Mechanical behavior of polycrystalline materials

From the mechanical point of view, polycrystalline materials have to be considered as a specific class of composites. They are composed of many grains, with grains size ranging from nm to cm scales. Grains are generally assembled in a random way, i.e. their size, shape, and lattice orientation do not depend on the size, shape, and orientation of the surrounding grains (figure 1). Therefore, the microstructure of polycrystals can hardly be described exactly. Most of the time, one can only access a statistical characterization of grain arrangement e.g. with the help of cross-correlation functions. In the Euler orientation space, microstructure description is generally limited to the distribution of crystal lattice orientations (Orientation Distribution Function, ODF, or crystallographic texture)

Multiscale modeling of upper mantle plasticity: From single-crystal rheology to multiphase aggregate deformation

We report a first application of an improved second-order (SO) viscoplastic self-consistent model for multiphase aggregates, applied to an olivine + diopside aggregate as analogue for a dry upper mantle peridotite deformed at 10 15 s 1 shear strain rate along a 20-Ma ocean geotherm. Beside known dislocation slip systems, this SO-model version accounts for an isotropic relaxation mechanism representing ‘diffusionrelated’ creep mechanisms in olivine. Slip-system critical resolved shear stress (CRSS) are evaluated in both phases – as functions of P, T, oxygen fugacity (fO2) and strain rate – from previously reported experimental data obtained on single crystals and first-principle calculations coupled with the Peierls–Nabarro model for crystal plasticity; and the isotropic-mechanism dependence on T and P matches that of Si selfdiffusion in olivine, while its relative activity is constrained by reported data. The model reproduces well the olivine and diopside lattice preferred orientations (LPO) produced experimentally and observed in naturally deformed rocks, as well as observed sensitivities of multiphase aggregate strength to the volume fraction of the hard phase (here diopside). It shows a significant weakening of olivine LPO with increasing depth, which results from the combined effects of the P-induced [100]/[001] dislocation-slip transition and the increasing activity with T of ‘diffusion-related’ creep. This work thus provides a first quantification of the respective effects of [100]/[001] slip transition and diffusion creep on the olivine LPO weakening inducing the seismic anisotropy attenuation observed in the upper mantle

Modeling and simulation of laser shock waves in elasto-plastic polycrystalline microstructures

We study the propagation of elasto-plastic shockwaves induced by high power laser impacts in 2D polycrystalline metallic alloys in order to investigate the influence of the material microstructure on the fields of plastic strain and subsequent residual stresses. Implementing a visco-plastic constitutive relation at the grain scale accounting for two dislocation slip systems into a finite volume numerical scheme, simulations on single crystal specimens with different lattice orientations show that plastic strain is concentrated in narrow bands originating at the edges of the laser impact and parallel to the slip planes. In the case of polycrystalline microstructures composed of randomly oriented grains, it is found that the microstructure morphology is the origin of a heterogeneous distribution of the residual plastic strain and stress fields, which thus departs from the residual stress fields usually modeled when the microstructure is not accounted for. To account for the random character of polycrystal microstructures, we perform a statistical analysis of the mechanical fields over a large number of microstructures to quantify the dispersion of the results. It is found that even though the residual stresses induced by a laser impact are in compression on average at the center of the laser impact, some realizations of the microstructures can lead to localized concentrations of less compressive, or even tensile, residual stresses at the surface, thus probably reducing the fatigue resistance of the shocked material

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

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

Foreword

La mécanique des matériaux, qu’il s’agisse d’alliages métalliques, de polymères, de composites, ou encore de minéraux, est un domaine de recherche vaste s’appuyant aussi bien sur la physique, la chimie, les mathématiques, les techniques numériques, que les sciences expérimentales. Elle a la particularité de traverser les échelles de l’atome au milieu continu macroscopique.En particulier, la prise en compte des mécanismes élémentaires de déformation aux échelles pertinentes permet la construction de modèles de comportement robustes, i.e. qui soient capables non seulement de reproduire fidèlement les observations mais aussi de prédire le comportement mécanique dans des conditions inexplorées ou inexplorables expérimentalement

Incremental homogenization approach for ageing viscoelastic polycrystals

An approximate self-consistent modelling is proposed to estimate the effective viscoelastic response of polycrystals presenting an ageing constitutive behaviour. This approach makes use of the equivalence between the Dirichlet series approximation of the viscoelastic functions and an internal variables formulation. An illustrative application is performed for model 2D polycrystals for which the exact expression of the continuous effective relaxation spectrum is give

An analytical finite-strain parametrization for texture evolution in deforming olivine polycrystals

Progressive deformation of upper mantle rocks via dislocation creep causes their constituent crystals to take on a non-random orientation distribution (crystal preferred orientation or CPO). The resulting anisotropy of the rock's elastic properties can be observed by seismic techniques, and provides a means to constrain mantle convective flow patterns. Existing methods for calculating the evolution of CPO in deforming olivine-dominated rocks rely on unwieldy discrete representations of the crystal orientation distribution in terms of a large number (103-104) of individual grains. Here we propose a more efficient method in which CPO is represented using three continuous analytical functions (structured basis functions or SBFs), each of which represents a virtual CPO produced by the action of just one of the three dominant slip systems of olivine. The SBFs are then combined using an appropriate weighting scheme to represent a realistic CPO that results from the simultaneous activity of all three slip systems. We assume that olivine CPO is a unique function of the finite strain experienced by the aggregate, which implies that the weights of the SBFs depend only on the two ratios of the lengths of the axes of the finite strain ellipsoid (FSE) and the two ratios of the strengths (critical resolved shear stresses) of the slip systems. Our preferred set of weighting coefficients is obtained by least-squares fitting of the SBF expansion to the predictions of a kinematic model (solved by the method of characteristics) in which the amplitudes of the crystallographic spins do not increase with strain. Calculation of CPO using this model is ≈107 times faster than full homogenization approaches such as the second-order self-consistent model, and the result fits the characteristics-based solution with a variance reduction ≥ 88.6 per cent for equivalent strains up to 0.9. Finally, we propose a simple modification of the FSE that prevents the CPO from becoming singular at large strains

Application of electron tomography of dislocations in beam-sensitive quartz to the determination of strain components

In this study we apply electron tomography of dislocations to quartz with a view to assess whether the von Mises-Taylor criterion is satisfied or violated in a deformed crystal of quartz. We propose a method to perform electron tomography with few projected images which allows extension of this technique to beam-sensitive materials such as quartz. The 3D characterization of the dislocation microstructure allows the evaluation of contributions to dislocation mobility with no ambiguity. From the geometrical characteristics of the dislocations and their Burgers vectors, we show how to identify the non-zero components of the strain tensor. We show that in the quartz grain investigated, the von-Mises-Taylor criterion is satisfied thanks to the climb of 〈c + a〉 dislocations.The TEM national facility in Lille (France) is supported by the Conseil Regional du Nord-Pas de Calais, the European Regional Development Fund (ERDF), and the Institut National des Sciences de l’Univers (INSU, CNRS). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under grant agreement 787198 – TimeMan. We thank A.K. Kronenberg and an anonymous reviewer for constructive comments