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= 1.38006488 × 10−23 |
J K−1) and N is the number of atoms per unit cell.Measurements of the electrical resistivity (at an accuracy of ±1%), the thermopower (at an accuracy of ±2%), and the thermal conductivity (at an accuracy of ±5%) in the temperature range 300–800 K were performed as described earlier To determine the relative density d as a percentage we used Archimedes’ principle for the density dmeas, which we compared with the calculated X-ray density dX-ray using the formulawhere M is the molar mass, Z is the number of formula units per unit cell, N is Loschmidt’s number and V is the volume of the unit cell.The lattice parameters of both starter alloys CayFe4Sb12 and BayFe4Sb12 () agree well with the data reported in the literature: CaxFe4Sb12, 0.9156 < |
a |
< 0.9176 nm . The almost linear compositional dependence of x on the lattice parameter a was then used to determine the filler ratio x from the lattice parameters in all those cases where it was impossible to employ EPMA due to a small grain size. plots the lattice parameters versus annealing time (left) and a close up of the X-ray patterns for Ca0.35Ba0.45Fe4Sb12 (sample A1, right) in the region 68.6° < 2θ |
< 69.8°. The lattice parameters of both phases, the Ba-rich phase (left peak) and the Ca-rich phase (right peak), smoothly fuse together after 28 h at 600 °C and the corresponding X-ray pattern shows a broad peak (e) in which the two phases are hardly distinguishable. After an additional annealing time of 164 h at 600 °C only one slim peak is visible, revealing a single-phase skutterudite with lattice parameter a |
= 0.91825(2) nm (f). This lattice parameter changes only within the error bar after an additional annealing time of 8 h (g) (total annealing time 200 h).After annealing sample A1 again for 4 weeks at 400 °C X-ray investigations interestingly showed two phases with skutterudite structure (h). The lattice parameter of the Ca-rich phase at a |
= 0.91624(3) is almost the same as before hot pressing, whereas a |
= 0.91997(3) for the Ba-rich phase is slightly lower than before hot pressing (see for all lattice parameters). The question was whether or not reversible decomposition had occurred at 400 °C. At that stage backscattered electron images (BSE) and element mapping clearly revealed the presence of two different phase regions. Subsequent heat treatment of sample A1(h) at 600 °C for 672 h produced a single-phase material again (A1(i)) with a |
= 0.91843(3), confirming a reversible phase transformation such as spinodal decomposition.In a second approach the annealing processes were repeated with another piece of Ca0.35Ba0.45Fe4Sb12 (sample A2). A2 was annealed at 600 °C for 120 h and was single-phase with almost the same lattice parameter as sample A1(f) after a similar heat treatment. The X-ray pattern after further annealing at 580 °C for 504 h (A2(n)) showed a Ca-rich and a Ba-rich phase, and further annealing at 450 °C for 200 h (A2(o)) resulted in separation into two skutterudite phases. After one more heat treatment at 600 °C the sample became a single-phase skutterudite A2(p) again, with almost the same lattice parameter as after the first treatment at 600 °C (A2(m)), showing that the transformation was fully reversible (see Sample A3 was prepared by mechanical mixing of Ca0.84Fe4Sb12 (lattice parameter a |
= 0.91686(2) nm) and Ba0.93Fe4Sb12 (lattice parameter a |
= 0.92088(1) nm) in the same way as sample A1. After hot pressing the sample also showed Ca- and Ba-rich phases (A3(a)), which became single-phase (A3(b)) after annealing at 650 °C for 312 h. Rietveld refinement and EPMA revealed a composition similar to that of sample A1, but with a slightly higher filling level Ca0.50Ba0.40Fe4Sb12. After annealing at 620 °C for 200 h it was still single-phase, however, annealing at 600 °C for 200 h resulted in two phases (A3(d)). This phase separation was confirmed after a heat treatment at 400 °C (A3(e)), showing decomposition of a large grain in the SEM image (see ). It should be noted that the sample with a slightly higher filling level (y |
= 0.9) needed a higher temperature (620 °C) to become single phase. shows the constitution of the (CaxBa1−x)yFe4Sb12 alloys with various substitution levels x as a function of the annealing temperature, revealing single-phase and decomposed states, in the form of an incoherent (equilibrium) binodal curve only slightly asymmetrical with respect to x |
= 0.5. The critical temperature was TC |
= 590 ± 5 °C for Ca0.35Ba0.45Fe4Sb12 and slightly higher at TC |
= 610 ± 5 °C for Ca0.50Ba0.40Fe4Sb12 with a higher filling level. Assuming a regular solution for the Gibbs free energy, Eqs. directly yield the interaction parameters α |
= 14.5 (A1) and α = 14.8 kJ mole−1 (A3) from the critical temperatures and the curves for binodal and spinodal decomposition. Despite approximation of the non-ideal heat of mixing by a regular solution term yielding a symmetrical binodal, this simple term describes our experimental data quite well. Only a minor discrepancy exists for the Ba-rich component of the Ca0.35Ba0.45Fe4Sb12 samples (A1(h) and A1(k) at 400 °C), which is associated with a slight asymmetry of the binodal and spinodal boundaries. The data available, however, do not warrant a thermodynamic treatment on the basis of non-regular or more complicated models.The effect of strain energy on spinodal decomposition was estimated from Eq. , which gives a value for the depression of the critical point TC |
− |
T on the spinodal curve. As the elastic parameters we take those measured earlier on a (Ca,Ba)Fe4Sb12 skutterudite: E |
= 120 GPa and ν |
= 0.24 The thermoelectric properties of sample Ca0.35Ba0.45Fe4Sb12 (A1) after different heat treatments are presented in . It is interesting to point out that the thermoelectric properties of sample A1(b) (a mixture of two skutterudite phases after hot pressing) are in the range of values reported for the single phase parent alloys CayFe4Sb12 and BayFe4Sb12) revealed metallic behaviour. The lowest resistivity was observed for sample B (Ca0.46Ba0.46Fe4Sb12 (x |
= 0.5, |
y |
= 0.92)), prepared by adding stoichiometric amounts of Ca and Ba directly to the master alloy, and is attributed to the higher density (97.2%) of this specimen. The resistivity of Ca0.35Ba0.45Fe4Sb12 decreased by about 16% in the single phase state (sample A1(g)), but after annealing at 400 °C returned to the original value when the single phase skutterudite (A1(g)) decomposed into two skutterudite phases (sample A1(h)). After annealing at 400 °C the density of the sample decreased by almost 3%, resulting in a higher resistivity. displays the decrease in average electrical resistivity as well as in the electrical resistivity at 800 K in the single-phase state and recovery when the sample decomposed. Higher resistivities are usually in line with finer grain sizes and, therefore, lie in the range of nanostructured skutterudites, e.g. CayFe4Sb12 and BayFe4Sb12 that the samples exhibit positive Seebeck coefficients, showing that the majority of the charge carriers are holes and that the thermopower increases with increasing temperature. It is notable that the values of the Seebeck coefficient for the single-phase samples (A1(g) and B) are about 20% higher than for microcrystalline CayFe4Sb12 and BayFe4Sb12 shows the highest values for both single-phase skutterudites (A1(g) and B), reaching a remarkably high value of 4.8–5.3 mW cm−1 |
K−1 at 800 K.) increases slightly with increasing temperature, reaching the highest value for sample B, in accordance with its low electrical resistivity. Whilst the thermal conductivities of the single-phase sample (A1(g)) and the sample with two phases (A1(b)) did not differ much, the spinodally decomposed two-phase sample (A1(h)) exhibited the lowest thermal conductivity.The phonon part of the thermal conductivity λph |
= |
λ |
− |
λe was calculated using the Wiedemann–Franz lawwith the Lorenz number L0 |
= 2.45 × 10−8 |
W Ω K−2.The highest values of λph are observed for sample A1(b) with two microcrystalline skutterudite phases, whereas the lattice thermal conductivities of samples B, A1(g) and A1(h) are, within the error bar, the same or much less (The sample with two phases (A1(b)) had the lowest ZT. Although the spinodally decomposed sample (A1(h)) had the lowest thermal conductivity, due to the high electrical resistivity ZT is only in the range of the single phase samples (A1(g) and B), with ZT = 0.80–0.86 at 800 K (). These values are in line with those of nanostructured single filled CayFe4Sb12 or BayFe4Sb12Investigation of double filled skutterudites (CaxBa1−x)yFe4Sb12 using XPD, LOM, SEM and EPMA established a binodal immiscibility gap with the critical point at x |
≈ 0.45 and critical temperatures depending on the filling level y (TC |
= 590 ± 5 °C for y |
= 0.8 and TC |
= 610 ± 5 °C for y |
= 0.9). Due to the small differences in the Ca and Ba parent skutterudite lattices suppression of the spinodal critical temperature due to coherency strain is insignificantly small, TC |
− |
T |
= 15 °C. Spinodal decomposition was found to be an efficient route to produce an ultrafine grain structure in skutterudite materials, which results in favourable thermoelectric properties. The microcrystalline mechanical mixture of CayFe4Sb12 and BayFe4Sb12 (weight ratio 1:1) shows Ca-rich and Ba-rich phases after hot pressing at 600 °C and 56 MPa for 2 h and becomes single-phase after annealing at 600 °C for 200 h. However, at temperatures below TC the solid solution demixes. This spinodal decomposition was not only reversible but was also confirmed by a second series of heat treatments with the same as well as with a new sample. The thermoelectric properties of Ca0.35Ba0.45Fe4Sb12 after different annealing temperatures were compared with the literature data for micro- and nanocrystalline CayFe4Sb12 and BayFe4Sb12.It was found that the single-phase (CaxBa1−x)yFe4Sb12 samples and the sample with spinodal decomposition showed increased thermopower accompanied by a decreased lattice thermal conductivity demonstrating a ZT similar to that observed for nanostructured skutterudites.Effect of carbon nanotubes content on crystallization kinetics and morphology of polypropyleneThermoplastic nanocomposites were prepared in a laboratory mixer using polypropylene (PP) and different amounts of single-walled carbon nanotubes (SWNT) in the range 0.25–2 wt%. The effect of SWNT content on the thermal and mechanical properties and also morphology of the PP/SWNT nanocomposites were studied. The results obtained from nonisothermal crystallization of PP and the nanocomposites, which were carried out using the differential scanning calorimetry technique, showed that not only the overall rate of crystallization of PP increased when SWNT was added to the polymer but also the rate of nucleation was higher and the crystallite size distribution was more uniform for the nanocomposites than for PP. From the optical microscopy studies, it was found that the PP spherulites decreased in size when SWNT was introduced into the polymer and also the mature spherical shaped crystals of PP changed in part to the immature kidney- or bean-shaped crystal forms in the nanocomposites. In addition, the crystallization kinetics was also studied by using isothermal spherulitic growth rate, and the values of nucleation constant, Kg, and end surface free energy, σe, were calculated for PP and the nanocomposites according to Lauritzen–Hoffman theory. The reductions of these two parameters were in agreement with the fact that the rate of crystallization of PP in nanocomposites was higher than that of the pristine polymer.Because of the exceptional electrical, thermal, chemical and mechanical properties of multi- (MWNT) and single-walled carbon nanotubes (SWNT), they have been considered as unique reinforcements for different polymers, and the results obtained by different research groups have been reported in many scientific papers Three methods have been used for incorporation of CNT into a polymer matrix. These are known as (a) melt mechanical mixing; (b) solution mixing or film casting and (c) in-situ polymerization of a monomer onto the nanotubes The main goal of this paper is to explore the thermal and mechanical properties of PP and its nanocomposites reinforced with different amounts of SWNT. The variation of spherulitic growth rate of PP in the nanocomposites at different temperatures has been used to calculate the crystallization kinetics parameters for PP and the nanocomposites. The nature of the impurities or agglomerations observed in the nanocomposites was also studied.The raw materials were obtained from commercial sources. The isotactic PP homopolymer was supplied as the grade Poliran PI0800 by Bandar Imam Petrochemical co. (Iran). The melt flow index and density were 8 g/10 min and 0.902 g/cm3, respectively. The SWNT was provided by Research Institute of Petroleum Industry (Iran). The SWNT was prepared using a chemical vapor deposition (CVD) process, via methane as a carbon source, with a cobalt and molybdenum catalyst system and reaction temperature in the range 800–1000 °C. The maximum length of the SWNT was less than 10 μm.Prior to the preparation of nanocomposites, PP and SWNT were dried in a vacuum oven for 12 h at 80 °C. Melt mixing of the components for the preparation of PP/SWNT nanocomposites was carried out in an internal mixer (Haake Rheomix; HBI SYS90) equipped with a pair of roller-type blades. After dry blending of PP granules with the selected amount of SWNT, the mixture was introduced into the mixer. The rotor speed and temperature were set at 120 rpm and 180 °C, respectively, and mixing continued for 10 min. A control PP sample without the nanotubes was also processed in the internal mixer under the same conditions for comparison. The mixtures were then compression molded in the shape of square plaques (0.5 mm thick) at 190 °C and 10 MPa for 5 min by using a Toyoseiki Mini Test Hydraulic Press (Japan). The sheets then were directly quenched in water at room temperature. The formulations of the nanocomposites are presented in Tensile testing was performed on a MTS tensile machine model 10/M at room temperature. Dumbbell-shaped specimens with 6 mm wide central section and a gauge length of 25 mm were cut from 0.5 mm thick molded sheets. All the tests were carried out at the rate of 50 mm/min. Ten specimens were used to obtain an average and standard deviation for each composition.Melting and crystallization studies were carried out using a Perkin–Elmer (Pyris 1, USA) differential scanning calorimeter (DSC) under nitrogen atmosphere to avoid any oxidation. Each sample of 5 ± 0.2 mg was taken from the molded sheet and encapsulated in an aluminium closed pan. The following procedure was used in nonisothermal conditions to reveal the crystallization and melting behavior. The sample was heated from 50 °C to 210 °C at a heating rate of 10 °C/min, held at 210 °C for 5 min to eliminate any previous thermal history, and then cooled to 50 °C at a cooling rate of 10 °C/min. The samples were kept at this temperature for another 5 min and heated again to 210 °C at a heating rate of 10 °C/min.Transmission electron microscopy (TEM) images were obtained using a Philips CM-200 TEM microscope operated at an accelerating voltage of 120 kV to observe the nanoscale structure of SWNT and the PP/SWNT nanocomposites. Ultra-thin sections of the nanocomposites were prepared by mounting the specimen in an epoxy (Araldite) resin and cutting with a diamond knife using a Riechert ultramicrotome to yield samples with a thickness of 40–80 nm. For SWNT, however, the nanotubes were first dispersed in ethanol by sonication for 1 min and then one drop of the solution was placed on a carbon-coated copper microscope grid for further examination by TEM. The TEM used was also equipped with an energy dispersive X-ray (EDX) analyzer system. Elemental analysis was performed on the impurities and possible agglomerates observed by TEM using this system.Morphology of the samples was examined using a Carl Zeiss Jena (Jenapol) polarized light microscope. A Linkam THMS 600 hot stage with a TMS 92 temperature controller was attached to the stage of the microscope. Thin films (ca. 10 μm thick) of each sample were first placed between two glass cover slips and then inserted into the oven of the hot stage. A television camera and a video recorder were used to record the crystal growth.The results obtained from tensile experiments for PP and the PP/SWNT nanocomposites are presented in . As can be seen, the introduction of SWNT increased the tensile modulus and yield stress of PP by 82% and 27%, respectively. This improvement of tensile modulus and yield stress can be attributed to several parameters, such as the inherent stiffness of SWNT, quality of dispersion, especially at low loading of SWNT, and also some adhesion of the nanotubes to the matrix. It was also found that the maximum tensile modulus and yield stress was achieved when 1 wt% and 0.75 wt% CNT were added to the pristine polymer, respectively. Beyond these values, the tensile modulus and yield stress started to decrease. However, the detrimental effect of SWNT in the nanocomposites became apparent such that SWNT decreased the toughness of the matrix by reducing the strain at break dramatically from about 1200% to less than 15% for the samples containing 1 wt% of SWNT and beyond. This could be related to the low interfacial adhesion between the filler and matrix and also the defects which might be created because of SWNT addition. Because of the high aspect ratio and high surface area of the nanotubes, it seems to be impossible to disperse the SWNT properly when higher amounts of filler are incorporated into a matrix, especially by the melt mixing method. Strain at yield also decreased with increasing amount of SWNT in the matrix.By analyzing the DSC crystallization exotherm of a sample crystallized from the molten state at a given cooling rate, some useful parameters can be obtained by which the nonisothermal crystallization behavior of the sample is described Tp is the crystallization peak temperature. Tonset is the temperature at the intercept of the tangents at the baseline and the high-temperature side of the exotherm and the difference between Tonset and Tp is inversely related to the general rate of crystallization. Si is the slope of the initial linear section of the exotherm, which is a measure of the rate of nucleation. Finally, Δw is the width at half-height of the exotherm peak and is related directly to the crystallite size distribution. The smaller the Δw, the narrower the crystallite size distribution will be. The melting temperatures at peak, Tm, and the enthalpy of melting, ΔHf, of the nanocomposites were both obtained from the DSC melting endotherms. The degree of crystallinity, Xc, was also determined using the following equation where 1 − |
ϕ is the weight fraction of polymer and ΔHfo is the theoretical enthalpy value for a 100% crystalline PP, which is taken to be 209 J/g shows the crystallization exotherms of PP and PP/SWNT nanocomposites. A summary of the nonisothermal crystallization parameters is reported in . All the Tonset and Tp values for the nanocomposites are higher than that of PP and they both increase with the amount of SWNT. At low SWNT content (0.25%), these temperatures increase abruptly. However, there was little increase in Tonset and Tp when the amount of SWNT was beyond 0.25%. The results show that Tonset, Tp and also Tm shift about 10, 11 and 2 °C, respectively, to higher temperatures for the nanocomposites containing 2 wt% of SWNT compared to PP. This can be attributed to the heterogeneous nucleation effect of the SWNT which facilitates the crystallization of PP chains when the nanocomposite is cooled down from a temperature above its melting point Optical light micrographs of the crystals produced by the crystallization of PP and the nanocomposites containing 0.25% and 0.5% SWNT at 132, 146 and 146 °C are shown in , respectively. Since PP has low nucleation density, the size of PP spherulites is large. However, it can be seen that for PP/SWNT nanocomposites the nucleation density of crystals is much higher than that of the pristine polymer. This is in agreement with the results obtained from the DSC experiments in which the TP shifted to higher temperature for the nanocomposites compared to PP alone, proving that the CNT act as nucleating agent in the polymer. It can be noted that not every nanotube can play the role of a nucleus to produce a crystal because in that case we would have seen many more crystals than are observed in the figures. It seems that a minimum size of nuclei stack (agglomeration) or impurities such as catalyst residue is needed to provide nuclei for crystal formation. These figures also show that for the nanocomposites many immature kidney- or bean-shaped crystals are formed along with some spherical shaped crystals in the temperature range studied.The radial growth rate, g, of the PP spherulites was measured at various temperatures for the pristine polymer and the nanocomposites containing 0.25 and 0.5% of SWNT. The results are shown in . The decrease of radial growth rate with temperature was consistent with nucleation controlled growth.An equation was developed by Turnbull and Fisher where g0 is a temperature independent quantity and depends upon molecular parameters. For the case of nucleation control of growth, g0 is also a function of crystal geometry. ΔG∗ is the work required to produce a nucleus with critical size, ΔE is the energy barrier for transport of material across the crystal-liquid interface, and its influence on the temperature dependence of the nucleation process can be neglected at small degrees of undercooling, T is temperature and R is the universal gas constant.Hoffman and coworkers proposed an equation based on the Turnbull and Fisher equation which is usually referred to as Lauritzen–Hoffman theory where Kg is the nucleation constant, T∞ is the temperature below which motions cease and is taken as T∞ |
= |
Tg |
− 30 K, TC is the crystallization temperature, ΔT=Tm0−TC is the degree of undercooling in which Tm0 is the equilibrium melting temperature and f is a factor that accounts for the variation in the enthalpy of fusion, ΔHf, with temperature, and is obtained byThe kinetics of crystallization of PP in its pure state and also in the nanocomposites was analyzed using equation . By rearranging this equation, equation where the n value depends on the crystallization regime according to Lauritzen–Hoffman theory. At regime I and III which occur at low and high under coolings, respectively, n |
= 4. However, at regime II, which occurs at medium undercooling, n |
= 2. σ and σe are the lateral and end surface free energies of the growing crystal, respectively. b0 is the molecular thickness and k is the Boltzmann constant.It was assumed that all the crystallizations were carried out in regime III where α was empirically obtained to be 0.1 and a0b0 represents the cross sectional area of the polymer chain shows the plot of lng+(ΔE/R(TC−T∞)) against (1/fTCΔT) from which the value of Kg can be directly calculated from the slope. Therefore, the value of σe was simply estimated by using equations . In order to plot this figure, the values of a0, b0, Tg, ΔE and Tm0 were taken to be 5.49 × 10−10 |
m, 6.26 × 10−10 |
m, 269.6 K, 6280 J mol−1. As can be seen, both parameters decreased in value with addition of SWNT into PP. These results show that the addition of the nanotubes to PP causes σe to decrease, and also by decreasing the work needed to create a new surface, increases the rate of crystallization of PP in nanocomposites A TEM image of the morphology of raw SWNT is shown in . The CNT are aggregated because of the Van der Waals forces. shows the TEM image of the nanocomposite containing 0.5% CNT. A few dark spots can be seen in the picture, which were examined by EDX in order to find their elemental composition. This showed that they mainly consist of carbon and also cobalt and molybdenum elements which were probably the remnants of the catalysts used for producing the SWNT. It was also found that the dark spots were 5-20 nm in diameter, on average.The thermal and mechanical properties as well as the morphology of the PP reinforced with different amounts of SWNT were studied. The results obtained from nonisothermal crystallization studies revealed that the overall rate of crystallization and also rate of nucleation were higher for the nanocomposites, and they all had more uniform crystallite size distribution compared to the pristine polymer. The morphological studies showed that the nucleation densities of the PP spherulites increased in the presence of SWNT, however, some immature kidney- or bean-shaped crystals were formed in the nanocomposites. The reduction of σe in the nanocomposites with increasing of SWNT content was in agreement with the higher rate of crystallization of PP in nanocomposites compared to that of PP alone. The mechanical properties studies showed that the maximum value of tensile modulus was obtained at 1 wt% and the highest yield stress was achieved at 0.75 wt% SWNT in PP.Reactive compatibilization of poly trimethylene terephthalate (PTT) and polylactic acid (PLA) using terpolymer: Factorial design optimization of mechanical propertiesA reactive extrusion route was employed to compatibilize blends of PTT and PLA by the addition of a random terpolymer of ethylene, methyl acrylate, and glycidyl methacrylate (EMAGMA) and multifunctional epoxy chain extender. Mixed level full factorial design was used to investigate the strength properties of the resulting blends. Using analysis of variance, main and interaction effects of terpolymer, chain extender and screw speed on mechanical properties of the blends were investigated. Multiple linear regression models were fitted and their adequacy was verified by checking residual plots. Most influencing factor for tensile strength was the terpolymer, while the impact strength was significantly affected by all three factors and one of the interaction effects. Phase morphology indicated a two-phase structure in which PLA-EMAGMA phase was dispersed as domains in the continuous PTT matrix. Domain size was found to decrease with the increasing concentration of the terpolymer at higher shear rates. Reduced particle size and interparticle distance was believed to be the main reason behind impact toughening in the blends. PTT70-PLA30/terpolymer (85/15) blends with 0.5 phr chain extender processed at 200 rpm with impact strength of 122 J/m and tensile strength of 44 MPa has been selected as the optimum blend formulation.Global plastic demand is expected to reach 335 million tons by 2020 and by the turn of the century, it could increase to 1 billion tons with growth in human population PTT is a partially biobased engineering thermoplastic polyester produced from condensation of propane diol with terephthalic acid or dimethyl terephthalate. Recent technological breakthroughs have made PTT production economically effective, offering opportunities in textile, carpet, packaging and other engineering applications. PTT has been shown to be a promising engineering plastic with unique combination of properties such as good tensile strength, elastic recovery, fast crystallization rate, electrical insulation, dimensional stability, and chemical resistance while retaining ease of processing Poly (lactic acid), PLA remains one of the most widely researched biopolymers owing to its renewability and biodegradability, in addition to high tensile strength and stiffness. PLA is being blended with other durable engineering polymers to widen the application areas of PLA. Miscibility and thermal properties of PTT and PLA blends have also been recently explored in some of the published work In several other studies, ethylene methyl acrylate glycidyl methacrylate (EMAGMA), a reactive terpolymer with epoxy functional groups has been blended with PLA PTT available under the tradename Sorona® 3301 BK 001 was kindly supplied by DuPont (Wilmington, DE, USA). DuPont™ Sorona® contains 35 wt% renewable resource content derived from corn. Weight average molecular weight (Mw) of Sorona is 56,300 g/mol -lactide content and Mw of 220,000 g/mol Reactive extrusion of PTT, PLA, and terpolymer, with and without chain extender was accomplished in a twin screw co-rotating micro compounder (Xplore®, DSM Research, The Netherlands). A DSM micro injection molder was used to mold test samples. PTT-PLA blend ratio of 70–30 was selected for compatibilization based on preliminary screening of mechanical and thermal properties of PTT-PLA blends at ratios varying in steps of 10 up to 50 wt% PLA. Reactive extrusion temperature was collectively controlled at 250 °C and screw rpm was varied for different formulations based on the standard order suggested by the factorial design of experiments. Polymer pellets in the calculated blend ratio was fed to the extruder and were melt mixed for 2.5 min to facilitate reactive compatibilization. In the following steps, melt mixed hot extrudate was collected through a heated piston cylinder assembly connected to the injection molding machine and the test samples were molded at 30 °C. Injection pressure for injection and holding stages was set at 3 and 6 bar, respectively; total injection time was 20 s. Samples were conditioned for 48 h at room temperature and 50% relative humidity prior to testing.Tensile strength of type IV samples were tested in Instron 3382 Universal Testing Machine (Norwood, MA, USA) according to ASTM standard D638 at 50 mm/min crosshead speed. Notched Izod impact strength of processed blends was measured using 43-02-01 Monitor Impact Tester from Testing Machines Inc. (New Castle, DE, USA) with 5 ft. lb. pendulum according to ASTM standard D256. Average measurement of 6 samples for impact test and 5 samples for tensile test are reported with standard deviations. Fourier transform infrared spectroscopy (FTIR) spectra were collecting using Thermo Scientific Nicolet™ 6700 (Waltham, MA, USA) under an attenuated total reflection infrared mode in the frequency range of 500 cm− 1 and 4000 cm− 1, averaging 32 scans. Scanning electron microscope (SEM) Phenom ProX (Phenom World BV, Netherlands) equipped with a back scattering electron (BSE) detector was used to observe the blend morphology. Impact fractured and cryogenically fractured surfaces before SEM imaging were gold coated using Cressington sputter coater 108 auto under an argon atmosphere for 15 s.Control of processing parameters and additives amount is the key to obtaining a compatibilized blend with optimum level of properties. It is therefore essential to identify the controlling parameters which predominantly determine performance of the blends produced. In some cases, effect of one parameter on the final properties could be different when other parameters are not varied or set at a different value, giving rise to interaction effects. Conventional univariate approach may take a higher number of experiments to find the optimum conditions; if significant interactions are present between the factors, conclusions from these experiments may be unsound or even misleading.Through factorial design of experiments, multiple controlling parameters can be systematically varied to study their effects on the response variable Control Factors: Terpolymer (5, 10, 15 wt%), chain extender (0, 0.25, 0.5 phr), screw speed (100, 200 rpm).Response Variables (y): Impact strength (MPa), Tensile strength (MPa).Control factors established in this study were selected based on preliminary screening experiments. Processing temperature is usually considered to have an effect on the reactive extrusion of the blends. Preliminary experiments revealed the difficulty in extruding PTT at temperatures below 250 °C because of the die zone being at lower temperature than the set barrel (processing) temperature. Preliminary Taguchi design revealed no significant effect when temperature was varied at the levels of 250, 255 and 260 °C in combination with various levels of screw rpm and additives content. There could be several reasons for this observation. Reaction kinetics may not be sensitive to temperature in the above selected range or the interfacial tension was not changed in this window of 10 °C. Properties were beginning to decline when processed at 270 °C indicating possible thermal degradation of the polymers. Therefore, processing temperature was held constant at 250 °C. Chain extender (CE) was added to the blend system mainly to offer melt stability to the polyesters and the maximum loading was limited to 0.5 phr based on preliminary experiments. Maximum screw speed of 200 rpm was selected once the preliminary experiments indicated a drastic decline in properties of the blends processed at 250 rpm. This could be attributed either to the potential increase in internal barrel temperature due to high shear or the opposing nature of dispersion and coalescence effects, this aspect is discussed further in reference to morphology of the blends. Therefore, a full factorial mixed level design with high design resolution was selected for this study. Minitab® software was used to generate and analyze the design of experiments. Design array and the process responses (objective functions) are presented in . Experiments were conducted in randomized order as suggested by the run order in the table to prevent any bias and nuisance factors affecting the processing and testing of blends. Only impact strength and tensile strength were considered as response variable in optimizing the blend formulations.ANOVA can be used to investigate the factors which are hypothesized to influence strength properties. Since there were several factors involved in our experiment, there were also several hypotheses to be tested; three for each of the main factors and one for interaction effect. Null hypothesis (Ho) for each of the main factor is: there is no significant difference in mean strength when the ‘factor’ level is increased. For the interaction factors, null hypothesis, Ho: there is no interaction between the factors. Analysis of variance was performed by comparing the variability between groups (mean squares, MS) to the variability within groups (mean square error, MSE). Assumptions of normality and equal variance (homoscedasticity) are the key requirements for analysis of variance shows the ANOVA for impact and tensile strength. P-values were compared with a α level of 0.05 to determine whether the observed data for each of the factors were statistically significant to reject the null hypothesis. Referring to ANOVA tables, all of the factors had significant effect on the mean impact strength, while only the terpolymer amount was significant for tensile strength. Interactions of the factors did not seem to affect tensile strength but, terpolymer and screw speed interaction did have significant effect on the impact strength. shows main effect of the selected parameters on the impact and tensile strength of the blends. A main effect is the difference between the mean responses of a factor measured in the levels specified. In other words, it is the change in strength properties when the levels of terpolymer, chain extender and screw speed are changed. When the difference between the maximum and minimum values of the average strength corresponding to each factor is higher, the effect of that factor on the resulting properties is higher. As shown in a, terpolymer amount has the most effect followed by screw speed and chain extender in increasing the impact strength. Only terpolymer had a significant effect on tensile strength; varying the chain extender amount and screw speed had no effect on the average tensile strength of the blends.Main effects plot adequately describes the relationship between the factors and the tensile strength of the blends. In the case of impact strength, ANOVA results suggested a strong interaction between terpolymer content and screw speed; hence the interaction plots for impact strength are examined. Interaction here refers to the effect of one factor being dependent on the level of other factor. Each point in the interaction plot shown in depicts the mean impact strength at different combinations of screw speed, terpolymer and chain extender content. Interaction is present between the factors when the lines are not parallel, i.e. slope of the lines is different. Interaction plot of terpolymer and screw speed indicates that processing of blends at a screw speed of 200 rpm seems to have a higher effect on impact strength when the terpolymer content is 20 wt% as the slope of the 200 rpm line is steeper beyond 15 wt%. There were no interactions seen between chain extender and screw speed. Slope of the blends containing 0.25 and 0.5 phr chain extender were different from the ones without them, however these interactions were shown to be of no significance in ANOVA results.Using the data acquisition software of the vertical twin screw extruder, axial force exerted on the material to push it downwards towards the die was measured. Recorded force values are plotted against time in for few selected formulations. This force value is an indirect measure of the melt viscosity of the blends at different conditions; it can also indicate degradation or any other reactions occurring in the blends Advantages of having higher shear rates in the reactive extrusion process is clearly evident from looking at the force curves for PTT70-PLA30/terpolymer (90/10) blend at 100 and 200 rpm. With increase in screw rpm, induction time for compatibilization reactions was reduced and the viscosity was increased. The residence time was however held constant at 2.5 mins to minimize the overall cycle time of the process. Complex flow field in co-rotating twin screw extruder may offer better mixing in less time. Higher shear stress resulting from higher screw speed may increase internal temperature and result in degradation of shear sensitive components. Although PLA is shear sensitive, force curves suggest no potential degradation.Reactive extrusion allows for the generation of in situ copolymer at the interfaces directly during melt blending. As shown through axial force curves previously, reaction between carboxyl, hydroxyl end groups of PTT/PLA and epoxide group of the terpolymer and chain extender proceeds within the time scale of melt processing. Well established reaction scheme compares the FTIR spectra of blends processed at different conditions. EMAGMA terpolymer can be characterized by epoxide ring vibration at 911 cm− 1; CO stretching vibrations at 1105 cm− 1 and 1192 cm-1; –CO stretching vibration at 1734 cm− 1; –CH vibrations at 2851 cm− 1and 2921 cm− 1O carbonyl stretching. PTT shows characteristic peaks at 1504 and 1408 cm− 1assigned to the CC stretching modes, while the peak at 723 cm− 1 is due to CC– stretching at 867 cm− 1 and 955 cm− 1. Peaks at around 1087 cm− 1, 1127 cm− 1 and 1180 cm− 1 are for –CCharacteristic peak for epoxy in oxirane ring (911 cm− 1) were not found in the compatibilized blend as shown in b, this can be assumed to be due to complete consumption of epoxy groups during the reactive extrusion process. Similar observations have been reported by various other researchers to confirm the compatibilization of blends using reactive terpolymers C stretching bonds pointing to the compatibilization reactions are overlapped with the characteristic peaks of the polyesters, however, changes in peak intensities were noticed. A small shift and broadening in the peaks related to the symmetric stretching of the CC bonds was observed in the compatibilized blend as shown in b. Quantitative determination of the epoxide conversion by IR spectroscopy is challenging. It is therefore safe to conclude based on the axial force values that the reaction was not complete within the selected processing time range for certain compositions and the residual epoxy groups present in the blends is hard to detect through FTIR.Morphology has a strong influence on the mechanical, physical and rheological properties of polymer blends shows the morphology of impact fractured PTT70-PLA30 blend, with clear indication of phase separation. Two or more particles of PLA were merging together exhibiting coalescence (shown through arrows in the images). Such sea-island morphology is typical for immiscible blends.Cryogenic fracture surface of selected blends processed at 100 and 200 rpm are show in c display the morphology of these blends with 0.5 phr chain extender at 200 rpm. Electron beam was found to etch away the PLA particles in spite of having a layer of gold coating; this is rather helpful in drawing meaningful conclusions. Reduction in PLA particle size was obvious in blend containing 15% terpolymer when the screw speed was increased from 100 to 200 rpm. After the addition of chain extender, PLA particle size is clearly observed to reduce further. As the amount of terpolymer increased to 20 wt% in the blends, coalescence of the PLA particles were predominant.Reduction in particle size of the PLA is believed to be caused by a combination of different phenomena At higher concentration of compatibilizer, reduction in particle size levels-off and the equilibrium concentration at which it occurs is referred to as critical concentration a. Such observations have also been reported to occur when the number of collisions between dispersed particles resulting in coalescence is higher than the droplet breakage Impact and tensile properties of the neat polymers and uncompatibilized PTT70-PLA30 blend are given in Interfacial adhesion and morphological parameters have interrelated effects on the impact strength. Uniform dispersion of the minor phase in the matrix can be promoted by increasing the interfacial adhesion. When interfacial adhesion is same between the samples, difference in morphological parameters greatly influence the impact strength Tensile strain at fracture, usually called the elongation is a conventional measure of ductility. Although no direct relationship exists between the ductility and performance in service, it serves as a good indicator of changes in formulations or processing conditions. Comparing the percentage elongation of neat polymers, uncompatibilized and compatibilized blends from , we can say the ductility of the PTT70-PLA30 blend is substantially increased with the addition of terpolymer. This could be attributed partly to the process of compatibilization and partly to the mere presence of a third component with higher intrinsic ductility. In the absence of chain extender, percentage elongation was observed to almost double when the screw speed was increased from 100 to 200 rpm. However, with the addition of chain extender such incremental trend was not observed in blends processed at low and high screw speed. This could be attributed to the increased density of crosslinked chains in the matrix resulting from the chain extension effect.On the other hand, increase in terpolymer content causes the blends to yield at lower applied stress. Few possible explanations for such reduction in tensile strength with higher amount of compatibilizer could be put forward. (i) Presence of discontinuities in the phase separated blends merely reduces the cross-section of the matrix available for external load transmission. (ii) After crossing a critical compatibilizer concentration, only part of the terpolymer enters the interface, the rest forms small droplets ANOVA table and factorial plots have assisted in determining which of the factors are important in affecting the strength properties; the next step is to model the effect of these significant factors. Method of least squares is typically used for estimating parameters and model fitting. In general, the response variable, y, can be related to predictor variables by a first order multiple linear regression model,y=βo+β1Ai+β2Bi+β3Ci+…βiAi*Bi…+βiAi*Ci…+βiBi*Ci…+εiThe deviations, εi, are assumed to follow a normal distribution with mean zero and standard deviation s. For regression model in our case, y represents mean strength; βi refers to the regression coefficients. Ai, Bi, and Ci represents the factors terpolymer, chain extender and screw speed respectively. Three different levels of the factors A and B, two different levels of factor C are represented by the subscript i. Only second order interaction terms are included in the model; third order interaction terms are not included on the assumption they are negligible and they are used to get an estimate of the random variation in response variable, strength. Based on the significant factors affecting each of the strength properties, models developed are expressed in In the above models the contrast coefficients for each level of the factor are normalized to make their sum zero. While predicting for one level of a factor other levels for the factor are taken as zero.R2 is a goodness-of-fit statistic determining how well the model fits the data. R2 denotes the percentage variation in the response variable explained by the developed model, it is always between 0 and 100%. Calculated values shown for R2 in are closer to 100% which explains almost all the variability in strength around its mean in the developed models. R2adj is adjusted for the number of predictors in the model. R2pred indicates how well the developed regression model predicts the strength properties for new observations indicate the models can predict valid responses for new observations very well. R2pred for impact strength is lower than the R2; reason for this could be due to higher number of terms in the model. Residual plots in have been used to show the goodness of model fit by checking the normality and equal variance assumptions. Satisfying the assumptions is necessary to produce unbiased estimates of the coefficients. Residuals refer to the difference between the experimental values and fitted or predicted values. Normal probability plot of residuals for tensile and impact strength of blends shown in a and b falls on the straight line indicating the residuals are normally distributed. Residuals versus fitted values plot for tensile and impact strength of blends in a and b shows random pattern of residuals as expected, ensuring the linear model adequacy.Standardized residuals were used as they are better indicators of outliers due to their constant variance as in this case the value of a residual is divided by an estimate of its standard deviation. Standardized residuals greater than 2 and less than − 2 are usually considered outliers. Spread of residual values in the plots fall within this range and on both sides of 0 indicating no outliers in the data collected for strength values at different factor levels. Residual versus order of data plot shown in a and b depicts all residuals in the data collection order. This plot is useful to ascertain the residuals are uncorrelated, no time or space related effects were noticed. Residuals were exhibiting normal random noise and were equally distributed with both positive and negative vales around the horizontal line (residual is 0).Contour plots are used to graphically explore the three-dimensional relationship between variables in two dimensions. In the contour plots shown in , terpolymer and screw speed are plotted on the x- and y-scales and the strength values are represented by contours while holding the chain extender value at 0.5 phr. Analysis in the previous section revealed the terpolymer content to be the only significant factor to affect the tensile strength of the blends, accordingly a proportional decrease in strength can be seen as the terpoylmer content increases. Contours in a clearly show the possibility of achieving impact strength over 160 J/m at screw speed higher than 150 rpm and terpolymer content higher than 18%. Both the contour plots are overlaid in c, the white region is where balanced tensile and impact strength can be achieved. The lower and upper bounds of the optimal values are shown in the legend. Depending on the requirements for a target application appropriate formulations can be selected to achieve desired performance.Response Optimization tool from Minitab software was used to find the global optimum points for each combination of terpolymer, chain extender, and screw speed. Value of 1 was selected to give equal emphasis to the target values of impact strength and tensile strength. Response optimizer works by searching for predictor variable combinations optimizing both the responses by satisfying the requirements set for each of them. Individual desirability (d) for impact and tensile strength are obtained first which are then combined to maximize the composite desirability (D) to provide optimum points of predictor variables. Goal for both impact and tensile strength was set to maximize but a compromise of one variable is required due to the inverse relationship in these properties with increasing content of terpolymer. Optimization of the responses is shown in , the red solid line points to the optimum level; blue dotted line is the maximum average response for impact and tensile strength. Optimum levels predicted for content of additives and screw speed to yield highest impact and tensile strength are 15 wt% terpolymer, 0.5 phr chain extender and 200 rpm for screw speed at a composite desirability of 0.5571.Parameters influencing the reactive compatibilization of PTT70-PLA30/terpolymer blend and the resulting strength properties are modelled using a mixed level full factorial design. This method allowed for the detection of statistically significant variation in mean impact and tensile strength upon varying the content of terpolymer and chain extender, and screw speed. Most influencing factor for tensile strength is the terpolymer, while the impact strength is significantly affected by all three factors and one of the interaction effects. Based on the requirement to strike a balance between the stiffness and toughness of the blends, PTT70-PLA30/terpolymer (85/15) blends with 0.5 phr chain extender processed at 200 rpm has been selected as the optimum formulation. The phase morphology of the developed blends was investigated as a function of screw speed and terpolymer concentration. Morphology indicated a two-phase structure in which PLA phase was dispersed as domains in the continuous PTT matrix. The coalescence behavior was much less prominent in blends having terpolymer. The compatibilzing action of terpolymer was associated with the reaction between the glycidyl epoxy group of EMAGMA terpolymer with hydroxyl and carboxyl group of PTT and PLA leading to the formation of a graft copolymer at the blend interface. The domain size of the dispersed phase was found to decrease with the increasing concentration of the terpolymer at higher shear rates. Reduced interparticle distance was believed to be the main mechanism behind impact toughening in the blends. Appropriate selection of additives and processing parameters in this work has resulted in blends with good balance of properties compared to previous works on PTT-PLA blends.Micro-mechanical modeling of machining of FRP composites – Cutting force analysisOrthogonal machining of unidirectional carbon fiber reinforced polymer (UD-CFRP) and glass fiber reinforced polymer (UD-GFRP) composites is simulated using finite element method (FEM). A two-phase micro-mechanical model with fiber assumed elastic and the matrix elasto-plastic is used to estimate the cutting forces during machining. A cohesive zone simulated the interface debonding between the fiber and matrix. Fiber failure was based on maximum principal stresses reaching the tensile strength. The matrix elastic modulus was degraded to include damage once yield strength was reached. The model assumes plane strain and quasi-static condition. The cutting forces during orthogonal machining were studied both experimentally and numerically for a range of fiber orientations (θ), depths of cut (t) and tool rake angles (γ). The contact forces developed between the tool and the fiber provided a good estimate of the cutting (Fh) and thrust (Fv) forces during the orthogonal cutting process. The failure of fiber is found to be a combination of crushing and bending, with the bending effect becoming more significant as the fiber orientation changes from 90° to 15°.unidirectional carbon fiber reinforced polymerunidirectional glass fiber reinforced polymerstress-opening displacement potential functionwork of separation in tangential directioncharacteristic length in the normal directioncharacteristic length in the shear directiondisplacement jump vector in the normal directiondisplacement jump vector in the tangential directionmodulus of elasticity along the fiber directionmodulus of elasticity across the fiber directiontensile strength along the fiber directioncompressive strength along the fiber directiontensile strength across the fiber directioncompressive strength across the fiber directionFiber reinforced polymer (FRP) composites are widely used in various applications, due to their high specific strength and high specific stiffness. Most of the FRP products are made to near-net-shape; however, postproduction removal of excess material by means of machining is often carried out to meet dimensional requirements and assembly needs. Machining of FRP products is difficult due to their material discontinuity, inhomogenity and anisotropic nature. Also various damage mechanisms such as fiber pullout, fiber fragmentation, delamination, matrix burning, matrix cracking and subsurface damage lead to poor cut surface quality. Compared to the machining of metals, studies on machining of composites are few and limited in number. Also, because of their inhomogeneous and anisotropic nature as also the various possible damage mechanisms, the process of material removal is different from that of machining single-phase material. An experimental work on cutting of UD-CFRP composites was presented by Koplev et al. . Very few researchers have used numerical analysis to investigate the material and machining response during orthogonal machining of UD-FRP composites (The numerical models cited here use an equivalent homogeneous material (EHM) for modeling of orthogonal machining operation and this is probably the prime source of deviation between the experimental and numerical results, especially the thrust force. Nayak et al. The matrix is considered elasto-plastic with isotropic hardening.The matrix undergoes damage and this is modeled by degrading the elastic modulus linearly to failure once the yield strength of the matrix has been exceeded.Debonding at fiber–matrix interface is modeled using cohesive zone model (CZM). GIC and GIIC the energies to fracture in Mode-I and Mode-II determine the debonding rather than strength An experimental and numerical study is performed to determine the cutting forces (Fh, |
Fv) and their variation with depth of cut (t), tool rake angle (γ) in UD-CFRP and UD-GFRP composites with fiber orientation (θ) varying between 15° and 90° with an increment of 15° with respect to cutting direction.The contact pressures (p) at the tool–composite work interface, stresses in the fiber and matrix, their variation with fiber orientation, possible fracture mechanisms of the fiber, damage in the matrix, interfacial debonding and consequent sub-surface damage are calculated numerically and discussed in detail.UD-carbon and glass fiber tapes, epoxy (LY 556) along with hardener (HY 951) are used to prepare specimens by lay-up procedure. The test specimens of 100 mm × 50 mm × 3 mm thick with 4 and 6 ply lay-up with desired fiber orientation (15°, 30°, 45°, 60°, 75° and 90°) were used for orthogonal machining experiments. The fiber volume fraction of the specimen as found to be 60% by Ignition Loss Method (ASTM D 2584). The fiber orientations are defined in clockwise with reference to the cutting direction as shown in . The cutting tool is made up of Solid Tungsten Carbide (Grade K-10) material with different rake angle (γ) at a constant edge radius (r) and relief angle (α). The tool geometry and the process parameters are listed in . The machining of composite specimens was carried out on a CNC machine. The signals of the cutting forces were picked up and recorded at every 0.01 s by a 4-Component Piezoelectric Dynamometer (Kistler Model-9272). shows a typical plot between the unit cutting force (force/unit width) and time for an UD-GFRP composite at θ |
= 60°, γ |
= 10° and t |
= 0.1 mm. The high frequency variation of cutting forces is an inherent characteristic of composites machining due to repeated fiber, matrix failure to form chips. For comparison with quasi-static finite element (FE) results an average of the cutting forces was calculated.The number of parameters during machining of composites is usually large. Besides, the process and tool geometry parameters, non-homogeneous and anisotropic nature of the material and machining direction with respect to fiber orientation are additional variables, which need to be investigated. Therefore, it is quite exhaustive, time consuming and un-economical to determine the desired machining response by experiments alone. Finite element method (FEM) is widely used to predict the machining response of metals and the same technique has lately been extended to composites. The advantage of this method lies in its ability to model the process in close detail and perform a parametric study by suitably varying the input variables.Commercially available finite element analysis software tool ABAQUS v6.5 The properties used during FE simulation are given in . The work material is composed of UD-CFRP and UD-GFRP composites; both the constituents are elastic and brittle. Carbon fibers are transversely isotropic; whereas both epoxy and glass fibers are isotropic. The Young’s modulus of carbon fiber in tension and compression in longitudinal direction is different. In the numerical model, to keep the problem tractable, only region of the work material close to chip formation zone was modeled. The displacements of the bottom of the work piece in both cutting and perpendicular direction were restrained in the FE model. The displacements of extreme left side were also restrained in the cutting direction.To simulate the cutting process the tool was displaced towards the work material. The tool displacement required to generate sufficient stresses in the fiber was unknown prior to the FE simulation. Therefore an iterative approach was used to find the appropriate tool displacement for maximum principal stress in the fiber to reach fiber strength. For understanding the origin and magnitude of cutting and thrust forces one can visualize the machining problem as a contact problem between a rigid indenter with an edge radius and a layered media as shown in a. Contact elements were used to prevent penetration of the tool into the fiber. The portion of the work piece adjacent to the tool is modeled using fiber and matrix separately, whereas, portions away from the tool have been modeled as EHM. Two fibers and three layers of matrix are shown in a and the tool is assumed to be in contact with the first fiber after the first layer of the matrix has been removed by machining. As the tool advances towards the work piece, there is a possibility of fiber–matrix debonding, matrix cracking and fiber breaking.The interface between the matrix and fibers is modeled using zero thickness cohesive elements, which allow for debonding to occur once the interfacial fracture energy between the fiber and matrix is exceeded. The elastic modulus of the matrix is degraded once the von Mises stress in the matrix element exceeds the ultimate strength of the matrix. To observe how far this matrix damage penetrates in the direction of the tool movement, another model with larger number of fibers and matrix layers as shown in b is used. The simulation of machining is initiated by giving a displacement to the rigid tool against the work material along the horizontal axis. Friction between the tool and fiber is assumed as Coulombic in nature and the coefficient of friction is taken as 0.3. Earlier Cohesive zone model (CZM) is a fracture mechanics approach to study the interfacial effects of either dissimilar material or in the same material when these are initially bonded together (Here, δn and δt are the normal and tangential interface characteristic lengths. The interfacial traction vector (T¯) is determined from potential function(ϕ), using the following relation:where (Δ¯) is a displacement jump vector across the surface. As the interfacial surfaces separate, the magnitude of the traction at first increases to a maximum and then approaches zero, as shown in Therefore, the interfacial surfaces tractions can be written as:The normal work of separation, ϕn and the shear work of separation, ϕt can be written as:where e |
= exp(1) = 2.718, σmax and τmax are the interfacial normal strength and tangential strength, respectively. From above, it is clear that CZM can be described by four parameters ϕn, ϕt, σmax and τmax. The solution convergence is very sensitive to the size of cohesive elements at the interface and a number of FE models with different element sizes were tested before finally deciding the element size of 1 μm × 1 μm at the interface. Four noded quadrilateral elements were used through out. The total number of elements in the mesh and solution time change from model to model depending on fiber orientation. The cohesive surface elements were implemented numerically as a user element in ABAQUS The matrix exhibits elastic and non-linear plastic behavior The friction between the cutting tool and fiber plays an important role in the machining of composites. The Coulomb friction law option is applied to the contact pair between the fiber and tool and relative motion (slip) between tool-fiber occurs at the contact point when fiber shear stress along the tool-fiber interface (τ) is more than or equal to the critical friction stress (μp) where ‘p’ is the normal pressure at the same point. For the present micro-mechanics, the coefficient of friction between the tool-fiber interfaces was taken as 0.3 for both UD-CFRP and UD-GFRP composites. However, it is understood that with higher fiber orientation this coefficient of friction will not remain constant at higher speed of machining and at higher normal load.The experimental observation of cutting force variations with different fiber orientation (θ), rake angle (γ) and depth of cut (t) is studied. All the experiments are conducted at constant cutting speed (V |
= 0.5 m/min) and relief angle (α |
= 6°). The cutting force mainly depends on fiber orientation (θ) and depth of cut (t), but is less affected by rake angle (γ) for this set of process parameters and material system. the principle cutting force (Fh) increases with fiber orientation (15–90°) for all depths of cut in both the material system. However, these forces are decreases with increased rake angle (5°, 10° and 15°); similar trend was observer for both the material system. These observations also support the earlier researchers (The contact pressure and frictional shear between the fiber and cutting tool for tool displacements resulting in the breaking strength of the fiber being reached are calculated by FE simulation for a range of fiber orientations. The initial contact point along the fiber from the cutting plane varies with fiber orientation (θ) and for the edge radius (r) of the cutting tool is given by length (L) = |
r[tan(θ/2)] and is plotted in . The contact pressures and frictional shear contribute to the chip release from work material and sum of their components normal to and along the cutting direction provide the thrust and the cutting forces, respectively. The maximum normal contact pressure did not vary much with fiber orientation and was found constant at 1350 MPa, and 1780 MPa for UD-CFRP and UD-GFRP composites, respectively, as shown in . The contact lengths, for various fiber orientations, are different as shown in a and b. For UD-GFRP composites the contact length is almost constant at 11 μm maximum for all fiber orientations whereas in UD-CFRP the contact length decreases from 13 μm to 10 μm as the fiber orientation decreases from 90° to 15°.The comparison of contact pressure and frictional shear distribution between the UD-CFRP and UD-GFRP composites was studied for the case of 90° fiber orientation. For this fiber orientation the tip of the tool moves normal to the fiber and fiber nodes may slip with respect to tool. In UD-CFRP composite both sticking and slipping took place at the tool-fiber interface, where as in UD-GFRP composites only sticking was observed as the critical shear stress at the fiber matrix interface was lower compared to the ‘μp’ value, where ‘p’ is the normal pressure. This phenomenon was true for all the depth of cut and rake angles.The contact forces induced due to cutting tool is a function of contact pressure and contact frictional shear stress. The principle cutting force is an algebraic sum of the horizontal component of forces contributed by the contact pressure and frictional shear stress. Similarly the thrust force is an algebraic sum of the vertical components of forces contributed by contact pressure and frictional shear stress. The principle cutting force increases significantly with increasing fiber orientation for all the depths of cut. From the experiments, it is observed that the principle cutting force decreases marginally with increase in the rake angle for all fiber orientations and depths of cut in both UD-CFRP and UD-GFRP composites. In numerical modeling these variations in cutting force due to change in rake angle could only be noticed for fiber orientations greater than 45°. These variations that are attributed primarily to larger indentation area and therefore bending and wrapping of the fiber around the tool edge in order to remain in touch with the rake face was not observed for lower fiber orientations. Cutting and thrust forces predicted by FE simulations matched well with the experimental results as shown in . It indicates that the cutting and thrust forces are lower in UD-CFRP as compared to UD-GFRP composites. While the thrust force keeps dropping in UD-GFRP for all fiber orientations they tend to reach an almost constant value beyond 60° fiber orientation. also shows the thrust forces predicted by an EHM model (macro-mechanical model) for UD-GFRP composites used by Nayak et al. For the case of 90° fiber orientation with interfacial debonding option the stresses along the fiber are typical of contact problems and are highly compressive in the contact region in both UD-CFRP and UD-GFRP composites. The maximum compressive principal stresses in the glass fiber (f1 in a) are observed on the front side of the fiber and maximum tensile principal stresses (3.59 GPa and 3.4 GPa in carbon and glass fiber, respectively) on the rear side at the interface with the matrix. These maximum principal stress distributions are similar in the two fibers till approximately 15 μm below the point where tool touches the fiber. But below this region the maximum principal stresses in the carbon fiber become compressive whereas they remain tensile in the glass fiber as shown in . This is attributed to the difference of elastic modulii between carbon fiber that is transverse isotropic and glass fiber that is isotropic. The magnitude of the stresses on the front side of the fiber also depends on the bonding at the fiber–matrix interfaces. If the bonding is perfect and no provision for debonding between the fiber and matrix exists then the tensile principal stress in the glass fiber on the front side is 1.4 GPa just above the cutting plane on the tool side and extends up to 10 μm below the cutting plane. However, if cohesive elements are used to represent debonding, this stress reduces to 0.7 GPa. Similar trend is observed with the carbon fiber also. This reduction of maximum principal stress can be attributed to extensive debonding, which occurs at the fiber–matrix interface on the fiber front side, similar trends are observed for other fiber orientations also.The stress distributions provide an indication as to where the fracture could initiate. However, it is very difficult to determine the actual crack path through the fiber. Chai The direction of the maximum principal stresses in the failed elements varies between −15° and +20° with respect to the fiber axis. It is true for both the materials at all the depth of cut and rake angle. This implies that the fiber is likely to break along a plane parallel to the fiber transverse axis, which agrees well with the experimental observation of chip formation process in UD-CFRP composites It is observed from the FE results that for a 50 μm tool edge radius, 100 μm depth of cut and with an imperfect bonding, the tensile principal stresses are highest at 35–40 μm above the trim plane which means that this much length of fiber will always remain uncut. This seems to agree with the experimental observations of Wang and Zhang For fiber orientations other than 90° the tool movement can be resolved normal and parallel to the tool surface. The indentation for the same horizontal movement of the tool is less as the orientation decreases. Also, as the fiber slides along the tool rake surface, the maximum compressive stresses are lower for lower fiber orientations and the location of this maximum compressive stress also shifts as shown in for various time steps in case of 30° fiber orientation (θ), 0.1 mm depth of cut (t) and 10° rake angle (γ) of UD-GFRP composites. The maximum principal stress contours for the case of 45° and 75° orientations are shown in a and b, respectively. It is observed from these that for both the composites the bending stress reaches the failure value before the compressive stress reaches its limiting value and therefore the bending of fiber become a more dominant failure mechanism as the fiber orientation changes from 90° to 15°.The forward movement of the tool can be resolved into a movement normal and along the fiber axis. Since the forward movement depends on the type of fiber material, fiber orientation, depth of cut, tool geometry and coefficient of friction, these factors can also decide the extent of sliding. The sliding results in shifting of the contact zone between the first fiber and the cutting tool.This shifting can be observed clearly for the fiber orientation 15°, 30°, 45°, 60° and 75°. The shifting is largest for 15° fiber orientation whereas for 90° fiber orientation the contact zone spreads over the fiber (front side) on both sides of the initial contact point and is almost symmetric about this point. To observe this phenomenon from the experiments is beyond the scope of this article, therefore, it was simulated using the finite element analysis and compared with chip size obtained from experiments. The results are shown in . These results show that for all the fiber orientation the shifting of the contact zone is more for UD-GFRP composites as compared to the UD-CFRP composites. This is due to the component of the forward movement of the cutting tool in the cutting direction being more in glass fibers for failure to initiate as compared to the carbon fiber. The variation is observed to be more for lower fiber orientations and almost negligible for higher fiber orientation. It was found that the chip size along the fiber direction completely depends on the shifting of contact zone. This size is equal to the distance, along the fiber direction, between the free surface of the work material and middle point of the final contact zone just prior to the fiber fracture.Sub-surface damage below the cutting plane in the work material during the composites machining process was studied. The damage occurred either in the matrix or as an interfacial debonding between the fiber and matrix. The damage in the matrix can be in the form of longitudinal or transverse cracks, and is numerically implemented by degrading the elastic properties once a yielding stress is reached. For interfacial debonding the cohesive elements allow both the initiation and propagation of the crack along the various matrix–fiber interfaces to be observed. Numerical simulations show that for all the fiber orientations, irrespective of tool rake angle and depth of cut, matrix damage rather than the interfacial debonding is the main mode of sub-surface damage. The sub-surface damage is found maximum for 90° fiber orientation and initiates in matrix (m2) behind the fiber in contact with the tool, even before the tool touches the matrix. Subsequently, interfacial debonding occurs at the interface between fiber (f1) and matrix (m1). Both modes of damage continue till the end of the first fiber failure and extend well below the cutting plane.The crack propagates along the interface due to both opening mode (Mode-I Fracture) as well as sliding mode (Mode-II Fracture). The location of crack front is based either on ‘Δn’ and referred to as opening crack location or based on ‘Δt’ and referred to as shear crack location. The time at which for a given node along the cohesive surface ‘Δn’ first becomes greater than or equal to ‘5δn’ defines the opening crack location. The tractions go to zero asymptotically at ‘∞’ and are extremely small for Δn |
= 5δn. Similarly, the time at which for a given node along the cohesive surface ‘Δt’ first becomes greater than or equal to ‘5δt’ defines the shear crack location. At the first fiber–matrix interface as the tool pushes the first fiber away from the first matrix (after the matrix above the trim plane has been machined) opening mode predominates for higher fiber orientations (60°, 75° and 90°) although shear mode is also quite significant. For lower fiber orientations (15°, 30° and 45°) Mode-II is more predominant compared to the Mode-I. This trend is similar in both UD-CFRP and UD-GFRP composites. The variations of interface crack size with orientation at the fiber (f1)-matrix (m1) interface for both UD-CFRP and UD-GFRP composite is shown in . Even though the slipping is observed at the second interface (between f1 and m2), the magnitude of the slipping is smaller than the characteristic length of the cohesive elements and therefore no crack was initiated for any orientation at this interface in both UD-CFRP and UD-GFRP composites.During analysis with the two fiber-three matrix model shown in a and used so far, it was observed that the large number of elements in the matrix underwent damage according to the failure criterion even before the fiber reached the failure strength. To observe how far into the work piece the matrix is damaged a new model with larger number of matrix–fiber layers as shown in b was used. It was noticed for UD-GFRP composites for 90° fiber orientation, although above the cutting plane the matrix damage extended well into fifth layer of the matrix, the damage below the cutting plane was restricted to the third matrix layer as shown in b. Compared to the degradation in second layer (48 μm), the sub surface damage in third layer is much less (11 μm). The sub-surface damage, due to matrix failure, is maximum for 90° fiber orientation which is also observed experimentally in other studies . Irrespective of the rake angle and depth of cut the damage increases as fiber orientation changes from 15° to 90°. The effect of rake angle on subsurface damage due to matrix degradation is not found significant; although, damage decreases with increasing rake angle for all the depths of cut. For the lower fiber orientation (15°, 30° and 45°) the depth of matrix failure is similar in both the composites, but for fiber orientation greater than 60°, matrix failure grows more rapidly in UD-GFRP composites as compared to the UD-CFRP composites.Although the cutting forces are measured from the contact pressure and frictional shear for the range of fiber orientation, depth of cut and rake angle. The mechanism of failure changes with fiber orientation. For the 90° fiber orientation, fiber crushing is predominant than bending. The fiber breaking may be due to the combination of crushing and bending stresses exceeding their corresponding properties of the fiber. For low fiber orientations, bending effect is more significant than crushing. The chip length also changes with fiber orientation even for the same depth of cut, this may be due to changing of initial contact point between the fiber and the cutting tool edge. For the 50 μm edge radius cutting tool, the initial contact point is 50 μm above the cutting plane for 90° fiber orientation, whereas it is only 6.6 μm for 15° fiber orientation. This initial contact point is also varying with other fiber orientation; which is true for all depths of cut and rake angles. Thus it can be suggested that the chip formation mechanism is dominated by a combination of crushing and tensile failure of the reinforcing fiber and the matrix, though isotropic, get influenced by the fiber failure even though it may try to get deform by shear mode.The experiments and simulations were performed on both UD-CFRP and UD-GFRP composites. The mathematical model improved upon an earlier existing model by including elasto-plasticity in the matrix, damage of matrix and fracture mechanics based debonding at the interface. The experimental and numerical investigations provide a better understanding of the origin of cutting forces, matrix damage, interfacial debonding and possible locations of fiber breakage during the orthogonal machining of UD-CFRP and UD-GFRP composites. The micromechanical finite element model is a better representation of the material for cutting process as compared to an EHM model as it explains the mechanism of machining. It provides a good agreement with the experimental cutting and thrust forces for both the material system investigated. The contact pressure varies with fiber orientation and is less effected by depth of cut and rake angle for both UD-CFRP and UD-GFRP composites. For 90° fiber orientation both bending at first fiber second matrix interface and crushing at fiber-tool interface causes fiber fracture in UD-CFRP whereas in UD-GFRP bending is the main failure mode. As the orientation changes from 90° to 15° bending increasingly becomes more significant for both the material system. Sub-surface damage mainly depends on fiber orientation, it is found maximum for 90° fiber orientation in both UD-CFRP and UD-GFRP composites, and is more in the UD-GFRP as compared to the UD-CFRP composites. The chip formation mechanism is dominated by a combination of crushing and tensile failure of the reinforcing fiber. The matrix, though isotropic, get influenced by these maximum principal stresses at the interface, however, the von Mises stresses are more predominant to deform and subsequently fail the matrix before fiber failure.Experimental and theoretical investigation on torsional behaviour of CFRP strengthened square hollow steel sectionCarbon fibre reinforced polymer (CFRP) has been used to strengthen steel members in bending and compression. There is a lack of understanding on behaviour of CFRP strengthened steel beams subject to torsion. This paper presents an experimental study on the behaviour of CFRP strengthened square hollow section (SHS) beams in pure torsion. A set of tests on CFRP strengthened steel specimens under torsion was carried out in which several different strengthening configurations were used. CFRP sheet wrapping consisted of different configurations including vertical, spiral, and reverse-spiral wrapping were used. The results showed that using CFRP could improve the elastic and plastic torsional strength of CFRP strengthened steel beam specimens. The number of layers of CFRP and the strengthening configurations were important factors for the improvement. Based on the measured values of the torsional moment at yielding and at ultimate, the corresponding twists, the torsional behavioural curves and the failure modes of the strengthened beam specimens, useful concluding remarks are presented.Over the last decade, strengthening and retrofitting of existing steel structures has become one of the important challenges for civil engineers. Fibre reinforced polymer (FRP) has a great potential to meet such challenges Several researchers have reported employing CFRP for strengthened thin-walled steel structures such as flexural strengthening An experimental program was therefore set up in this study in order to gain an understanding of the behaviour of square hollow section (SHS) beams subject to torsion load. In this paper the experimental procedure including detail of specimens, test setup and the results obtained are explained. Influence of the important parameters that may affect the behaviour of the strengthened specimens are also elaborated.The type of used steel is mild steel, and its measured elasticity modulus is 200,000 N/mm2. They are hot-formed SHS. Dimensions of the section are presented in . The dimensions and material properties of SHS steel section are given in The type of CFRP sheet used in the tests is SikaWrap®-200C with unidirectional woven carbon fibres fabric. The properties of the used CFRP sheet are shown in . The epoxy used in this research was provided by the same supplier. This epoxy is used for a SikaWrap®-200C which is called Sikadur®-330 (Six steel beam specimens with the SHS used in this study were produced in Malaysia. Four beam specimens of them (shown in ) were strengthened using CFRP at the laboratory of University of Malaya and were tested under pure torsion. The length of all the beam specimens was 1400 mm and the test region length was approximately 1160 mm.Two specimens without strengthening scheme were designed as the control beam specimens. They were called Type 1. The rest beam specimens were strengthened by carbon fibre in different configurations. Four types of strengthening configuration were used in this study. Type 2 was wrapped with five layers of CFRP vertically with respect to the longitudinal axis of the specimen. Type 3 was wrapped with two layers of CFRP reverse-spirally with respect to the longitudinal axis of specimen. The strengthening configuration of Type 4 was a combination of three layers of CFRP reverse-spirally and one layer of CFRP spirally wrap with respect to the longitudinal axis of specimen. The strengthening configuration of Type 5 was a combination of two layers of CFRP spirally and two layers of CFRP reverse-spirally wrap with respect to the longitudinal axis of the specimen. A schematic view of the different types of strengthening configurations is shown in The first step was to have the surface preparation process which was completed before applying the CFRP wrap. The surface of the beam specimens was removed from the galvanised coating and any oil, rust, paint, and impurities using grinding. The tube surface was then cleaned using acetone before applying adhesive. For applying CFRP wrap on the surface of the specimens, the two components of the epoxy were mixed according to the weight ratio given by the manufacturer. The mix ratio was 4:1 by volume of component A to component B. The epoxy was applied onto the surface of the beam specimens using a brush. It was then spread using a paint brush. After applying the epoxy, the CFRP sheets roller was used along the direction of the fibre to remove excess adhesive and air bubbles (). The specimens were kept at room temperature for one week.The torsion testing rig comprised of a fixed grip and a pivoted rotating grip, between which a length of specimen could be caused to twist about its longitudinal axis (). The apparatus was designed to function correctly and safely up to a torque of 10,000 Nm. All tests were controlled and data were collected using computer U60 software which displayed the result in the form of a graph plotting the torsion load vs. torsion angle under the specified parameter conditions. This machine is used to carry out torsion test steel or concrete specimen or other rod specimen and designed in accordance with client's requirements.In this study in order to improve the visibility of the distribution of stress, the control beam specimen was coated with a lime wash (also a primitive form of brittle coating) so that the dark coloured lines show up against the white background Using the rosette strain gauge mounted on one of surfaces of the steel control beam specimen (at the middle of the specimen length), the strains were monitored. shows torque–strain curves for the control beam specimen. The curves in this figure are plotted based upon the strain in strain gauges no. 1, 2, 3, 4 and 5. shows the yield and ultimate torque values for the control beam specimen. The yield and ultimate torques were 2643 Nm and 2782 Nm, respectively (b shows configuration of the strain gauges on surface of the control beam. It can be observed in a and b that the values of strains corresponding to the strain gauges no. 3, 4 and 5 are close to zero. These values can be attributed to pure shear stresses. When a beam is subjected to a pure torsional moment, normal stresses are negligible in longitudinal and transverse directions of the beam. The shear stresses can be caused principal stresses in direction ±45° with respect to the longitudinal axis of the beam. The strain gauges no. 1 and 2 are in direction ±45° with respect to the longitudinal axis of the control beam. shows the experimental results in terms of the torque versus strain of CFRP sheets. In this figure, typical torque–strain curves for the strengthened specimens with different strengthening configurations are plotted. By qualitative study of , it can be seen that for a given torque, strain levels of strengthened specimen Type 5 is less than those of specimens Type 3 and Type 4 in the plastic region. For Type 2, negligible strain is recorded in the elastic and plastic region.Investigating the torque–twist angles throughout the tests for all specimens was another goal of this experimental study. The values of twist angle versus the applied torque are presented in , the difference observed in the initial stiffness of the specimens can be attributed to a less-than- perfect fixed condition achieved in the setup. The authors believe that such difference does not substantially affect the result of the torsional strengthening of the specimens., three different zones can be seen on each curve. The first zone represents the torsional stiffness of un-yielded specimen, the second zone represents the stiffness of the yielded specimen and the last zone corresponds to the damaged cross-section with yielded torsional steel and ruptured CFRP sheets., the torque–twist curves for all specimens are linear with a constant slope until yielding. After yielding, the torsional stiffness decrease significantly while affected by volumetric ratio and orientation angle of CFRP sheets.The best orientation angle for fibres is in direction of the principal tensile stresses. Therefore, spirally CFRP wrap is the best strengthening configuration. also shows that the strengthened specimens Type 4 (RRRS) and Type 5 (SRSR) provide much higher ultimate torque comparing to the specimens Type 2 (V5) and Type 3 (RR). The reason of deficiency of the strengthened specimen Type 3 in comparison with specimens Type 4 and Type 5 is that the orientation angle of fibres is almost in direction of the principal compressive stresses. For specimen Type 2, since the fibres direction is perpendicular to the longitudinal axis of the specimen, so it cannot sustain much higher load than specimen Type 1 (the control beam).A combination of spiral and reverse-spiral CFRP wraps could be useful to resist cyclic torque caused by earthquake. In this study, specimens Type 4 and Type 5 were strengthened with combinations of spiral and reverse-spiral CFRP wrap around the specimens. For specimens Type 4 and Type 5, the gain in ultimate torsional capacity is 59.7% and 60.4% compared to the control specimen, respectively. shows the strengthened beam specimen during the test. For all the strengthened beam specimens, the ultimate torques along with their increase percentage comparing to that of control beam specimen and modes of failure are listed in shows the failure modes for all the strengthened specimens. In specimen Type 2, splitting of the CFRP occurred in the direction perpendicular to the longitudinal axis of the specimen, (Which is parallel to the CFRP direction). It is due to deficiency of the strengthening configuration. In this specimen, the CFRPs cannot sustain the additional applied torque compared to the control specimen. For specimens Type 3, Type 4 and Type 5, CFRP rupture occurred and eventually failures followed by yielding in the specimen body. CFRP rupture occurred in direction of the principal tensile stresses.In this section a proposed method for determining plastic torsional capacity of SHS are presented. The plastic torsional capacity (Tpl) for a box section can be determined by taking into account the flow of uniform plastic shear around the cross-section, given aswhere t is thickness of the SHS, τ is the shear stress which is equal to 0.6fy and fy is the yield stress of the SHS. Ah is the enclosed area (where rext is external corner radius, rint is internal corner radius and rm is the mid-corner radius given byWhen CFRP is applied, the proposed method considers equivalent thickness approach. The CFRP thickness can be equivalent to steel thickness as given bywhere ECFRP is Young's modulus of CFRP and Esteel is Young's modulus of the steel, n is the number of layers and tfibre is the thickness of the fibre. b shows the dimensions of the equivalent SHS with CFRP, then the equivalent dimensions becomeAh,eq=(b−2rext)(heq−teq)+2(h−2rext)rm,eq+πrm,eq2Then, the torsional capacity, Tpl can be calculated by using Eq. ). The value τ should be increased because of the strain hardening. The extreme case will be 0.6 fu where fu is the ultimate tensile strength of steel SHS. Thus torsional capacity of the strengthened beam with CFRP is given byThe calculated torsional capacity for Type 3, Type 4 and Type 5, where fibre direction is along the shear direction are presented in . By comparing the experimental results and the calculated values using the simplified expression, it was found that the values are in good agreement. It should be noted that the strengthening scheme using vertical fibres alone was found not efficient. Therefore no predictions are included in the paper for this strengthening scheme.Based on the limited tests on the SHS steel specimens strengthened using CFRP, the following conclusions can be drawn:The ultimate torques of all strengthened steel specimens are greater than that of the control specimens. The increase in magnitude depends on CFRP's reinforcement ratio and the strengthening configuration.The best orientation angle for fibres is in the direction of the principal tensile stresses. This direction is related to spirally wrap configuration. Using this configuration, CFRP contribution to ultimate torque is greater than that of the strengthened specimens with vertical orientation of CFRP.In order to resist cyclic torque, the best orientation angle for torsional strengthening of steel structures is combination of spiral and reverse-spiral CFRP wraps.For strengthened specimens with the same volumetric ratios of CFRP reinforcement (Type 4 and Type 5), the torsional resistance increases as the strengthening configuration is changed from spirally-reverse wrap to spirally wrap.The proposed method of the torsional capacity prediction is in good agreement with the experimental results.Machine learned metaheuristic optimization of the bulk heterojunction morphology in P3HT:PCBM thin filmsWe discuss results from a machine learned (ML) metaheuristic cuckoo search (CS) optimization technique that is coupled with coarse-grained molecular dynamics (CGMD) simulations to solve a materials and processing design problem for organic photovoltaic (OPV) devices. The method is employed to optimize the composition of donor and acceptor materials, and the thermal annealing temperature during the morphological evolution of a polymer blend active layer composed of poly-(3-hexylthiophene) (P3HT) and phenyl-C61-butyric acid methyl ester (PCBM), for an increased power conversion efficiency (PCE). The optimal solutions, which are in qualitative agreement with earlier experiments, identify correlation between the design variables that contributes to an enhanced material performance. The framework is extended to multi-objective design (MOCS-CGMD) to attain a Pareto optimality for the blend morphology, and enhance concurrently the exciton diffusion to charge transport probability and the ultimate tensile strength of the material. The predictions reveal that a higher annealing temperature enhances the exciton diffusion to charge transport probability, while a PCBM weight fraction between 0.4 and 0.6 increases the tensile strength of the underlying blend morphology.Polymer-based materials have been employed for organic photovoltaic (OPV) applications due to their low-temperature solution processability, inherent flexibility and environ-friendly synthesis and electricity generation Intractable (a.k.a. black-box) objective functions are difficult to optimize using gradient based algorithms such as gradient descent or conjugate gradient We integrate the CS scheme with classical CGMD simulations to optimize representative design parameters such as composition of donor and acceptor materials and thermal annealing temperature for targeted properties. The results from the CGMD simulations of a typical solvent-free mixture of poly-(3-hexyl-thiophene) (P3HT) and phenyl-C61-butyric acid methyl ester (PCBM) that compose the BHJ morphology provide feedback to the CS scheme iteratively to facilitate the search for the optimal solution. The CS-CGMD method, discussed herein, is extended to a bivariate and multi-objective optimization scheme (MOCS-CGMD) based on the CS-MD framework established in a previous effort The original CS single objective optimization At a given time, a cuckoo lays one egg and deposits it in a random nest.The best nest consisting of a high-quality egg (solution) is passed on to the next generation.An alien egg is discovered by a host bird with probability pa∈[0,1]. If the host bird identifies an alien egg it will get rid of it by either abandoning the nest or evicting the egg out of the nest. The total number of nests in each generation remains constant.The MOCS with N different objectives can be achieved by adapting the first and third rules At a given time, each cuckoo lays N eggs corresponding to N possible solutions and deposits them in a random nest.Each nest will be discarded with probability pa∈[0,1] and a new nest with N eggs will be generated.CS leverages the efficient global Lévy flight mechanism whose step length is determined from a Lévy distribution, Ls,λ=λΓλsin(πλ2)πs1+λ,s≫0 where Γλ is the gamma function. Consequently, the global random walk is represented as xit+1=xit+αL(s,λ) where α > 0 is the step-size scaling factor related to the boundary of the defined design landscape and xit+1,xit are eggs (solutions) from the consecutive generation. On the other hand, the progression of nests by local random walk is represented as xit+1=xit+αs⊗H(pa-ε)⊗(xit-xkt)where Hx is a Heaviside function, εis a random number, xit,xkt are solutions selected from random permutations and ⊗ represents entry wise product. We select the switching parameter pa = 0.2 as the convergence of the CS optimization has been found to be minimally dependent on the choice , involves optimizing one or more design variables for the targeted property such as the exciton diffusion to charge transport probability of a thin film active layer morphology. During each optimization generation, the CS-CGMD scheme compares different solutions amongst the different nests and retains a fraction of the best candidates. All the ill-performing solutions are replaced with newer alternatives from global and local explorations in the design space leveraging the efficient Lévy flights to eliminate the local saddle points.Nevertheless, predictions from a large set of computationally-expensive CGMD simulations remain unutilized during the metaheuristic search. Inspired by the promise of machine learning (ML) in the device optimization , supervised learning is employed using SVR libraries implemented in Scikit-learn . Nonequilibrium simulations are employed to model the mechanical deformation of thermally annealed BHJ blend under a constant velocity of deformation boundary condition along the longitudinal (x-) direction , following the recently developed protocol in our earlier effort The objective functions in our CS-CGMD optimization algorithm is implemented from the evaluation of exciton diffusion to charge transport probability (P) and ultimate tensile strength (UTS). The molecular trajectories from the CGMD simulations are utilized to analyse the exciton diffusion to charge transport probability (P) and the UTS of the BHJ morphology under constant deformations. Exciton diffusion, charge dissociation and charge transport in BHJ layers depend on three key morphological features, viz., average domain size, interfacial area and percolation ratio. Despite the low photon absorption in fullerene-based acceptors relative to the donor P3HT phase, we assume all of the solar energy absorbed by both donor and acceptor phases can generate excitons. The exciton diffusion to charge transport probability can be defined as,P=Pdiff∗Pdiss∗Pperc, where the probability of exciton diffusion Pdiff=1Nbox∑ve(-dεexciton), probability of charge dissociation Pdiss=AintVbox∗tint, probability of charge transportPP3HT and PPCBM are the corresponding percolation ratios of P3HT and PCBM phases, while d, SA and SCare respectively the shortest distances that an exciton needs to travel until it reaches an interface, a hole needs to travel to reach the anode, and that an electron needs to travel to reach the cathode. εexciton, εh and εe are diffusion lengths of exciton, holes and electrons, respectively; Aint and tint are interfacial area and interface thickness; Vbox is volume of the simulation box and Nbox is the number of voxels after discretizing the simulation box by finite element scheme A feature importance analysis based on results from our earlier efforts A, reveals relative impact of the different design parameters on the exciton diffusion to charge transport probability. The results suggest that PCBM weight fraction is perceived as the most influential quantity affecting the morphology with ~ 60% overall contribution followed by the annealing temperature (~30%). Hence, optimizing the PCBM weight fraction and annealing temperature to establish the processing to performance relationship through the CS-CGMD framework is the key design problem. Here, the coupled CS-CGMD scheme is evaluated for three different optimization problems in accord with the parameters listed in . First, we implement the univariate CS-CGMD method where the PCBM weight fraction is optimized for enhanced exciton diffusion to charge transport probability. The results presented in B show an increase in exciton diffusion to charge transport probability over the several optimization generations. The globally optimal solution for PCBM weight fraction ~ 0.45 is obtained after 7 CS generations. Each objective function evaluation involves a complete CGMD simulation, where for a given PCBM weight fraction, a BHJ morphology is evolved from a ternary mixture following solvent evaporation and thermal annealing procedures. For the one-dimensional univariate problem, ~ 40 objective function evaluations are performed before the global optimum is attained. Likewise, annealing temperature also has a pronounced effect on the morphology due to molecular rearrangements of the donor polymers upon annealing C-D present results from a bivariate (2-dimensional design space) optimization problem where PCBM weight fraction and thermal annealing temperature are concurrently optimized for the targeted exciton diffusion to charge transport probability (in principle when the probability approaches ~ 1.0, the PCE approaches ~ 100%). We compare the effect of the number of nests (n) on the overall performance of the CS optimization, by executing simulations with n = 5 and 10. While the ensuing effect on the efficiency of the traditional CS-CGMD method is inconclusive, the convergence of the ML-guided CS-CGMD scheme to the global optimum is accelerated with n = 10. The data-enabled global convergence is attained within 35 objective function evaluations, outperforming the traditional CS-CGMD scheme. For the bivariate optimization problem, the ML-guided CS-CGMD predicts an optimum PCBM weight fraction (~0.48) and thermal annealing temperature (~450 K) that effectively enhances the performance by ~ 10% from the optimum solution obtained from univariate analyses. Although the correlation between the design space and the underlying morphology is complex, we note that the global optimum determined from the ML-guided CS-CGMD concurs with earlier experimental reports Subsequently, we extend our data analytics model to a multi-objective optimization problem enabled by the MOCS algorithm (i.e., MOCS-CGMD) portrays the progression of two objective functions during the MOCS-CGMD optimization generations.A illustrate the convergence of ultimate tensile strength to attain the global solution while the charge transport probability is compromised. On the other hand, in E the trend in the progression is completely reversed due to the trade-off between the two objective functions. The approximated Pareto front generated by 5 subservient solutions after 10 generations of optimization run, leading to ~ 500 objective function evaluations, is shown in A. Predictions from the SVM assisted model over 10 generations of MOCS runs reveal the Pareto optimality situation. We find that no individual solutions from the Pareto front can be considered as the global optimum for one of the targeted properties without compromising the other. B-F illustrate the converged ROIs on the 2-dimensional design landscape for different combinations of the targeted objective as a function of PCBM weight fraction and annealing temperature. When mechanical strength is prioritized, in lieu of the exciton diffusion to charge transport probability, as the desired objective function (B), the global optimum is identified around PCBM weight fraction between 0.4 and 0.6 and annealing temperature ~ 340 K. In contrast, when the exciton diffusion to charge transport probability is considered as the preferred objective function (F) suppressing the need for an enhanced tensile strength, the global optimum migrates around new ROI (PCBM weight fraction < 0.5 and annealing temperature ~ 420 K).The predicted trends intuitively correlate to the molecular arrangements of the annealed polymers. With an increase in annealing temperature, the polymers tend to align themselves with each other enhancing the crystallinity and hence the overall charge transport through the blend. Although the crystalline domains inside a pure P3HT phase tend to increase the ultimate tensile strength, P3HT:PCBM blend exhibits increased strength until the PCBM weight fraction approaches a threshold ~ 0.6 C-E reveal the migration of the ROIs and the global optimum when the objective functions are prioritized according to their corresponding weights. Based on these results, it is evident that an ideal OPV BHJ layer comprises of a trade-off between the performance and mechanical strength, which necessitates a robust predictive modeling to establish PSP relationship across the vast landscape of design parameters.In summary, we employ CGMD simulations coupled with the metaheuristic Cuckoo Search optimization (CS-CGMD) to correlate solution processing parameters with the morphological evolution consisting of electron-donor P3HT and electron-acceptor PCBM molecules. A ML-guided approach to augment the traditional CS-CGMD is observed to significantly enhance the convergence of the 2-dimensional design space to attain the global optimum solutions. Based on the success of the ML-guided approach in contrast to the traditional optimization scheme, we extend the machine learned metaheuristic search algorithm to define a multi-objective optimization framework leveraging CGMD simulations (MOCS-CGMD) on the fly, to attain faster convergence to the global solution. Results from the optimization run based on ~ 500 objective function evaluations reveal a Pareto optimality situation consisting of subordinate solutions. While an increase in annealing temperature is observed to enhance the exciton diffusion to charge transport probability, a PCBM weight fraction between 0.4 and 0.6 is recommended for increased tensile strength of the underlying blend morphology. Thus, the SVM assisted MOCS-CGMD optimization framework, implemented in this investigation, demonstrates remarkable capability to identify complex correlations of the vast design landscape with the targeted properties and can be integrated with high-throughput framework for novel materials discovery to accelerate the design of efficient organic solar cells and quasirandom nanostructured materials.Joydeep Munshi: Methodology, Coding, Computational modeling, Manuscript preparation. Wei Chen: Discussion of results, Manuscript editing. TeYu Chien: Discussion of results, Manuscript editing. Ganesh Balasubramanian: Conceptualization, Supervision, Review and Editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Supplementary data to this article can be found online at The following are the Supplementary data to this article:Role of isothermal omega phase precipitation on the mechanical behavior of a Ti-Mo-Al-Nb alloyThe formation and the evolution of the athermal and isothermal omega phase precipitates in a commercial metastable β–titanium alloy, β-21S, under controlled heat treatments, and its consequent impact on tensile properties has been presented in this paper. The structural and compositional changes of the omega precipitates have been tracked using SEM, TEM, and atom probe tomography (APT). Upon quenching from above the β-transus, the microstructure consisted of a single phase β without any discrete athermal omega precipitates and this condition exhibited the highest tensile ductility. Following β -solutionizing, when the samples were aged below the omega solvus temperature, there was an increase in the size scale of the omega precipitates with increasing time period. The larger and more solute-depleted omega precipitates, resulted in increased tensile strength and reduced ductility. The details of the deformation behavior were further analyzed using electron backscattered diffraction (EBSD) and TEM. Two different modes of deformation were noted in the system, depending on the initial microstructure. While the single phase condition (β solutionized sample) exhibited deformation occurring mainly via (110)β slip, the presence of larger isothermal omega precipitates in the aged condition (β solutionized + 350 °C/100H) resulted in the activation of not only (110) β slip but also (112) β slip. The reasonably high tensile ductility noted in this aged condition has been attributed to the activation of both these slip systems.Owing to a richness in their microstructural features, a unique combination of high specific strength and ductility, excellent hardenability, good fatigue performance, and corrosion resistance makes beta (β)-titanium alloys a viable candidate for many applications, including aerospace, automobile, and orthopedic implants []. A number of researchers have worked on understanding and improving the microstructural features, and their subsequent influence on the mechanical properties of these alloys, either by changing the alloying elements or via a series of thermomechanical treatments []. The mechanical properties of these β alloys depend a lot on the precipitate phases forming in them, namely the metastable omega (ω) phase and/or the stable alpha (α) phase []. The size scale, morphology, and the volume fraction of these precipitates influences the physical and mechanical properties. It is therefore important to understand the formation, growth, and the mechanical behavior of these precipitate phases. While most of the work in literature has focused on α formation and its influence on the mechanical properties [], not much has been reported in terms of the microstructural and mechanical features of ω phase based microstructures []. The present work focuses on understanding the evolution of the ω phase and its subsequent influence on the mechanical behavior of the alloy.The ω phase can form either when quenched from the high temperature β phase or under high pressure []. This phase has been observed extensively in titanium, zirconium, and hafnium alloys, wherein the ω phase formed under high pressure is a stable phase, while the former is metastable in nature []. Two types of ω phase are present in the titanium alloys; athermal and isothermal ω. As the names suggest, while the former forms via a diffusionless transformation mechanism when quenched in from above the β transus, the latter forms when there is a solute diffusion-taking place due to the effect of temperature. For the formation and growth of the isothermal ω phase, the samples are usually aged below the ω solvus temperature. Depending on the alloying elements, the isothermal ω precipitates are either cuboidal or ellipsoidal in nature []. When the misfit between the ω phase and the β phase is large, cuboidal precipitates are formed, like in the case of Ti-V systems []. Conversely, the Ti-Mo system, wherein there is a lower misfit between the two phases, ellipsoidal ω formation takes place []. Non-uniformly distributed plate-like ω have also been reported in previous studies. These plate-like ω precipitates are usually noted to form under mechanical loading [The initial interest in the study of ω phase, since its discovery by Frost in 1954, was due to its deleterious effects on the mechanical properties. Gysler et al. and Williams et al. did the first comprehensive study on binary Ti-V and Ti-Mo alloys []. Later on, Banerjee et al. studied the mechanical behavior of Ti-Mo system with ω precipitates at both room and elevated temperature and noted considerable changes in the mechanical behavior, depending on the volume fraction of the ω phase, and the temperature at which the test was conducted []. Recent work by Sun et al. shows that if carefully controlled, the ω precipitation can be very beneficial in terms of both strength and ductility. Using low temperature annealing techniques, a controlled precipitation of the ω phase was obtained, where in a TWIP/TRIP effect leads to enhanced ductility []. The ability of an alloy to TWIP/TRIP depends on the β phase stability. While dislocation slip dominates the deformation in near β and β stabilized alloys, twinning is the more common phenomenon in less stabilized alloys [The present work involves β-21S a heavily β-stabilized alloy where in a controlled growth of ω was studied, both in terms of structural and compositional evolution, and their influence on the mechanical behavior []. It is a metastable β titanium alloy developed by TIMET in 1988 to satisfy the need for a titanium alloy with good high-temperature behavior. Though initially developed for metal matrix composites on the NASP, the alloy's unique combination of high ambient strength, producibility, good elevated temperature properties, and extraordinary environmental degradation resistance has proven useful for both civil and military aero-engine exhaust components [Sheets of β-21S, ~1.22 mm thick, were provided by the TIMET Company. Nominal composition of this alloy was Ti-15Mo-3Nb-2.7Al-0.2Si wt. % or Ti-9Mo-5.4Al-1.6Nb-0.3Si in at. %. Same stock was used for all the experiments in the present study. The samples were first heat treated above the β transus temperature of β-21S, at 1173K (900 °C), for 30 min followed by water quenching. The choice of β solutionizing temperature was guided by the work of Chaudhuri et al. []. As such, β solutionizing was the first step for all the heat treatments. The samples were further subjected to isothermal annealing at 623K (350 °C) for periods ranging from 0H to 100H. The schematic of all these heat treatments has been shown in All samples were investigated in detail using scanning electron microscopy (SEM) carried out in a FEI NovaNano SEM 230 TM instrument operating at 20 kV. Transmission electron microscopy (TEM) was carried out in a FEI Tecnai F20-FEG TEM operated at 200 kV. In addition, nanometer-scale compositional analysis of the same samples was done using 3D atom probe tomography (APT) in a local electrode atom probe (LEAP™) system from Cameca Inc. SEM samples were prepared by conventional mechanical grinding and polishing routes. TEM samples were also prepared via conventional routes, consisting of mechanical thinning and polishing of 3 mm diameter discs, followed by mechanical grinding of the central region of these discs using a Gatan 656 Dimple Grinder™, and finally ion-beam milling was done using Gatan 691 Precision Ion Polishing System to electron transparency. To avoid oxygen contamination TEM foils were extracted away from edges from the samples. Site-specific samples for deformed studies were obtained via a dual-beam focused ion beam (FEI FIB-Nova Nanolab 200). For APT analysis, samples were prepared using the dual-beam focused ion beam (FIB-Nova Nanolab 200 system) from FEI. Subsequently, these samples were used for APT studies, carried out in a LEAP™ 3000 HR microscope. All atom probe experiments were carried out in the electric-field evaporation mode at a temperature of 50–60 K, with an evaporation rate of 0.5–1.0% and a pulsing voltage at 20% of the steady-state applied voltage [Dog-bone shaped tensile specimens of gage length ~3 mm, width ~1 mm and thickness ~0.4–0.6 mm were extracted from the heat-treated plates using a Mitsubishi FX-10 Wire electrical discharge machining (EDM). The mechanical testing was done under uniaxial tension at room temperature with a strain rate of 10-3 s-1. Details of the setup for the mechanical testing are presented elsewhere []. For each heat treatment condition, four dog-bone specimens were strained to failure following which fractography was performed.A systematic series of heat-treatments were conducted to examine microstructural evolution after annealing at a ω-solvus temperature (623K or 350°C). Observations from the microstructural characterization after each heat-treatment are reported in this section.The inverse pole figure (IPF) map presented in (a) shows that the β-solutionized microstructure consisted of equiaxed β grains with an average diameter 94 ± 34 μm. The SEM image did not provide any further information and to further identify the presence of precipitate phases after water quenching, TEM examination was carried out on thin foils extracted from three separate β-solutionized specimens. A representative dark-field TEM (DFTEM) recorded along the [011]β zone axis is shown in (b). The [011]β SADP (inset) indicated only reciprocal lattice streaking (RLS) in addition to the primary bcc β phase reflections. Recent studies on Ti-Mo, Ti-Mo-Al, Ti-Nb and Ti-Nb-Zr alloys have suggested that such RLS in β-stabilized Ti-alloys result from instabilities within the bcc lattice; leading to the formation of a nanoscale orthorhombic phase in some cases []. However, the presence of such a phase in β-21S needs further investigation using atomistically resolved aberration corrected microscopy. Furthermore, the absence of discernable discreet precipitate reflections suggests that either the athermal ω precipitates has not formed after water quenching, or the volume fraction of athermal ω is too less to allow sufficient sampling.The β-solutionized specimen was further examined with atom probe tomography (APT) to check for any compositional partitioning within the β matrix. (c) shows the raw ion maps of Ti, Mo, Al, and Nb in 3D reconstructed atom probe tips. A qualitatively assessment of the ion maps did not reveal any discernable partitioning within the β phase. Therefore, Langer-Baron-Miller (LBM) analysis was performed on the raw data of the Mo ions and statistically compared to a theoretical binomial distribution (a random distribution). The concentration of Mo was calculated in every 100 ion bins, and the Mo-rich section of the histogram frequency vs. Mo concentration is plotted in (c). In the same plot, the binomial distribution is also shown and it can be seen that both the distributions are almost similar. shows the composition obtained from the atom probe data. The composition was determined using five different spheres within the reconstruction and averaged out. There was no discernable change from the original alloy composition. In other words, APT could not detect composition partitioning in the WQ condition, and for all practical purposes the β-solutionized microstructure can be considered as a compositionally homogeneous bcc β matrix.The β-solutionized specimens were further annealed at 623K (350 °C) for 20H and 100H to develop the isothermal ω precipitates. The microstructure obtained after 20H of annealing is presented in . After annealing for 20H, a dark-field (DF) TEM image – (a) – was recorded by selecting the four ω reflections (shown in the inset); corresponding to four variants of ω). The DFTEM clearly revealed ellipsoidal ω precipitates, and the length of these precipitates varied form ~10–20 nm along the major axis of the ellipsoids. The [011]β SADP (shown as inset) exhibited discreet ω reflections at 1/3 and 2/3 {112}β positions – unlike the β-solutionized condition. Such ω reflections are an outcome of the orientation relationship between the ω (space group: P6/mmm) and β (space group: Im3‾m) phases: [211‾0]ω || [011]β and [0001]ω || [1‾11‾]β. The presence of some amount of early stage α was also noted and has been shown in the inset [Compositional partitioning between the constituent phases, after 20H of annealing, was examined using APT. The raw ion maps of the reconstructed atom probe tips showed regions depleted in Mo, Al, and Nb. (circles in (b)). These solute depleted regions are identified as ω precipitates, and their morphology is depicted as an inset in (c) via 85 at. %Ti iso-concentration surface (or isosurface). The diameter of the ω precipitates (~5–10 nm) were consistent with the TEM observations ((b)). The isosurface further allowed us to quantify elemental partitioning across ω/β interfaces via a proximity histogram (or proxigrams). The calculated proxigram, presented in (c), indicated that the ω precipitates are enriched in Ti, but lean in Mo and Al along with other minor elements (e.g. Nb and Si). A summary of APT based compositions of ω and β phases after 20H of annealing is listed in . Thus, the TEM and APT results demonstrate that 20H of annealing at 623K (350 °C) resulted in fine scale isothermal ω precipitates, which were depleted of solute elements.The microstructure after 100H annealing is shown in . The [011]β SADP showed intensity maxima at 1/3and 2/3{112}β typically associated with the ω phase (inset in (a)). DFTEM image obtained by capturing all the four reflections of isothermal ω (encircled in the SADP) showed that the ellipsoidal ω precipitates have coarsened to ~40 nm in length. Additionally, extremely fine (~100 nm long and ~8 nm wide shown in the inset of (4)) lath-like features were also noted alongside ω precipitates. A closer inspection of the [011]β SADP in (a) revealed faint intensity maxima at 1/2 {112}β (arrow in (a)), which corresponds to hcp α phase. The lower intensity of α reflections, compared to ω reflections, is possibly due to comparatively lower volume fraction of α - also consistent with the DF image presented in (a). The solute content of β and ω phases was further investigated using APT. Similar to the 20H condition ((b)), the raw ion maps of Mo, Al, and Nb, after 100H of annealing, indicated that the ω precipitates are solute depleted pockets. Compositional partitioning across ω/β interfaces is plotted via proxigram analysis in (c) and the relevant ω precipitates are depicted with 85 at. %Ti isosurface as an inset. The proxigram quantitatively confirms that ω precipitates are depleted in solutes, while the surroundings becomes solute-rich. The proxigram also detected a Mo pile-up at the ω/β interfaces, which was evident in the 20H annealed specimen (see (c)). The composition of the ω and β phases were also extracted 100H annealed specimen (listed in ). A comparison of the ω and β compositions for the two heat-treatment conditions (20H and 100H annealed) did not show any substantial changes in the composition of β or ω phases.Results from the microstructural characterization are summarized as follows:β-Solutionizing did not result in any observable ω precipitation; the microstructure largely consists of bcc β matrix.Isothermal ω precipitates were noted after annealing the β-solutionized microstructure at 350 °C for 20 and 100H. The lengths of these precipitates after 20 and 100H of annealing were ~10–20 and ~40 nm respectively.After annealing, extremely fine scale α precipitation was also noted. However, the volume fraction of such α precipitates was substantially smaller compared to ω.Results from APT reconstructions further indicated that the overall composition of the β matrix remained largely unchanged even after the formation of well-developed ω precipitates and substantial partitioning across the ω/β interface (The mechanical properties of the β (β-solutionized) and β+ω (after 20 and 100H of annealing at 350 °C) microstructures were examined by subjecting them to quasi-static tensile loading conditions (strain-rate ~10-3s-1). The measured engineering stress-plastic strain plots for the three conditions are presented in (a). These representative stress-strain plots show striking resemblance in the tensile response of the conditions. After reaching yield point, in each case, the flow curves decrease monotonically– indicating the absence of any strain hardening during plastic deformation. A summary of average mechanical properties (UTS and strain-to-failure or ductility) is plotted in (c). The β-solutionized condition exhibited an excellent ductility ~30% and reasonable UTS, ~1000 MPa or 1 GPa. Annealing for 20H at 350 °C retains the YS (i.e. ~1 GPa), but, compared to the β-solutionized condition, the ductility reduces to ~20%. After 100H of annealing, the strength increased to ~1172 MPa while the ductility reduced to ~15%. A discussion regarding the differences in the UTS between the three conditions will be delayed until a latter section. Regardless, it is also worth pointing out that although 100H of annealing at 350 °C causes a noticeable reduction in ductility (compared to β-solutionized condition); the alloy (containing well-developed ω precipitates) still retained an excellent combination of strength and ductility. The increase in the overall strength, due to the precipitation of ω phase, can be rationalized based on the interaction of dislocations with these precipitates. When the dislocations meet the precipitates, they can either shear through them or bypass them via Orowan looping. According to Gysler et al. [], whose work closely matches the present work in terms of the alloy composition, the stress required to shear through the ω precipitates is lower than the stress required for bypassing them. We have calculated the values of stress required for both the aforementioned cases, based on previous work by Gysler et al. and more recently Chen et al. [The stress required for the bypass to occur is given by the formulawhere ν: Poisson's ratio = 0.33; G: Shear modulus of the matrix = 39.5 GPa []; r: radius of the precipitates = 20 nm; b: Burgers vector = 0.283 nm. Based off of these values, the calculated stress values would be closer to 2135 MPa, which is much higher than the observed values of 1175 MPa. Thus, shearing of the precipitates seemed a more feasible mechanism and the stresses required to shear through the precipitates were calculated based of the following equationWhere γ is the “antiphase boundary energy” and f is the volume fraction of the precipitate phase, ω. G, b, and r are the same as in the case for the bypass. The value of γ is estimated to be around 0.3J/m2 [42]and the value of f (from APT and TEM calculations) is estimated to be around 0.3. By plugging in the values in equation , the stress required is calculated to be around 287 MPa, giving an overall strength of ~1287 MPa, which is closer to the observed value. In order to check whether the theoretical calculations done in the system where accurate, deformation studies using TEM were done in the case of the β+ω sample and will be further discussed in the relevant sections.Thus, the mechanical characterization of the three microstructures allowed us to infer two key features regarding role of microstructural constituents on the deformation behavior:The tensile ductility is reduced after annealing at 350 °C – from 20 to 100H of annealing, while the β-solutionized condition exhibited the maximum ductility. The reduction in ductility may be attributed to the growth of isothermal ω precipitates during annealing. Notwithstanding, the ω containing microstructures showed remarkable ductility (ranging from ~15 to 20%) even in the presence of this embrittling phase.The flow curves did not reveal any strain hardening, regardless of the presence of ω precipitates (specimens annealed at 350 °C for 20 and 100H).These two features were further examined in detail in the following sections.For this purpose, tensile specimens from the three conditions (β-solutionized and subsequent annealing at 350 °C for 20 and 100H) were mechanically polished, and then deformed to failure under tension. Subsequently, SEM observations were performed near the necking region and the fracture surfaces. (a)-(c) shows the fracture surface of all the three conditions. In each case, the fracture surface revealed the presence of dimples due to ductile fracture (consistent with the tensile response ). The inset shows higher magnification images of the same. In order to get a statistical correlation between the size and depth of these dimples to the mechanical properties, i.e. strain to failure, further analysis was done. shows a plot of the same and a good linearity can be seen between the dimple size and strain to failure. As can be seen, with an increase aging time, there was a decrease in the size and shallowness of the dimples []. Similar observations have been made in the past in Ti-Mo systems with similar Mo equivalency.The surface manifestation on the pre-polished surface also provided useful insights into the prevailing deformation modes, shown in . The stress axis is marked with σX in each case. The β-solutionized and 20H annealed microstructures ( and respectively), both, exhibited extensive slip band formation, and the β grains were noticeably elongated along the tensile stress axis. Interestingly, in the β-solutionized condition, the slip-bands were continuous across the grain-boundaries in several cases (blue arrows in (a)). But unlike, as in the case of the gum metal work, reported recently by Lai et al. [], there was no noticeable offset between the slip lines when going across the grain boundaries. In the 20H annealed condition, although there were some instances of such slip-band continuity (blue arrows in (b), the surface manifestation of deformation was not as homogenous as in the β-solutionized specimen. Such subtle differences in the deformation features, in the two conditions, suggest the presence of additional deformation modes in the ω containing microstructures. This was further confirmed by noting the deformation features in the 100H annealed specimen ((c)), which were strikingly different from the β-solutionized and 20H annealed microstructures. In (c), the slip-bands were predominantly confined within individual grains, and interestingly, intragranular cracks (marked with dotted ellipses) were noted in few grains. Thus, (a)–(c) suggest that the prevalent plastic deformation modes are affected by the presence of ω precipitates, and that such modes may be accentuated in the presence of coarse well-developed ω particles (e.g. after 100H of annealing, Deformation features in ω and non-ω containing microstructures were further examined by carrying EBSD analysis on the deformed surfaces of all three specimens. In case of the β-solutionized condition, EBSD analysis was performed on a region in the gauge section, which was far away from the fracture surface since it allowed indexing of the Kikuchi-bands (from the parent β-matrix) with higher confidence index. (b) shows the SEM image of the region of interest (ROI) and (c) shows the superimposed image quality (IQ) and inverse pole figure (IPF) map of the ROI. The IQ + IPF map clearly shows slip on several grains, and two such grains are shown in (d). Trace-analysis performed on the two grains revealed that the slip-bands were predominantly parallel to the {110}β planes of the bcc β-matrix. (e) compares the pre-deformation and post-deformation textures using {001}β, {011}β and {111}β pole figures. The differences in the crystallographic orientations are apparent in the two sets of pole figures in (e), and the maximum texture intensity changes from 5.56 to 7.50 after deformation. The differences in texture in pre- and post-deformation conditions may be attributed to lattice rotations in the elongating β grains during tensile deformation. Such rotations are necessary for maintaining five operative slip-modes (without twining) required for plastic deformation. The evidence of grain rotation is also present as surface manifestations near the grain boundary regions in the SEM images in (b). Similar to the β-solutionized condition, the EBSD analysis for the 20H sample was also done away from the fracture site in order to get a higher confidence index ((b) shows the SEM image of the area from which the EBSD was done, 10(c) shows the IPF + IQ map of the highlighted region in 10(b). Trace analysis was performed on two grains (shown in (d)) and as expected the slip lines were noted to be parallel to the {110}β planes []. As the deformed surface in this condition was very similar to the β-solutionized condition, no major differences were noted between the two. shows the EBSD analysis of the deformed specimen, which was previously annealed for 100H: the location of ROI in the gauge section is indicated in is the SEM image of the ROI showing an intragranular crack, and (c) presents that IQ + IPF map of ROI. Trace analysis revealed the crack edges were parallel to the {112}β planes, which suggested that the cracks may have formed presumably via shear localization on non-closed packed {112}β planes. It should be noted here that the sampling was done across many grains which showed intragranular cracking and all of them revealed the slip traces to be along the {112}β plane. Slip on {112}β planes is also likely in the β-solutionized condition; specially near necking regions (close to the fracture surface) where intense slip-bands were noted ((a)). Nonetheless, the EBSD results demonstrate that the presence of well-developed ω precipitates clearly influences the operative slip systems during the plastic deformation of the β-matrix.Finally, the results from SEM and EBSD analysis can be summarized as follows:Fracture surfaces of all specimens exhibited dimpled features, which indicated that even ω containing microstructures experienced ductile fractureThe β-solutionized condition exhibited homogeneous deformation via the formation of inter and intra-granular slip bands. These slip band appeared to form on {110}β planes. Grain elongation and lattice orientation during plastic deformation was also evident.The 20H annealed tensile specimen exhibited similar deformation features as the β-solutionized condition. However, the surface manifestation of deformation was not as homogeneous as the β-solutionized condition.The 100H annealed specimens also consisted of slip-bands, but they were predominantly confined within grains. In addition, intragranular cracks were also noted, which appeared to form on the {112}β planes.Twinning was not observed in any of the deformed microstructures.The distinct lack of strain hardening in the flow curves of the β-solutionized (pure β-matrix without isothermal ω), and 20 and 100H annealed (with well-developed isothermal ω) conditions suggests that such a mechanical response ((a)) may be attributed to the deformation behavior of the parent β-matrix. Consequently, TEM analysis was carried out on a β-solutionized tensile specimen, which was partially strained beyond the yield-stress (marked with arrow in (a)). It may be emphasized that precipitation-free β-solutionized condition was chosen because it allowed us to clearly image strain-contrast associated with dislocations in only the β-matrix, and avoid complications arising from dislocation entanglements with prior precipitation. TEM foil was extracted from the deformed region containing slip bands.Results from the TEM observations are summarized in via bright-field TEM (BFTEM) images. The BFTEMs were recorded with a two-beam condition by systematically exciting three g vectors: 10(a)-(b) g = 2‾00, 10(c)-(d) g = 11‾0 and 10(e) g = 11‾0, corresponding to the reflections in the [001]β zone axis. A “+” sign indicates the point of reference in each BFTEMs. The TEM observations indicated distinct slip bands dominating the deformed β-matrix ((a) and (c)), and trace analysis suggested that these bands lie on the {011}β planes (indicated with bold lines in (a) and (c)) – consistent with the EBSD observations, and also previously reported literature. Finer scale slip bands (indicated with dotted lines) were also noted, which crisscrossed the prominent bands and each other. The imaging conditions utilized to record the BFTEMs further allowed us to visualize dislocations both within the deformation bands and between them. As depicted in (b), (d) and 12(e) - majority of the dislocations were concentrated within the slip bands, and comparatively fewer dislocations were observed in the β regions between such bands.An application of the g.b = 0 invisibility criteria using the three imaging g vectors (= 2‾00, 11‾0 and 11‾0 in (b), (d) and 12(e) respectively) indicated that Burgers vectors of the dislocations in the β-matrix (between the bands) were ½ [111‾] and ½ [11‾1]. The g.b analysis is listed in , and, we further emphasize that such an analysis valid only for viewing only screw dislocations [ref]. The g.b = 0 invisibility criteria is further highlighted with the dotted ellipse in (b), (d) and 12(e), where dislocations are visible in (b), the dotted ellipse indicated multi-planar slip on (110)β; presumably the early stages of deformation band formation.TEM based deformation analysis was also done on the sample which was aged for 100H. This was done in order to understand the tensile ductility noted in this condition, as it has generally been reported that the higher volume fraction of ω precipitates exhibit very poor strain to failure values. (a) shows the SEM image from which the TEM sample was obtained. The sample orientation was approximately 45° to stress axis (maximum CRSS is obtained here). A high magnification DFTEM image (inset shows the [110]β SADP from which the dark field image was obtained), shown in (b) shows the deformation band similar to the ones observed in the β-solutionized sample. Trace analysis performed here revealed the band to be along {112}β. High magnification image of the same region clearly shows the shearing of the ω precipitates taking place, leading to a small ω free channel. The dislocations when moving through the β matrix can either shear through the ω precipitates or by-pass them, and as Gysler et al. reported the energy needed to by-pass is higher than the energy required to shear; which is consistent with the current study. The shearing of these ω precipitates and consequent formation of the ω free channels, indicating no dislocation pile-up, could account for the higher ductility values than generally reported for ω forming systems. Recently Lai et al. have shown in their work that the ω transforms back into β during this type of deformation wherein a reverse shear transformation leads to the collapse reversing from ω back to β. This was talked in terms of the partials reuniting during the straining of the sample. The model proposed talks about the ½{111} dislocation disassociating into three partials due to the presence of the ω phase. While we are on agreement with the aforementioned theory regarding the {112} slip plane and the shearing of the ω precipitates and their subsequent transformation, the presence of {111} slip noticed in the EBSD remains unanswered. It is believed that in the present case, slip simultaneously takes place on both the planes. The {111} slip is not able to completely shear through the ω precipitates, the case of precipitation hardening, leading to an increased UTS value. On the other hand, the ω free channels created by the {112} plane lead to the increased ductility as the dislocations are easy to pass through without a need for dislocation pile-up or localized stress concentration.On quenching from above the β transus the presence of any athermal ω was not detected in the β matrix. The 3D APT results also did not reveal any compositional difference.The aging treatment at 350 °C for different time periods resulted in the growth of the ω precipitates. The structural growth was tracked using transmission electron microscopy wherein the ω precipitates grew from ~10 to 20 nm to about ~40–50 nm in size along the longer axis. 3D APT results showed compositional partitioning following the formation of the ω precipitates. The ω precipitates in both conditions rejected Mo, Nb, and Al.The mechanical behavior of these microstructures, tested at room temperatures was discussed. Increase in the ω size resulted in an increase in the tensile strength, but the strain to failure was noted to go down.While the single phase condition (β solutionized sample) exhibited deformation occurring mainly via (110)β slip, the presence of larger isothermal omega precipitates in the aged condition (β solutionized + 350 °C/100H) resulted in the activation of not only (110) β slip but also (112) β slip. The reasonably high tensile ductility noted in the aged condition is attributed to the same.Effects of thermo-mechanical treatments on mechanical properties of AA2219 gas tungsten arc weldsFusion zone of AA2219 alloy gas tungsten arc welds was subjected to compressive deformation by rolling the crown of the weld in the welding direction. Twelve percent compressive deformation improved the as-weld hardness from 75 to 100 VHN. The yield strength increased from 125 to 220 MPa. The welds made by pulsed current technique exhibited better strength and ductility compared to their continuous current weld counterparts, both in the as-welded condition and the deformed condition. The improvement in strength was found to be due to dislocation loops formed near the grain boundaries in the fusion zone. Direct aging of fusion zone at 190 °C, increased the yield strength significantly from 125 to about 200 MPa. Aging of the deformed fusion zone did not improve tensile strength further.), explained the process of planishing wherein the first set of wheel electrodes create a weld joint and the second set depending on the shape, area, and pressure of the wheels, either reduced the weld thickness, tempered the weld joint, or both.This technique has many applications in aerospace industry; it offers multiple solutions to the problems encountered when conventional cold forming processes are applied to integrally stiffened structures (). It was found to reduce residual tensile stresses. reported the decrease in residual stresses in steel weld metals. Another U.S. patent issued in 1999 () claimed that weld residual stresses were relieved by planishing in case of an external propellant tank of the space shuttle made of 2195 aluminum–lithium alloy. Similar results were reported by where compressive deformation of the fusion zone was found to change the stress patterns.Such plastic deformation prior to artificial aging in Al–Cu–Li alloys has been found to enhance the strength, ductility and aging kinetics over non-deformed material through the introduction of dislocations, which act as preferential matrix nucleation sites for the primary strengthening phase θ′ ( that crushing or cold working of the fusion zone by planishing improves the yield and tensile strengths of the welded joint by reducing porosity. on inert gas arc butt welds of stainless steel 304 showed noticeable improvement in strength and significant improvement in ductility by roll planishing the weld in the welding direction. Investigations by on austenitic–martensitic stainless steels highlighted the usefulness of rolling the fusion zone in terms of the response of the material to hardening during subsequent aging. After rolling and aging the strength of the joint was found to be 50% higher. They have also concluded that the rolling pressure controls the mechanical properties, the greater the rolling pressure the better the strength.Methods such as cold rolling, shot blasting, roll planishing and machining were reported () to improve the mechanical properties including fatigue limits. have concluded that local mechanical compression is an extremely effective method of increasing the endurance limit of some types of welded joints. It was reported by that 40% reduction in weld bead thickness by rolling and subsequent aging resulted in equalizing the hardness of fusion zone, HAZ and the base metal in stainless steel and Cr–Mo steel welds. Application of an elastic stress during the aging process of age hardenable aluminum alloys was also reported to improve the mechanical properties by altering the distribution of strengthening precipitates This effect was also observed in Al–Cu alloys by Copper containing alloys such as AA2219 are used for their excellent weldability and cryogenic applicability. Increased precipitation can be produced in AA2219 alloy by strain hardening after solution heat treatment and artificial aging. The increased density of precipitation caused by strain hardening is reflected in the high strength (475 MPa) of the alloy in T87 temper. However, AA2219 welds suffer from relatively poor fusion zone and HAZ hardness and strength compared to their base metal counterpart in T87 condition. However, the loss of HAZ hardness in the case of AA2219 in T6 condition is found to be much more than that noticed in AA2219-T87. The hardness in the HAZ of AA2219-T87 tungsten inert gas welds was found to be 94 VHN (), whereas the fusion zone hardness was found to be about 75 VHN.The joint efficiency of AA2219 achieved is only about 40%, mainly because the fusion zone gets softened significantly during the melting and re-solidification. The loss of strength is due to the dissolution of strengthening precipitates and the material in the fusion zone is as good as solution treated material. Another reason for the lower strength of the fusion zone is the segregation of copper to grain and dendrite boundaries. The copper–aluminum eutectic (α-Al + CuAl2), which contains about 32% Cu, forms at the grain boundaries, resulting in depletion of Cu in the matrix. Due to the low fusion zone strength, AA2219 welded sections are designed to be twice or thrice thicker, compared to the rest of the sections in a structure. Fabrication starts with a thicker plate and it is machined at sections which are away from the welding area. Chemical milling or CNC pocket milling is employed to cut away the portions and reduce the total weight of the tank or a shell. The whole fabrication becomes costly and cumbersome. If the strength of the fusion zone can be increased to any extent, by any means, the cost and weight savings would be significant. In view of the expected benefits of compressive deformation, the current work was taken up to study the effects of compressive deformation on the mechanical properties of the fusion zone of aluminium–copper alloy (AA2219-T87) gas tungsten arc welds.Material used in this study was an aluminum alloy AA2219-T87 plate of thickness 8.4 mm and AA2319 filler wire of 1.6 mm diameter was used to make gas tungsten arc welds where high purity argon was used as shielding gas. Chemical composition of materials is given in . Gas tungsten arc (GTA) alternating current (AC) welding process was used. Welding was done with continuous current (CC) and pulsed current (PC) modes. Welding parameters employed are given in . The parameters were selected based on their effectiveness to change the solidification structure from columnar to equiaxed grains in the fusion zone. Welding speed was kept constant at 120 mm/min in all cases to maintain the heat input approximately the same. In case of PC welding, time at peak current was equal to time at base current.X-ray spectral analysis was conducted for quantitative chemical analysis of all the elements. Aging studies were conducted on both CC and PC welds. The experiments were designed in such a way that the effect of deformation, aging and deformation followed by aging could be evaluated. Four different aging temperatures 100, 130, 160 and 190 °C were considered. Aging time was up to 100 h. The full factorial matrix of all the deformation, aging and deformation + aging parameters investigated is given in Polished surfaces of the fusion zones were etched with Keller's reagent for optical metallography. The Electron Probe Micro Analysis (EPMA) was used for qualitative chemical analysis of different phases by elemental X-ray mapping and by X-ray line scan techniques. The line scan technique was also used for studying the variation of solute content (Cu) across the grains. For transmission electron microscopic (TEM) studies, the Jet Polisher required a 30% nitric acid solution in methanol, cooled to −30 °C, and was operated at a potential of 4.5 V. TEM-EDX analysis was undertaken to find the composition of specific phases. Hardness was measured using a Vickers hardness testing machine, in the thickness direction of the weld fusion zone, using a 5 kg load and dwell time of 20 s. Welds were tested for hardness in the as welded, deformed and aged conditions. Results were averaged over a minimum of 5 tests per sample. The crown and the root reinforcement of the welds were compressively deformed by sending the joint through rollers in the welding direction. The percent compressive deformation was calculated based on the initial thickness of the fusion zone including the crown and root reinforcement. Depending on the amount of deformation needed 2–6 roll passes were employed.Transverse tensile tests were conducted in a computer controlled servo hydraulic universal testing machine with extensometer attachment on sub-size samples made according to ASTM E-8M standard. Before making the tensile specimens all the welds were machined to a thickness of 6 mm (plate thickness was 8.4 mm), completely removing the crown and part of the root of the weld. All tensile values presented were the average values of at least 3 specimens. The yield strength values presented were 0.2% proof strength values as computed by the computer program that controls the machine.Back scattered electron images of 2219 CC and PC weld metals are given in . Some of the particles found in the CC fusion zone were thick but not connected with other thicker particles as can be seen from (a). Pulsed current welding resulted in very fine unconnected eutectic particles; many of them were small and spherical in shape as shown in (b). A quantitative estimation of copper content using EPMA line scan is presented in (c). The graph shows that the copper content is about 30% at the two peaks shown for CC welds, indicating that the particle found in the back scattered electron (BSE) images were eutectic particles. In case of PC welds the peaks show only ∼15% copper, which only means that the beam is measuring partially on the eutectic particle and partially on the matrix, because the particles were very fine. An observation of the base of these curves reveals that the average copper content of the PC weld metals in the interior of the grains or the matrix is slightly higher than that in the CC weld metals.It can also be observed from the line scans that there are troughs before and after the peaks, suggesting that the copper depletion occurs around the eutectic particles. The line scan was taken over a distance of 80 μm, at every 2 μm distance. Average copper content of the grain interiors was calculated by removing the peak values which are higher than the actual copper content (6.5%) of the base metal.The average matrix copper content in the case of CC weld was thus found to be 2.96% by weight, while that of the PC weld was found to be 3.61%. It was concluded that the grain interiors or the matrix of the PC weld fusion zone contains higher copper content.Constant current weld fusion zone of 2219 alloy exhibited a hardness value of 74–76 VHN which is nearly 50% of that of 2219-T87 base metal (150 VHN). As the amount of deformation increased the hardness of the fusion zone also increased. About 24% rise in hardness of the fusion zone was noticed at 5% compressive deformation (The results of transverse tensile tests are given in . It is evident that the 12% compressive deformation of the fusion zone resulted in about 70% improvement in yield strength of the joint. The UTS was also improved by about 23%. However, the ductility of the joint dropped from 4.7 to 3.3%. PC fusion zones responded better to the compressive deformation. Deformed PC welds exhibited noticeably better yield and tensile strength values than the deformed CC welds. The real gain for PC welds was in ductility of the joint, which was 6.5% compared to 3.3% of the deformed CC weld. The better ductility exhibited by PC welds even after post weld treatments could be attributed to the finer eutectic morphology in the fusion zone.Transmission electron microscope (TEM) studies showed that the increase in hardness of the fusion zone was purely due to the strain hardening because no precipitates were found. Lot of dislocation loops were found close to grain boundaries as is common in the case of deformed materials and are shown in . The TEM specimen was examined in several tilted angles and no precipitates were found as shown in (c) which was taken after tilting the specimen to defocus the dislocation loops.Earlier studies on the effect of deformation of welds () showed that uniform hardness could be obtained along the joint in the case of stainless steel and Cr–Mo steel welded pipes. Studies on deformation of the fusion zone by roller planishing () showed that substantial improvement in the strength can be obtained in steels as well as aluminum alloys. It was concluded that the process offsets a high percentage of longitudinal and lateral shrinkage by crushing down the seam, and relieves the stress patterns. In the present study it is found that the hardening of the fusion zone is due to the dislocation looping and pile up.As described earlier, in EPMA line scans for as-welded specimens (c), the copper content in the grain interiors was only 2.5–3.5%, which was not high enough to cause natural aging. CC and PC welded joints were tested for hardness soon after the welding and monitored for change in hardness value over a period of about 2 years. It was found that no perceptible change has occurred in the hardness values of these fusion zones and it was concluded that the 2219 welds do not significantly age at room temperature. Therefore, the weld joints were subjected to artificial aging at four different temperatures 100, 130, 160 and 190 °C up to 100 h. The hardness values were measured at every 3 or 4 h up to 40 h and later at intervals of 10 h. The results of hardness testing of the fusion zone were presented in the form of a graph in . The graph shows the binomial best-fit curves for the hardness data obtained.It can be seen from the graph presented in (a) that the fusion zone age hardens at all the four temperatures considered; only the extent of hardening differs. At 160 and 190 °C the fusion zone reached a hardness value of ∼110 VHN in 60 h. It would be interesting to note that the base material 2219T6 would attain a hardness value of 120 VHN in 36 h when aged at 190 °C during the processing of the material. It is clear that the weld fusion zone does not age as fast as and as much as a solutionized 2219 wrought material. It is different from its solutionized wrought counterpart in terms of solute segregation and eutectic morphology. As shown in , in the as-welded fusion zone copper was segregated to the extent of 30% making it difficult to respond to aging. At temperatures 100 and 130 °C fusion zone hardened very slowly and the peak hardness values were also lower compared to a solutionized and aged wrought counterpart. It was concluded that aging at 160 or 190 °C can be employed to quickly improve the fusion zone hardness to its peak value.The tensile properties of directly aged CC and PC welds are presented in . Direct aging of the CC welds resulted in significant improvement in yield and tensile strength and noticeable reduction in percent elongation. The PC welds responded better by exhibiting relatively better strength and ductility. Relatively better tensile properties were obtained by aging at 190 °C for an aging time of 24 h. In case of CC welds there was a significant improvement in yield strength (125–180 MPa) and tensile strength (230–270 MPa) and a reduction in %elongation (from 4.7 to 2.0) due to aging.It was found that like in the case of deformation of welds, pulsed current welds respond better and exhibit better properties upon aging. In case of PC welds there was a significant improvement in yield strength (∼55%) and tensile strength (∼23%). The PC welds exhibited better ductility (∼4%) compared to their CC counterparts in aged condition, though they also experienced significant loss of ductility due to aging. This better response of the PC welds to direct aging could be attributed to the higher copper content in the grain interiors and finer unconnected eutectic network (Transmission electron micrographs presented in shows the progression of precipitate formation at 190 °C. After 20 h of aging small and thinner CuAl2 precipitates could be seen to grow to full sized plates after 60 h of aging where the peak hardness occurs.Age hardening behavior of the deformed fusion zones is shown in (b). It can be seen that higher deformation faster the aging and higher the peak temperatures. Tensile properties of deformed and aged welds were given in . A comparison of tensile properties of deformed and aged welds with as-deformed welds shows that there is not much advantage in aging the deformed welds.Transmission electron microscopy revealed the presence of CuAl2 precipitates in the deformed and aged welds. Formation of precipitates due to aging seems to nullify the effect of strain hardening. No dislocation loops were found in the aged welds, and the strength of the deformed and aged welds seems to result from the enhanced precipitation on the dislocation sites with the loss of strain hardening effect. This could be the reason why the properties did not improve much after deformation followed by aging.A 10–12% compressive deformation of fusion zone of AA2219 gas tungsten arc welds resulted in significant improvement in hardness (from 75 to 100 VHN) and yield strength (from 125 to 220 MPa).Deformed Pulsed Current GTA welds exhibited relatively better yield and tensile strength values and ductility (6.5%) compared to the deformed Continuous current welds (3.3%).The increase in strength in AA2219 fusion zone was found to be due to the dislocation looping and pile up.GTA weld fusion zone of AA2219 did not age as fast as and as much as a solutionized wrought counterpart. At 190 °C the fusion zone reached a hardness value of ∼110 VHN in 60 h, whereas its base metal counterpart reached 120 VHN in 36 h at 190 °C.Direct aging of CC welds resulted in significant improvement in yield (125–180 MPa) and tensile strength (230–270 MPa) and noticeable reduction in percent elongation (4.7–2%). The PC welds responded better by exhibiting better strength values (195 MPa YS and 280 MPa TS) and ductility (4%).Deformation followed by aging did not contribute much to the increase in strength values already attained by deformation.Three-dimensional discontinuous deformation analysisThree-dimensional discontinuous deformation analysis (3-D DDA) using a new contact resolution algorithmThis paper presents a new contact calculating algorithm for contacts between two polyhedra with planar boundaries in the three-dimensional discontinuous deformation analysis (3-D DDA). In this algorithm, all six type contacts in 3-D (vertex-to-face, vertex-to-edge, vertex-to-vertex, face-to-face, edge-to-edge, and edge-to-face) are simply transformed into the form of point-to-face contacts. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. In this paper, formulations of normal contact, shear contact and frictional force submatrices based on the new method are derived and the algorithm has been programmed in VC++. Examples are provided to demonstrate the new contact rule between two blocks.Three-dimensional discontinuous deformation analysisThe discontinuous deformation analysis (DDA) is a numerical method for blocky systems In this paper, a new model of geometric resolution in contact detection is developed and formulations of normal contact, shear contact and frictional force submatrices based on this new model of contact for 3-D DDA are presented. This contact model has been implemented into a 3-D DDA computer program, and numerical results from several test cases demonstrate the validity of the model and the capabilities of the program.Contact detection in discrete element method (DEM) and discontinuous deformation analysis method (DDA) is usually performed in two independent stages. The first stage, referred to as neighbor search, is merely a rough search that aims to provide a list of all possible polyhedra in contact. Among the most recent algorithms available for neighbor searching are the spatial partitioning algorithm In the second stage, called geometric resolution, pairs of contacting polyhedra obtained from the first stage are examined in more detail to find the contact points (or contact area, if distributed contact forces are considered) and calculate the contact forces. Cundall The Lin–Canny closest features algorithm In the contact theory for the 3-D DDA, the first step is to determine the type of contact between any two arbitrary shaped blocks. The type of contact is important because it determines the mechanical response of the contact. There are six types of contact for 3-D blocks including vertex-to-vertex, vertex-to-edge, vertex-to-face, edge-to-edge, edge-to-face and face-to-face. In this paper, we describe an algorithm for computing the distance between two approaching polyhedra to derive the topological information about two nearest points (e.g. closest point type) of the two contacting convex polytopes (see Section ). Such topological information can be used to determine the contact type. For two contacting convex polyhedra, there are four cases for the closest point types such as vertex-to-vertex, vertex-to-edge, vertex-to-face, and edge-to-edge as shown in . In each types the contact plane can be computed as follows:In the vertex-to-face case two closest points P and Q are located on the vertex of polyhedron A and the face of polyhedron B, respectively (In the edge-to-edge case, two closest points P and Q are located on the edges of polyhedron A and polyhedron B, respectively (In the vertex-to-edge case, two closest points P and Q are located on the vertex of polyhedron A and the edge of polyhedron B, respectively (For the vertex-to-vertex case, two closest points P and Q are located on the vertices of polyhedra A and B, respectively (Contact types can be calculated from the above topological information about two nearest points between the polyhedra. Contact planes and types are described as follows:If the vertex-to-face closest point type is identified, the contact plane would be simply the face of the reference block and normal vector of that face would be the normal vector of the contact plane. In this case, if the distance of any vertex of another block falls within the tolerance of the contact plane (in this study, the tolerance level is set at twice the magnitude of maximum displacement in each time step) similar to Cundall’s method If three or more vertices fall within the tolerance, a face-to-face contact type is applicable (If two vertices fall within the tolerance, an edge-to-face contact type is applicable (If one vertex falls within the tolerance, a vertex-to-face type is applicable (In the edge-to-edge, vertex-to-vertex and vertex-to-edge closest point types, first, the vector between the two closest points should be obtained. Then, a plane perpendicular to that vector, referred to as the mid-plane, should be determined. In order to calculate the contact plane, the distances from the mid-plane to the vertices of each block are computed. The contact types and the position of contact plane depend on the number of vertices that fall in the tolerance as follows:If more than two vertices of each block fall within the tolerance, face-to-face contact type happens and the contact plane would be one of those faces.If more than two vertices of one block and two vertices of the other block fall within the tolerance, edge-to-face type of contact happens and the contact plane would be the face of the first block.If more than two vertices of one block and one vertex of the other block fall within the tolerance, vertex-to-face type of contact happens and the contact plane would be the face of the first block.If two vertices of one block and two vertices of another block fall in tolerance, edge-to-edge contact type happens and the contact plane can be computed by passing the mid-plane through one of the edges (a and b). If the two edges are parallel or the two vertices of one edge lie on another edge, the contact normal vector can be computed by taking the average between the normal vectors of the faces neighboring one of those edges.If one vertex of one block and two vertices of the other block fall within the tolerance, vertex-to-edge contact type happens and the contact normal is given by a line from the nearest point on the edge of the second block to the vertex of the first block. If the vertex lies on the edge, the normal of contact can be computed from average normal vector of neighboring faces of the edge.If one vertex of each block falls in tolerance, vertex-to-vertex contact type happens and the contact normal is given by a line from the vertex to the vertex. If one vertex lies on another vertex (in which case the distance between the two will be zero), the contact normal vector can be computed by taking the average between the normal vectors of the faces neighboring one of those vertices.If two contacting polyhedra overlap, then there are four possible cases for the pair of nearest point approach. These are vertex-to-vertex, vertex-to-edge, vertex-to-face, and edge-to-edge. In the vertex-to-face case, the contact normal is simply the face normal. In the edge-to-edge case, the cross product of the edge direction vectors is the contact normal. The vertex-to-vertex and the vertex-to-edge cases are degenerated in the sense that for two contacting objects, the possibility of their occurrence is remote. However, in order to accommodate such possibilities we need to separate the two polyhedra in the direction normal to the point/line of contact. In the vertex-to-edge case, the contact normal is given by taking the average between the normal vectors of the faces neighboring the edge. For the vertex-to-vertex case, the contact normal could be taken as the normal vector of either vertex, which is computed by taking the average between the normal vectors of the faces neighboring the vertex.Contact planes and types are computed and restored at the beginning of each step. If two blocks tend to intersect each other, depending on the type of contact, a reaction force is activated to keep the blocks separated. The complete DDA algorithm is described in Discontinuous deformation analysis algorithm |
Find the nearest point between probable blocks in contact |
Create the contact plane between the two nearest points |
Find the vertices which fall within the set tolerance |
Compute the type of contact using the number of approaching vertices |
Compute the contact forces between the blocks including frictional, normal and shear forces |
Assemble the generalized stiffness, K, and force, F, matrices; integrate over time and solve |
Update the stresses in the blocks: apply the stress incrementsWhen determining the distance between two polyhedra, the most intuitive approach consists of computing and comparing the distances between their boundary features (vertices, edges, and faces). Computing the closest point between two polyhedra can be estimated with just vertex-to-face and edge-to-edge search between two objects. These two contact types will encompass all possible occurrences of closest points between any two polyhedra such as vertex-to-face, vertex-to-edge, vertex-to-vertex and edge-to-edge. Searching through all possible edge-to-edge and vertex-to-face contacts between two objects would be costly when there are numerous vertices, edges and faces involved in the contact search. To overcome this problem in the first step, the nearest vertices for the two approaching polyhedra are determined and the search is continued among all faces of the two polyhedra that share those vertices. As shown in , if P and Q are the closest vertices of the two polyhedra A and B, searching for the closest point should be sought only on the neighboring faces of P and Q (i.e. the faces that share each vertex) as is presented in the following sections.In DDA applications, the change in blocks’ positions between two time steps is very small. As a result, the change between contact type in one step can be neglected with good approximation as shown in the following examples (see Section In order to compute the closest point of vertex P to face (polygon) f as shown in Let ∏ denote the plane passing through the face f. Then the projection of vertex P (P′) on the plane ∏ is obtained.Check whether the point P′ is inside a given polygon f. If so, then the point P′ would be the nearest point of face f to vertex P (vertex-to-face category) but if point P′ is outside the polygon f, the nearest point would be located on one of the edges or vertices of face f.To find the nearest point from vertex P′(the projection of point P on plane ∏) to boundary of face f, the nearest vertex of face f and P′ should be obtained first. Then, the nearest point (e.g. P″ in b) is sought only on two edges that share that vertex. If the nearest point is located on an edge, then the contact is of the vertex-to-edge type. If the nearest point is located on a vertex, the vertex-to-vertex contact would occur.The above three steps will allow three categories of nearest point including vertex-to-face, vertex-to-edge and vertex-to-vertex to be obtained.If two edges are located in one plane the nearest points between these two edges would be located on the vertex of one edge and the vertex or the edge of the other (). Either possibility would coincide with either of the vertex-to-vertex or vertex-to-edge category described in Section . Therefore, after a simple search if the two edges are coplanar, the algorithm should skip to another pair search. But if the two edges are not located in one plane, the nearest points between them can be located as follows:Let H1 and T1 be the head vertex and tail vertex of the edge E1 respectively. Similarly, H2 and T2 represent the head vertex and tail vertex of the edge E2. Vectors e1 and e2 are defined as e1 |
= |
H1 |
− |
T1 and e2 |
= |
H2 |
− |
T2. We can find the nearest point pair P and Q on E1 and E2 by the following:P=H1+s(T1-H1)=H1-se1Q=H2+u(T2-H2)=H2-ue2where s,u |
∈ [0, 1] indicate the relative location of P and Q on the edges E1 and E2, respectively. Let nˆ=P-Q and |nˆ| is the shortest distance between the two edges E1 and E2. Since nˆ must be orthogonal to the vectors e1 and e2, we have〈nˆ,e1〉=〈(P-Q),e1〉=0〈nˆ,e2〉=〈(P-Q),e2〉=0s=〈e1,e2〉[〈(H1-H2),e2〉]-〈e2,e2〉[〈(H1-H2),e1〉]detu=〈e1,e1〉[〈(H1-H2),e2〉]-〈e1,e2〉[〈(H1-H2),e1〉]detwhere det = (〈e1, |
e2〉 ∧ 〈e1, |
e2〉) − (〈e1, |
e1〉 ∧ 〈e2, |
e2〉). However, to make sure P and Q lie on the edges E1 and E2, s and u are truncated to the range [0, 1] which gives the correct nearest point pair (P; |
Q). As shown in , if s, |
u |
∈ (0, 1) the type of closest points is edge-to-edge. If not, either vertex-to-vertex or vertex-to-edge type of contact would occur, which is included in the vertex-to-face search (Section ) and therefore should not be considered as nearest points.Assuming linear elasticity and homogeneous deformation, the displacement (u, |
v, |
w) of any point (x, |
y, |
z) of a block can be represented by 12 displacement variables. In the 12 variables, (u0, |
v0, |
w0) is the rigid body translation of a specific point (x0, |
y0, |
z0), r1, r2 and r3 are the rotation angles (in radians) of block around z-axis, x-axis and y-axis, respectively. The parameters εx, εy, εz, γxy, γyz, γzx are the normal and shear strains in the block. The displacement of any point (x, |
y, |
z) in the block can be represented by Eq. uvw=[Ti][Di]=100-(y-y0)0(z-z0)(x-x0)00(y-y0)20(z-z0)2010(x-x0)-(z-z0)00(y-y0)0(x-x0)2(z-z0)200010(y-y0)-(x-x0)00(z-z0)0(y-y0)2(x-x0)2·u0v0w0r1r2r3εxεyεzγxyγyzγzxAssuming that n blocks are defined in a block assembly, the system of simultaneous equilibrium equations can be written in the matrix form asK11K12K13…K1nK21K22K23…K2nK31K32K33…K3n⋮⋮⋮⋱⋮Kn1Kn2Kn3…KnnD1D2D3⋮Dn=F1F2F3⋮FnSubmatrices Kii depend on the material properties of block i, and Kij, where i |
≠ |
j is defined by the contacts between blocks i and j. Since each block i has twelve degrees of freedom defined by the components of Di in Eq. is a 12 × 12 sub-matrix. Also, each Fi is a 12 × 1 sub-matrix that represents the loading on block i. The system of Eq. can also be expressed in a more compact form as KD |
= |
F where K is a 12n |
× 12n stiffness matrix, and D and F are 12n |
× 1 deformation and force matrices, respectively. The total number of unknown deformations is the sum of the degrees of freedom of all the blocks. The total potential energy Π is the summation over all potential energy sources; stresses and forces. The simultaneous equations are derived by minimizing the total potential energy Π of the block system.kijrs=∂2Π∂dridsj,r,s=1,2,…,12Fir=-∂Π(0)∂dri,r=1,2,…,12dri={d1id2id3i…d12i}T={uiviwir1ir2ir3iεxiεyiεziγxyiγyziγzxi}Tdsj={d1jd2jd3j…d12j}T={ujvjwjr1jr2jr3jεxjεyjεzjγxyjγyzjγzxj}Tand the subscripts i and j represent the i-th block and the j-th block, respectively. The solution to the system of Eq. is constrained by a system of inequalities associated with block kinematics (e.g. no penetration and no tension between blocks) and Coulomb’s friction for sliding along block interfaces. The system of Eq. is solved for the displacement variables and the final solution to this system is obtained as follows: At first, the solution is checked to see how well the constraints are satisfied. If tension or penetration is found along any contact location, the constraints are adjusted by selecting new locks and constraining positions. The procedure of adding and removing stiff springs depending on the changes in contact states is known as “open–close” iteration The matrices K and F are updated accordingly from which a new solution is obtained. This process is repeated until no tension and no penetration are found along all of the block contacts. Hence, the final displacement variables for a given time step are actually obtained by an iterative process.In this section, formulation of normal contact, shear contact and frictional force submatrices based on the new method are presented as follows: shows a schematic of a moving block in 3-D in which P1(x1, |
y1, |
z1) and P1∗ represent the locations of a vertex of block i before and after a displacement increment, respectively. P0(x0, |
y0, |
z0) denote the projection of P1 on the contact plane and P0∗ represents this point after the displacement increment. The displacement increments of points P1 and P0 are given by (u1, |
v1, |
w1) and (u0, |
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