Molecular dynamics simulations were used to study deformation mechanisms during uniaxial tensile deformation of an amorphous polyethylene polymer. The stress-strain behavior comprised elastic, yield, ...strain softening and strain hardening regions that were qualitatively in agreement with previous simulations and experimental results. The chain lengths, number of chains, strain rate and temperature dependence of the stress-strain behavior was investigated. The energy contributions from the united atom potential were calculated as a function of strain to help elucidate the inherent deformation mechanisms within the elastic, yield, and strain hardening regions. The results of examining the partitioning of energy show that the elastic and yield regions were mainly dominated by interchain non-bonded interactions whereas strain hardening regions were mainly dominated by intra-chain dihedral motion of polyethylene. Additional results show how internal mechanisms associated with bond length, bond angle, dihedral distributions, change of free volume and chain entanglements evolve with increasing deformation.
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The response surface methodology (RSM), which typically uses quadratic polynomials, is predominantly used for metamodeling in crashworthiness optimization because of the high computational cost of ...vehicle crash simulations. Research shows, however, that RSM may not be suitable for modeling highly nonlinear responses that can often be found in impact related problems, especially when using limited quantity of response samples. The radial basis functions (RBF) have been shown to be promising for highly nonlinear problems, but no application to crashworthiness problems has been found in the literature. In this study, metamodels by RSM and RBF are used for multiobjective optimization of a vehicle body in frontal collision, with validations by finite element simulations using the full-scale vehicle model. The results show that RSM is able to produce good approximation models for energy absorption, and the model appropriateness can be well predicted by ANOVA. However, in the case of peak acceleration, RBF is found to generate better models than RSM based on the same number of response samples, with the multiquadric function identified to be the most stable RBF. Although RBF models are computationally more expensive, the optimization results of RBF models are found to be more accurate.
Geometrically necessary twins in bending of a magnesium alloy McClelland, Z.; Li, B.; Horstemeyer, S.J. ...
Materials science & engineering. A, Structural materials : properties, microstructure and processing,
10/2015, Letnik:
645
Journal Article
Recenzirano
Evidence for the formation of geometrically necessary twins (GNTs), or twins that accommodate a strain gradient in a multi-axial stress state, in quasi-static, room temperature three-point bending of ...a rolled magnesium alloy is presented. Electron backscatter diffraction analysis showed that {101¯2}<101¯1¯> extension twins (rather than {101¯1}<101¯2¯> contraction twins) form in arcs in the tension zone, and that twinned grains have very low Schmid factors. The main tensile stress component in the tension zone was nearly perpendicular to the c-axis of the parent grains. The mechanism for such unusual twinning behavior was analyzed from the perspective of strain components that are generated by {101¯2}<101¯1¯> twinning. After twinning, an extension strain component along the c-axis and a contraction strain component perpendicular to the c-axis of the parent lattice are generated simultaneously due to the misfit between the parent and the twin lattice. The contraction strain component by twinning provided an extra strain accommodation for the compressive strain in the tension zone produced by the bending, despite the fact that the local stress state strongly disfavored the {101¯2}<101¯1¯> twinning. Thus, the {101¯2}<101¯1¯> twins in the arcs in the tension zone of the bent specimen present the characteristic of being geometrically necessary, similar to geometrically necessary dislocations and boundaries.
► Anisotropy in rod-textured Mg was studied by compression and predicted by VPSC. ► Anisotropy and slip–twin interactions are different from those in spotty texture. ► Observations suggest minimum ...effect of Hall–Petch induced by twin boundaries. ► Contraction twinning triggered at different CRSSs upon changing loading direction. ► Contemporarily crystal plasticity could not capture this non-Schmid’s effect.
We experimentally and numerically investigated the effect of twinning on plasticity using an extruded rod-textured magnesium alloy. The rod-texture is a
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-axis fiber texture that presents a fundamentally different anisotropy correlated to twinning with respect to the widely discussed
c-axis fiber texture generated by clock rolling. We quantified a profuse
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extension twinning along the extrusion direction (ED) that consumed the entire parent before the inflection point in the stress–strain behavior. However, under compression along the extrusion radial direction (ERD), the twinning model in the viscoplastic self-consistent formulation still predicts substantial extension twinning. However, in this case the stress–strain curve did not inflect, and Regime II hardening was absent. We demonstrate via EBSD analyses that the absence of Regime II hardening along the ERD was due to a non-Schmid effect by multivariant “stopped” twinning. The intersecting variants of stopped twins incurred twin–twin interactions that limited the twin growth. Profuse
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double twinning occurs both under ED and ERD but peculiarly triggered earlier under ERD than under ED, so the Voce model under VPSC could not capture their effect. The complex networks of stopped twins in the ERD clearly negate a possible Hall–Petch effect on Regime II by twin segmentation, since otherwise Regime II would be more marked in the ERD. Rather, the stopped twins suggest preferential latent hardening within the twinned regions by parent dislocation transmutation upon their incorporation in the twins. In fact, since twin–twin interactions mitigate the growth rates of sweeping extension twin boundaries, dislocation transmutation could be limited to the extent that Regime II hardening will be eliminated.
Textured hexagonal close packed double-lattice structures show stronger anisotropy than textured cubic structures. The reason lies behind the necessity to activate deformation twinning and hard slip ...dislocation modes. Although the mechanisms behind activation of dislocations with non-basal Burgers vectors are still not fundamentally understood, the effect of twinning on hardening presents the most substantial challenge to polycrystal plasticity modelers. The origin of the increasing strain hardening rate regime (Regime II) upon profuse twinning is still not fundamentally clear. Previous successful attempts to fit the stress–strain behaviors based on a Hall–Petch effect by twin segmentation had systemically led to discrepancies in predicting intermediate textures and/or twin volume fraction evolutions. A recent dislocation-based hardening rule incorporated into the Visco-Plastic Self-Consistent (VPSC) model allows slip and twinning to be physically coupled in the simulations. In this paper, we investigate hardening mechanisms in pure magnesium and apply a dislocation based formalism to model anisotropy. In contrast to magnesium alloys, we show that pure magnesium under large strains develops substantial multivariant twinning and multifold twinning. These twinning phenomena are accompanied by a marked grain refinement and blunting of former twin boundaries. This blunting suggests severe accommodation effects in the soft matrix that caused the twin boundary to lose coherency. Thus, multivariant and multifold twinning take place to accommodate further deformation, but the subsequent twin–twin interactions arise to contribute in material hardening. The strain path anisotropy related to the saturation stresses revealed major missing links for comprehending hardening by twinning and substantiated dislocation transmutation effect by twinning shear.
The growth and coalescence of voids in magnesium single crystals at the nanoscale have been investigated using molecular dynamics simulations and the embedded atom method. One void and two void ...specimens with identical initial void volume fractions were utilized to study the mechanism of void growth and coalescence. In order to study the influences of material length scale on void evolution in single crystals four specimen sizes with the same initial volume fraction of voids were considered. Investigations of the effects of temperature and strain rate were also performed. Uniaxial stress–strain curves were monitored during increasing employed strain. The simulation results show that the specimen size, loading strain rate and temperature had apparent influences on the twin or dislocation pattern, void evolution shape and uniaxial stress–strain responses, but negligible effects on the initial slopes of the uniaxial stress–strain curves. Furthermore, the nucleation stress of twin bands in orientation A –
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was much higher than that of plastic deformation in orientation B –
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The generalized stacking fault energy (GSFE) curve plays a major role in predicting the properties of materials. In the present paper we estimate this GSFE curve for pure Mg and Mg with several ...alloying/solute elements, focusing on the pyramidal slip system of Mg. First-principles density functional theory can be used to calculate the GSFE curves to link continuum-scale dislocation properties and stacking fault widths, on pyramidal slip systems. Within the pyramidal slip systems, we specifically have considered pyramidal type I {101¯1}〈1¯21¯0〉, with 〈a〉, and {101¯1}〈1¯1¯23〉, with 〈a+c〉 dislocation, and type II {112¯2}〈1¯1¯23〉, with 〈a+c〉 dislocation. Solute effects on these slip systems’ GSFE curves have been calculated for nine alloying elements: Al, Ca, Li, Gd, Ce, Si, Sn, Zn and Zr. The strength and ductility of these novel alloys can be qualitatively estimated in the light of pyramidal slip systems. Finally an approximate method to increase formability has been introduced by adding these solutes.
This paper describes a numerical, hierarchical multiscale modeling methodology involving two distinct bridges over three different length scales that predicts the work hardening of face centered ...cubic crystals in the absence of physical experiments. This methodology builds a clear bridging approach connecting nano-, micro- and meso-scales. In this methodology, molecular dynamics simulations (nanoscale) are performed to generate mobilities for dislocations. A discrete dislocations numerical tool (microscale) then uses the mobility data obtained from the molecular dynamics simulations to determine the work hardening. The second bridge occurs as the material parameters in a slip system hardening law employed in crystal plasticity models (mesoscale) are determined by the dislocation dynamics simulation results. The material parameters are computed using a correlation procedure based on both the functional form of the hardening law and the internal elastic stress/plastic shear strain fields computed from discrete dislocations. This multiscale bridging methodology was validated by using a crystal plasticity model to predict the mechanical response of an aluminum single crystal deformed under uniaxial compressive loading along the 4
2
1 direction. The computed strain-stress response agrees well with the experimental data.
The energetics and length scales associated with the interaction between point defects (vacancies and self-interstitial atoms) and grain boundaries in bcc Fe was explored. Molecular statics ...simulations were used to generate a grain boundary structure database that contained asymptotically =170 grain boundaries with varying tilt and twist character. Then, vacancy and self-interstitial atom formation energies were calculated at all potential grain boundary sites within 15 Angstrom of the boundary. The present results provide detailed information about the interaction energies of vacancies and self-interstitial atoms with symmetric tilt grain boundaries in iron and the length scales involved with absorption of these point defects by grain boundaries. Both low- and high-angle grain boundaries were effective sinks for point defects, with a few low- capital sigma grain boundaries (e.g., the capital sigma 3{112} twin boundary) that have properties different from the rest. The formation energies depend on both the local atomic structure and the distance from the boundary center. Additionally, the effect of grain boundary energy, disorientation angle, and capital sigma designation on the boundary sink strength was explored; the strongest correlation occurred between the grain boundary energy and the mean point defect formation energies. Based on point defect binding energies, interstitials have asymptotically =80 % more grain boundary sites per area and asymptotically =300% greater site strength than vacancies. Last, the absorption length scale of point defects by grain boundaries is over a full lattice unit larger for interstitials than for vacancies (mean of 6-7 Angstrom versus 10-11 Angstrom for vacancies and interstitials, respectively).
A computational framework is developed to investigate the process-structure-property relationship for additive manufacturing (AM) of Ti–6Al–4V alloy. The proposed model incorporates experimentally ...informed two-phase α+β morphologies within prior β-grains, which are widely observed in the as-built AM components. Specifically, the temperature-dependent phase-field model (PFM) is used to simulate the evolution of various grain morphologies, e.g., columnar and equiaxed grain structures. The proposed PFM taking into account both of the epitaxial grain growth and the constitutional cooling-driven heterogeneous nucleation enables us to capture the columnar to equiaxed transition (CET) of grain structures. The thermal fields concerned with the scanning strategies and manufacturing parameters are simulated using a finite-element model (FEM). The Burgers orientation relation (BOR) is further utilized to generate two-phase α+β morphologies within prior β-grains, accompanied by the transformation of crystal orientations, i.e., (0001)α//{101}β and <112‾0>α// β. Finally, a fast Fourier transform-based elasto-viscoplastic (EVP-FFT) model is employed to predict the micromechanical behaviors and properties for the two-phase α+β microstructures. The presented PFM-based formulation is generally applicable to predict the process-structure-property relationship for additive manufacturing of a variety of alloy systems, e.g., titanium alloys, aluminum alloys and nickel-based superalloys.
•Two-phase lamellar α+β morphology for Ti–6Al–4V are considered in the computational framework.•High travel speed and low power provide the equiaxed β-grain structures and fine α-lath microstructures.•Equiaxed β-grain structures provide higher tensile strength than that of columnar β-grain structures due to shorter effective slip length.•Fine α-lath microstructure and small colony size reduce the effective slip length, and thus provide high tensile strength.•Stress concentrations due to dislocation pile-ups induce the crack and thus reduce the ductility of columnar β-grains in Rx-direction.
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