Large scale finite element simulations of polycrystalline aggregates: applications to X-ray diffraction and imaging for fatigue metal behaviour

International audienceLarge scale finite element simulations of the elastoviscoplastic behaviour of polycrystalline aggregates have become a standard technique to study the stress-strain heterogeneities that develop in grains during deformation. For a long time, comparison between continuum crystal plasticity and experimental field measurements was confined to the observation of surface behaviour. As for example the study of the development of intense deformation bands at the free surface of a polycrystal. Recent 3D experimental techniques open new perspectives in computational crystal plasticity. After reviewing how to define a representative volume element for polycrystal properties and showing that actual 3D computations, including grain shapes and orientations, are really needed to accurately determine the stress and strains distributions, two examples of applications of large scale simulations are described in this paper. First the simulation of 3D coherent X-ray diffraction in a polycrystalline gold sample is detailed. Based on the real geometry of the grains and their columnar nature, a 3D avatar is reconstructed. FE computations are then carried out to evaluate the effect of mechanical and thermal strain of the diffraction pattern resolved in the reciprocal space by complex FFT. Qualitative comparison with the experimental diffraction patterns shows that such computations can help understand the true nature of strain heterogeneities within the material. The second example of application deals with short fatigue crack propagation in polycrystals. One fundamental problem caused by short fatigue cracks is that despite decades of research, so far no reliable prediction of the crack propagation rates, comparable to the well-known Paris law in the long crack regime, could be established. This ``anomalous'' behaviour of short cracks is commonly attributed to factors like their complex three dimensional shapes and the influence of the local crystallographic environment affecting their propagation behaviour via a combination of physical mechanisms. Crystal plasticity computations based on the real grain shapes and orientations obtained thanks to diffraction contrast tomography are carried out using an ideal crack shape. The stress concentration at the crack tip is analysed with respect to possible crack growth directions

A MULTI-SCALE CRYSTAL PLASTICITY FINITE ELEMENT MODELING FRAMEWORK FOR PREDICTING STRAIN-RATE SENSITIVE DEFORMATION OF HEXAGONAL METALS

This work presents improvements to the methods used in crystal plasticity simulations. It shows how these improvements can be used to accurately predict the deformation behavior of two magnesium alloys, WE43, and AZ31. The first improvement to the methodology is guidance on the type of finite elements to use in explicit grain crystal plasticity simulations. This study found that quadratic tetrahedral and linear hexahedral elements are the most accurate element types included in the study. The study also concluded that tetrahedral elements are more desirable due to fast mesh generation and flexibility to describe geometries of grain structures. The second improvement made was the addition of a numerical scheme to enable the use of any rate sensitivity exponent in the fundamental power-law representation of the flow rule in crystal visco-plasticity. While allowing the use of even very large exponents that many materials exhibit, this numerical scheme adds little to no increase in computational time. This crystal plasticity model was used to accurately predict the deformation behavior of both WE43 and AZ31 under quasi-static and high rate deformation, predicting the stress-stain response and the evolution of texture, twinning and the relative activities of the various deformation modes

Investigation of the grain-scale deformation in a polycrystalline aluminum alloy

A finite element based crystal plasticity implementation is employed to study an aluminum polycrystal subjected to uniaxial loading. The emphasis is put on the effect of the representation of the microstructure on the strain accumulation and intra-granular misorientation field. To better capture the crystal-scale behavior, each grain in the mesh is discretized into many finite elements. It is found that irregular tessellations based on Voronoi schemes provide similar responses whereas regular solids show some differences. An extended investigation of the role of the grain boundaries in the development of strain heterogeneity and in the re-orientation of parts of the grains is also provided according to an original averaging procedure

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