C.N. Tomé

Application of texture simulation to understanding mechanical behavior of Mg and solid solution alloys containing Li or Y

Abstract The viscoplastic self-consistent model was used to interpret differences in the mechanical behavior of hexagonal close packed magnesium alloys. There are only subtle differences in the compression textures of magnesium and its solid solution alloys containing lithium or yttrium. However, the plane strain compression textures of the alloys showed an increasing tendency for the basal poles to rotate away from the “normal direction” towards the “rolling direction”. Texture simulations enabled these distinctions to be attributed to the increased activity of the non-basal 〈 c + a 〉 slip mode. The alloys had improved compressive ductilities compared to pure magnesium, and the increased c + a slip mode activity provides a satisfying explanation for this improvement, since it can accommodate c-axis compression within individual grains. Accounting for individual deformation mode hardening enabled the flow curves to be simulated and the anisotropic plastic response of textured wrought alloys to be mechanistically understood and predicted.

Study of slip mechanisms in a magnesium alloy by neutron diffraction and modeling

Abstract Internal strains within a polycrystalline magnesium alloy plate have been measured during tensile and compression testing in situ by neutron diffraction. Using an elasto-plastic self-consistent simulation code, information about the operation of slip and mechanical twinning modes as a function of strain has been obtained.

Statistical analyses of deformation twinning in magnesium

To extract quantitative and meaningful relationships between material microstructure and deformation twinning in magnesium, we conduct a statistical analysis on large data sets generated by electron backscattering diffraction (EBSD). The analyses show that not all grains of similar orientation and grain size form twins, and twinning does not occur exclusively in grains with high twin Schmid factors or in the relatively large grains of the sample. The number of twins per twinned grain increases with grain area, but twin thickness and the fraction of grains with at least one visible twin are independent of grain area. On the other hand, an analysis of twin pairs joined at a boundary indicates that grain boundary misorientation angle strongly influences twin nucleation and growth. These results question the use of deterministic rules for twin nucleation and Hall–Petch laws for size effects on twinning. Instead, they encourage an examination of the defect structures of grain boundaries and their role in twin nucleation and growth.

MECHANICAL RESPONSE OF ZIRCONIUM—I. DERIVATION OF A POLYCRYSTAL CONSTITUTIVE LAW AND FINITE ELEMENT ANALYSIS

Simulating the forming of anisotropic polycrystals, such as zirconium, requires a description of the anisotropy of the aggregate and the single crystal, and also of their evolution with deformation (texture development and hardening). Introducing the anisotropy of the single crystal requires the use of polycrystal models that account for inhomogeneous deformation depending on grain orientation. In particular, visco- plastic self-consistent models have been successfully used for describing strongly anisotropic aggregates. As a consequence, using a polycrystal constitutive law inside finite element (FE) codes represents a considerable improvement over using empirical constitutive laws, since the former provides a physically based description of anisotropy and its evolution. In this work we develop a polycrystal constitutive description for pure Zr deforming under quasi-static conditions at room and liquid nitrogen temperatures. We use tensile and compressive experimental data obtained from a clock-rolled Zr sheet to adjust the constitutive parameters of the polycrystal model. Twinning is accounted for in the description. The polycrystal model is implemented into an explicit FE code, assuming a full polycrystal at the position of each integration point. The orientation and hardening of the individual grains associated with each element is updated as deformation proceeds. We report preliminary results of this methodology applied to simulate the three-dimensional deformation of zirconium bars deforming under four-point bend conditions to maximum strains of about 20%. A critical comparison between experiments and predictions is done in a second paper (Kaschner et al., Acta mater. 2001, 49(15), 3097-3107). Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.

Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations

We present a detailed description of the numerical implementation, within the widely used viscoplastic self-consistent (VPSC) code, of a rigorous second-order (SO) homogenization procedure for non-linear polycrystals. The method is based on a linearization scheme, making explicit use of the covariance of the fluctuations of the local fields in a certain linear comparison material, whose properties are, in turn, determined by means of a suitably designed variational principle. We discuss the differences between this second-order approach and several first-order self-consistent (SC) formulations (secant, tangent and affine approximations) by comparing their predictions with exact full-field solutions. We do so for crystals with different symmetries, as a function of anisotropy, number of independent slip systems and degree of non-linearity. In this comparison, the second-order estimates show the best overall agreement with the full-field solutions. Finally, the different SC approaches are applied to simulate texture evolution in two strongly heterogeneous systems and, in both cases, the SO formulation yields results in better agreement with experimental evidence than the first-order approximations. In the case of cold-rolling of low-SFE fcc polycrystals, the SO formulation predicts the formation of a texture with most of the characteristic features of a brass-type texture. In the case of polycrystalline ice, deforming in uniaxial compression to large strain, the SO predicts a substantial and persistent accommodation of deformation by basal slip, even when the basal poles become strongly aligned with the compression direction.

Modeling texture and microstructural evolution in the equal channel angular extrusion process

Abstract In this work, we develop a modeling framework for predicting the visco-plastic deformation, microstructural evolution (distributions of grain shape and size) and texture evolution in polycrystalline materials during the equal channel angular extrusion (ECAE) process, a discontinuous process of severe shear straining. The foundation of this framework is a visco-plastic self-consistent (VPSC) scheme. We consider a 90° die angle and simulate ECAE up to four passes for four processing routes, (A, C, B A and B C , as denoted in the literature) for an FCC polycrystalline material. We assume that the FCC single crystal has a constant critical resolved shear stress (CRSS), so that hardening by dislocation activity is suppressed, and the influence of grain shape distribution and texture as well as their interaction can be isolated. Many deformation microstructural features, such as grain size and shape distribution, texture, and geometric hardening–softening, were highly dependent on processing route. Using a grain subdivision criterion based on grain shape, route A was the most effective, then route B A and route B C and lastly route C, the least effective for grain size refinement, in agreement with redundant strain theory. For producing refined equiaxed grains, route B C was more effective than routes B A and A. We show that grain–grain interactions tend to weaken texture evolution and consequently geometric hardening and softening in all routes.

Measured and predicted intergranular strains in textured austenitic steel

Tensile specimens were machined from heat-treated austenitic stainless steel plate prior to and after 70% reduction by uni-directional rolling. In addition to a single specimen cut from the as-received plate, two specimens were cut from the rolled plate, with axes parallel and perpendicular to the rolling direction, respectively. In situ measurements of the strain response of multiple hkl lattice planes to an applied uniaxial tensile load were made using neutron diffraction, to macroscopic plastic strains of around 1%. The experimental results are compared with predictions from a self-consistent Hill–Hutchinson model. The measured texture in the plate was approximately three times random; however, its effect on the hkl response was small compared to the residual strains left by rolling. The apparent elastic modulus of the planes is affected by the residual strains, which is attributed to the effect of micro-plasticity. Interpretation of residual stress measurements, for both single peak and Rietveld measurements is considered in light of these results.

Self-consistent polycrystal models: a directional compliance criterion to describe grain interactions

Viscoplastic self-consistent polycrystal models have been successful in addressing and explaining features of plastic deformation which cannot be treated with the Taylor condition of isostrain. In particular, these models have been applied to the simulation of plastic deformation and texture development in materials with hexagonal, trigonal, orthorhombic and triclinic symmetry. An important assumption required to solve the equilibrium equation within self-consistent formulations is that the strain-rate varies linearly with the stress in the homogeneous effective medium surrounding the inclusion. The characteristic of such a linear relation has been a matter of debate and two extreme cases can be identified: the tangent and the secant approaches. The secant approach has associated with it a stiffer inclusion-matrix interaction than the tangent approach and is closer to the Taylor approach. In this work we perform a systematic study of the implications of both assumptions on the response of cubic and hexagonal materials (texture development, system activity, stress and strain-rate deviations). In addition, we argue that the strength of the matrix-inclusion interaction should not be constant but should depend on the capability of each orientation to accommodate the particular deformation mode imposed externally. As a consequence, we propose a relative directional compliance (RDC) criterion for defining a variable interaction between grain and matrix depending on their relative compliances and compare the predictions of the RDC approach with the predictions of the secant and the tangent schemes.

Effects of texture, temperature and strain on the deformation modes of zirconium

Clock-rolled, high-purity, textured polycrystalline zirconium exhibits significant plastic anisotropy for compression along the through-thickness and in-plane directions and strong temperature dependence of flow stress for both orientations. Orientation imaging microscopy in a scanning electron microscope and defect analysis via transmission electron microscopy are used to characterize the defect microstructures as a function of initial texture, deformation temperature and plastic strain. The observed deformation mechanisms are correlated with the measured mechanical response.

Twinning and De-twinning via Glide and Climb of Twinning Dislocations along Serrated Coherent Twin Boundaries in Hexagonal-close-packed Metals

The (1¯012) twin boundaries experimentally observed in hexagonal-close-packed metals are often serrated rather than fully coherent. These serrated coherent twin boundaries (SCTBs) consist of sequential (1¯012) coherent twin boundaries and parallel basal–prismatic planes serrations (BPPS). We demonstrated that the formation of BPPS is geometrically and energetically preferred in the SCTBs, and an SCTB thus migrates by glide and climb of twinning dislocations, combined with atomic shuffling. Particularly, the climb mechanism, combined with the density and the height of BPPSs in the SCTBs, could be crucial in controlling twinning and de-twinning, and twinning-associated hardening.