Surya R. Kalidindi

Crystallographic texture evolution in bulk deformation processing of FCC metals

Abstract A Taylor-type polycrystalline model, together with a new fully-implicit time-integration scheme has been developed and implemented in a finite element program to simulate the evolution of crystallographic texture during bulk deformation processing of face centered cubic metals deforming by crystallographic slip. The constitutive equations include a new equation for the evolution of slip system deformation resistance which leads to macroscopic strain hardening behavior that is in good accord with experiments performed on OFHC copper. The good predictive capabilities of the constitutive equations and the time-integration procedure for simulating the stress-strain behavior and the evolution of texture under both homogeneous and non-homogeneous deformation conditions are demonstrated by comparing numerical simulations against experimental measurements in simple shear and a simple plane-strain forging experiment on copper.

Polycrystalline plasticity and the evolution of crystallographic texture in FCC metals

A Taylor-type model for large deformation polycrystalline plasticity is formulated and evaluated by comparing the predictions for the evolution of crystallographic texture and the stress-strain response in simple compression and tension, plane strain compression, and simple shear of initially ‘isotropic’ OFHC copper against (a) corresponding experiments, and (b) finite element simulations of these experiments using a multitude of single crystals with accounting for the satisfaction of both compatibility and equilibrium. Our experiments and calculations show that the Taylor-type model is in reasonable first-order agreement with the experiments for the evolution of texture and the overall stress-strain response of single-phase copper. The results of the finite element calculations are in much better agreement with experiments, but at a substantially higher computational expense.

Strain hardening of titanium: role of deformation twinning

Abstract The purpose of this study is to investigate the role of deformation twinning in the strain-hardening behavior of high purity, polycrystalline α-titanium in a number of different deformation modes. Constant strain rate tests were conducted on this material in simple compression, plane-strain compression and simple shear, and the true stress (σ)-true strain (e) responses were documented. From the measured data, the strain hardening rates were numerically computed, normalized by the shear modulus (G), and plotted against both normalized stress and e. These normalized strain hardening plots exhibited three distinct stages of strain hardening that were similar to those observed in previous studies on low stacking fault energy fcc metals (e.g. 70/30 brass) in which deformation twinning has been known to play an important role. Optical microscopy and Orientation imaging microscopy were conducted on samples deformed to different strain levels in the various deformation paths. It was found that the onset of deformation twinning correlated with a sudden increase in strain hardening rate in compression tests. The falling strain hardening rate correlated with saturation in the twin volume fraction. In shear testing a much lower rate of strain hardening was found, at all strains, and this correlated with a lower density of deformation twinning.

Incorporation of deformation twinning in crystal plasticity models

Abstract A new constitutive framework, together with an efficient time-integration scheme, is presented for incorporating the crystallography of deformation twinning in polycrystal plasticity models. Previous approaches to this problem have required generation of new crystal orientations to reflect the orientations in the twinned regions or implementation of “volume fraction transfer” schemes, both of which require an update of the crystal orientations at the end of each time step in the simulation of the deformation process. In the present formulation, all calculations are performed in a relaxed configuration in which the lattice orientation of the twinned and the untwinned regions are pre-defined based on the initial lattice orientation of the crystal. The validity of the proposed constitutive framework and the time-integration procedures has been demonstrated through comparisons of predicted rolling textures in low stacking fault energy fcc metals and in hcp metals with the corresponding predictions from the earlier approaches as well as through qualitative comparisons with the measurements reported previously.

Microstructure sensitive design for performance optimization

Abstract The accelerating rate at which new materials are appearing, and transforming the engineering world, only serves to emphasize the vast potential for novel material structure, and related performance. Microstructure-sensitive design (MSD) aims at providing inverse design methodologies that facilitate design of material internal structure for performance optimization. Spectral methods are applied across the structure, property and processing design spaces in order to compress the computational requirements for linkages between the spaces and enable inverse design. Research has focused mainly on anisotropic, polycrystalline materials, where control of local crystal orientation can result in a broad range of property combinations. This review presents the MSD framework in the context of both the engineering advances that have led to its creation, and those that complement or provide alternative methods for design of materials (meaning ‘optimization of material structure’ in this context). A variety of definitions for the structure of materials are presented, with an emphasis on correlation functions; and spectral methods are introduced for compact descriptions and efficient computations. The microstructure hull is defined as the design space for structure in the spectral framework. Reconstruction methods provide invertible links between statistical descriptions of structure, and deterministic instantiations. Subsequently, structure–property relations are reviewed, and again subjected to representation via spectral methods. The concept of a property closure is introduced as the design space for performance optimization, and methods for moving between the closures and hulls are presented as the basis for the subsequent discussion on microstructure design. Finally, the spectral framework is applied to deformation processes, and methodologies that facilitate process design are reviewed.

Work-hardening/softening behaviour of B.C.C. Polycrystals during changing strain paths : I. An integrated model based on substructure and texture evolution, and its prediction of the stress-strain behaviour of an if steel during two-stage strain paths

Abstract For many years polycrystalline deformation models have been used as a physical approach to predict the anisotropic mechanical behaviour of materials during deformation, e.g. the r -values and yield loci. The crystallographic texture was then considered to be the main contributor to the overall anisotropy. However, recent studies have shown that the intragranular microstructural features influence strongly the anisotropic behaviour of b.c.c. polycrystals, as revealed by strain-path change tests (e.g. cross effect, Bauschinger effect). This paper addresses a method of incorporating dislocation ensembles in the crystal plasticity constitutive framework, while accounting for their evolution during changing strain paths. Kinetic equations are formulated for the evolution of spatially inhomogeneous distributions of dislocations represented by three dislocation densities. This microstructural model is incorporated into a full-constraints Taylor model. The resulting model achieves for each crystallite a coupled calculation of slip activity and dislocation structure evolution, as a function of the crystallite orientation. Texture evolution and macroscopic flow stress are obtained as well. It is shown that this intragranular–microstructure based Taylor model is capable of predicting quantitatively the complex features displayed by stress–strain curves during various two-stage strain paths.

Modeling anisotropic strain hardening and deformation textures in low stacking fault energy fcc metals

Abstract The main issues and challenges involved in modeling anisotropic strain hardening and deformation textures in the low stacking fault energy (SFE) fcc metals (e.g. brass) are reviewed and summarized in this paper. The objective of these modeling efforts is to capture quantitatively the major differences between the low SFE fcc metals and the medium (and high) SFE fcc metals (e.g. copper) in the stress–strain response and the deformation textures. While none of the existing models have demonstrated success in capturing the anisotropy in the stress–strain response of the low SFE fcc metals, their apparent success in predicting the right trend in the evolution of deformation texture is also questionable. There is ample experimental evidence indicating that the physical mechanism of the transition from the copper texture to the brass texture is represented wrongly in these models. These experimental observations demonstrate clearly the need for a new approach in modeling the deformation behavior of low SFE fcc metals. This paper reports new approaches for developing crystal plasticity models for the low SFE fcc metals that are consistent with the reported experimental observations in this class of metals. The successes and failures of these models in capturing both the anisotropic strain hardening and the deformation textures in brass are discussed in detail.

The process of shear band formation in plane strain compression of fcc metals: Effects of crystallographic texture

Abstract The recent advances in the development of constitutive equations for large deformations of ductile single crystals and the development of robust finite element procedures for solving non-homogeneous boundary-value problems using these constitutive models, provide a foundation for understanding and predicting many features of the localization of deformation into shear bands. This paper presents the results of a numerical simulation of the effects of crystallographic texture evolution on the process of shear band formation in plane strain compression of initially isotropic OFHC polycrystalline copper. An aggregate of single crystals is used to represent a polycrystal. The calculations are two-dimensional plane strain at the macroscopic level, but they use the actual slip system structure for fee materials with twelve {111} 110 type slip systems. In the calculations an element of the finite element mesh represents either a single crystal or a part of a single crystal, and the constitutive response at an integration point is given by the single crystal constitutive model. The calculation procedures enforce equilibrium and compatibility throughout the polycrystalline aggregate in the weak finite element sense. No initial material or geometric imperfections are prescribed, but the initial lattice orientations are different from one grain to the next. The localization of deformation in the simulations is found to be a natural outcome of large deformation processes in ductile polycrystalline materials, and associated with the concurrent evolution of crystallographic texture. Comparison of results from the numerical simulations against experimental measurements shows that the resolution of grain-scale micro-shear bands requires very fine finite element meshes. The limitations of our computers are such that at present even very refined finite element meshes are too coarse to capture grain-scale shear bands. However, our simulations do capture the major features that are observed experimentally. In particular, the averaged global stress-strain behavior, the crystallographic texture, and the orientation of macroscale shear bands predicted by our simulations are close to those measured in our experiments.

Key computational modeling issues in Integrated Computational Materials Engineering

Designing materials for targeted performance requirements as required in Integrated Computational Materials Engineering (ICME) demands a combined strategy of bottom-up and top-down modeling and simulation which treats various levels of hierarchical material structure as a mathematical representation, with infusion of systems engineering and informatics to deal with differing model degrees of freedom and uncertainty. Moreover, with time, the classical materials selection approach is becoming generalized to address concurrent design of microstructure or mesostructure to satisfy product-level performance requirements. Computational materials science and multiscale mechanics models play key roles in evaluating performance metrics necessary to support materials design. The interplay of systems-based design of materials with multiscale modeling methodologies is at the core of materials design. In high performance alloys and composite materials, maximum performance is often achieved within a relatively narrow window of process path and resulting microstructures. Much of the attention to ICME in the materials community has focused on the role of generating and representing data, including methods for characterization and digital representation of microstructure, as well as databases and model integration. On the other hand, the computational mechanics of materials and multidisciplinary design optimization communities are grappling with many fundamental issues related to stochasticity of processes and uncertainty of data, models, and multiscale modeling chains in decision-based design. This paper explores computational and information aspects of design of materials with hierarchical microstructures and identifies key underdeveloped elements essential to supporting ICME. One of the messages of this overview paper is that ICME is not simply an assemblage of existing tools, for such tools do not have natural interfaces to material structure nor are they framed in a way that quantifies sources of uncertainty and manages uncertainty in representing physical phenomena to support decision-based design.

Strain hardening regimes and microstructure evolution during large strain compression of high purity titanium

Abstract The sudden increase of strain hardening rates seen after small strains in titanium, was shown to correlate with the onset of deformation twinning. This result appears to match quantitatively with Hall–Petch grain size strengthening. The new twin boundaries appear to reduce the effective grain size.