Fast Fourier transform-based modelling for the determination of micromechanical fields in polycrystals

International audienceEmerging characterization methods in Experimental Mechanics pose a challenge to modelers to devise efficient formulations that permit interpretation and exploitation of the massive amount of data generated by these novel methods. In this overview we report on a numerical formulation based on Fast Fourier Transforms, developed over the last 15 years, which can use the voxelized microstructural images of heterogeneous materials as input to predict their micromechanical and effective response. The focus of this presentation is on applications of the method to plastically-deforming polycrystalline materials

Influence of microstructure variability on short crack growth behavior

Fatigue life in metals is predicted utilizing regression analysis of large sets of experimental data. Furthermore, a high variability in the short crack growth (SCG) rate has been observed in polycrystalline materials, in which the evolution and distribution of local plasticity is strongly influenced by the microstructure features. We aim to identify relationships between the crack driving force and the materials microstructure; specifically addressing variability of microstructure features and slip activity near a crack-tip as a means to account for the variability in the SCG behavior. To investigate the effects of microstructure variability on the SCG rate, sets of different microstructure realizations are constructed, in which cracks of different length are introduced to mimic quasi-static SCG. Through fatigue indicator parameters within crystal plasticity models, scatter within the SCG rates is related to variability in the microstructural features as a means to quantify uncertainty in fatigue behavior

Modeling microstructural effects in dilatational plasticity of polycrystalline materials

In a recent paper [1] we presented a new constitutive model for the viscoplastic response of polycrystalline aggregates accounting for local anisotropy induced by crystal plasticity and dilatational effects associated with the presence of intergranular cavities. In this contribution we provide a summary of our findings, as well as previously unpublished details of the numerical algorithm underlying this novel formulation. The formulation is based on homogenization and captures microstructural effects on the dilatational plastic behavior of polycrystalline materials. These effects are relevant to many engineering problems in which the presence of cavities embedded in a heterogeneous and anisotropic polycrystalline matrix must be accounted for, and for which standard polycrystalline models of incompressible plasticity, or dilatational plasticity formulations for voided materials with uniform properties of the matrix, have been proven to be insufficient. The present approach makes use of variational linearcomparison homogenization methods to develop constitutive models simultaneously accounting for texture of the matrix, porosity and average pore shape and orientation. The predictions of the models are compared with full-field numerical simulations based on fast Fourier transforms to study the influence of different microstructural features (e.g. overall porosity, single-crystal anisotropy, etc.) and triaxiality on the dilatational viscoplastic behavior of voided fcc polycrystals.Facultad de Ingenierí

Full-field vs. homogenization methods to predict microstructure-property relations for polycrystalline materials

In this chapter, we review two recently proposed methodologies, based on crystal plasticity, for the prediction of microstructure-property relations in polycrystalline aggregates. The first, known as the second-order viscoplastic self-consistent (SC) method, is a mean-field theory, while the second, known as the fast Fourier transform (FFT)-based formulation, is a full-field method. The main equations and assumptions underlying both formulations are presented, using a unified notation and pointing out their similarities and differences. Concerning mean-field SC homogenization theories for the prediction of mechanical behavior of nonlinear viscoplastic polycrystals, we carry out detailed comparisons of the different linearization assumptions that can be found in the literature. Then, after validating the FFT-based full-field formulation by comparison with available analytical results, the effective behavior of model material systems predicted by means of different SC approaches are compared with ensemble averages of full-field solutions. These comparisons show that the predictions obtained by means of the second-order SC approach-which incorporates statistical information at grain level beyond first-order, through the second moments of the local field fluctuations inside the constituent grains-are in better agreement with the FFT-based full-field solutions. This is especially true in the cases of highly heterogeneous materials due to strong nonlinearity or single-crystal anisotropy. The second-order SC approach is next applied to the prediction of texture evolution of polycrystalline ice deformed in compression, a case that illustrates the flexibility of this formulation to handle problems involving materials with highly anisotropic local properties. Finally, a full three-dimensional implementation, the FFT-based formulation, is applied to study subgrain texture evolution in copper deformed in tension, with direct input and validation from orientation images. Measurements and simulations agree in that grains with initial orientation neartend to develop higher misorientations. This behavior can be explained in terms of attraction toward the two stable orientations and grain interaction. Only models like the FFT-based formulation that account explicitly for interaction between individual grains are able to capture these effects

Dislocation interactions in olivine control postseismic creep of the upper mantle.

Changes in stress applied to mantle rocks, such as those imposed by earthquakes, commonly induce a period of transient creep, which is often modelled based on stress transfer among slip systems due to grain interactions. However, recent experiments have demonstrated that the accumulation of stresses among dislocations is the dominant cause of strain hardening in olivine at temperatures ≤600 °C, raising the question of whether the same process contributes to transient creep at higher temperatures. Here, we demonstrate that olivine samples deformed at 25 °C or 1150-1250 °C both preserve stress heterogeneities of ~1 GPa that are imparted by dislocations and have correlation lengths of ~1 μm. The similar stress distributions formed at these different temperatures indicate that accumulation of stresses among dislocations also provides a contribution to transient creep at high temperatures. The results motivate a new generation of models that capture these intragranular processes and may refine predictions of evolving mantle viscosity over the earthquake cycle

Modeling the mechanical response of polycrystals deforming by climb and glide

This paper presents a crystallographically-based constitutive model of a single crystal deforming by climb and glide. The proposed constitutive law is an extension of the rate-sensitivity approach for single crystal plasticity by dislocation glide. Based on this description at single crystal level, a homogenization-based polycrystal model for aggregates deforming in a climb-controlled thermal creep regime is developed. To illustrate the capabilities of the proposed model, we present calculations of effective behavior of olivine and texture evolution of aluminum at warm temperature and low strain rate. In both cases, the addition of climb as a complementary single-crystal deformation mechanism improves the polycrystal model predictions

Subgrain rotation recrystallization during shearing: insights from full-field numerical simulations of halite polycrystals

We present, for the first time, results of full-field numerical simulations of subgrain rotation recrystallization of halite polycrystals during simple shear deformation. The series of simulations show how microstructures are controlled by the competition between (i) grain size reduction by creep by dislocation glide and (ii) intracrystalline recovery encompassing subgrain coarsening by coalescence through rotation and alignment of the lattices of neighboring subgrains. A strong grain size reduction develops in models without intracrystalline recovery, as a result of the formation of high-angle grain boundaries when local misorientations exceed 15°. The activation of subgrain coarsening associated with recovery decreases the stored strain energy and results in grains with low intracrystalline heterogeneities. However, this type of recrystallization does not significantly modify crystal preferred orientations. Lattice orientation and grain boundary maps reveal that this full-field modeling approach is able to successfully reproduce the evolution of dry halite microstructures from laboratory deformation experiments, thus opening new opportunities in this field of research. We demonstrate how the mean subgrain boundary misorientations can be used to estimate the strain accommodated by dislocation glide using a universal scaling exponent of about 2/3, as predicted by theoretical models. In addition, this strain gauge can be potentially applied to estimate the intensity of intracrystalline recovery, associated with temperature, using quantitative crystallographic analyses in areas with strain gradients