Table of contents

This special issue contains selected contributions from invited speakers to the 'Polycrystal Modelling with Experimental Integration: A Symposium Honoring Carlos Tomé', held as part of the 2011 TMS Annual Meeting and Exhibition, that took place on February 27–March 3, 2011 in San Diego, CA, USA.

This symposium honored the remarkable contributions of Dr Carlos N Tomé to the field of mechanical behavior of polycrystalline materials, on the occasion of his 60th birthday. Throughout his career, Dr Tomé has pioneered the theoretical and numerical development of models of polycrystal mechanical behavior, with emphasis on the role played by texture and microstructure on the anisotropic behavior of engineering materials. His many contributions have been critical in establishing a strong connection between models and experiments, and in bridging different scales in the pursuit of robust multiscale models with experimental integration. Among his achievements, the numerical codes that Dr Tomé and co-workers have developed are extensively used in the materials science and engineering community as predictive tools for parameter identification, interpretation of experiments, and multiscale calculations in academia, national laboratories and industry. The symposium brought together materials scientists and engineers to address current theoretical, computational and experimental issues related to microstructure–property relationships in polycrystalline materials deforming in different regimes, including the effects of single crystal anisotropy, texture and microstructure evolution. Synergetic studies, involving different crystal plasticity-based models, including multiscale implementations of the latter, and measurements of global and local textures, internal strains, dislocation structures, twinning, phase distribution, etc, were discussed in more than 90 presentations.

The papers in this issue are representative of the different length-scales, materials, and experimental and modeling techniques addressed in the symposium. The special issue starts with two papers by Wang et al presenting molecular dynamics studies of the interaction of dislocations with grain and twin boundaries in hcp crystals. The papers by Vu et al and Mercier et al that follow present novel formulations based on non-linear homogenization for viscoelastic and elasto-viscoplastic polycrystals, respectively. Next, two papers by Merkel et al and Beaudoin et al report on synchrotron x-ray measurements of lattice strains in hcp-iron and Al–Li (fcc) polycrystals, respectively, interpreted by means of polycrystal plasticity models. The following two papers by Field et al and Lefebvre et al show how orientation images of polycrystalline cubic metals obtained by electron backscatter diffraction can be used as direct input of models for quantification of dislocation density fields and surface roughness, respectively. Finally, the papers by Jeong et al and Vanna Yang et al show applications of physically-based models of polycrystal plasticity to the analysis of the anisotropic plastic response of stainless steels, and the strain-hardening of Mg–Al alloys, respectively.

In this paper, we study the kinetics and energetics involved in the nucleation and propagation of $\{\bar {1}\,0\,1\,1\}$ and $\{\bar {1}\,0\,1\,3\}$ twinning dislocations (TDs) in Mg using atomistic simulations. We demonstrate that for both twins, a 2-layer TD of mixed character nucleates as a result of the interaction of a basal dislocation with a twin boundary. The favorability of the 2-layer TD over a 4-layer TD of edge character can be explained by its greater mobility. The twin boundary likely translates by nucleating and propagating 2-layer TDs with opposite-signed screw components in equal amounts on average.

Using molecular dynamics (MD) simulations, the dislocation structures of $[1\,\bar {2}\,1\,0]$ symmetric tilt grain boundaries (STGBs) in hexagonal close packed (hcp) crystal structures are studied. STGBs over the entire range of possible rotation angles θ from 0° to 90° are found to have an ordered atomic structure. Formation energy calculations reveal four local minimum-energy boundaries that correspond to coherent grain boundaries (GBs). Deviations in tilt from the basal plane (θ = 0°, $P_{\rm B}^{(1)} )$, prismatic plane (θ = 90°, $P_{\rm B}^{(6)} )$, or one of these four minimum-energy boundaries, $P_{\rm B}^{(2)} ,P_{\rm B}^{(3)} ,P_{\rm B}^{(4)} ,P_{\rm B}^{(5)}$, result in the formation of a tilt wall (edge-type grain boundary dislocations, GBDs) superimposed on the nearest GB structure $P_{\rm B}^{(i)}$ in θ-space. As θ deviates far from the rotation angle of one $P_{\rm B}^{(i)}$ and draws closer to that of an adjacent $P_{\rm B}^{(j)}$, an abrupt transition in STGB base boundary structure and GBD Burgers vector occurs. For all θ, the sign and spacing of GBDs depend on θ, and their Burgers vector is either one or two times the interplanar spacing of P_B. We present a simple model that generalizes the results to other c/a ratios. Subsequent MD simulations show that (1) the model forecasts the STGB structure to first-order and (2) STGBs with two distinct atomic structures can have remarkably different responses when interacting with basal lattice dislocations originating from the adjoining crystals.

The correspondence principle is customarily used with the Laplace–Carson transform technique to tackle the homogenization of linear viscoelastic heterogeneous media. The main drawback of this method lies in the fact that the whole stress and strain histories have to be considered to compute the mechanical response of the material during a given macroscopic loading. Following a remark of Mandel (1966 Mécanique des Milieux Continus(Paris, France: Gauthier-Villars)), Ricaud and Masson (2009 Int. J. Solids Struct.46 1599–1606) have shown the equivalence between the collocation method used to invert Laplace–Carson transforms and an internal variables formulation. In this paper, this new method is developed for the case of polycrystalline materials with general anisotropic properties for local and macroscopic behavior. Applications are provided for the case of constitutive relations accounting for glide of dislocations on particular slip systems. It is shown that the method yields accurate results that perfectly match the standard collocation method and reference full-field results obtained with a FFT numerical scheme. The formulation is then extended to the case of time- and strain-dependent viscous properties, leading to the incremental collocation method (ICM) that can be solved efficiently by a step-by-step procedure. Specifically, the introduction of isotropic and kinematic hardening at the slip system scale is considered.

Homogenization of linear viscoelastic and non-linear viscoplastic composite materials is considered in this paper. First, we compare two homogenization schemes based on the Mori–Tanaka method coupled with the additive interaction (AI) law proposed by Molinari et al (1997Mech. Mater.26 43–62) or coupled with a concentration law based on translated fields (TF) originally proposed for the self-consistent scheme by Paquin et al (1999Arch. Appl. Mech.69 14–35). These methods are also evaluated against (i) full-field calculations of the literature based on the finite element method and on fast Fourier transform, (ii) available analytical exact solutions obtained in linear viscoelasticity and (iii) homogenization methods based on variational approaches. Developments of the AI model are obtained for linear and non-linear material responses while results for the TF method are shown for the linear case. Various configurations are considered: spherical inclusions, aligned fibers, hard and soft inclusions, large material contrasts between phases, volume-preserving versus dilatant anelastic flow, non-monotonic loading. The agreement between the AI and TF methods is excellent and the correlation with full field calculations is in general of quite good quality (with some exceptions for non-linear composites with a large volume fraction of very soft inclusions for which a discrepancy of about 15% was found for macroscopic stress). Description of the material behavior with internal variables can be accounted for with the AI and TF approaches and therefore complex loadings can be easily handled in contrast with most hereditary approaches.

Internal elastic strains and textures are measured using monochromatic x-ray diffraction in -Fe plastically deformed up to 17.5 GPa and 600 K in the deformation-DIA. We observe the development of a strong 0 0 0 1 compression texture along with a strongly non-linear behavior of 0 0 0 2 lattice strains. We then use an elastoplastic self-consistent polycrystal model to simulate the macroscopic flow curves, internal strain and texture development within the sample. Input parameters are single-crystal elastic moduli, critical resolved shear stresses, and hardening behavior of the slip and twinning mechanisms. The model is found to reproduce the experiment data with basal slip as the easiest and most active deformation mechanism. Other active mechanisms are tensile twinning, prismatic and pyramidal 〈c + a〉 slip. Tensile twinning is most active at lower temperatures (e.g. 400 K) and a higher strain rate. In most cases, the twinning activity occurs early in the deformation and later saturates. It is also responsible for the non-linear behavior of 0 0 0 2 lattice strains. Later in the deformation, the plastic activity of -Fe is controlled by basal, prismatic and pyramidal 〈c + a〉 slip.

High energy diffraction microscopy is used to measure the crystallographic orientation and evolution of lattice strain in an Al–Li alloy. The relative spatial arrangement of the several pancake-shaped grains in a tensile sample is determined through in situ and ex situ techniques. A model for crystal plasticity with continuity of lattice spin is posed, where grains are represented by layers in a finite element mesh following the arrangement indicated by experiment. Comparison is drawn between experiment and simulation.

Plastic deformation in polycrystalline materials involves a complex interaction of dislocations with defects in the lattice. The geometrically necessary component of the dislocation density can be quantified to some extent using data obtained from automated electron backscatter diffraction scans over planar regions or volumes using the three-dimensional imaging techniques that are currently available. Reliable measurements require that the step size of the orientation data used in determination of geometrically necessary dislocation densities be on the scale of the microstructural information. Measurements were performed in deformed Cu, Al and steel specimens. Geometrically necessary dislocation density in Cu deformed 10% in compression was about 15–30% of the overall estimated dislocation density. Measurements in Al demonstrate that three-dimensional estimates are on the order of 1.2–2 times the values obtained from 2D measurements on the same structures. Analysis of interstitial free steel specimens shows an increase in average geometrically necessary dislocation density by an order of magnitude for specimens deformed to 12% tensile deformation elongation.

The effect of the spatial distribution of crystallographic orientations on roping amplitude and wavelength in ferritic stainless steel has been evaluated. The through-thickness mechanical behaviour of a sheet deformed in tension has been tested experimentally and simulated using a full-field viscoplastic fast Fourier transform formulation. These crystal plasticity simulations use orientation imaging microscopy data as input, allowing for large-scale simulation domains to be investigated while accounting for the clustering of orientations with similar deformation behaviour. The simulations predict both the local deformation response as well as the macroscopic surface roughness. The latter is compared quantitatively with experimental measurements and is shown to predict both the wavelength and amplitude of the observed roping. The results of these simulations have also been compared with previously proposed mean-field crystal plasticity simulations of roping, performed using the viscoplastic self-consistent code, in which each crystal orientation is, at most, influenced by the behaviour of a homogenized matrix, but not by its local neighbourhood. Comparison between these two kinds of approaches thus allows us to assess the significance of the local neighbourhood on the macroscopic prediction of roping.

The visco-plastic self-consistent (VPSC) model is applied to a 304 austenitic stainless-steel sheet sample to investigate its suitability as a constitutive model for sheet metal forming simulations. The factors to which the model prediction is sensitive are explored. In particular, the influence of the textures obtained at three different depths on the in-plane variation of the r-value (Lankford coefficient) and the yield stress is investigated. Then, the grain number sensitivity in the representative volume element is analyzed. Moreover, the influence of the linearization scheme for the crystal constitutive power law on the simulation result is discussed. For simulation, discrete crystallographic orientation distributions are calculated from the pole figures obtained at different depths. Several mechanical experiments are conducted, namely, uniaxial tension, in-plane biaxial and the bulge tests. The mechanical response of the material is simulated using the VPSC model and compared with the model predictions.

The Kocks–Mecking method was used to compare the strain-hardening behavior at low strains of high pressure die cast Mg-9 mass% Al alloy and gravity cast fine grained pure Mg specimens. The alloy specimens exhibited a rounded flow curve in contrast with the pure metal's for which macroscopic yielding occurred at a well-defined stress. Microhardness mapping of the cross-section of an alloy specimen showed a surface layer, or skin, with hardness values ∼20 HV above those of the centre or core region. On the assumption that the core strain hardens at the same rate as the pure Mg specimen, it was estimated that ∼20% of the alloy specimen's cross-section was still elastic when the core reached full plasticity. The micromechanics of the elasto–plastic transition in the alloy specimens are discussed.