Finite element modeling of periodic polycrystalline aggregates with intergranular cracks

Abstract

a b s t r a c tThe present study addresses the prediction of the mechanical response of model polycrystalline aggregates in which the anisotropy of individual crystals induces high internal stresses as well as microcracks. A novel procedure is proposed in order to automatically generate finite element (FE) meshes that conform to the polycrystalline microstructure. The meshes obtained are periodic in 3-D and they contain cohesive zone elements along all grain boundaries. The FE model is applied to two materials with significant elastic anisotropy at the crystal level: stainless steel and graphite. A self-consistent equivalent inclusion solution is shown to produce a valid mean-field estimate of the effective stiffness of the polycrystal. This reference solution is used in order to optimize the assignment of lattice orientations to individual grains prior to the FE simulations. It is demonstrated that relying on such model polycrystals increases the accuracy of FE predictions at an affordable computational cost. The influence of internal cracks on the macroscopic response depends on the anisotropy of individual crystals.

Atomistic and mean-field estimates of effective stiffness tensor of nanocrystalline copper

“…This result is in agreement with other literature studies, e.g. [61,63]. Figure 4 compares the CS/MT model predictions with the corresponding results of atomistic simulations for nano-grained polycrystals.…”

Elastostatic field distributions in polycrystals and cracked media

“…which suggests an extended Van Hove singularity P * xx = P * yy ∼ t −1/3 , as hinted by (26). This is a less singular behavior at the origin than that of the probability distribution P yy obtained for parallel cracks (Eq.…”

“…Using FFT computations, they showed that the field distributions in the matrix are well approximated by Gaussian distributions in the linear case but strongly deviate from the latter when dealing with strong nonlinearities such as perfect plasticity. The distribution of elastic fields in polycrystals is considered in [26].…”

From Architectured Materials to Large-Scale Additive Manufacturing

“…As a matter of fact, advanced models are often restricted to a limited variety of materials. Although isotropic and anisotropic polycrystalline metals, for instance, have been extensively studied by the means of both analytical and computational tools (Cailletaud et al 2003;Kanit et al 2003;Madi et al 2007;Berdin et al 2013;Fritzen et al 2013;Hor et al 2014;Kowalski et al 2016;Amodeo et al 2016;Schindler et al 2017), architectured materials bring up new challenges regarding the determination of effective properties.…”