a pin, as shown in . In each weld the forces against the welding tool were recorded and plotted as a function of spindle speed, as shown in . All welds produced were free of volumetric defects. The resultant in-plane force was observed to initially decrease, reach a minimum value, and then increase with increasing spindle speed. At the same time, the spindle torque was observed to continuously decrease, while the weld power and specific energy increased. The direction cosine of the in-plane force is plotted as a function of spindle speed in . As the spindle speed increases, the in-plane force becomes more aligned with the welding direction. These observations can be examined within the context of the conceptual model, shown in . In this figure, upward influence is indicated by a heavy dark line, downward influence is shown as a heavy gray line, and neutral influence is shown as a dotted line. that increasing the spindle speed resulted in decreased torque, which, according to the conceptual model, would exert a downward influence on the power and specific energy., the increase in spindle speed also exerts an upward influence on the power and specific energy. It was observed in that the power and specific energy actually increased with increasing spindle speed, in spite of the decreasing torque. Since no change was made to the heat loss characteristics, the increasing power and specific energy would be expected to increase the maximum temperature and the temperature distribution, although these were not measured in the present study.The model predicts that the increasing temperature distribution increases metallurgical alteration in advance of the welding tool, exerting a downward influence on the flow stress and the friction force.Increasing the spindle speed also has the effect of increasing thermal softening by deformation heating, exerting an additional downward influence on the friction force and flow stress at the tool. The effect on flow stress is counteracted, to some unknown extent, by the presumed increase in strain rate. However, it has been shown that the torque continues to decrease with increasing spindle speed, even beyond the point at which no additional far-field temperature distribution increase is expected, and the deformation heating effect is stronger than the effect of increasing strain rate, resulting in a continued decrease in flow stress with increasing spindle speed The model shows a positive relationship between local compressive force and the friction force. It was observed that as the spindle speed increased, the net in-plane force also increased and the direction of the in-plane force became more aligned with the welding direction, exerting an upward influence on the friction force that competes with the negative influence of the increased metallurgical alteration and deformation heating. The local compressive force also includes the effect of the plunge force, but in a fixed-gap bobbin tool this force is internal to the tool and could not be measured.The decreasing flow stress and friction force would be expected to reduce the torque, as was observed. The model also predicts the downward influence of the decreasing travel per feature per revolution, although it is impossible to isolate the effect in the data collected in the present experiment. However, a previous discussion of this conceptual model It is speculated that the increasing in-plane force with respect to spindle speed is the direct result of the decreasing friction coefficient predicted by the model. In the bobbin-welding experiment, as the spindle speed increased, the in-plane force became almost entirely composed of force required to push the tool in the welding direction, which implies high compressive force between the leading edge of the welding tool pin and the workpiece. It is conceivable that the increasing in-plane force provides a mechanism for regulating the production of heat as the spindle speed increases, thus perpetuating the welding process. It is notable that in the present experiment, the power and specific energy continue to increase with increasing spindle speed, instead of staying constant. This is an area where additional fundamental research into the mechanics of the process is needed.It is interesting that at low spindle speed the in-plane force was observed to decrease with increasing spindle speed, as shown in . It seems logical that at a spindle speed of zero, all material transfer around the pin would be due to extrusion and the in-plane force would be very high. It can be supposed that as the spindle speed increases it begins to assist in material transfer and to produce thermal softening, causing the in-plane force to decrease. Eventually, a minimum force condition is reached where further increase in the spindle speed causes the in-plane force to increase due to the reduced friction coefficient, as discussed above. Perhaps the minimum in-plane force point offers a convenient indicator of optimum spindle speed for a given travel speed, since this point minimizes the force on the tool. Higher spindle speeds only serve to increase heat input and in-plane force.For modeling of heat input and material flow, a critical input required is the coefficient of friction during the friction stir process. To date, a framework for coefficient of friction during the friction stir process has not been adequately developed. The metalworking literature primarily relies on either the Coulomb friction model (τ |
= |
μσn, where the shear stress τ is proportional to the normal stress σn with a proportionality constant μ, the coefficient of friction) or the constant shear model (τ |
= |
mσy, where the shear stress τ is proportional to the material yield stress σy with a proportionality constant, m) shows the variation of coefficient of friction with modeled torque for two aluminum alloys. The values for the coefficient of friction range from 0.35 to 1.3 for these alloys. This data and the procedure for repeating the results with other alloys will be described in a future publication As emphasized above, the temperature generation, material flow strength and coefficient of friction are all intertwined. The modeling and simulation efforts can use experimentally obtained empirical relations to obtain more realistic information.In spite of the apparent simplicity of the FSW process, there are still many aspects of the process that remain unexplained. This study proposes a conceptual model of the mechanisms of heat generation in FSW for the purpose of facilitating a general understanding of the process. However, in describing the process, several questions emerge. For example, an adequate description of the mechanics of frictional heat generation under the conditions of FSW does not exist. In addition, quantitative study of the effects of different variables could lead to assigning weighting factors to the interactions between variables. This work could, for example, yield valuable insight into the relative magnitude of the role of friction vs. plastic work in heat generation and the relative importance of strain rate effects.Ultra-high strength and ductility from rolling and annealing of a Ni-Cr-Co superalloyA new processing route is demonstrated for producing a nickel-based alloy with 1099 MPa tensile yield strength and 30% elongation. A chromium- and cobalt-rich commercial alloy was solution-annealed, cold-rolled, and aged at different temperatures and times to develop partially-recrystallized microstructures with ordered Ni3(Al,Ti) γ′ precipitates. These were tested in uniaxial tension and compared to alloys given the same heat treatment without rolling to assess the contributions of different strengthening mechanisms. Orientation mapping showed the development of a modest 〈111〉 and 〈100〉 double-fiber texture. Scanning transmission electron microscopy also revealed the development of exceptionally large dislocation densities including wall structures.The last two decades have produced substantial progress in developing materials with outstanding combinations of high strength and ductility, largely through research involving twinning-induced plasticity (TWIP) and transformation-induced plasticity (TRIP) steels [] and more recently “high-entropy” multi-principal element (MPE) alloys []. It is now common for these alloys to attain ultimate true tensile strengths exceeding 1200 MPa while retaining >30% elongation to fracture. Recent attention has therefore been extended to increasing the yield strengths of these alloys, which often remain in the more modest range of 400–600 MPa [Most efforts to enhance room-temperature yield strength have focused on changes in processing and chemistry that exploit mechanisms like deformation twinning. In TWIP steels, one successful avenue involves cold-rolling the material to produce a microstructure with a high density of deformation nanotwins and subsequently annealing at a moderate temperature. The recovery during the annealing step is thought to reduce the dislocation density (thereby restoring some ductility) while the deformation twins, which are stable up to ~625 °C, remain unaffected []. The twinning substructure then substantially enhances the yield strength of the alloy on further testing. Using this method, TWIP and TWIP-TRIP steels have exhibited outstanding combinations of yield strength and elongation of, for example, 798 MPa/41% [In contrast, yield strength enhancement in MPE alloys has primarily focused on changes in composition. The early emphasis in MPE alloys was on compositions that avoided precipitation of deleterious, embrittling phases and derived their strength from solid solution hardening. This produced alloys like single-phase equimolar FeNiCoCrMn [], which have high work-hardening rates and excellent ductility like the baseline TWIP alloys. However, very recent work has shown that conventional precipitation hardening in MPE alloys using the B2 [] can significantly enhance the yield strength with only marginal compromises in ductility. The composition chosen by Zhao et al. in [] is particularly interesting as a derivative of equimolar CrCoNi, which exhibits exceptionally high hardening rates due to formation of nanoscale HCP regions along deformation twins and stacking faults [In this work, we combine processing lessons from TWIP-TRIP alloys with the compositional benefits conferred by the CrCoNi + (Al,Ti) composition space. The alloy chosen for study was commercially available Inconel 740H, which has the nominal composition (in wt%) Ni – 25Cr – 20Co – 1.35Al – 1.35Ti – 1.5Nb – 0.1Mo. This corresponds to an atomic composition of approximately Ni48.5Cr27.0Co19.0Nb0.9Ti1.6Al2.8Mo0.1. This composition has several advantages: 1) large Cr and Co contents reduce the stacking fault energy of the alloy and produce a composition similar to thoroughly-studied equimolar CrCoNi; 2) additions of Al and Ti enable precipitation of the well-known γ′ phase that has been thoroughly studied in Ni-based superalloys; and 3) the (Al + Ti) content is low so precipitation can be avoided with a fast quench from the solution-annealing heat treatment. Developed for elevated-temperature applications, alloy 740H is typically used in the aged, precipitation-hardened condition []. In this work, it was cold-rolled in the solutionized (precipitate-free) state and subsequently heat treated, which achieved dual purposes of annealing the highly deformed microstructure to restore ductility and inducing precipitation to enhance the yield strength. This combination of chemistry and processing produced an alloy with ultra-high yield strength and large ductility.Commercial alloy Inconel 740H was supplied by Special Metals Corporation in the solutionized condition, which consisted of a precipitate-free face-centered cubic (FCC) matrix and a low volume fraction of MC-type carbides containing primarily Nb or Ti. The material was rolled to a 65% reduction in thickness and annealed for 1 or 2 h at temperatures ranging from 600 °C–900 °C. To compare the strengthening increment from precipitation alone, material was also aged for the same times and temperatures without the intermediate rolling step. Following thermomechanical processing, tensile specimens were cut via electrical discharge machining (EDM) and tested in uniaxial tension on an Instron Electro-Thermal Mechanical Tester (ETMT) with engineering strain rates of 10−3 s−1. Strain measurements were made using digital image correlation (DIC) with paint patterns applied to the surface of the specimens. Full-field strain maps were produced with Correlated Solutions VIC2D software using subset and step sizes of approximately 0.65 mm and 0.01 mm, respectively. Engineering strain was determined through conversion of the average Lagrangian strain in the gauge section as calculated by VIC2D.Pre- and post-deformation specimens were characterized using an FEI Apreo scanning electron microscope (SEM) and an FEI TF-20 Tecnai 200 kV transmission electron microscope (TEM). Electron backscatter diffraction (EBSD) was performed on the SEM using an EDAX Hikari Super EBSD camera in conjunction with acquisition software EDAX TSL DC7 and analysis software EDAX TSL OIM 8. Scans were acquired using an accelerating voltage of 20 kV and a beam current of 6.4 nA at a working distance of 20 mm. The deformation structures were studied in the TEM using foils prepared via focused ion-beam (FIB) milling.The mechanical responses produced by several selected processing conditions are shown in . The as-received solution-annealed specimen, which was fully recrystallized and had a large grain size of approximately 90 μm, had the lowest strength and largest ductility of any tested specimens. Note that the material was free of prior deformation and precipitates in this state. Aging the solutionized material at 900 °C for 2 h induced precipitation of the γ′ phase. Due to the modest quantities of γ′-forming elements Al and Ti, the volume fraction remained low at ~6.5% with average particle diameter 31 nm. These precipitates increased the yield strength from 300 MPa in the solutionized specimens to approximately 550 MPa. The ductility decreased but still achieved a uniform elongation of about 29% (true strain) and elongation to failure of 39% (engineering strain).The most outstanding properties were achieved for specimens that were cold-rolled and annealed at 900 °C for 1 and 2 h. All rolled samples that were annealed at temperatures below 900 °C retained properties similar to the as-rolled condition, which had very high strength but negligible uniform elongation. In contrast, rolled specimens processed at 900 °C for 2 h had an average yield strength of 1099 MPa with 15% uniform elongation and 30% elongation to failure. Note that for non-rolled and rolled specimens given the same 900 °C/2 h heat treatment, the addition of the intermediate rolling step increased the yield strength by 550 MPa (doubling the value in the non-rolled material) with only a modest change to the total elongation, from 39% to 30%. shows the microstructural evolution for specimens aged at 900 °C for 2 h with and without prior rolling. The inset inverse pole figure (IPF) triangles for each figure give the crystal orientation parallel to the specimen tensile axis, which has previously been associated with strong texture development in CrCoNi and other FCC alloys. Prior to deformation, the non-rolled specimen had large equiaxed grains with a substantial area fraction of annealing twins and no substantial texture (a). Deformation in uniaxial tension produced a strong double-fiber texture with 〈111〉 and 〈100〉 components parallel to the tensile axis (In contrast, the rolled and aged specimen showed highly elongated grains with extensive intragranular rotation and deformation even after annealing (c). Many regions also recrystallized to form fine grains free of orientation gradients, which are marked with arrows on the inset in c. Although there was some evidence for residual texture with preferred orientations near 〈111〉, the overall texture was relatively weak due to the large fraction of recrystallized grains. After tensile deformation (d), the IPF maps showed large intragranular rotations with grains even more highly elongated and partitioned than in the pre-deformed state. Separation of data from the recrystallized and non-recrystallized grains clearly showed substantial rotation of the latter during the tensile experiment. This observation is critical as it suggests that even grains with considerable prior cold work retained their capacity for plastic deformation.The remainder of this work focuses more closely on the specimens that were rolled and aged at 900 °C for 2 h, which exhibited superior mechanical properties. shows a more detailed view of the microstructure immediately prior to tensile testing. These images were acquired after rolling and aging. a shows a higher magnification image of a region containing recrystallized grains, most of which were several microns in diameter. These did not display any preferred orientation and were primarily observed along prior grain boundaries, although some were occasionally noted in the apparent interior of other grains. Precipitation of the ordered Ni3(Al,Ti) γ′ phase also occurred during aging. b shows an SEM micrograph with fine γ′ precipitates revealed by etching (dark features). In non-recrystallized regions, γ′ precipitation was relatively homogeneous; however, recrystallized grains were denuded of the precipitates in the grain interiors and formed coarsened particles along grain boundaries. While not shown here for brevity, the ordered structure and composition were confirmed via superlattice reflections using selected area diffraction in the TEM. STEM energy dispersive spectroscopy also confirmed partitioning of Al and Ti co-located with reduced Co and Cr on a size scale consistent with the precipitate structure indicated in the SEM image of At finer length scales, the residual deformation from rolling was apparent. c shows a bright-field STEM diffraction contrast image ([]) from a non-recrystallized region exhibiting extremely high dislocation densities. Many of the dislocations were concentrated in high-density dislocation walls, which tended to be elongated parallel to the trace of a single set of {111} planes. Imaging of individual dislocations proved difficult; but, the inset d gives some indication of the very high density that exists even between the ultra-high density walls. Although very fine deformation twins were observed in the rolled and annealed microstructure in one instance (d, bottom right corner), these were very rare and did not appear in other scans with similar magnifications and step sizes. Likewise, no twin reflections were visible in TEM diffraction patterns from this condition.The post-deformation microstructure (following uniaxial tension) is shown in a shows a BSE-SEM image of the highly elongated and partitioned deformation structure. Nearly all high-angle grain boundaries were aligned approximately parallel to the common rolling and tensile axis. Additionally, many intragranular striations were also visible parallel to {111} planes, which are consistent with features visible in the bright-field STEM image shown in b. As in the post-rolling/aging, pre-deformed condition, these are dislocation walls of exceptionally high density. Although some areas appear to have substantially lower dislocation densities, this is actually a manifestation of large intragranular rotations that result in the loss of a strong diffraction condition. Tilting of the specimen to restore a locally strong diffraction condition confirmed a uniformly high density. Analysis of EBSD data and TEM diffraction patterns did not reveal any evidence for deformation twinning. Apart from the higher dislocation density after tensile deformation, STEM observations did not show any substantial differences between the pre- and post-tensile deformation structures.The apparent lack of deformation twinning in this alloy is not an expected result given its compositional similarity to equiatomic CrCoNi, and its high hardening rates and elongation, which are properties that have been associated with TWIP steels. Although the presence of ordered γ′ precipitates would be expected to deter twinning, even the solution-annealed specimens without precipitates did not show any evidence for extensive deformation twinning when examined with very fine EBSD scans and STEM. This suggests that higher Ni concentration at the expense of Cr and Co, or the presence of Al, Ti, or Nb, sufficiently raises the stacking fault energy to promote slip of perfect dislocations rather than dissociated partials that can later develop into twins. Further work is needed to explain how IN740H can achieve such outstanding strength, elongation, and hardening rates without involving twinning. Deformation twinning is usually considered as being fundamental to those same characteristics in mechanically similar alloys like CrCoNi [For the rolled and annealed alloy exhibiting ultra-high strength and ductility, the strengthening mechanisms can be separated based on results from different processing routes. In addition to the inherent solid solution hardening, the primary strengthening modes are work hardening (σw) and precipitation hardening (σp). The work hardening contribution can be obtained by comparing the solution-annealed and as-rolled tests, which show a yield strength increase σw = 980 MPa. The precipitation hardening contribution is likewise given by comparing the solution-annealed specimens to the aged (but non-rolled) samples, which gives an increase σp = 250 MPa. This suggests the total strengthening increment for the rolled and aged sample should be the sum of those contributions, 1230 MPa; however, recovery at elevated temperature reduces the observed strengthening increment to 815 MPa (the difference between the solution-annealed and rolled + aged specimens). This suggests a loss of 415 MPa to recovery and recrystallization, which contributes substantially to the restored ductility and hardening behavior. The relative contribution of recrystallized and non-recrystallized grain regions to the total strain during tensile deformation is presently unknown, but the fact that texture development occurs in both clearly indicates that they are active and deforming compatibly. Based on images of the specimen after failure (e.g, ), it is also clear that deformation structures and non-recrystallized grains from rolling are quite stable at room temperature and remain present through the duration of tensile testing. Although the high-temperature stability of these structures requires further study, post-rolling heat treatments of 600 °C–800 °C/1 h did not produce substantial recrystallization.As a final note, this alloy showed outstanding properties despite the large grain size in the solutionized state. The yield strength in the solution-annealed specimen was approximately 300 MPa. CrCoNi is often reported as having a higher yield strength, but using specimens with a smaller grain size; based on the Hall-Petch coefficients developed by Zhao et al., a grain size of 90 μm (similar to the as-annealed alloy 740H in this work) would produce a yield strength of only ~276 MPa in CrCoNi []. Large grains may also contribute substantially to the lower hardening rates observed in this work, which warrants further study in recrystallized material with smaller grains. This influence of grain size will be critical to separate given results from the present study that indicate deformation twinning and plasticity-induced phase transformations might not be necessary to achieve large uniform elongations.In conclusion, this work presents the development of a processing route on a commercial superalloy Inconel 740H that produced ultra-high tensile strength and ductility (1099 MPa yield strength/30% elongation), which compares favorably to recent advanced TWIP steels (e.g, 700 MPa yield strength/30% elongation in []) and other high-entropy alloys (for example, 1005 MPa yield strength/17% elongation in []). These properties were achieved using a combination of alloy chemistry, which enabled precipitation of the ordered γ′ phase, and processing via rolling and annealing. Despite a partially recrystallized microstructure with a high dislocation density, substantial elongations were still attained. This process is easily implemented and tailored to specific combinations of strength and ductility.Positron annihilation studies of the interaction between oxygen impurities and nanovoids in neutron-irradiated vanadiumVanadium samples with controlled oxygen impurity of up to 2460 at. ppm were irradiated with fast neutrons to a fluency of 8.3×1018ncm-12 at 150 °C. The irradiation-induced nanovoids and the interaction between the defects and the oxygen impurities are studied systematically by combining the positron lifetime technique, the coincidence Doppler broadening technique and the first-principles calculations. The nanovoids are seen to be decorated with the oxygen impurities, which play a significant role in the dynamic processes of the formation of the nanovoids by irradiation and their subsequent recovery by post-irradiation annealing. The decoration with oxygen impurities not only enhances the nanovoid formation but also stabilizes them during low-temperature annealing (<400 °C). The oxygen impurities dissociate from the nanovoids by annealing above 400 °C and the irradiation-induced nanovoids recover on the annealing at 650 °C.Vanadium and its alloys have been considered as promising candidates for fusion first-wall-blanket materials since they have good mechanical properties, low irradiation-induced activity, and good resistance to irradiation-induced swelling and damage The positron annihilation technique is a powerful tool with which to study vacancy-type defects in solids Recently, the coincidence Doppler broadening (CDB) technique, which was originally introduced by Lynn et al. In this work, we combine the positron lifetime and CDB methods to study the fast neutron irradiation-induced defects in oxygen-doped vanadium samples. We have observed that, in all the samples with various oxygen concentrations, longer positron lifetimes of about 380–480 ps are obtained. This shows the formation of nanovoids clearly. The sizes of nanovoids are further estimated based on the positron lifetime calculation. In highly oxygen-doped vanadium, more nanovoids are formed when the isochronal annealing temperature is increased to 350 °C. From the CDB measurements, the fingerprint of oxygen impurities was found in the high momentum region. These results suggest that nanovoid formation and swelling are affected by oxygen impurities, in particular when annealing temperature is increased.The vanadium samples with oxygen content up to 2460 at. ppm were prepared by a zirconium-foil wrapping technique . The samples were irradiated by fast neutrons at the Japan Materials Testing Reactor to a fluency of 8.3×1018n/cm2 at 150 °C. To investigate the effect of increasing oxygen impurities on the annealing behavior of irradiation-induced defects and the defect–oxygen interaction on heating, the specimens with a low (6 at. ppm) and a high (1980 at. ppm) oxygen concentration were isochronally (30 min) annealed up to 700 °C under vacuum (10-6Torr) by increasing the temperature in 50 °C steps, and the results for these two specimens were compared.The positron lifetime spectra were measured by using a fast–fast lifetime spectrometer with a time resolution of about 198 ps. For each spectrum, more than a million counts were collected at room temperature. After positron source corrections, the lifetime spectra were decomposed into two exponential components using the computer program PATF1T In this work, the usual shape parameters of a Doppler-broadening (DB) spectrum, namely the S-parameter and the W-parameter, were also evaluated from the CDB spectrum. The S- and W-parameters are defined as the ratio of low momentum (|pL|<4×10-3m0c) and high momentum (18×10-3m0c<|pL|<34×10-3m0c) regions in the Doppler-broadening spectrum to the total region, respectively. Thus, the S-parameter (W-parameter) is a measure of the momentum density at low (high) momentum.First, positron lifetime and CDB measurements were performed for the as-irradiated samples. It was found that all the lifetime spectra can be decomposed well into two components. The variations in the positron lifetimes and their intensities with the oxygen impurities are shown in . For comparison, the positron lifetime and CDB profile for the unirradiated vanadium sample are also presented together.For the unirradiated standard vanadium sample, only a single lifetime of 123 ps is obtained, which is consistent with the previous experiment ). In particular, it was found that the lifetime τ2 systematically decreases with the increase in the oxygen concentration, while the intensity I2 rapidly increases from 35% to about 72% when the oxygen concentration increases from 6 to 460 at. ppm.In order to clarify the positron annihilation sites responsible for the observed lifetimes, we performed first-principles calculations of positron lifetime based on the two-component density functional theory within the local density approximation Because of the size limitation of the supercell, we performed first-principles calculations for the positron lifetimes at the bulk and at some small vacancies and vacancy–oxygen complexes (i.e. V1,V2 aligned along the [1 1 1] direction, V2 aligned along the [1 0 0] direction, V1–(tetrahedral)–O complex and V1–(octahedral)–O complex) (). We found that the calculation could reproduce the experiment for the bulk well, while the theoretical lifetimes (164–214 ps) for the calculated small defects are only comparable with the experimental τ1 (about 160 ps). We thus concluded that the experimentally observed τ1, which was nearly constant at 160 ps for all the samples with various oxygen concentrations, was mostly produced by a mixture with a small bulk component and other components of positron annihilation at some small vacancies (such as monovacancies and divacancies) and vacancy–oxygen complexes.However, in addition to the shorter lifetime τ1, another longer lifetime component τ2 of about 400 ps was observed in the experiments (). Obviously, such a longer lifetime component cannot be attributed to the positron annihilation at the small defects, as shown in ; instead, it may arise from the positrons annihilating at some larger defects induced by neutron irradiation. In order to clarify these larger vacancy clusters or nanovoids, we employed the superimposed atomic charge scheme proposed by Puska and Nieminen presents the calculated positron lifetimes as a function of number of vacancies in the simulated defect in vanadium (the decoration with oxygen and its effects on the positron lifetime are neglected in the calculations). The calculations show that the positron lifetime at the nanovoid consisting of about 25 vacancies is around 400 ps (). Therefore, the average size of the nanovoids induced by neutron irradiation in our vanadium samples was estimated to be approximately V25.The formation of nanovoids is further supported by the CDB profiles. A narrower Doppler-broadening component (namely a larger S-parameter) compared with that for the bulk is widely observed for defects in materials. In the present experiments, the FWHMs of the CDB profiles for the as-irradiated samples are about 10.5×10-3m0c, narrower than that for the standard vanadium sample (12.8×10-3m0c) (). This change clearly indicates the formation of irradiation-induced nanovoids., the positron annihilation parameters for the as-irradiation vanadium samples exhibit an interesting dependence on the oxygen concentration. The intensity of the longer positron lifetime at the nanovoids (I2) is found to increase rapidly from 35% for the 6 at. ppm oxygen sample to 70% for the 460 at. ppm oxygen sample, then this intensity stays nearly constant even when the oxygen concentration increases to 2460 at. ppm, while the positron lifetime for the nanovoids decreases continuously. This oxygen dependence clearly shows that the oxygen impurity plays an important role in the nanovoid formation, especially when its concentration is low (<460 at. ppm).It has been well established that hydrogen impurities block the formation of vacancy clusters in electron-irradiated tantalum and niobium indicate that this blocking effect is especially significant when the oxygen concentration is lower than 460 at. ppm. Moreover, oxygen impurities are found not only to block the formation of larger nanovoids but also to decorate the nanovoids. In order to explain this, we obtained the ratio curves of the CDB spectra for the as-irradiated samples relative to standard vanadium, and compared these results with the ratio curve of the neutron-irradiated SiO2 (). In the latter, it is believed that the positrons are mainly annihilated with the electrons of the oxygen atoms (, the shapes of the ratio curves for all the vanadium samples are broadly similar to each other and to that for the irradiated SiO2. There is a characteristic valley around 15×10-3m0c and a high-momentum peak around 22×10-3m0c observed in the irradiated SiO2, which originated from the positron annihilation with the core electrons of the oxygen atoms and are the fingerprints of oxygen. Such features clearly indicate that the irradiation-induced nanovoids are decorated with the oxygen impurities in all the samples. Nevertheless, it is noteworthy that the ratio data presented in also show some fluctuations with increasing oxygen concentration. Namely (i) the ratio for the 460 ppm oxygen sample in the low (high) momentum region is larger (smaller) than all of the others and (ii) the ratio for the 1980 ppm oxygen sample is larger (smaller) than that of the 2460 ppm sample in the low (high) momentum region. These fluctuations imply that other oxygen-free defects may also exist in the samples after irradiation.To highlight the oxygen-decorated nanovoids, we further estimated the areas of the characteristic peak (21–24×10-3m0c) and valley (14–17×10-3m0c) of the oxygen fingerprints in the CDB profiles. Although the shape parameters of the CDB ratio curves defined here do not directly represent the amount of the oxygen decorating the nanovoids as some oxygen-free defects exist in the samples, the ratio of the peak relative to the valley is specific to the amount of oxygen impurities. In , the ratio is plotted as a function of the total oxygen concentration. From , it is observed that the amount of the decorating oxygen in the low oxygen-doped (6 at. ppm) sample is very small, and the decoration with oxygen in the nanovoid increases linearly with the increase in the total oxygen concentration within the experimental range (up to 2460 at. ppm).For a better understanding of the interaction between oxygen impurities and nanovoids, we made isochronal annealing experiments (30 min) from 200 °C up to 700 °C in vacuum. At each annealing temperature step (50 °C), lifetime and CDB measurements were performed. shows the annealing behavior of the positron lifetime for the low oxygen-doped (6 at. ppm) and highly oxygen-doped (1980 at. ppm) vanadium samples. An interesting difference between them was observed. For the low oxygen-doped sample, the lifetime τ2 was nearly constant (around 475 ps) below 400 °C and decreased to about 300 ps when the annealing temperature was increased to 650 °C, while the intensity I2 decreased continuously with increasing annealing temperature. These results indicate that recovery of the nanovoids takes place even during the early stage of annealing, though the shrinking of the nanovoids occurs later, and almost all the irradiation-induced nanovoids are recovered on annealing at 650 °C. However, for the highly oxygen-doped sample, the annealing behavior exhibited two quite distinct stages. In the first stage (from the as-irradiated state to the 400 °C annealing), the lifetime τ2 was nearly constant at about 390 ps and the intensity I2 increased from 75% for the as-irradiated state to 90% at around 350 °C. In the second stage (from 400 to 650 °C), the lifetime τ2 increased slightly while the intensity I2 decreased rapidly to near zero around 650 °C, at which temerature almost all of the nanovoids were recovered, as observed for the low oxygen-doped sample.The above difference is highlighted even more in the CDB experiments. a and b shows the correlation between the S-parameters and the W-parameters of the CDB profiles for these two samples. In general, the recovery of one type of defect or several types of similar defects will result in a linear relationship between the S-parameter and the W-parameter. From the S–W correlation shown in a, such a linear relationship is indeed observed for the low oxygen-doped sample, where the concentration of the oxygen dopants is very low and only few oxygen impurities decorate the nanovoids. However, for the highly oxygen-doped sample (b), two distinguishable lines, namely two clear stages of annealing behavior, are observed. From the as-irradiated state to 400 °C annealing, the (S, W) points are distributed along a line where the W-(S-)parameter decreases (increases) with increasing annealing temperature. In contrast, the annealing above 400 ° C (b) causes the W-(S-)parameter to increase (decrease) with increasing annealing temperature.The physical origin of the above-mentioned two stages of annealing behavior is the dynamics of the oxygen impurity. To clarify this, we evaluated the area ratio of the peak relative to the valley of the oxygen fingerprints at each annealing temperature (). For the highly oxygen-doped sample, we found that the oxygen impurity decorating the nanovoids increased after annealing at the low temperature, while the oxygen impurity rapidly dissociated from the nanovoids and resolved into the matrix after annealing at above 400 °C. Since the oxygen atom has only a 1s core state, the high momentum density of this impurity is lower than that of the vanadium atom, where the 2s and 2p core electrons especially contribute significantly to the density in the high momentum region. Thus the increase in the oxygen decorating the nanovoids during the first stage increases the probability of positrons sampling the oxygen valence electrons and 1s core electrons, resulting in an increase (decrease) in the positron–electron momentum densities in the low (high) momentum region, i.e. the S-(W-)parameter increases (decreases) after annealing during the first stage. With further increasing annealing temperature, the oxygen impurities dissociate from the nanovoids and the nanovoids are recovered. As a result, the number of positrons trapped in the nanovoids decreases with annealing in the second stage and thus a linear S–W correlation is observed.However, for the low oxygen-doped sample, since only a few oxygen impurities decorate the nanovoids their amount changes slightly even when the annealing temperature is increased up to 700 °C. The chemical environment around the positron annihilation site shows almost no change during all the annealing, and thus a linear relationship between the S-parameter and W-parameter is expected.The above results show that the CDB technique is a very powerful tool with which to explore the dynamic behavior of the oxygen impurity. The positron lifetime at the first stage was found to be nearly a constant, indicating that the lifetime of the positrons trapped at a nanovoid was insensitive to the impurities at the nanovoid’s inner surface. This is because the positron lifetime measures the total positron annihilation rate λ(=1/τ) with both the valence and core electrons, but the CDB can highlight the positron annihilation with the core electrons, which contributes only a small fraction to the total annihilation rate.Finally, we combined the lifetime and CDB measurements to consider the role of oxygen impurity in the nanovoid recovery. For the low oxygen-doped sample, the intensity I2 decreased even during the early stage of the annealing (below 400 °C), while this intensity increased for the highly oxygen-doped sample. This result indicates that the decoration with the oxygen atoms increases the stability of the nanovoids and assists the additional formation of nanovoids in the first stage. Moreover, oxygen migration at low temperature increases the oxygen impurities trapped in the small vacancies, which may block the traps that compete with the nanovoids for positrons and thus contributes partly to the increase in I2 at the first stage for the highly oxygen-doped sample. In the second stage, the oxygen impurities dissociate from the nanovoids, and then the nanovoids rapidly get recovered until the annealing at 650 °C. It is noteworthy that the lifetime τ2 for the highly oxygen-doped sample increased a little in the second stage, indicating that the nanovoids became slightly larger after the oxygen impurities dissociated from the inner surfaces of the nanovoids. Another reason for increase in nanovoid size is the reduction of the blocking effect after the oxygen dissociation, which could result in further growth of the nanovoids. This is consistent with our analysis for the oxygen dependence of the lifetime τ2 of the as-irradiated sample.Vanadium samples with controlled oxygen impurity up to 2460 at. ppm were irradiated with fast neutrons to a fluency of 8.3×1018ncm-12 at 150 °C. The irradiation-induced nanovoids and the interaction between the nanovoids and the oxygen impurities were studied systematically by combining the positron lifetime technique, the coincidence Doppler broadening technique and first-principles calculations. We observed that, in all the samples with various oxygen concentrations, longer positron lifetimes of about 380–480 ps were obtained after neutron irradiation, unambiguously indicating the formation of nanovoids. Two of the samples were further isochronally annealed (30 min) from 200 °C up to 700 °C in vacuum. It was found that when the annealing temperature was increased to 350 °C more nanovoids were formed in the highly oxygen-doped vanadium samples. From the CDB measurements, the fingerprint of oxygen impurities was observed in the high momentum region.By combining the first-principles calculations of positron lifetime, the sizes of the nanovoids were estimated. It was clearly shown that the nanovoids were decorated with the oxygen impurities, which play a significant role in the dynamic processes of the formation of the nanovoids by irradiation and their recovery by post-irradiation annealing. The decoration with oxygen impurities not only enhanced the nanovoid formation but also stabilized them at the low-temperature annealing (<400 °C). The oxygen impurities dissociated from the nanovoids by the annealing above 400 °C and the irradiation-induced nanovoids recovered on annealing at 650 °C. These results suggest that nanovoid formation and swelling are affected by oxygen impurities, in particular when the annealing temperature is increased.Blending polybenzimidazole with an anion exchange polymer increases the efficiency of vanadium redox flow batteriesPBI membranes are recently discussed as stable, well performing membranes for vanadium redox flow batteries (VRFB). Blending meta-PBI with an anion exchange polymer (FAA3i) slightly reduces the coulomb efficiency from 99.7 to 97.8%, but strongly increases the voltage efficiency from 82.5 to 88.2%, leading to an increased energy efficiency (86.2% at 80 mA cm−2), exceeding that of meta-PBI (82.2%) and N212 (83%). Apparently, since the conductivity of sulfuric acid has a maximum around a concentration of 3.8 M, the concentration of the absorbed acid has a dominant influence on the conductivity. Addition of FAA3i decreases the concentration of the acid absorbed by PBI membranes. Furthermore, an ex-situ stability test in 1.5 M V5+ solutions in 2 M sulfuric acid for 87 days showed a very high stability for meta-PBI and Nafion 212, while the commercial FAA3 membrane disintegrated into pieces. Blending of meta-PBI and FAA3 decreased the stability, as proven by formation of V4+, but all tested blend membranes retained their membrane shape and could still be handled. Blending with FAA3 reduces the tensile strength and Young's modulus of meta-PBI, and doping with sulfuric acid leads to a further decrease in the mechanical strength. However, an acid doped PF-21 still showed a tensile strength of 37 MPa and a Young's modulus of 0.7 GPa.In flow batteries, redox active species flow over the electrodes, which are separated by a membrane to prevent direct contact between the anolyte and catholyte. While the concept is nearly 70 years old [], work on this type of batteries gained momentum with the research on vanadium redox flow batteries, started by Skyllas-Kazacos []. Here, the electrolytes consist of vanadium ions dissolved in 2–4 M sulfuric acid (H2SO4). During the charging process, V4+ ions in the positive electrolyte are oxidised to V5+, and V3+ ions in the negative electrolyte are reduced to V2+ []. When the battery is discharged, the opposite reactions occur. Therefore, the storage capacity depends on the volume of electrolyte tanks and the solubility of redox-active species, and the power depends on the active area of the device and the electric current. In recent years, work on VRFBs has been accelerated because VRFBs are considered to be one of the best ways to store large amounts of renewable energy originating from fluctuating, intermittent renewable resources, like solar or wind power.One of the key components, which strongly affect the performance and durability of VRFBs, is the membrane, which should transfer protons or other electrochemically inert ions, but block the diffusion of redox-active species. Furthermore, the membrane should withstand the highly oxidative environment, i.e. contact with V5+ ions when the VRFB cell is fully charged. The requirements and implications of such a membrane were well described by Schwenzer et al. [], a review of the more recent developments was published by Chen et al. [] In short, while perfluorinated Nafion is one of the most stable membrane materials and shows a low resistance, it is a cation exchange membrane and therefore its vanadium crossover is severe. Although this can be partially compensated by using thicker membranes, this also increases the resistance, weakening the voltage efficiency of the VRFB.One approach to substitute Nafion membranes is to fill the pores of inert porous substrates with ion conducting materials. Examples are porous PVC [], where the pores are filled with silica particles. Especially the latter membrane (which had smaller pores) showed a very high coulomb efficiency, and the charge capacity loss was lower than for Nafion 117 []. However, long-term stability tests of microporous separators still need experimental validation []. One potential problem which could arise from aforementioned structures would be loss of filler over time, widening the pores and thereby decreasing the coulomb efficiency. In that aspect, dense, homogeneous membranes would be preferred.Among dense, homogeneous membranes, anion exchange membranes are very promising because their vanadium ion crossover is strongly reduced []. However, since they are typically produced from non-fluorinated hydrocarbon materials, they are prone to be degraded by the attack of highly charged vanadium ions. For instance, it was suggested that the ether bonds in aromatic poly(ether sulfones) are cleaved []. Finally, the most recent class of materials that was tested for its properties in the VRFB is polybenzimidazole (PBI). PBI is practically non-conductive, but its basic imidazole groups strongly interact with mineral acids, allowing to produce acid doped membranes []. While most work on acid doped PBI focused on phosphoric acid doped PBI for use in high temperature polymer electrolyte membrane fuel cells [], it is also possible to dope PBI with sulfuric acid []. In 2015, Zhou et al. reported that sulfuric acid doped PBI membranes worked well in VRFBs and showed a similar stability as Nafion in ex-situ tests []. The most striking feature of PBI is the low vanadium crossover, which is attributed to the positively charged protonated polymer backbone (repelling vanadium ions) and the narrow channel size (low distance between the polymer chains), which excludes vanadium ions. Li and Zhang et al. [] tested the stability of PBI in the operating system and used a PBI membrane for over 13,500 charge-discharge cycles. In the test, they initially fixed the current density at 80 mA cm−2, and then sequentially increased to 100 and later 120 mA cm−2. Also at this high current density, the system showed a stable performance, with an energy efficiency of ca. 80% []. In our previous paper, we showed that the vanadium blocking effect of PBI is practically independent of the thickness, and that the coulomb efficiency remains close to 100% also when the thickness is decreased from 35 μm to 15 μm. In addition, it appears that the reduced charging potentials even further increase the coulomb efficiency of thin membranes, probably by suppressing side reactions and reducing the potential over the membranes, which affects ion migration []. Hong et al. showed that the sulfuric acid uptake (which is inversely correlated with the resistance) can increase when the regular structure of mPBI is broken up by side groups, leading to reduced crystallinity [In this work, we blend mPBI with a commercial anion exchange polymer (FAA3i) to increase the conductivity (chemical structures are shown in ). The conductivity of anion exchange membranes increases with the water contents, and in the sulfate exchanged form, each quaternary ammonium group in FAA3i binds about 20 water molecules []. We expect that blending of FAA3i into mPBI will break up the morphology of PBI, which should increase the water contents in the membrane, making it more similar to that of the external solution. Assuming that the coulomb efficiency is not much affected because both PBI and anion exchange membranes show high coulomb efficiency, it is expected that the lower resistance will increase the voltage efficiency and the energy efficiency because energy efficiency is a product of voltage efficiency and coulomb efficiency. Two materials are prepared: PBI/FAA3i blend membranes of a weight ratio of 2:1 (called “PF-21”), and membranes of a weight ratio of 3:1 (denominated as “PF-31”).Before membrane conductivity was measured, all samples were washed in DI water at 70 °C for 24 h, dried in the vacuum at 60 °C for 48 h, and immersed in 2 M sulfuric acid for at least 48 h. After that, through-plane conductivity was measured by immersing the samples in 2 M sulfuric acid between two gold coated disc electrodes (active area 1.767 cm2). Impedance was measured with a Zahner IM6 potentiostat. The conductivity was calculated bywhere t is the thickness of the acid doped membrane, A the active area, and Rmem = R(cell with membrane) - R(cell without membrane). For Nafion 212, which responds sensitively to traces of metal cations (e.g. from corrosion of the electrode), the electrolyte was continuously refreshed at a flow rate of 1 ml/min.For measuring the acid uptake, PBI containing membranes were washed and dried to get the dry weights. Then they were immersed in sulfuric acid for 48 h. After blotting with a tissue paper, the wet weights were noted. In turn, samples were immersed in 20 ml 0.05 M KOH for 48 h, and the solutions were titrated with 0.1 M HCl solution, while the membrane samples remained in the solution. Some amount of KOH remains in the membrane in this process; this amount was estimated by “doping” samples in DI water, and the fictitious “sulfuric acid uptake” was subtracted from the titrated sulfuric acid uptake values. The water uptake was calculated by subtracting the amount of absorbed sulfuric acid from the weight gain, and adding the weight of bromine lost by total ion exchange, assuming an ion exchange capacity of 1.9 (IEC based on the specification sheet). The concentration of the absorbed sulfuric acid is based on the weights of absorbed acid and water. Data for FAA3i was obtained by immersing membranes in 2 M sulfuric acid solution (for ion exchange and weight gain in sulfuric acid). Then the membranes were dried (water contents of the absorbed acid). After that, membranes were washed in pure water (water uptake of the sulfate exchanged membrane) and dried (dry weight of the sulfate exchanged membrane form).The permeability of VO2+ ions was determined by assembling the membranes between two compartments, which were stirred by magnetic bars. One of the compartments contained 1.5 M VO2+ in 2 M sulfuric acid, the other 1.5 M MgSO4 in 2 M sulfuric acid. The diffusion driven permeation of vanadium ions was monitored by UV/vis spectroscopy [Stability against VO2+ ions was tested by immersing membrane samples in a solution containing 1.5 M VO2+ and 2 M H2SO4 (prepared by charging a VO2+ solution in a flow battery) for 87 days. The membranes were inspected visually for defects, and the solutions were analysed by UV/vis for the content of VO2+, which is formed when VO2+ reacts with organic compounds, e.g. the membranes. To compensate for traces of unreacted initial VO2+ and potential reactions between VO2+ and impurities in the solution, the amount of VO2+ formed in the bottle containing Nafion 212 was subtracted as a base line. To compensate for slightly different membrane thicknesses, the molar amounts of formed VO2+ were divided by the respective membrane weights.For VRFB cell tests, the membranes were immersed in 2 M sulfuric acid for 24 h before assembly. Then they were assembled together with JNT GF-040 carbon felts (JNT, Korea; 4.0 mm thick). The active area was 4 cm2. The electrolyte consisted of 1.5 M VOSO4 in 2 M sulfuric acid, and the positive and negative storage tanks were filled with 17 and 15 mL electrolyte, respectively, to avoid overcharging. While higher acid concentrations up to 4 M sulfuric acid would be advantageous with respect to the electrolyte resistance (e.g. good results in the lab), the given conditions were chosen to both maximise the concentration of V2+ and to reduce the minimum operating temperature, which is an important consideration for real applications in countries with cold winters []. The system was pre-activated by a first charging step up to a potential of 1.75 V using a WBCS3000K8 potentiostat from Won-A Tech (Korea). Then, the fully charged catholyte was quickly exchanged with a fresh solution to maximise the cell potential of the VRFB system. During testing, the flow rate was fixed at 15 mL min−1 [The conductivity of acid doped PBI membranes correlates with the acid uptake []. For mPBI, the weight gain (including contributions from water and sulfuric acid) increased from about 68% to 103% when the sulfuric acid concentration increased from 2 M to 8 M (a). Titration shows that these values refer to an acid doping level of 1.0–2.3 mol sulfuric acid per repeat unit, which is about 1 lower than reported by Jones et al. [] The difference could be related to the different analytical methods, elemental analysis and titration, but most probably is related to the different membrane formation and hygrothermal history of the samples. As expected [], a higher acid concentration in the doping bath leads to a higher weight gain (a), based on both higher sulfuric acid uptake (c). One exception for this trend is the initial drop of the water uptake for mPBI when the concentration is raised from 2 M to 3 M sulfuric acid. One possible explanation is that the morphology changes in this regime, e.g. crystalline domains may start to dissolve when the amount of absorbed acid increases. While the weight gain and acid uptake increase with the PBI contents in the membranes, the water uptake follows the opposite trend, and increases with the amount of FAA3. In general, the concentration of absorbed acid increases both with the amount of PBI in the blend and the sulfuric acid concentration in the doping bath (d). However, while the concentration of absorbed acid constantly increases with the doping bath concentration for blend membranes, the concentration for mPBI shows a strong initial increase between 2 M and 3 M sulfuric acid in the doping bath, and then remains practically constant around 73% (13 M). A similar behaviour was reported for the concentration of absorbed phosphoric acid, which is around 85% (14 M) for doping bath concentrations between 3 M and 11 M []. Addition of VOSO4 reduces the weight gain for all tested membrane types, but especially for mPBI.The conductivity of sulfuric acid solutions is known to have a maximum around 4 M (30 wt%, see ]. For phosphoric acid, a similar curve shape was reported, with a maximum at around 45 wt% at room temperature []. At 160 °C, the temperature used in high temperature polymer electrolyte fuel cells (HT PEMFCs), the maximum conductivity can be estimated to be at around 80-90 wt%, the equilibrium concentration of the acid inside doped mPBI []. Therefore, although a quantitative, exact correlation cannot be expected (e.g. some molecules will not behave as bulk solution but will strongly interact with the imidazole groups of PBI, and the polymer morphology will play a role), the concentration of the absorbed acid should have an important impact on the membrane conductivity and also increase up to a certain maximum, and then again decrease. When the concentration of the sulfuric acid absorbed by different membranes is marked in the conductivity against concentration plot (), one can see that the expected conductivity increases with increasing addition of FAA3. The highest value is reached by FAA3i. A slight deviation from this trend is only observed for mPBI and PF-31 without addition of vanadium ions, which could also be due to slight measurement errors, since these values are very close to each other.In our previous work, we found a through-plane conductivity of 4.9 mS cm−1 for mPBI immersed in 2 M sulfuric acid []. Here, we used a different cell setup, but obtained a very similar conductivity for mPBI, 4.8 mS cm−1 (). As predicted, the addition of FAA3 increased the conductivity. A very high conductivity was measured for pure FAA3i. At first glance, this is unexpected. However, Chen et al. [], reported that the conductivity of an AEM increased by a factor of four when the solvent was changed from water to 2.5 M sulfuric acid, because the membrane took up also protons and excess sulfate ions. An FAA3 membrane in the chloride form showed a conductivity of ca. 15 mS cm−1 in water [], and FAA3i is specified by the producer to have an unusually high ion exchange capacity of 2.4–2.9 mmol Cl−∙g−1In conclusion, the measured conductivity indeed follows the trend predicted in . This shows that not only the amount of the absorbed acid, but also its concentration needs to be considered. As an anion exchange membrane, FAA3 is expected to absorb more water than acid. As mentioned before, FAA3 was reported to absorb ca. 20 water molecules per ammonium group, but is expected to absorb only one sulfate molecule per 2 ammonium groups. For FAA3i, we even measured a water uptake of 153%, ca. 45 water molecules per ammonium group. This should reduce the concentration of the absorbed acid in the analysed blend membranes. An open question is why the contributions of the polymers to water and acid absorption do not simply add up. A possible explanation is based on the fact that PBI is highly oriented, as observed by anisotropic swelling during doping with acids and bases []. In blends, the swelling is less anisotropic, supporting interaction of the two polymer chains []. The resulting entanglement of the two chains and different preference for water and sulfate probably lowers the overall swelling.The mechanical properties correlate well with the composition (). mPBI has the highest tensile strength, Young's modulus, Elongation at break, and proportional limit stress among all the tested membranes, and the values decrease with the addition of FAA3. Consequently, the FAA3-30 has the lowest values, but higher than would be expected from the trends observed for the blend materials. This interesting region between pure FAA3 and blend with 67% PBI (PF-21) could not be analysed, because casting solutions for PF-11 showed a tendency to gel. Doping with 2 M sulfuric acid shows the expected effect and reduces the tensile strength, Young's Modulus and proportional limit stress, while the elongation at break values are increased. Also for the doped membranes, the earlier mentioned properties correlate with the amount of FAA3 in the blends. The only property which does not follow a trend is the proportional limit strain.The chemical stability of membranes was assessed by immersing them in solutions of 1.5 M VO2+ in 2 M sulfuric acid, and checking the UV/VIS spectra after 87 days ( top). With the exception of FAA3, which disintegrated into several pieces, all other membranes remained intact. For Nafion 212, only a slight discoloration was observed. In the test solutions, the presence of VO2+ (formed by reduction of VO2+) was seen in the UV/VIS spectra as an intensive peak around 770 nm. To compensate for the different mass of polymer samples, the measured VO2+ concentrations were divided by the membrane sample weights ( bottom). This representation seems not to be correct, since FAA3 (which even visibly strongly degraded) appears to be similarly stable as PBI. While Skyllas-Kazacos reported the formation of VO2+ when Nafion membranes were immersed in VO2+ solutions [], others reported that no VO2+ was formed []. Since the solutions were stored in poly(tetrafluoroethylene) bottles, it is reasonable to assume that the chemically similar Nafion backbone is fully resistant against VO2+ within the period of the test. Therefore, the amount of VO2+ formed in the solution containing Nafion was taken as a blind value. It may stem from the oxidation of impurities in the VO2+ solutions, or more probably, simply was already present at the begin, e.g. VO2+ which was not oxidised during the electrochemical preparation of the VO2+ solution. This blind value was subtracted from the measured VO2+ values, and the corrected values were divided by the weight of the samples ( bottom). This representation indicates that mPBI and Nafion show a similar ex-situ chemical stability, supporting the findings from Zhou et al., who found a similar weight loss during chemical degradation for Nafion (2.1%) and PBI (2.9%) []. When the amount of FAA3 in the blend materials increases, the formation of VO2+ increases., all PBI based membranes showed a very low (not reliably measureable) permeation, whereas FAA3 showed a noticeable permeability of 1.7·10−08 cm2/s, one order of magnitude lower than that of Nafion 212. It is well known that AEMs repel vanadium cations due to the fixed positively charged groups on the polymer back bones (Donnan exclusion). While mPBI is not an AEM (e.g. immersion of HCl doped mPBI in KBr solution would not lead to an exchange of the anions, but mainly leach out the absorbed acid), it has fixed positively charged groups on the polymer chain in the protonated state, and should also show Donnan exclusion. In comparison to FAA3 (IEC of ca. 2 mmol Cl/g), mPBI protonated by HCl would have an IEC of 5.3 mmol Cl/g, and thus a 2.5 times higher density of charged groups.The prepared blend membranes were tested in a VRFB single cell, and their performances were compared with those of mPBI, FAA3 and Nafion 212 (, the VRFB single cells were cycled between 0.8 and 1.7 V. For the initial 23 cycles, they were tested at 80 mA cm−2, then the current density was increased to 90, 100, 110 and 120 mA cm−2, after which it was again reduced to 80 mA cm−2. At each step, five charge-discharge cycles were carried out.For all tested membranes, voltage efficiency decreased as current density increased, due to the ohmic resistances of the VRFB single cell. The VRFB single cells using Nafion 212 and 15 μm thick PF-21 showed the highest VEs, much higher than those of the cells using mPBI or FAA3. This result well agrees with our hypothesis that blending PBI with FAA3 will enhance the VE. Because 15 μm thick PF-21 has a higher coulomb efficiency and similar voltage efficiency to Nafion 212, it shows the highest energy efficiency of all the tested VRFB single cells, reaching 86% at 80 mA cm−2. For mPBI, we recently achieved an energy efficiency of 92% at 40 mA cm−2 and 3 M H2SO4 in the electrolyte []. At 80 mA cm−2, the apparent record so far is 90.11%, as reported recently by Li and Zhang et al. for a 34 μm thick porous O-PBI membrane []. For comparison, other highly developed systems reached energy efficiency values of 88.3% [When comparing the ex-situ conductivities of Nafion 212 and PF-21 (obtained in 2 M sulfuric acid) with the voltage efficiencies in the flow battery, it is striking that 50 μm thick Nafion 212 and 15 μm thick PF-21 show such a similar voltage efficiency. There are two reasons for this: a) The voltage efficiency depends not directly on the conductivity but on the related area specific resistance, which scales with the membrane thickness. b) While PBI repels vanadium ions, Nafion is a cation exchange membrane and absorbs vanadium ions. For Nafion, it was reported that the substitution of protons with vanadium ions reduces the conductivity by about 25–40% []. For acid doped PBI membranes, the influence of vanadium ions is expected to be lower, because it hardly affects the acid uptake (Another interesting difference between ex-situ and in-situ data is the observation that all PBI based membranes are practically impermeable for VO2+ ions, while the CE is <100% for all tested blend membranes, and decreases with decreasing membrane thickness and increasing amount of FAA3. This is because the ex-situ test only measures diffusion of VO2+ ions, while in the real cell also migration in the electric field, permeation of V2+, V3+ and VO2+ and side reactions (hydrogen evolution) need to be considered. summarises the efficiencies of all tested VRFB single cells, as measured over 20 charge-discharge cycles at 80 mA cm−2. When comparing the series of 15 μm thick membranes, it is seen that the addition of FAA3 to PBI lowers the CE. At the same time, the addition of FAA3 clearly increases the VE. The same trend is also observed for the 25 μm thick membranes, which in general have a lower voltage efficiency due to the increased resistance. The relatively low VE of FAA3-30 is unexpected at first glance, considering the high conductivity of FAA3i as shown in . Since FAA3 is an anion exchange membrane, its conductivity strongly relies on its water contents. This is lower for FAA3-30 (which is crosslinked) than for the FAA3i parent material, and the addition of 1.5 M vanadium ions to 2 M sulfuric acid roughly doubles its ionic strength. The resulting osmotic pressure difference further reduces the water uptake of FAA3-30. As shown in , this effect is not strong for PBI containing membranes.mPBI shows negligible diffusion of VO2+ in ex-situ tests, and addition of FAA3 does not change this, even though FAA3 itself showed noticeable diffusion (). In the real system, however, also migration in the electric field and diffusion and migration of other ions need to be considered. Therefore, the CE decreases when the amount of FAA3 is increased in the blends (). This effect is less pronounced for 25 μm thick membranes than for 15 μm thin membranes, because diffusion typically decreases when the membranes get thicker. Therefore, the negative effect of FAA3 on crossover can be compensated by increasing the membrane thickness.Analysis of the charge-discharge curves () allows to plot the charge capacities for each cycle (). Based on the electrolyte concentration, the theoretically maximum possible capacity is 40.2 Ah∙L−1. FAA3-30 and Nafion 212 showed the highest initial charge capacities of 30.2 and 30.9 Ah∙L−1, respectively. All other VRFB single cells had a lower initial charge capacity of 27.5-26.7 Ah∙L−1. At the 23rd cycle, FAA3-30 (25.9 Ah∙L−1) and mPBI (24.33 Ah∙L−1) showed the highest capacity, followed by Nafion 212 (23.79 Ah∙L−1) and 25 μm thick PF-31 (23.09 Ah∙L−1). In order to better compare the capacity degradation rates, the capacities were also normalised to the initial values (b bottom) and this normalization indicates that mPBI has the lowest capacity degradation, followed by FAA3. While most membranes showed rather linear capacity degradation, Nafion 212 degraded most rapidly over the first 15 cycles, after which the degradation rate decreased. Therefore, after 10 cycles, Nafion 212 has the poorest capacity retention, but after 50 cycles, it shows the 3rd highest remaining capacity. Unfortunately, the highest capacity degradation rate was observed for 15 μm thick PF-21, which performed best in terms of voltage efficiency and energy efficiency. Within the series of the blend membranes, it is seen that the addition of FAA3 increases the capacity loss, while an increase in thickness stabilizes the capacity.When comparing the discharging and charging capacities, it is observed that the discharging capacities are usually lower, as expected (). For mPBI, the discharging capacity is just 0.3% lower than the charging capacity. This value increases for the blend membranes, with values between 0.9 up to 2.1%. Due to the high crossover of vanadium ions, Nafion 212 has the highest difference, and the discharging capacity is 6.0% lower than the charging capacity.The hypothesis of this work was that blending a commercial anion exchange polymer (FAA3) into mPBI leads to membranes with improved voltage efficiency and only slightly reduced coulomb efficiency, resulting in an improved energy efficiency. This hypothesis was proven successfully and quantitatively. It appears that the concentration of the absorbed acid (considering only acid and water) plays a dominant role. According to the analysis, a 15 μm thick PF-21 membrane resulted in outstanding VRFB single cell performance that was represented as a coulomb efficiency of 97.8%, a voltage efficiency of 88.2%, and an energy efficiency of 86.3%. Compared with other data, the obtained energy efficiency was higher than that obtained in VRFB single cells using commercial Nafion 212 (83.0%), commercial FAA3-30 (82.6%), commercial mPBI (82.2%), or any of the other tested blend membranes. Taken together, as expected, thicker blend membranes showed higher CE, but lower VE.The work is related to a patent application (KR2017-0030148).The following is the Supplementary data to this article:Supplementary data to this article can be found online at Controllable friction and wear of nitrided steel under the lubrication of [DMIm]PF6/PC solution via electrochemical potentialThe friction and wear properties of the nitrided steel at different electrochemical potentials of the rubbed surface have maintained interesting and still an unsolved problem. This study systematically investigated the friction and wear behavior under different potentials for the nitrided AISI 4340 low alloy steel lubricated by propylene carbonate with an additive of imidazolium ionic liquid. A nitrided layer ~170 nm thick, composed of nitrogen expanded austenite (γN) phase, nitrogen-containing martensite (α′) phase and chromium nitride (Cr2N) precipitate, was formed onto the steel substrate via plasma source ion nitriding. The nitrided layer exhibited a higher hardness and corrosion resistance than the steel substrate. It was found that the friction and wear for the nitrided sample could be controlled via electrochemical potential. A stable low friction coefficient, 0.16, was obtained within the potential range of −1 V to −0.6 V, and almost no wear appeared at −1 V for the nitrided sample. The potential controlled friction was due to the modulation of the adsorption of the lubricant ions ([DMIm]+ cations or [PF6]− anions) by the potential, and the potential controlled wear was due to the adjustment of the anti-wear ability of the lubricant by the potential. The saturated adsorption of [DMIm]+ cations at −1 V led to the improved anti-wear ability compared to that at OCP, and the anodic corrosion of the rubbed sample surface was responsible for the degraded anti-wear ability at +1 V. Also, the nitrided sample exhibited a much milder wear than the un-nitrided sample at each tested potential, ascribed to the higher hardness and corrosion resistance of the nitrided sample compared to those of the un-nitrided sample.Surface modification of steel materials via nitriding treatments has attracted much attention because the nitriding process has strengthening effect on the steel surfaces and can improve their hardness and wear resistance All these studies presented above have demonstrated that the nitrided steels have better friction and wear properties than those of the un-nitrided steels. For further improving the friction and wear properties of the nitrided steels, people might use some effective lubrication strategies. For instance, Borghi et al. Specifically, the sliding friction and wear behavior of the nitrided AISI 4340 steel surface has been experimentally investigated under different loads and electrochemical potentials, with the lubrication of 0.5 mM [DMIm]PF6/PC solution. The micro-structure and hardness of the nitrided steel surface have been characterized via XPS, XRD, SEM and Vickers hardness measurements. Also, the corrosion resistance of the nitrided sample has been investigated in the non-aqueous ionic liquid environment via the electrochemical test. Meanwhile, the comparison of the nitrided with un-nitrided steels has been made in terms of the corrosion resistance, the friction and wear properties under different electrochemical potentials. The experimental results show that the nitrided steel has a better corrosion resistance and higher wear resistance than the un-nitrided steel under different electrochemical potentials, and the nitrided steel exhibits a stable lower friction at negative potentials from −1 V to −0.6 V and a higher wear resistance at −1 V compared to those at open circuit potential (OCP).AISI 4340 steel was selected as the sample material. All samples were quenched in oil for ~2.5 h at 850 °C before tempered for 2 h at 200 °C. Then, they were polished using silicon carbide paper and diamond paste. Some of these samples were cleaned with acetone and ethanol, dried with air, and then modified on surface by performing the plasma source ion nitriding process, which was described elsewhere 1-decyl-3-methylimidazolium hexafluorophosphate ([DMIm]PF6, ≥99% purity) was dissolved into propylene carbonate (PC, 99% purity) to prepare test solution with 0.5 mM concentration, which was also used in the previous study White light interferometry (MicroXAM-3D, AEP Technology, USA) was employed to characterize the three-dimensional wear morphologies of the surfaces of worn samples after wear tests. For each tested sample, the morphology of a segment of the circular wear track was recorded, and the wear depth and average volume loss were approximately calculated from the corresponding data of the wear profile. X-ray photoelectron spectroscopy (XPS; PHI Quantera SXM, Ulvac-Phi, Japan) was used to make the atomic concentration depth profiles of some typical elements beneath the surface of the nitrided sample, to determine the chemical states of some typical elements in the nitrided layer, and to examine the atomic concentration depth profiles of some typical elements beneath the worn surfaces after the wear tests. In the XPS tests, Al Kα radiation was used as the excitation source. The binding energies of the target elements were determined at a pass energy of 55 eV, with a resolution of ±0.1 eV, and using the binding energy of contaminated carbon (C1s: 284.8 eV) as the reference. Before characterizing the sample surfaces via white light interferometry or XPS, the sample surfaces were cleaned with acetone and ethanol, and then dried with air jet. X-ray diffraction (XRD; D8 Advance, Bruker, Germany) with Cu Kα (40 kV and 40 mA) in the θ−2θ mode was used to detect the structure information of the nitrided layer of the sample. Field emission scanning electron microscopy (SEM; Quanta 200FEG, FEI, USA) was utilized to observe the surface morphologies of the nitrided and un-nitrided samples and the transverse cross-sectional morphology of the nitrided sample. Vickers hardness tester (Tukon 2500, Wilson, USA) was used to measure the surface hardness of steel samples at a test load of 0.5 kg maintained for 10 s.Cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) tests were performed in a three-electrode cell, which contained a platinum counter electrode and a silver/silver chloride (Ag/AgCl) reference electrode, and the working electrodes were made of nitrided and un-nitrided AISI 4340 steels, respectively. The electrolyte was 0.5 mM [DMIm]PF6/PC solution. A commercial potentiostat/galvanostat (PGSTAT302N, Metrohm, Switzerland) was employed to control and monitor the electrochemical potential and current. CV tests were conducted with the scan rate of 5 mV s–1 in the potential range from −1 to +1 V vs. Ag/AgCl, which was similar to the case in our previous study The friction and wear tests were performed on a standard rotating tribometer (Plint TE92, Phoenix Tribology, UK) in a ball-on-disc configuration, as shown in . In the configuration, a steel disc, graphite counter electrode and Ag/AgCl reference electrode formed a three-electrode system to impose a desired electrochemical potential to the steel disc surface via PGSTAT302N potentiostat/galvanostat. During the tribological tests, the surface of the stationary steel disc rubbed against a ZrO2 ball sliding along a wear track of 11 mm in diameter at a limited speed of 11.5 mm s–1 (20 rpm). The rubbing steel disc and ZrO2 ball were both cleaned with acetone and ethanol, and then dried with air jet before each test. The used lubricant was 0.5 mM [DMIm]PF6/PC solution. Normal loads of 100 N and 200 N were employed for the friction or wear tests. Under the point contact condition with the ball diameter of 10.318 mm, loads of 100 N and 200 N yielded respectively Hertz pressures of 1.6 GPa and 2.0 GPa at the ball/disc interface respectively, calculated from the Hertz contact theory. In this study, the sliding velocity of the ball relative to the disc, the lubricant viscosity and the Hertz pressure over the contact region were almost similar to those adopted in the previous study XPS detection provided the atomic concentration depth profiles of nitrogen, chromium and iron elements beneath the surface of the nitrided sample (see shows that the nitrogen element diffuses into the steel surface after the plasma source ion nitriding, and possesses a maximum concentration of 15 at% at the depth of 80 nm. The nitrided layer has a thickness of ~170 nm, same as the maximum depth at which the nitrogen concentration is higher than 3 at% shows the existence of nitrogen expanded austenite (γN) phase and chromium nitride (Cr2N) precipitate in the nitrided layer. XRD patterns (see ) verify the formation of γN phase and Cr2N precipitate in the nitrided layer, and suggest that the nitrogen-containing martensite (α′) phase appears as well in the nitrided layer, evidenced by the shift of the diffraction peak of α′ phase to lower Bragg angle than that for un-nitrided sample. The above XPS and XRD results indicate that the nitrided layer is a diffusion layer ~170 nm thick, including γN phase, Cr2N precipitate and nitrogen-containing α′ phase, while the un-nitrided substrate is composed mainly of austenite (γFe) and α′ phases. Further, the surface morphology and the transverse cross-sectional morphology of the nitrided sample were observed via SEM, as shown in b and c, respectively. As contrast, the surface morphology of the un-nitrided sample is displayed in a and b, it can be seen that the uniformly distributed pearl-like nanostructures appear on the steel substrate after nitriding, producing a larger roughness (Ra~20 nm) for the surface of the nitrided sample compared to that (Ra~10 nm) for the un-nitrided sample. The result of c confirms that the diffusion layer is formed onto the AISI 4340 steel substrate by the plasma source ion nitriding.The surface hardness measurements revealed a hardness of approximately HV4.9 N 601 for the nitrided sample, ~30% higher than that of the un-nitrided sample, which had a value of approximately HV4.9 N 476. Here, the measured surface hardness of the nitrided sample characterized the combined hardness effects of the nitrided layer and substrate, because the hardness measurement for the nitrided sample produced an indentation depth of 5–6 µm, larger than the thickness of the nitrided layer. This suggests the hardness of the nitrided layer could be much higher than HV4.9 N 601, ascribed to the hardening effects of γN phase, Cr2N precipitate and nitrogen-containing α′ phase on the nitride layer presents the surface hardness values of the nitrided, un-nitrided AISI 4340 steel samples and ZrO2 rubbing ball. The hardness is typically around 2.8 times the yield stress CV test was conducted to evaluate the corrosion resistance of the nitrided sample in 0.5 mM [DMIm]PF6/PC solution, and the electrochemical measurement was done for un-nitrided sample for comparison. displays the cyclic voltammograms of the nitrided and un-nitrided samples in 0.5 mM [DMIm]PF6/PC solutions. The current densities are lower than 10 μA cm–2 for both of the test samples over the potential range from −1 V to +1 V, indicating a very slow corrosion rate for the un-nitrided and nitrided samples. From , we can also see that the nitrided sample has a smaller current density compared to that of the un-nitrided sample, revealing the higher corrosion resistance of the nitrided sample. This point is attributed to the corrosion-resisting effects of γN phase and nitrogen-containing α′ phase in the nitride layer to coincide with the potential range of −0.6 V to +0.6 V, over which the current density undergoes a little change and is lower than 5 μA cm–2. present the relationship between the coefficient of friction and electrochemical potential for the nitrided and un-nitrided samples at loads of 100 N and 200 N, respectively. For the nitrided sample, the values of friction coefficient (asterisks in ) under different potentials at 100 N are almost similar to those (asterisks in ) at 200 N, and both of the friction coefficients at 100 N and 200 N follow the same declining trend when the potential varies from OCP to −0.6 V. For the un-nitrided sample, when the load turns from 100 N to 200 N, the value of friction coefficient under each tested potential becomes larger, but both of the friction coefficients at 100 N and 200 N follow the same changing trend within the potential range from −0.6 V to +0.6 V (see empty squares in display the morphologies of the wear tracks under different electrochemical potentials for the nitrided and un-nitrided samples at 100 N and 200 N, respectively. For the nitrided sample, no apparent wear is observed under each tested potential at 100 N (a–c). When the load turns to 200 N, mild wear occurs at OCP (b), and a relatively apparent wear appears at +1 V (c). For the un-nitrided sample, mild wear appears under each tested potential at 100 N (see d–f), while prominent wear is found under any given potential at 200 N (see d–f). Also, the wear for the un-nitrided sample at 200 N becomes increasingly severe with the positively shifting of the potential (see , it can be seen that regardless of the nitrided or un-nitrided sample, the wear resistance increases in the following order in terms of potential: +1 V, OCP, −1 V. It is also seen that at any given potential, the wear resistance for the nitrided sample is higher than that for the un-nitrided sample. These points can be further supported by the wear depth-potential relationship and average volume loss-potential relationship for the nitrided and un-nitrided samples (see It is well known that many aspects, such as plowing ), and loads of 100 N and 200 N produces Hertz pressure of 1.6 GPa and 2.0 GPa, respectively, so no apparent plastic deformation happens for both tested loads. Thus, the friction coefficient for 100 N or 200 N is mainly determined by the shear strength of the nitrided layer and the lubricity of the boundary films. The load has no influence on the shear strength or the lubricity, so the friction coefficient (asterisks in ) for 100 N almost coincides with that (asterisks in ) for the nitrided sample show the effect of the potential on the friction coefficient at both 100 N and 200 N, indicating the influence of the potential on the lubricity of boundary films within the potential range from OCP to −0.6 V, which is similar to that for the un-nitrided sample For the un-nitrided sample, it has the yield strength of 1.7 GPa (see ), so the load of 100 N (Hertz pressure of 1.6 GPa) does not result in apparent plastic deformation, while the load of 200 N (Hertz pressure of 2.0 GPa) leads to considerable plastic deformation. Therefore, besides the shear strength and lubricity, which is responsible for the friction result at 100 N, the plowing effect should also be considered to contribute to the friction coefficient at 200 N. Thus, the friction coefficient (empty squares in ) at 200 N is higher than that (empty squares in also show that the friction coefficient curves exhibit a similar trend within the potential range of −0.6 V to +0.6 V for the un-nitrided samples at both 100 N and 200 N, indicating the effect of the potential on the lubricity of the used ionic liquid, as pointed out in our previous study , we can see that for the un-nitrided or nitrided sample, the lubrication behavior undergo a similar tend within the same potential range despite the different loads. For the un-nitrided sample, the boundary lubrication is modulated within two different potential ranges of OCP to −0.6 V and OCP to +0.6 V. This potential-dependent lubrication has been considered to be attributed to the effect of the potential on the adsorption of [DMIm]+ cations and [PF6]− anions of the used ionic liquid shows the EIS results of the nitrided and un-nitrided samples under open-circuit potentials (OCPs). OCP is −50 mV for the nitrided sample and −40 mV for the un-nitrided sample. The negative values of OCPs indicate the presence of the adsorption of the [PF6]− anions at OCPs for the nitrided and un-nitrided samples ), the much larger diffusion resistance (~ 46 kΩ cm2) for the nitrided sample (asterisks in ) suggests the prohibiting effect of the nitrided layer on the adsorption of the [PF6]− anions at potentials more positive than the OCP, leading to the almost invariable adsorption amount of the anions on the nitrided sample within the potential range from OCP to +0.6 V, and thus the substantially same boundary lubricity within this potential range for the nitrided sample. A good and almost stable lubricity is reached at negative potentials lower than −0.6 V for either the nitrided or the un-nitrided sample, as attributed to the saturated adsorption of the long-alkyl-chain [DMIm]+ cations It should be pointed out that the oxidation layers are detected beneath the worn surfaces for both samples under different tested potentials (see ). These oxide layers are usually capable of reducing friction at the rubbed surfaces, and the oxygen concentration at the location of 5 nm beneath the worn surface reaches its peak at the positive potential of +1 V for either the nitrided (see c) sample, but unexpectedly the measured friction at +1 V is higher than that at −1 V. This inconsistence between the potential dependent friction and the potential-oxidation concentration relation suggests that the potential dependent friction is little related to the change of the oxidation layer under different potentials.To understand the wear mechanism at different potentials for the nitrided and un-nitrided samples lubricated by the used model lubricant, it is suggested that the plastic deformation effect show the influence of different loads, different samples and different potentials on the wear extent. A more apparent wear occurs at the larger load, which results from the fact that the rubbed surface deform plastically more easily under the corresponding larger contact pressure. Also, the un-nitrided sample undergoes a more considerable wear compared to the nitrided sample, because the un-nitrided sample tends to plastically deform more easily due to its lower yield stress. Further, the potential exhibits a similar effect on the wear extents in spite of the different loads and the different samples, indicating that the anti-wear property of the used lubricant can be affected by the potential for either the nitrided or the un-nitrided sample. The change trends of the anti-wear property with respect to the potential are similar for both samples, which indicates that the potential dependent anti-wear property for the nitrided sample originates from the same mechanism as it does for the un-nitrided sample , the anti-wear property of the lubricant for the nitrided sample increases with the potential negatively shifting from +1 V to −1 V. This point is verified by the results of nitrogen concentration at the location of 5 nm beneath the worn surfaces under different potentials (see a). The observed nitrogen concentration increases with the potential negatively shifting, consistent with the change trend of the anti-wear property with respect to the potential, which suggests that the nitrided layer is better protected at −1 V due to the improved anti-wear property, and the nitrided layer is destroyed more severely at +1 V because of the degraded anti-wear property. It is interesting that a high oxygen concentration of 20–40% is observed on the worn surfaces or at the location of 5 nm beneath the worn surfaces for the nitrided (see c) samples under different tested potentials. The measured high oxygen concentration on the worn surface is considered to include the contribution of the surrounding contamination when preparing the tested samples. The oxygen concentration measured at the location of 5 nm beneath the worn surface, which includes no influence of the undesirable contamination, increases in the following order in terms of potential: OCP, −1 V, +1 V. The change trend of the oxygen concentration with respect to the potential differs from that of the anti-wear property with respect to the potential, indicating that the potential dependent anti-wear property has little correlation with the varying oxygen amounts at the rubbed surface under different potentials. The improved anti-wear ability at −1 V is considered to be resulted from the saturated adsorption of the [DMIm]+ cations with long alkyl chains, which provides a better protection for the rubbed surface comparing with the case at OCP, where [PF6]− anions adsorb on the rubbed surface. The degraded anti-wear property at +1 V is suggested to be due to the anodic corrosion of the rubbed steel surface, which is evidenced by the results of CV measurements (see b and c suggest an oxidation layer with high oxygen concentration to be formed beneath the worn surfaces for the nitrided and un-nitrided samples at the positive potential of +1 V, which means that the corrosion resistance, as provided by the oxide layer, is weakened at +1 V comparing with that at OCP by the trans-passivation due to such a positive potential. Further, the smaller extent of corrosion wear at +1 V is observed for the nitrided sample than that for the un-nitrided sample (see ), as ascribed to the higher corrosion resistance of the nitrided sample comparing with the un-nitrided sample (see This study has successfully achieved a nitrided layer ~170 nm on the AISI 4340 steel via plasma source ion nitriding. The nitrided layer is physically a diffusion layer including nitrogen expanded austenite (γN) phase, nitrogen-containing martensite (α′) phase and chromium nitride (Cr2N) precipitate. This structure of the nitrided layer ensures it to possess the higher hardness (>5.89 GPa) and better corrosion resistance than the steel substrate.The nitrided sample shows controlled friction and wear properties by adjusting the electrochemical potential of the sample surface, which is similar to the case for the un-nitrided sample. The potential-controlled friction behavior is attributed to the modulation of the adsorption of the lubricant ions, [DMIm]+ cations or [PF6]− anions, by the potential. The more negative potential than −0.6 V causes the [DMIm]+ cation adsorption to reach a saturation and thus a stable low value of friction coefficient, 0.16, is obtained for the nitrided sample within the potential range of −1 V to −0.6 V. At potentials more positive than OCP, the adsorption of [PF6]− anions remains always saturated for the nitrided sample, leading to a steady high friction coefficient of 0.28 within the potential range of OCP to +1 V. For the un-nitrided sample within this range of positive potentials, the adsorption of the [PF6]− anions reaches a saturated state at +0.6 V and the saturated adsorption remains within the potential range from +0.6 V to +1 V, resulting in a stable high friction.The potential-controlled wear property is ascribed to the modulation of the anti-wear property of the ionic liquid lubricant by the potential. The improved anti-wear property at –1 V is due to the saturated adsorption of [DMIm]+ cations, which can better protect the rubbed samples against wear than the film of the adsorbed [PF6]− anions does at OCP. Compared to the case at OCP, the degraded anti-wear property at +1 V results from the anodic corrosion of the rubbed samples at such a positive potential. Further, the nitrided sample undergoes a smaller corrosion wear comparing with the un-nitrided sample, which is attributed to the higher corrosion resistance of the nitrided sample. Also, the wear resistance of the nitrided sample is higher than that of the un-nitrided sample at any tested potential, as ascribed to the hardening effect of the nitriding process on the steel surface.Microstructure and mechanical properties of Ti–V–Al–Cu shape memory alloy by tailoring Cu contentThe microstructure, martensitic transformation behavior, mechanical and shape memory properties of the Ti–V–Al–Cu light weight shape memory alloys were investigated systematically. The results showed that the phase constitution gradually evolved from single α″ martensite phase to the complete β phase with the Cu content increasing in the solution treated Ti–13V–3Al-xCu alloys at room temperature. The spear-like martensite variant constituted the typical self-accommodation configuration, and {111} type I twins and <211> type II twins coexisted in the Ti–V–Al–Cu alloys. Moreover, Ti2Cu precipitate can be observed in the Ti–V–Al–Cu alloys with the higher Cu contents. The martensitic transformation temperature of Ti–V–Al–Cu alloys decreased continuously with the increased Cu content. The Ti–V–Al–Cu alloys with the higher transformation temperature and higher strength as well as the superior shape recovery characteristics can be obtained by tailoring Cu content. It was the perfect combination of solid solution strengthening, grain refinement and precipitation strengthening to promote the enhancement of matrix strength. The maximum recoverable strain was 4.4%, for 6% pre-strain and the reverse martensite transformation temperature was 334 °C in the optimal Ti–13V–3Al-0.5Cu alloy.During the past few decades, shape memory alloys have been paid extensive attentions, based on their novel functional properties such as shape memory effect and superelasticity []. Till date, Ti–Ni alloys are the most promising and commercial materials, which has been widely used in many fields such as aerospace applications and automotive actuators []. However, some drawbacks also exist in the Ti–Ni shape memory alloys and limit their widespread application. On the one hand, the martensite transformation temperature (Ms) of binary Ti–Ni shape memory alloys is below 100 °C, which restricts their application in the high temperature fields. On the other hand, the binary Ti–Ni alloys possess the relatively high density (6.7 g/cm3). However, it is the best choice to adopt the light weight alloys as the aircraft materials in the aerospace industry. Thus, Ti–Ni alloys can't meet the requirement of weight reduction of aircraft. So far, the higher transformation temperature shape memory alloys primarily consist of Ni–Ti-X (X = Hf, Zr, Pd, Pt), Cu–Al–Ni, Ni–Mn-Ga and Zr–Cu alloys etc []. However, their densities are ranging from 6.4 g/cm3 to 9.0 g/cm3, which is equivalent to or higher than that of binary Ti–Ni alloys. Recently, Mg–Sc shape memory alloys have been developed owing to its lower density []. The density of Mg–Sc alloy is 2 g/cm3, which is only one third of the density of Ni–Ti alloy. Nevertheless, both the lower transformation temperature (Ms«100 °C) and the excessively price are its inherent nature, which impedes its application in the aerospace industry. Relatively, Ti–V–Al alloy has the lower density (4.5 g/cm3) and the higher transformation temperature (As»300 °C), which become a great candidate for the light weight high temperature shape memory alloy.Initially, Wayman et al. found that Ti-16.1V–4Al (wt.%) alloy exhibited a fully recoverable strain of 3%, which was significantly lower than that of Ti–Ni alloy (~8%) []. Yang et al. adjusted the martensitic transformation temperature and optimized the shape memory effect by changing Al contents []. They found that the solution-treated Ti–13V–3Al alloy had the higher martensite transformation temperature and a good shape memory effect. A recoverable strain of 4.2% with a pre-strain of 6% can be achieved in the solution-treated Ti–13V–3Al alloy. In addition, the quaternary Fe element was added into the Ti–V–Al alloy to improve the shape memory effect of the Ti–V–Al light weight high temperature shape memory alloy []. The Ti–13V–3Al–1Fe alloy showed the recoverable strain of 5.8% in pre-strain of 6% and the excellent elongation of 30%. However, the martensite transformation temperature decreased rapidly with Fe content increasing. The reverse martensite transformation start temperature of the Ti–13V–3Al–1Fe alloy was close to 100 °C. Hence, it can be concluded that adding alloying element is an effectively methods to improve the performance of the Ti–V–Al alloy.It has been reported that Cu acts as powerful solution-strengthening element and increases the critical slip stress in Ti–Nb–Cu alloy []. In addition, Ti2Cu phase is also beneficial to the improvement of the alloy strength []. For shape memory alloys, the higher strength can hinder dislocation movement during deformation and further promote to the enhancement of shape memory effect [Therefore, we expect to improve the mechanical and functional properties of Ti–V–Al alloy by tailoring the quaternary Cu element. Moreover, the effect of Cu content on the microstructure, martensitic transformation behavior, mechanical properties and shape memory properties of Ti–V–Al–Cu alloys were systematically investigated.Ti–13V–3Al-xCu (x = 0.2, 0.5, 1.0, 1.5, 2.0, 2.5, 5.0) ingots were prepared from the high-purity elements (99.99% Ti, 99.99% V, 99.99% Al, 99.95% Cu) by non-consumed arc-melting furnace under an argon atmosphere. Each ingot was remelted at least six times to achieve the homogeneous chemical composition. The samples for the subsequent measures were processed from the ingots by means of electro discharge machining. All samples were solution treated at 900 °C for 2 h under the higher vacuum atmosphere, and followed by rapid quenching in ice water.In order to analyze the transformation behaviors, differential scanning calorimeter (DSC; PerkinElmer Diamond) with a heating and cooling rate of 100 °C/min were used. The start temperature (As), peak temperature (Ap) and finish temperature (Af) of reverse martensite transformation on heating were determined by tangent technology in the DSC curve. The identification of phase constitution was conducted by adopting X-ray diffraction (XRD) with Cu Kα radiation at room temperature. The microstructure of the Ti–V–Al–Cu alloy was performed on an Olympus optical microscope. Moreover, transmission electron microscope (TEM) was carried out on a Talos F200X microscope operating at 200 kV. The specimens for TEM observation were prepared by jet polishing. The electrolyte was the mixture of 6% perchloric acid, 60% methyl alcohol and 34% n-butyl alcohol (in volume). The temperature of the electrolyte was kept at about −30 °C. The tensile tests were conducted with an Instron 5569 testing system at a strain rate of 0.4 mm/min at room temperature. In addition, three samples of each alloy were performed to ensure the reliability of the tensile tests. shows the XRD patterns of Ti–13V–3Al-xCu (x = 0.2, 0.5, 1.0, 1.5, 2.0, 2.5, 5.0) alloys at room temperature. It is found that the phase constitutions are largely dependent on the Cu content in the Ti–13V–3Al-xCu alloys. It has been reported that the Ti–13V–3Al alloy is in fully monoclinic α″ martensite at room temperature []. Ti–V–Al–Cu alloys with the minor Cu addition are still sole α″ martensite at room temperature, which indicates that minor Cu addition has no significant influence on the phase constitutions of Ti–V–Al alloy. When the Cu content is ranging between 1.0 at.% and 1.5 at.%, the monoclinic α″ martensite and the β parent phase with a body-centered cubic structure coexist in the Ti–V–Al–Cu alloys at room temperature. With the content of Cu increasing, (110) diffraction peak corresponding to the β parent phase appears and its intensity gradually becomes stronger and stronger. Moreover, the intensity of the diffraction peak corresponding to the α″ martensite begins to weaken. As the Cu content is up to 2.0 at.%, the diffraction peaks corresponding to α″ martensite almost vanish and only β parent phase diffraction peak can be observed. With the Cu content further increasing, the Ti–V–Al–Cu alloys are fully in the β parent phase state. shows the dependence of lattice parameters of the α″ martensite phase and the β austenite phase on the Cu content in the Ti–13V–3Al-xCu alloys. The results reveal that the value of b of the α″ martensite continuously decreases with the Cu content increasing. However, the value of a and c is almost equal, when the Cu content changes. In addition, the dependence of a0 of β austenite on the Cu content in the Ti–13V–3Al-xCu (x = 0.2, 0.5, 1.0, 1.5, 2.0, 2.5, 5.0) alloys can be formulated by the following equation:The reduction of lattice parameter a0 of β austenite as a result of Cu addition is quite acceptable from the viewpoint of Goldschmidt radii (0.147 nm for Ti, and 0.128 nm for Cu) []. Furthermore, Cu element can play an important role in the solid solution strengthening as a result of the smaller atomic size of Cu, which is favor of the improvement of the mechanical and functional properties of Ti–V–Al alloys. shows the optical images of the Ti–V–Al–Cu alloys with the different Cu contents. For the Ti–13V–3Al-0.2Cu alloy, the microstructure is characterized by a large amount of lath-like α″ martensite. It has been reported that the crosshatched pattern are likely related to variant selections during the austenite to martensite phase transformation []. When the Cu content is increased to 1.0 at.%, featureless grain with the size of 196 μm can be observed, except from grain filled with the lath-like α″ martensite. The featureless grain corresponds to β parent phase. Furthermore, the amount of the lath-like martensite α″ phase gradually decrease and the number of the β parent phase continuously increase with the increasing of the Cu content. Besides, the grain size is obviously refined from 2.5 mm to 160 μm owing to the addition of Cu. The evolution of microstructure with the changing of Cu content is well consistent with the preceding XRD results of Ti–V–Al–Cu alloys.(a) and b shows the bright-field TEM image and the corresponding selected area electron diffraction (SAED) pattern of Ti–13V–3Al-0.2Cu alloy. It is observed that the microstructure of Ti–13V–3Al-0.2Cu alloy is characterized by α″ martensite with a spear-like morphology, which is well in accordance with the former XRD results. What's more, no twinning substructure is observed based on a series of tilts in multiple directions, which can be confirmed by the corresponding SAED pattern. This phenomenon can be explained by the tertiary principal transformation strain (η3). When the η3 is close to zero, the elastic energy is lower. In turn, the lattice mismatch between martensite phase and parent phase is small. Hence, the constant strain of the lattice does not occur. shows the bright-field TEM images of the different zone and the corresponding SAED patterns of Ti–13V–3Al-0.5Cu alloy. It can be seen that the martensite variants show self-accommodation configuration with the spear-like morphologies, as shown in (a) and (c). The corresponding SAED pattern in (b) and (d) reveal that the spear-like martensite variants are {111} type I twins and <211> type II twins related. The bright-field TEM image and corresponding SAED pattern of Ti–13V–3Al-2.5Cu alloy are shown in . It can be seen that the higher density of ω phase uniformly disperses in the β phase matrix, which can be confirmed by the SAED pattern in (b). The SAED pattern is characterized by the diffuse scattering at 1/3 {112} positions corresponding to the athermal ω phase, in addition to the primary reflections of the β matrix. (c) and (d) display the bright-field TEM image of another area and corresponding SAED pattern in the solution treated Ti–13V–3Al-2.5Cu alloy. The second phase showing rectangular shape can be observed and its size is 0.5 μm in width and 1 μm in length. The analysis results of SAED pattern reveal that the second phase may be Ti2Cu phase. Similarly, the Ti2Cu is also detected in the Ti–Nb–Cu alloy [ shows the DSC curves of the Ti–13V–3Al-xCu (x = 0.2, 0.5, 1.0, 1.5, 2.0, 2.5, 5.0) alloys. It can be seen that only an endothermic peak corresponding to β→α″ transformation appears in the DSC curves for Ti–V–Al–Cu alloys and no exothermic peak is observed in the cooling process, when the Cu content is not beyond 1.5 at.%. In addition, with the Cu content increasing, the endothermic peak shifts towards the lower temperature. To date, the reason for the absence of the exothermic peak during cooling in Ti-based shape memory alloys can be concluded as follows. On the one hand, the enthalpy of martensitic transformation from β phase to α″ phase is relatively low, which is beyond the limitation of DSC. On the other hand, martensitic transformation from β phase to α″ phase during cooling is only partial, which makes the transformation heat peak too small to be detected by DSC. The similar phenomenon is also reported in Ti–Nb alloys, Ti–Zr alloys and so on []. Upon the Cu content is more than 1.5 at.%, both the endothermic peak and exothermic peak fully disappear during the heating and cooling within the testing temperature ranging from 200 °C to 400 °C. This may be related to the lower transformation temperature in the Ti–V–Al–Cu alloy with the major Cu content, which can be confirmed by the XRD results and optical images. Transformation temperatures of the Ti–13V–3Al-xCu alloys with the Cu content of 0.2 at.%~1.5 at.%. are listed in . For the β-Ti based shape memory alloy, a convenient manner is proposed to consider the overall beta stability of an alloy with various alloying additions []. By arbitrarily using molybdenum as a baseline, the “moly equivalent” (Mo Eq.) are defined as following:Mo Eq. = 1.00(wt.% Mo) + 0.67(wt.% V) + 0.44(wt.% W) + 0.28(wt.% Nb) + 0.22(wt.% Ta) + 2.86(wt.% Fe) + 1.54(wt.% Cr) +0.77(wt.% Cu) + 1.11(wt.% Ni) +1.43(wt.% Co) + 1.54(wt.% Mn) – 1.00(wt.% Al)The Mo Eq. of the Ti–13V–3Al-xCu alloys is calculated and listed in . The results reveal that the Mo Eq. increases with the increasing of the Cu content, which means that β parent phase would become more stable with the increasing of the Cu content. Consequently, the reverse transformation temperature would decrease with the increasing of the Cu content.Furthermore, for the Ti–V–Al–Cu alloys with the Cu content ranging from 0.2 at.% to 1.5 at.%, the relationship between Mo Eq. and the martensitic transformation temperature (As, Ap, Af) can be formulated as:It has been proposed that β phase stability can be evaluated by the Bo and Md (see ). For a β-type Ti alloy, the average values of Bo and Md are defined simply by taking the compositional average of each parameter, and are denoted Bo‾andMd‾, respectively. The β/β + ω phase boundary in the Bo‾−Md‾ diagram has been developed by Saito, Mohamed et al. []. In addition, the alloy which is away from the β/β + ω phase boundary has a better β phase transition stability. The Bo‾andMd‾ of the present Ti–13V–3Al-xCu alloys are calculated and plotted in . For comparison, other quaternary Ti–13V–3Al-0.5Y (Y = Fe, Co, Zr, Sn) alloys are also added. It can be seen that the Ti–V–Al–Cu alloys with the higher copper content is away from the β/β + ω phase boundary, which indicates that the β phase stability of the alloys with a high copper content is improved. Thus, the transformation temperature of Ti–V–Al–Cu alloys decreases with the increasing of Cu content, which is consistent with the DSC results. Besides, compared to the other quaternary element such as Fe, Co, Zr etc., the same content of Cu can significantly suppress the precipitation of ω phase. The Ti–13V–3Al-0.5Sn alloy is further away from the phase boundary, which may control the precipitation of ω phase. The similar situation has been reported in Ti–Ta–Sn alloys []. Nevertheless, the minor Sn doping can lead to the remarkable decrease of strength [The stress-strain curves of the solution treated Ti–13V–3Al-xCu alloys are shown in (a). The deformation mechanism of the Ti–V–Al–Cu shape memory alloys changes with the changing of Cu content. When the Cu content is lower, the Ti–V–Al–Cu alloys are in α″ martensitic state and the deformation mechanism of Ti–V–Al–Cu alloys can be divided into the three stages. The first stage is the elastic deformation, the second stage is the reorientation of the martensite phase, and the third stage is the plastic deformation stage of the martensite. With the increasing of the Cu content, the phase constitutions of Ti–V–Al–Cu alloys consists of the α″ martensitic and β parent phase at room temperature. Hence, the second stage should be changed into the reorientation of the martensite phase and the stress-induced martensitic transformation. In addition, both the critical yield stress and tensile fracture stress almost increase continuously with the Cu content increasing. As shown in (b), the fracture strength of the Ti–13V–3Al–5Cu alloy can be up to 859 MPa, which is significantly higher than that of Ti–13V–3Al-0.2Cu alloy (763 MPa). The yield strength of the Ti–13V–3Al–5Cu alloy is about 671 MPa, which is increased by about 39.2%, compared to the Ti–13V–3Al-0.2Cu alloy. Moreover, the yield strength and fracture strength of Ti–V–Al–Cu alloys is higher than that of the reported Ti–V–Al–Fe alloys []. These results mean that the addition of Cu can significantly enhance the mechanical strength of Ti–13V–3Al alloy. The main mechanisms of the improvement of matrix strength can be concluded as the grain refinement strengthening, solid solution strengthening as well as the precipitation strengthening. In Section , it has been revealed that Cu addition results in the reduction of grain size and presence of Ti2Cu and ω precipitate in the Ti–V–Al–Cu alloys. However, the fracture strain of the Ti–V–Al–Cu alloys decreases with the increasing of Cu content. The maximum fracture strain of 15.1% can be achieved in the quaternary Ti–13V–3Al-0.2Cu alloy. The worsening of the elongation is mainly related to the presence of athermal ω phase in the Ti–V–Al–Cu alloys with the higher Cu content [In order to evaluate the effect of Cu content on the shape memory effect of the Ti–V–Al alloys, the tensile loading-unloading tests are carried out. The shape memory effect is characterized by performing the tensile loading-unloading tests to 6% strain, followed by heating to (Af + 30) °C and hold for 3 min for strain recovery. The shape memory effect (SME) strain of the quaternary Ti–V–Al–Cu alloys as a function of Cu contents is shown in . The lines with an arrow represent the strain recovered by heating. Obviously, Ti–V–Al–Cu alloys show a certain shape recovery by heating, when the Cu content is not more than 1.5 at.%. Moreover, the shape memory effect of Ti–V–Al–Cu shape memory alloys increases firstly and then decreases with the increasing of Cu content. The maximum shape memory effect strain is about 4.4% in Ti–V–Al–Cu alloy with the Cu content of 0.5 at.%. The initial increase of shape memory effect strain can be related to the matrix strength stemmed from grain refinement and solution strengthening. However, the deterioration of strain recovery in the Ti–V–Al–Cu alloys with the 1.0 at and 1.5 at.%Cu can be ascribed to the presence of ω phase. Besides, the decrease of proportion of α″ martensite phase with the Cu content increasing also should be responsible for the can be deterioration of strain recovery in the Ti–V–Al–Cu alloys with the 1.0 at and 1.5 at.%Cu. Upon the Cu content is beyond 1.5 at.%, no strain recovery is observed after heating for Ti–V–Al–Cu alloys. The absence of the strain recovery in the Ti–V–Al–Cu with the higher Cu content can be attributed to the primary β phase rather than the α″ martensite phase at room temperature.Although the yield strengthen of the Ti–V–Al–Cu alloys is improved by tailoring Cu contents, the perfect shape memory effect with the larger recoverable strain is not realized in the solution treated Ti–V–Al–Cu alloys due to the presence of ω phase. Nevertheless, other techniques (such as cold working and moderate annealing treatment as well as further modifications to the composition to optimize the volume fraction of precipitate phase) can be used to improve the shape memory properties of Ti–V–Al–Cu alloys.In order to obtain the light weight Ti–V–Al–Cu higher temperature shape memory alloys with the higher strength and superior strain recovery characteristics, the effect of Cu content on the transformation behaviors, microstructure, mechanical and functional properties of the solution treated Ti–13V–3Al-xCu alloys were investigated. Ultimately, the composition of Ti–V–Al–Cu alloy with the excellent performance is optimized and the corresponding results can be obtained.The phase constitution of the Ti–13V–3Al-xCu alloys evolved with the changing of Cu content. With a minor Cu addition, Ti–V–Al–Cu alloy was composed of single α″ martensite phase. Both α″ martensite phase and β parent phase coexisted in the Ti–V–Al–Cu alloys with Cu content of 0.5–1.5 at.%. Further increasing Cu content, Ti–V–Al–Cu alloys completely changed into β parent phase. In addition, Ti2Cu precipitate and high densities of ω phases were observed in Ti–V–Al–Cu alloys with higher Cu content. The grain size is reduced owing to the Cu addition.Cu addition had a great influence on the martensitic transformation of Ti–V–Al–Cu alloys. Reverse martensitic transformation temperature decreases, as the Cu content increases.The yield strength and the fracture strength were enhanced owing to Cu addition, which can be attributed to the solution strengthening and precipitation strengthening as well as grain refinement. The highest yield strength of 671 MPa and the largest fracture tensile strength of 859 MPa can be achieved in Ti–V–Al–Cu alloy with the Cu content of 5 at.%.With the Cu content increasing, the shape memory effect firstly increased and then decreased. The moderate Cu addition of 0.5 at.%. resulted in Ti–13V–3Al-0.5Cu alloy showing the largest recoverable of 4.1% with the pre-strain of 6%.The authors declare that they have no competing financial interests for the publication of “Microstructure and mechanical properties of Ti–V–Al–Cu shape memory alloy by tailoring Cu content”.Experimental and analytical characterization of transverse cracking behavior in carbon/bismaleimide cross-ply laminates under mechanical fatigue loadingTransverse cracking behavior in high temperature bismaleimide-based carbon fiber reinforced plastics (CFRP) laminates under fatigue loading was observed. Three types of cross-ply laminate, [0/902/0], [02/903/02] and [02/904/02], were tested to study the effect of ply thickness. Damage observation was conducted using two methods. Optical microscopy and soft X-ray radiography were used for edge and internal damage observation, respectively. Variational approach was used to derive the energy release rate associated with transverse cracking. Multiplication of transverse cracks was modeled based on modified Paris-law approach.High temperature carbon fiber reinforced plastics (CFRP) are candidate structural materials for super sonic transporter (SST). Many heat resistant polymers, such as thermoplastic polyimide and thermoset bismaleimide were developed and evaluated Previous studies on the fatigue behavior of composite laminates mainly focused on the measurement of fatigue life and stiffness and residual strength degradation due to fatigue loading In the present study, microscopic damage behavior in bismaleimide-based CFRP laminates under tensile fatigue loading was investigated. To discuss the effect of laminate configurations, three types of cross-ply, [0/902/0], [02/903/02] and [02/904/02] laminates were tested. Quantitative observation was conducted using both an optical microscope and a soft X-ray radiography. Then a variational method Material system used was carbon fiber (G40-800) reinforced bismaleimide (5260), G40-800/5260 (. Bismaleimide is heat resistant polymer, which is considered to be a potential material system for future SST structure. Laminate configuration tested were three types of cross-ply laminates, [0/902/0], [02/903/02] and [02/904/02] to study the effect of 90° ply thickness on the transverse cracking behavior. The specimen size was 150 mm long and 25 mm wide. GFRP tabs were glued on the specimens, which resulted in specimen gauge length of 80 mm. Both free edges of specimens were polished for the observation using optical microscopy. All specimens were stored in a desiccator to avoid the moisture effects.Tension–tension fatigue tests were conducted using an electro-hydraulic testing machine (MTS, Table Top System 858). All the tests were run at the stress ratio, R=0, at a frequency of 5 Hz, at room temperature and with a sinusoidal waveform under load control condition. The maximum stress levels were selected to correspond to the initial laminate strain, εinit of 0.4, 0.5, 0.6, 0.7 and 0.8% for each laminate. During the test, the testing machine was periodically stopped, and the edges of specimens were observed by optical microscopy directly. The specimens were also observed by soft X-ray radiography to detect transverse crack progress in the width direction. The number of transverse cracks per unit observed length was defined as transverse crack density, which was measured as a function of number of cycles, n. All fatigue tests were conducted until n=1,000,000.The first microscopic damage observed was transverse cracking in 90° ply. shows a transverse crack observed by optical microscopy. Transverse cracks in 90° ply initiate at the free edge and go through the thickness, instantaneously. As the number of cycles increased, the number of cracks increased. Then, cracks in the matrix rich region between 0 and 90° plies and the fiber breaks in 0° plies at the matrix crack tip were observed. show the cracks in the matrix rich region and fiber breakage, respectively. Cracks in the matrix region are inclined to the tensile direction, which means the existence of high shear stress in the interlaminar layer.show the microscopic damage progress in [0/902/0], [02/903/02] and [02/904/02] laminates observed by soft X-ray radiography, respectively. Transverse cracks grew in the width direction with increase in number of cycles. Crack growth rates in the width direction were almost constant; however, several cracks were arrested at some point and grew again as the cycles increased. shows the example of crack progress in the width direction and the relation between crack length and number of cycles, respectively. Crack was arrested at region. To clarify the mechanism of such a cracking manner, the specimen was cut in the loading direction to observe crack path. shows the observation results of cross-section. Crack shape changed as progress. Especially, crack shape was deformed in , which corresponds to crack arrested point. This is attributed to fiber misalignment as shown in . That is, crack growth rate largely depend on the fiber alignment.Splittings in 0° plies were observed in [02/903/02] and [02/904/02] laminates at εinit=0.5∼0.8%. Delamination was not observed in all laminates until n=1,000,000.shows the transverse crack density as a function of number of cycles. Only the transverse cracks, which went through the width were counted. Crack densities increased as the number of cycles increased, and saturated at some levels. Crack densities became larger in each laminate as the εinit became larger until n=1,000,000.No transverse cracks were observed in [0/902/0] laminates at εinit=0.5%. On the other hand, transverse crack progress was observed in [02/904/02] laminates at εinit=0.5%. The stress condition was the same for [0/902/0] and [02/904/02] laminates at the same value of εinit. This shows the size effect on transverse cracking and, therefore, energy balance approaches were necessary to analyze the transverse cracking behavior under fatigue loading.Based on the Nairn model, energy release rate associated with matrix cracking, Gm, is expressed aswhere D is the transverse crack density, σ0 is the laminate stress, T is the temperature difference between stress free temperature and test condition, Ex(1) is the Young's modulus of 90° ply, Δα is the difference between transverse and longitudinal thermal expansion coefficients, C1 and C3 are the constants defined by laminate configuration and material constants, t1 is half of the 90° ply thickness and Y(D) is the calibration function.For matrix cracking, the modified Paris-law equation is written aswhere n is number of cycles, A and γ are constants, and σmax and σmin are the maximum and minimum stresses, respectively. In the present analysis, the energy release rate is calculated by using Assuming that crack density growth rate is constant at one cycle and integrating in terms of number cycles, crack density is written aswhere σmax |
n and σmin |
n are the maximum and minimum stresses during cycle n, respectively. Nf is first cracking cycle.where k and C are constants. Once A, m, k and C are determined at a certain condition, transverse cracking behavior at any stress condition can be predicted for arbitrary laminate configuration.In this study, all the parameters are determined from [02/903/02] results. show the stress in 90° plies as a function of first cracking cycles and transverse crack density growth rate as a function of the energy release rate range, respectively. All the parameters obtained are listed in corresponds to S–N curves of 90° plies of G40-800/5260 laminates. The master curve in corresponds to the resistance to transverse crack formation in 90° plies during fatigue loading for the G40-800/5260 laminates. shows comparison between the experimental results and the analytical predictions of transverse crack density. Predictions agree with the experimental results at the initial region corresponding to the constant growth region Microscopic fatigue damage progress was observed in three types of cross-ply G40-800/5260 laminates. Transverse crack densities were measured as functions of the cyclic stress level and the number of stress cycles. To characterize the damage progress, the energy release rate associated with transverse cracking was calculated using variational analysis. The modified Paris-law approach was used to model the transverse cracking. It was proved that initial transverse crack behavior could be predicted using the present analysis.Enhanced electron field emission from ZnO nanoparticles-embedded DLC films prepared by electrochemical depositionZnO nanoparticles-embedded diamond-like amorphous (DLC) carbon films have been prepared by electrochemical deposition. Transmission electron microscopy (TEM) and high-resolution TEM (HRTEM) results confirm that the embedded ZnO nanoparticles are in the wurtzite structure with diameters of around 4 nm. Based on Raman measurements and atomic force microscope (AFM) results, it has been found that ZnO nanoparticles embedding could enhance both graphitization and surface roughness of DLC matrix. Also, the field electron emission (FEE) properties of the ZnO nanoparticles-embedded DLC film were improved by both lowering the turn-on field and increasing the current density. The enhancement of the FEE properties of the ZnO-embedded DLC film has been analyzed in the context of microstructure and chemical composition.► ZnO nanoparticles were embedded within DLC matrix by electrochemical deposition. ► The ZnO nanoparticles were in wurtzite structure. ► ZnO embedding enhanced both surface roughness and graphitization of the films. ► The FEE properties of the films have been enhanced by ZnO embedding.Diamond-like carbon (DLC) films are considered as good electron emitters for field emission displays due to negative electron affinity, high thermal conductivity and chemical inertness Zinc oxide (ZnO), an n-type semiconductor with a wide bandgap (3.37 eV) and a large exciton binding energy (60 meV), has drawn renewed attention due to its promising integration into optoelectronic devices, sensors, spintronics and so on In this work, ZnO nanoparticles were embedded within DLC films by electrochemical deposition. Method for DLC fabrication based on electrochemical deposition has demonstrated such advantages as the relative simple equipment required, low production cost and the possibility of doping by various elements The DLC and ZnO–DLC films were fabricated using an electrolytic cell system described in detail in Ref. The chemical states of the typical elements of the samples were examined by X-ray photoelectron spectroscopy (XPS, Perlin–Elmer PHI-5702). The Raman measurements were carried out on a Jobin–Ivon LabRam HR800 Raman apparatus with a laser source wavelength of 532 nm. Additional structural characterization was carried out using transmission electron microscopy (TEM, JEM-1200EX). The surface morphologies of the films were examined using atomic force microscope (AFM, CSPM4000). The FEE properties of the films were measured in a parallel plate configuration with a stainless steel anode at a pressure of ∼10−6 Torr. The anode–cathode distance was 100 μm. The testing area was 4.15 mm2. The applied voltage was gradually increased from 0 to 2350 V. The electric field is defined using a formula E = V/d (V is the applied voltage and d is anode-to-cathode separation). The field emission current density is defined using the formula J = I/S (I is the field emission current and S is the entire area of samples exposed to the anode screen).The chemical composition of DLC and ZnO–DLC films electrochemically deposited on Si substrates was investigated by XPS. The survey spectrum of a DLC film indicate that the film contains mainly carbon and a small amount of oxygen, while the ZnO–DLC film contains 8.9 at% zinc besides 80.1 at% carbon and 11.0 at% oxygen, suggesting that Zn element has been successfully doped into DLC films. The appearance of the O 1 s peak, which is common for the spectra of this kind of films, might be designated to the contamination of the samples for the exposure to air and the absorption in the deposition process (a), the Zn2p peaks of the ZnO–DLC film present the binding energies of Zn2p1/2 and Zn2p3/2 at around 1045.4 eV and 1022.4 eV, respectively, coinciding with the characteristics of ZnO (b) and (c). The spectra were fitted with three peaks obtained at 284.2–284.7, 285.2–285.7 and 286.8–289.2eV, which have been assigned to graphite (284.4 eV), diamond (285.2 eV) and CO-contaminated, respectively. Since the area of each peak is directly related to the concentration of the corresponding phase, the sp3 content could be estimated by taking the ratio of diamond peak area over the sum of diamond and graphite peak areas. It has been found that the doping of ZnO decreased the sp3 content from 0.67 of the DLC sample to 0.61 of the ZnO–DLC sample. This can be interpreted in terms of the graphitization of the DLC matrix induced by ZnO dopping. (a) and (b) show the 3D AFM surface micrographs of DLC and ZnO–DLC films, respectively. As evidenced in , the ZnO–DLC film exhibits a relatively rougher surface with an rms roughness of 76 nm than that of the DLC film with an rms roughness of 35 nm.Apparently, ZnO doping greatly changed the intrinsic structure of amorphous carbon films, which could be further analyzed by Raman analysis. Raman spectra of DLC and ZnO–DLC films are given in (a) and (b), respectively. Obviously, the main characteristics of D band, corresponded to the breathing modes of sp2 ring structure in disorder graphite, and G band, attributed to E2g vibration mode arising from the bond stretching of all pairs of sp2 atoms in both rings and chains, both appear in the range of 1200−1–1700 cm−1 for the two samples, indicating the existence of mixed sp2 and sp3 bonding in the deposited films (a) shows two peaks as G peak at around ∼1580 cm−1 and D peak at around ∼1350 cm−1, with an integrated intensity ratio I(D)/I(G) of 0.58. For the composite ZnO–DLC film, as shown in (b), compared with those of the DLC film, both D and G peaks move to higher wavenumbers and the I(D)/I(G) increases to 0.76. This is attributed to the graphitization of DLC matrix resulted from ZnO embedding. In addition to D and G peaks, a number of LO multiphonon peaks corresponding to ZnO nanoparticles are observed in the Raman spectrum of the ZnO–DLC film. The peak at 577 cm−1 is related to longitudinal optical (LO) phonon mode of ZnO nanoparticles. In the high-frequency region, LO overtones and combinations involving LO modes induce a second-order feature peak near 1140 cm−1(a) and (b) shows the TEM and HRTEM images of the ZnO–DLC composite film, respectively. The spherical ZnO nanoparticles (dark spots) with diameters of around 4 nm were uniformly embedded in amorphous carbon matrix (bright area), and show no agglomeration. This may interpreted the rougher surface of the ZnO–DLC film observed by AFM. During the deposition process, the inhomogeneity of film-forming associated with ZnO doping may induce the increase of surface roughness of the DLC film. In the HRTEM image, the lattice spacings between adjacent lattice planes are approximately 0.27 nm, in agreement with the distance between two (002) crystal planes of hexagonal wurtzite structured ZnO presents the FEE curves of DLC and ZnO–DLC films. It can be seen that the FEE current density from the ZnO–DLC film is higher than that from the DLC film. In addition, the turn-on field, under which a 2.5 μA/cm2 current density is extracted, is reduced from 13.5 V/μm for the DLC film to 7 V/μm for the ZnO–DLC composite film. The figure reveals that the highest current density is about 1.5 mA/cm2 at the electric field of 23.5 V/μm from the ZnO–DLC film. The possible reason for the above observations is the joint effect of surface roughness and microstructure variation. Previous AFM studies of DLC and ZnO–DLC films have indicated that the embedded ZnO nanoparticles induce surface protrusions on the ZnO–DLC film, which could act as a source of geometric field enhacement. Simultaneously, ZnO embedding enhances the graphitization of DLC matrix. It is known that sp2-bonded carbon would form conducting channels and provide sufficient electrons to the sp3-bonded carbon acting as emission sites. The presence of abundant sp2-bonded carbon may advantage the current forming and flowing in the film.The emission current is determined by the Fowler–Nordheim (FN) equation where J is the emission current density, φ is the work function called the emission barrier, E is the electric field, and β is the field enhancement factor at sharp geometries. By ploting ln(J/E2) against (1/E), the inset shows the corresponding FN plots of the sample. Assuming the field enhancement factor β to be 1, the slopes of the plots give barriers of 69 and 43 meV for DLC and ZnO–DLC films, respectively. Actually, the real value of the work function should be larger because of the underestimation of the field enhancement factor β.ZnO nanoparticles with a wurtzite structure were embedded within DLC films by electrochemical deposition. The embedding of ZnO nanoparticles could enhance both surface roughness and graphitization of the DLC films. The FEE properties of the ZnO–DLC films have been improved with the turn-on field fall and the FEE current density rise by ZnO embedding. The results show that the electrochemical deposited ZnO–DLC composite films can be a promising candidate as field emission emitters.Computational methods for creep fracture analysis by damage mechanicsSome mechanical problems of the computational method of creep fracture analysis based on continuum damage mechanics are discussed. After brief review of the local approach to creep crack growth analysis by means of finite element analysis and continuum damage mechanics, intrinsic feature of the fracture analysis in the framework of continuum theory and the causes of mesh-dependence of the numerical results are discussed. Then, a series of numerical analyses are performed for a plate specimen with a central crack to show the characteristics of the mesh-dependence. In view of these results, the effects of stress-singularity at the crack tip as an essential cause of the mesh-dependence are discussed by analyzing the magnitude of stress in the finite element at the crack-tip. As another major cause of the mesh-dependence of the numerical results, ill-natured stress-sensitivity of the constitutive and the evolution equation of the conventional Kachanov–Rabotnov creep damage theory is elucidated by performing sensitivity analysis of the relevant equations. In order to suppress this singular stress sensitivity at the critical stage of damage, a new creep damage model is developed. Finally, the effects of the preceding damage field on stress singularity of the asymptotic stress field at mode I creep crack are analyzed to furnish a criterion to overcome the mesh-dependence in computational method for creep fracture analysis.Conventional method of fracture analyses is to evaluate the rate or the stability of crack growth by correlating them with some global fracture mechanics parameters. However, advances of the computational methods have given another framework of fracture analysis by pursuing the local field of stress, strain and damage at a crack tip, and this method is usually called a Local Approach of FractureThe present paper is concerned with the discussion on the intrinsic feature of the fracture analysis in the framework of continuum theory and with the problems of the mesh-dependence in the local approach to creep fracture analysis by FEM. After a brief review of the notion and the procedure of the local approach, the essential causes of the mesh dependence are discussed in some detail. Then, two major causes of the mesh-dependence in creep crack analyses will be analysed, i.e., the effects of stress-singularity at crack-tip and those of the stress-sensitivity in constitutive and evolution equations at the critical damage state. New constitutive and evolution equations of creep damage are proposed to regularize the mesh-dependence. Finally, the effects of the preceding damage field on the stress-singularity in the asymptotic stress field at the creep crack tip is discussed.Fracture in materials usually originates from the initiation and development of some microscopic defects and cavities, and is induced by the nucleation and growth of macroscopic cracks brought about by the coalescence of these microscopic cavities.According to the notion of CDM, it is assumed that the damaged state at a point x characterized by the development of the microscopic defects and cavities can be described by a properly defined Damage Variable in the usual framework of continuum mechanics, where the states |D|=0 and |D|=Dcr represent the undamaged and the completely fractured state, respectively. Thus, if a crack is characterized by the region where the state of damage has attained to its critical state |D|=Dcr as shown in the process of damage development and crack growth can be analyzed directly by the local states of stress, strain and damage. This scheme is usually called Local Approach of FractureOne of the most important issues of the FEM analysis of the initial- and the boundary-value problems of continuum mechanics is the accuracy and the convergence of the numerical results. The mesh-dependence and its regularization in FEM analysis, especially of the strain localization, bifurcation and of the singular and discontinuous stress field, have been extensively discussed. The factors leading to the mesh-dependence in these problems may be attributable mainly to:(A1) Stress singularity and discontinuity in stress field.(A2) Bifurcation and strain localization due to material softening.(B2) Incorporation of strain-rate dependence (artificial viscosity).(B3) Incorporation of Cosserat continua.(B4) Use of non-local or gradient theory.In the local approach to fracture based on CDM and FEM analysis, besides the above problems (A1)–(A3), additional features intrinsic to the crack growth analysis will arise. Namely, though the physical phenomena of fracture are intrinsically dependent on the characteristic length of the microstructure of the material (C2) Stress concentration at the tip of growing crack.(C3) Localization of damage distribution.As regards (C1), one of the most successful model of a crack in local approach is the non-local damage theory The cause (C4) may be discussed partly in relation to the cause (A2), and partly to (C3). Moreover, bifurcation due to material softening does not occur in the case of rate-dependent materials In order to examine the characteristic features of mesh-dependence in local approach to creep fracture, we analyze first the initiation of crack growth and its subsequent growth in a cracked plate.Let us assume that the total strain εij is given as the sum of elastic strain εeij and creep strain εcijAccording to the conventional creep-damage theory of Kachanov–Rabotnov, the constitutive and the evolution equation are given as follows where εcij and D are the creep strain and the damage variable, while sij=σij−(1/3)σkkδij, , and σI are deviatric stress, stress, equivalent stress and maximum principal stress, respectively. The symbols B, A, n, p, q and α are material constants.The elastic constitutive equation coupled with damage may be expressed as follows:where Cijkl(D) is the material stiffness tensor dependent of the damage variable D. For the isotropic elastic material, we havewhere E(D) is the damage-dependent Young's modulus, and ν is the Poisson ratio. In the practical application, two kinds of E(D) are usually employed where E0 is the Young's modulus of the undamaged material and Dcr is the critical value of damage. Since FEM analysis by the use of the fully coupled approach of needs considerable amount of computation, we will employ here the partly coupled approach of The FEM analysis is performed for a cracked plate shown in The material is type 316 stainless steel at 650°C. A constant tensile load pe=50 MPa is applied to the specimen. The material constants for where the unit of stress is (MPa) and that of time is (hr).In order to examine the mesh-dependence in the local approach to creep fracture analysis, we employ different finite element meshes of To elucidate the effects of mesh-size, four kinds of the crack-tip element sizes Δe=0.01, 0.12, 0.50 and 1.00 mm are used.The results of the creep crack analysis described above are shown in shows the mesh-size dependence of the crack growth initiation timetig for three types of the elements shown in , and gives the relation tig∝(Δe)1.57. The initiation of crack growth is specified as the failure of the Gaussian point P(rm) that is the closest to the initial crack-tip, and the failure of an element is defined by the state D=Dcr., there is no significant influence of the type of the crack-tip element on the mesh-size-dependence behavior. Thus only eight-node isoparametric element of (b) is used in the subsequent analysis and discussion. The mesh-size-dependence will be referred to as mesh-dependence hereafter. shows the crack growth rate da/dt as a function of crack growth length Δa, for four different meshes. For a specific crack length, different mesh-sizes result in quite different crack growth rates, and the largest difference among da/dt attains to 10 times. However, it will be observed that the curves come close to each other as crack growth length Δa increases. This means that, after sufficient growth of the crack, the mesh-size-dependence of crack growth rates may disappear in this case. This feature may be understood in view of the effects of the preceding damage on the crack-tip stress field which will be discussed in Under certain conditions, the initial stress for the integration of the damage evolution may be the steady-state creep stress field rather than elastic one. Namely, if the transition time ts should be in fact the steady-state creep. In view of this situation we carried out another set of calculation. Namely, the elastic-creep analysis without damage was carried out first. Then after steady creep state was attained, the damage coupled analysis was started, and continued until the initiation and the growth of a crack. This series of calculation will be called C-calculation, while the analysis based directly on show the relevant results obtained by C-calculation. The calculation was performed only by the use of the eight-node isotropic elements, because the choice of the type of the elements has not much influence also in C-calculation. In the crack growth initiation time tig obtained from C-calculation is plotted as a function of Δe in log–log coordinates. It can be seen that the regression to the numerical results show that the slope of the line is 0.60. , on the other hand, shows the numerical results of the crack growth (Δa−t) curves for the four different mesh sizes. It will be observed that the incipient growth rate ȧ decreases as the mesh-size decreases. This feature will be discussed in the following.Which of the E-calculation or the C-calculation gives better understanding will depend on the mechanical properties of the material of the relevant problem.In the numerical calculation by means of finite element analysis, as the size of the crack-tip element decreases, the stress in this element (or at some Gaussian points in the element) will tend to the singular stress fields of the ideal crack. For the cases of linear elasticity and power-law creep, the singular stress fields of the maximum principal stress σI are given by the KI- and HRR-stress field defined as follows and r is the stress intensity factor, a parameter to describe the stress-intensity at the crack-tip in a non-linear material and the distance from the crack-tip, respectively. is governed by the local stress, the damage state in front of the crack-tip depends directly on the mesh-size. Thus, a singular stress field at the crack-tip can be one of the most essential causes for the mesh-dependence of the local approach.We now discuss the effects of stress singularity, on the mesh dependence in some detail.By postulating the maximum principal stress criterion, the damage evolution applied to a Gaussian point P(rm) will lead to a simpler form:where σI(t,rm) is the maximum principal stress at time t, and will vary during the total life time tf of the point P; i.e., during the crack growth initiation time tig at the tip of the initial crack. Integrating this equation from t=0, D=0 to t=tig, D=1.0, and by using a non-dimensional variable τ=t/tig, we haveIn view of the results of the preceding FEM analysis, we can write the principal stress of the numerical solution in the form ofwhere σ0(rm) is the initial stress of σI(t,rm) and g(τ,rm) is an unknown function of τ at the point P(rm). Then, we have the following relations:In both cases of E-calculation and C-calculation, the theoretical (asymptotic) solution of the crack-tip stress fields σ(r) are given by the KI-field of , respectively. Obviously, the numerical solution of the initial stress σ0(rm) should be approximately in agreement with these analytical results. According to Since rm is proportional to the crack-tip mesh-size Δe for the present mesh series (see This equation clearly shows the strong influence of the mesh-size Δe on the value of the initial stress σ0(rm). Thus, the value of local stress in front of the crack-tip will not tend to a definite value even the mesh is divided infinitesimally.where Ip has been rewritten as the function of Δe. This equation shows the dependence of the initiation time tig on the mesh-size Δe. Since the dimensionless history g(τ,Δe) is indeed not very sensitive to the change of mesh-size Δe, the influences of Ip(Δe) on tig may be neglected, and thus will leads to a very simple approximate relation between tig and ΔeThis equation predicts that the initiation time tig of a cracked specimen will decrease with mesh-size at crack-tip following a power law of an exponent p/k.In E-calculation, we already observed (see ) that tig was proportional to 1.57th power of Δe. According to , if we take k=2.0 (elastic initial field) and use the material constant p=2.8 of , we obtain tig∝Δe1.40. This is in approximate agreement with the numerical results, and the difference between the theoretical exponent 1.40 and the numerical one 1.57 is due to the mesh-size effects on Ip(Δe). predicts the power law dependence of the initiation time tig on Δe with the exponent index p/(n+1), or 0.62 for the present material. In , on the other hand, tig obtained from C-calculation is plotted as a function of Δe in log–log coordinates. It can be seen that there also exists an approximately linear relation between . The slope of the regression line 0.60 agrees well with the predicted value of 0.62. This good agreement is because of the very weak influences of mesh-sizes on Ip(Δe) in the C-calculations.The above results shows that, the simple relation of can describe the mesh dependent behavior of the crack growth initiation time tig quite well in the present calculations. Namely, is a proper expression of the fact that, in the existence of the crack-tip singularity, the initiation time tig of the cracked specimen predicted by the use of local approach will be subject to mesh-dependence that is governed by the stress concentration due to stress singularity. In the practical calculation, relation can be easily used to estimate the initiation time tig for different meshes, provided the singularity power k and the damage index p are known.The mesh-dependence of crack growth analysis is much more complicated than that of its initiation. However, an approximate estimation to the incipient crack growth rates can be obtained by the use of the previous analysis of the crack growth initiation. As observed from (e), the incipient crack growth increment Δa0 is proportional to the mesh-size Δe, and thus the incipient crack growth rate This equation shows that, the incipient crack growth rate also will be subjected to a mesh-size-dependence which is associated with the stress singularity. It is interesting to note from that, depending on the value of p/k, there exist two opposite behaviors of the mesh-dependence of the predicted crack growth rate. In the case of will decrease as Δe decreases in the case of k>p. In particular, when p=k, predicts that a0 will be independent of mesh-size. will tend to infinity as mesh-size tends to zero according to . It implies that we cannot obtain a definite value of from the numerical calculations if the meshes of different sizes are used. The E-calculation in the present analysis is an example of this case, in which we have k=2 and p=2.5, and hence k>p. In , the calculated growth rates da/dt was plotted as a function of crack growth length Δa, with mesh-size Δe as a parameter. The strong mesh-size dependence is observed in this figure. One of the essential reasons for such mesh-size dependence is that, the incipient crack growth rate based on different meshes could become arbitrarily large according to . In such cases, we cannot expect the existence of a unique relations among the different meshes. The obvious non-uniqueness of curves for different mesh-sizes was also found in the previous papers predicts that the incipient crack growth rates will decrease when the mesh-sizes are decreased. This is also in agreement with our numerical results. In C-calculation we have shows the calculated crack growth (Δa−t) curves for the four different mesh-size, in which we can see that the incipient growth rate is a useful relation for the qualitative estimation of the mesh dependent behavior of crack growth. Especially, this relation can be used to judge if the calculated growth rates will increase or decrease when mesh-size is continuously decreased. The opposite tendencies of numerical results in the present E-calculations and C-calculations are in agreement with the prediction of . Furthermore, this also shows that, the initial crack-tip singularities have important influences on the mesh-dependent behavior of crack growth. is valid only for the incipient crack growth rate, suggests that it will be applicable also for the later stage unless the crack ligament becomes considerably small.In the case of the conventional creep damage theory of Kachanov–Rabotnov represented by , besides the strain localization as a result of bifurcation referred to (A2) in , strain and damage localization due to numerical instability of the constitutive and evolution equations can be another major cause of mesh-dependence. Namely, at the final stage of damage where the damage variable D approaches 1, the rates of creep and damage given by tend to infinity. Thus, a small difference in stress, or a small numerical error may induce an eventual localization of strain and damage; this numerical instability, or singular stress sensitivity in constitutive and evolution equations may be another significant cause of mesh-dependence.In order to elucidate this feature in more detail, we will start with the evolution gives the damage history as a function of stress historyLet us consider the variation of D(t) due to a small variation of stress history δσD(t). Taking variation of both sides of Since A[σD(t)]p is always larger than 0, by the use of the mean-value-theorem of integration, the above equation can be rewritten as follows has been replaced by the function of D(t) by the use of represents the relative variation of stress at time implies that, when D tends to 1.0, δD can be unlimitedly large by an infinitesimal variation of stress. In other words, the damage evolution employed in this analysis is very sensitive to a small change of stress when the damage variable D is close to its maximum value 1.0. and p=q=3.5 implies that the variation of damage δD(t) can be 107 times larger than the relative variation of stress . This singular stress sensitivity can be often an essential cause of the damage localization.Kachanov–Rabotnov creep damage theory of has been originally proposed to describe the relation between creep strain and time under specific constant tensile stresses , in particular, are originated from the effective stress concept However, it should be emphasized that the accelerating damage rate in the final stage of creep rupture in usual creep tests is brought about mainly by the instantaneous elastic–plastic damage, not by the creep damage. The stable damage rate in the final stage of creep rupture is confirmed also in the creep fracture modeling based on Voronoi simulation of grain boundary cavities have been introduced to represent the elastic–plastic damage at the final fracture rather than to represent the creep damage. This feature accounts for the above mentioned singular stress sensitivity of Kachanov–Rabotnov equation.More appropriate creep damage model will be necessary not only for accurate description of creep damage evolution, but also to avoid the ill-natured stress sensitivity in the creep damage model and hence to suppress the mesh-dependence in local approach to creep fracture. has been observed for the metallographical parameters such as cavity density, cavity fraction of grain boundary, A-parameter, etc. Experimental results of cavity area density of Nimonic 80 A It will be observed that the damage D of the Kachanov–Rabotnov model of can not correctly describe these metallographically observed damage evolution since usually the material parameter q≫1.In order to improve this feature of singular stress sensitivity, a modified form for the damage evolution has been proposed by the present authors where A, p and q2 are material constants. The solid line in and the observed results of cavity area density.Since the damage evolution is closely related to the stress field, the marked stress sensitivity in the creep constitutive equation also has significant effects on the damage localization. In order to eliminate this difficulty, the following creep constitutive equation has been derived by the present authors where c, B′, n′, B, n are material constants, while t̄ is a fictitious time to be eliminated from the fictitious creep relation under constant uniaxial stress σ(t)=σEQ(t)., similar to that of Art. 4.2, gives the following result:According to this equation, the damage variation remains finite even for D=Dcr=1.0. By the use of the typical material constants of p=q=5 and Dcr=0.99, gives the stress sensitivity factor, δD/(δσD/σD)=8.33×109 for the conventional damage evolution (3). In contrast, by the use of p=5, q2=q+2=7 and Dcr=1.0, gives the factor δD/(δσD/σD)=782.6 which is several orders smaller than that of In order to examine the improvement in the damage localization and mesh-dependence in local approach achieved by the proposed , we will now apply them to the creep crack analysis of a perforated copper plate under uniaxial tension.Finite element analysis are conducted for a thin copper plate containing a circular hole as shown in a) by the similar procedure as in Art. 3.1. The specimen is under the state of plane stress, and is subjected to a constant tensile load pL=50 MPa under 250°C. The material constants of were specified as follows for the material by fitting the equations to the experimental results:Because of the symmetry, only 1/4 of the specimen is modeled in finite element calculations. The finite element mesh consists of eight-node isoparametric element with reduced (2×2) Gaussian integration.In order to examine the influences of mesh size, three different meshes, i.e., mesh-1/1, mesh-1/8 and mesh-1/64 were employed, where the minimum mesh-sizes Δe in front of notch root are 1/1, 1/8 and 1/64 mm, respectively. A typical finite element mesh (mesh-1/8) is shown in and (b) give the damage distribution around the growing crack (i.e. CDZ where D=Dcr) for mesh-1/64, the finest mesh employed in the present calculations. Marked damage localization around the crack can be observed in (a) for Kachanov–Rabotnov model; damage D increases steeply to its critical value in a very close vicinity of the crack-tip. In contrast, a quite moderate damage distribution is obtained for the proposed exponential type model as shown in (b). Obviously, this damage delocalization effect is due to the improvement of the damage evolution and damage-coupled creep behavior in the proposed model. shows the effects of mesh sizes on the calculated crack growth rates. As discussed in the previous papers (a) calculated by Kachanov–Rabotnov model of . Even between two fine meshes, mesh-1/8 and mesh-1/64, there is almost two order differences in the predicted growth rates. On the other hand, it is found that the mesh-dependence is greatly improved by the use of the proposed exponential model of (b), where the difference of crack growth rates between mesh-1/8 and mesh-1/64 has been considerably reduced. This improvement in mesh dependence is because the moderate damage distribution shown in (b) can relax the stress concentration (or even stress singularity) in front of crack-tip that is usually very sensitive to the mesh-size., the stress singularity of the asymptotic stress field plays an essential role in the mesh-dependence of the crack initiation times and the crack growth rates. , in particular, showed that the mesh dependence of the creep growth rate decreases as the crack extends, and this implies that crack-tip singularity varies significantly as the development of the damage field.Recently, the present authors analyzed the effects of the damage field on the stress singularity of a Mode I creep crack in steady state growth Let us first take a moving coordinate system o–x1x2x3 or o–rθz with the origin at the crack tip as shown in where the x1-axis and the θ=0 direction are in the direction of creep crack growth.The governing equations of the boundary value problems are given as follows:where (·) denotes material derivative with respect to time.where ν represents the rate of creep crack growth.where φ(r,θ,z) is the Airy stress function. was solved by a semi-inverse method. In view of the results of the creep crack analysis of represented by the following power function of radius r:where ℓ and r0 are an exponent characterizing the damage distribution and a constant representing the size of the damage region, respectively.In order to solve the above equations, we assume the following asymptotic solution for crack-tip stress:where λ=s−2 represents the exponent of the stress field, and furnishes a two-point boundary-value problem of non-linear ordinary differential equations for the unkown function F(θ). The unknown exponent ℓ and crack-growth rate ν were determined so that the resulting stress field σij(r,θ) and the assumed damage field (34) satisfy the evolution equation of damage (31) in front of the crack tip r⩾0 and θ=0.shows the exponent λ of the asymptotic stress field at the crack tip in relation to the creep exponent n and the exponent p of the damage evolution obtained by the analysis. The results for the creep of plane strain and plane stress were shown in (a) and (b), and the circles o and the solid lines represent the numerical results of the analysis and the corresponding approximate expressions:, furthermore, represents the stress singularity exponent of HRR stress field of undamaged material , when damage develops before the crack tip (p>0), the value of the stress singularity exponent λ is always larger than that of the undamaged case of , and thus the stress field may become nonsingular (λ>0) even for finite value of the creep exponent. The effects of the damage field, furthermore, depend largely on the value of the exponent p of the damage evolution equation. This result is in clear contrast to the undamage material of , where the stress field is always singular for the finite value of n., the mesh-dependence of the numerical results gives serious limitation to the applicability of the computational methods to fracture analysis, and the stress singularity of the asymptotic stress field at the crack tip is one of the most essential causes of the problem. Thus, it should be emphasized that the results of may give a very important criterion to estimate the degree of the mesh-dependence in local approach of creep fracture based on FEM and CDM.Computational method and the related numerical problems for creep fracture analysis based on damage mechanics and FEM were discussed. Special emphasis was placed on the causes of the mesh-dependence of the numerical results because it is one of the most crucial problem for the accuracy and the reliability of the analysis.After detailed discussion of the mesh-dependence due to the stress singularity at the crack tip, ill-natured stress sensitivity in the damage evolution equation was shown to be another major cause of the mesh-dependence. Thus, a new creep damage model appropriate for creep fracture calculation was proposed. Finally effects of preceding damage field on the stress-singularity of mode I creep crack was elucidated to furnish a criterion to estimate the mesh-dependence in local approach of creep fracture based on FEM and CDM.Since extensive work has been published to regularized the mesh-dependence problem, the details of the specific method should be referred to the relevant Refs. Nonlinear forced vibration of damped plates by an asymptotic numerical methodThis work deals with damped nonlinear forced vibrations of thin elastic rectangular plates subjected to harmonic excitation by an asymptotic numerical method. Using the harmonic balance method and Hamilton’s principle, the governing equation is converted into a static formulation. A mixed formulation is used to transform the problem from cubic nonlinearity to quadratic one sequence. Displacement, stress and frequency are represented by power series with respect to a path parameter. Equating the like powers of this parameter, the nonlinear governing equation is transformed into a sequence of linear problems with the same stiffness matrix. Through a single matrix inversion, a considerable number of terms of the perturbation series can easily be computed with a limited computation time. The starting point, corresponding to a regular solution, is obtained by the Newton–Raphson method. In order to increase the step length, Padé approximants are used. Numerical tests are presented and compared with numerical and analytical results in the literature, for different boundary conditions, excitations and damping coefficients.To minimize the structural weight, thin plates are widely used in many industrial fields such as aeronautic, mechanics and civil engineering. These structures are often forced into high-amplitude vibrations, inducing significant geometrical nonlinearity, which is a source of complex instability phenomena. To reduce the effect of such problems, a common approach consists in introducing a damping component into the structure. But the principal difficulty, in the analysis of such problems, lies in the presence, on the one hand, of nonlinearity, source of complex phenomena such as bifurcations, jumping and chaos, and on the other hand of damping, which generally leads to complex solutions.In the literature, most investigations which take damping into account are limited to linear vibrations, leading to a complex eigenvalue problem. Only a few works combine both geometrical nonlinearity and damping: Amabili made an experimental and numerical study of plates with viscous damping and subjected to harmonic excitation This paper deals with the nonlinear vibration of damped plates by an asymptotic numerical method (ANM). In previous works using this method As it is well known, in the investigation of thin plates’ behavior, one assumes that the rotations are moderate and the use of von Karman model was validated in several previous referenced works Using this theory, the harmonic balance method and Hamilton’s principle, the initial governing motion equation is converted into an operational form.Coupling a perturbation technique and the finite element method, the nonlinear problem is transformed into a sequence of algebraic linear problems. Padé approximant method was used Let us consider a thin rectangular plate with a coordinate system (O;x,y,z), the origin O being situated at one corner. The displacement components of the plate’s middle surface are denoted by u, v and w, where u and v are the in-plane displacements and w the transverse displacement in the x, y and z directions, respectively. The associated Green–Lagrange strain varies linearly with respect to the thickness:where γ |
= |
γl |
+ |
γnl is the generalized membrane strain which can be broken down into a linear and nonlinear part, and k is the bending strain.The nonlinear strain–displacement relationships associated with the von-Karman plate theory are given by:γl=∂u/∂x∂v/∂y∂u/∂y+∂v/∂x,γnl=12(∂w/∂x)2(∂w/∂y)22(∂w/∂x)(∂w/∂y),k=-∂2w/∂x2∂2w/∂y22∂2w/∂x∂yThe strain can be written by an operator notation as follow:where U is the displacement vector given by U |
= {u, |
v, |
w}t; Bl and Bnl are the linear and nonlinear strain–displacement operators, respectively. In our case: BlU |
= |
γl |
+ |
zk and 12Bnl(U)U=γnl.The generalized stresses N are related to the strain for homogeneous and isotropic material by:where D is a symmetrical matrix containing material properties.Neglecting the rotary inertia terms, the kinetic energy is given by:where S0 is the plate’s middle surface, ρ is a density, h is the plate’s thickness and the dot is a derivation with respect to the time ‘t’.Neglecting transverse stress σz under Kirchhoff’s hypotheses, the elastic strain energy V of a plate is given by:, taking into account the damping coefficients and using Hamilton’s principle, the governing equation is obtained in the following form:∫S0t[Bl+Bnl(U)]NdS+CU˙-MU¨=FN=DBl+12Bnl(U)Uwhere M is the mass matrix, F is the external force vector and C is the viscous damping matrix of Rayleigh’s type C |
= |
αM |
+ |
βK (α and β are two parameters and K is a stiffness matrix). in which the unknowns are the displacement vectors, the stress vectors and the frequencies.The considered harmonic excitation is given by:It is assumed that the response of the plate is harmonic and can be written down in the following form:U(t)=∑j=0H-1Ucjcosjωt+UsjsinjωtN(t)=∑j=0H-1Ncjcosjωt+NsjsinjωtNew vectors U¯ and N¯ are introduced, containing all the harmonics and defined by:U¯=Uc0,Uc1,Us1,…,Uci,Usi,…,UcH-1,UsH-1N¯=Nc0,Nc1,Ns1,…,Nci,Nsi,…,NcH-1,NsH-1where “c” denotes the co-sinus factor, “s” the sinus factor and i the harmonic i |
= 0, H |
− 1. and using the harmonic balance method, the system ∫S0t[B¯l+B¯nl(U¯)]N¯dS+ωC¯U¯-ω2M¯U¯=F¯N¯=D¯B¯l+12B¯nl(U¯)U¯where matrices M¯,C¯,D¯,B¯l and B¯nl are derived from matrices M, C, D, F, Bl and Bnl, respectively (see for a definition). The vector F¯ is derived from F and written in the form is cubic with respect to the displacement and frequency, as our objective is to solve it using an asymptotic numerical method, it is written in a quadratic form with respect to an unknown vector (Λ, |
ω, |
Ω):〈LΛ,δΛ〉-ω2〈M¯Λ,δΛ〉+Ω〈C¯Λ,δΛ〉+〈Q(Λ,Λ),δΛ〉=〈F¯,δΛ〉where L(·) is a linear operator and Q(·,·) is a quadratic one defined by the following expressions:〈LΛ,δΛ〉=∫S0tB¯lN¯dS〈Q(Λ,Λ),δΛ〉=∫S0tB¯nl(U¯)N¯dSΛ=t[U¯,N¯]is the mixed displacement–stress vectorΩ=ω2Let us consider a regular solution (Λ0, |
ω0, |
Ω0) of the nonlinear problem , the basic idea of the ANM consists in searching for the solution path in the vicinity of this point, by power series with respect to a path parameter ‘a’:Λ(a)=Λ0+aΛ1+a2Λ2+⋯+anΛnω(a)=ω0+aω1+a2ω2+⋯+anωnΩ(a)=Ω0+aΩ1+a2Ω2+⋯+anΩnwhere (Λp, |
ωp, |
Ωp) is the new unknown parameter to be computed. can be identified as the projection of the displacement increment (U¯-U¯0), and the frequency increment (ω |
− |
ω0), on the tangent vector (U¯1,ω1):where 〈·,·〉 designates the Euclidian scalar product. and equating like powers of ‘a’, one gets the following set of linear problems:Lt(Λp)=∑i=0p-1(Ωp-iM¯-ωp-iC¯)Λi-∑i=1p-1Q(Λi,Λp-i)〈U¯1,U¯p〉+ω1ωp=0As well known, in the literature of ANM, to solve the problems by a classical finite element method, one returns to a displacement formulation using behavior law K¯t0{q1}=ω1[2ω0M¯-C¯]{q0}〈q1,q1〉+ω12=1{N¯1}=[D¯][B¯l+B¯nl(q0)]{q1}Ω1=2ω0ω1K¯t0{qp}=ωp[2ω0M¯-C¯]{q0}+Fpnl〈q1,qp〉+ω1ωp=0{N¯p}=[D¯][B¯l+B¯nl(q0)]{qp}+12[D¯]∑i=1p-i[B¯nl(qp-i)]{qi}︸N¯pnlΩp=2ω0ωp+∑i=1p-1ωiωp-i︸Ωpnlwhere K¯t0 denotes the tangent matrix at the starting point (Λ0, |
ω0, |
Ω0) and {qp} is the discretized form of the displacement U¯p andFpnl=Ωpnl[M¯]{q0}+∑i=1p-1[Ωp-iM¯-ωp-iC¯]{qi}-∫S0t[B¯l+B¯nl(q0)]N¯pnl+∑i=1p-1t[B¯nl(qi)]{N¯p-i}dSNote that the plates are modeled with the classical triangular shell elements DKT So, all unknown parameters of the series can be determined by successively solving Eqs. coincide almost perfectly within the convergence radius, but they diverge out of this zone of validity. This limit can be computed automatically by using the following simple criterion proposed by Cochelin et al. can be improved using rational fractions named Padé approximants {qp(a)}={q0}+∑i=1n-1fi(a)ai{qi}ωp(a)=ω0+∑i=1n-1fi(a)aiωiwhere fi(a) are rational fractions admitting the same denominator. is defined by the maximal value ‘amp’ of the path parameter “a”. The relative difference between the displacements at two consecutive orders must be smaller than a given parameter μ, which leads to:The iterative application of the ANM makes it possible to determine the whole of a complex nonlinear branch.In this part of our study, different examples of plates with various excitation types and boundary conditions are presented. Some of these examples are taken from the literature to validate our method. The material is aluminum with Young’s modulus E |
= 70 × 109 |
Pa, density ρ |
= 2778 kg/m3 and Poisson’s ratio υ |
= 0.3. The plates are modeled with DKT triangular shell elements with three nodes and six degrees of freedom per node (u, |
v, |
w, |
θx, |
θy, |
θz). For symmetry reasons, only a quarter of the plate has been discretized with 121 nodes (i.e. 726 dof for one harmonic). Based on previous studies, the accuracy parameter η |
= 10−4, the truncation order n |
= 15 In order to validate our program, the nonlinear response of an undamped fully-clamped square plate is considered in . The length of the plate is equal to 240 times its thickness, the applied load is assumed to be non-dimensional with an amplitude P0d=0.2. Our results are extremely similar to the ones found in the literature In this section, two isotropic homogenous plates are analyzed. Their geometrical characteristics and the used damping coefficients are given in . The first plate is rectangular with simply-supported boundary conditions and it is subjected to a vertically-distributed harmonic excitation. The second one is a square plate subjected to a vertically-distributed harmonic excitation. It is simply-supported with immovable edges where Mx and My are the bending moments per unit length according to x and y directions, respectively. shows the maximum vibration amplitudes of plate 1, due to a harmonic distributed force with amplitudes of 5 and 10 N/m2, and frequencies around the first resonance frequency. Considering the case of damping coefficients β |
= 10−3 and β |
= 10−4, it can be noted that the present approach gives the same results as those computed by HFEM and shooting methods u(x,y,t)=∑i=1m∑j=1nu2i,j(t)sin2πilxsinπjLyv(x,y,t)=∑i=1m∑j=1nvi,2j(t)sinπilxsin2πjLyw(x,y,t)=∑i=1mˆ∑j=1nˆwi,j(t)sinπilxsinπjLyMx=Eh312(1-ν2)(∂2w/∂x2+ν∂2w/∂y2)=0atx=0,LMy=Eh312(1-ν2)(∂2w/∂y2+ν∂2w/∂x2)=0aty=0,lTherefore, the geometric boundary conditions associated to are exactly satisfied by the expansions of u, v and w given by The asymptotic numerical method is applied to obtain the variation of displacement with respect to frequency. After that, the first generalized component of transversal displacement w11 is compared with that given by previous works (a). It can be noted that our results coincide perfectly with those found in the literature , the responses of fully-clamped plates (CC) and simply-supported plates (SS) are compared. As in the previous section, non-dimensional forces are adopted, and the free response is also computed using the asymptotic numerical method. It appears clearly that the simply-supported boundary conditions yield a larger nonlinear response than the clamped ones.In addition to principal resonances, the present approach makes it possible to obtain higher harmonics resonances. presents the responses of the structures with various harmonics numbers. In these tests, the adopted ANM parameters are: n |
= 20, η |
= 10−4 and μ |
= 10−4 (see Section for more details about the choice of these parameters). It can be noted that with four harmonics, only one higher harmonic resonance is detected for a frequency ω |
≈ 0.3ωl, while the use of six harmonics gives two higher harmonic resonances, the first situated at ω |
≈ 0.2ωl, and the second at ω |
≈ 0.3ωl. Hence, to have a complete study of the geometrical nonlinear response, more harmonics are required. However, the computation time increases with the number of harmonics as detailed in the next section.For the first example, several tests were performed with different truncation orders, tolerance coefficients and excitation frequencies, so as to choose the adequate parameters. An excitation amplitude F |
= 40 N/m2 and a damping factor of β |
= 10−4 were considered. The analysis was performed around the first mode (0 ⩽ |
ω |
⩽ 2ω1). In each test, one parameter was changed to see its influence on the solution’s quality. The harmonic number H |
= 3 was adopted in all these tests. Taking first the tolerance η |
= 10−4, and changing truncation order n (), it can be noted that with the truncation order n |
= 20, one gets smallest steps number and the better final residual. Then, for the second test, taking the truncation order n |
= 20 and changing the tolerance η (), it can be noted that with tolerance η |
= 10−3, one obtains the smallest steps number but a bad final residual. This tolerance can be taken into account and corrective steps added at the end of the computation. η |
= 10−4 was finally adopted for our tests.Based on the results of these test, the following parameters of ANM are selected: truncation order n |
= 20 and tolerance η |
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