Representative volume element size determination for viscoplastic properties in polycrystalline materials

Abstract

The size of representative volume element (RVE) for 3D polycrystalline material is investigated. A statistical RVE size determination method is applied to a Voronoi tessellation-based pure copper microstructure. The definition of RVE has remained problematic in the literature for properties related to nonlinear viscoplastic behavior, e.g. apparent viscoplastic parameter, intrinsic plastic dissipation. Computational homogenization for elastic and plastic properties is performed within a crystal plasticity finite element framework, over many realizations of the stochastic microstructural model, using periodic boundary conditions. The generated data undergoes statistical treatment, from which RVE sizes are obtained. The method used for determining RVE sizes was found to be operational, even for viscoplasticity. The microscale analysis of the full-field simulation results reveals microstructure-relate heterogeneities which shed new light on the problem of RVE size determination for nonlinear properties.

Generating polycrystalline microstructures with prescribed tensorial texture coefficients

“…We start with the case of a unique grain-size and a uniform orientation distribution, corresponding to mechanically isotropic behavior [86][87][88]. For the results to be representative, it is necessary to determine the number of grains which ensure an isotropic effective material response, see for example Kanit et al [15] and Yang et al [17]. In this spirit, we investigate microstructures with an increasing number of grains and study their effective stiffness.…”

“…Instead, using synthetic representative volume elements (RVE) [15,17] provide a way to generate periodic computational cells within a reasonable amount of time. However, using these RVEs comes with the challenge of accurately reproducing the investigated microstructure, or at least the important characteristics of it.…”

Effect of defects and reinforcements on the mechanical behaviour of a bi-layered panel

“…According to Hill’s definition [16], for a composite sample, the RVE should contain sufficient microstructural details to adequately represent the composites. Some efforts have been devoted to quantifying the minimum dimensions of RVE [17]: (i) Kanit et al [18] applied a statistical approach to determine dimensions of RVEs based on desirable precision and deduction with four to five realizations; (ii) Terada et al [19] presented the variational formulae for homogenization and employed the convergence of several macro and micro parameters, i.e. stresses in inhomogeneity, to reduce the dimension of an adequately large RVE.…”