Polycrystal models for the analysis of intergranular crack growth in metallic materials

Modelling Polycrystalline Materials: An Overview of Three-Dimensional Grain-Scale Mechanical Models

“…3D Voronoi polyhedra have been employed by Diard 60 for studying the plasticity of polycrystalline aggregates through crystal plasticity finite elements and by Zhang et al 61 , who simulated microplasticity-induced deformations in uniaxially strained ceramics. Threedimensional Voronoi tessellations have also been used by Kamaya et al 62 , who performed a statistical analysis of grain-boundary stresses in a microstructure comprised of 100 grains, by 63,64,65,32 , who modeled bainitic steel with crystal plasticity finite elements, by Luther and Könke 66 , who developed an algorithm to generate polycrystals with arbitrary grain size distribution functions for studying brittle intergranular damage in metallic polycrystals, by Musienko and Cailletaud 67 , to study intergranular stress corrosion cracking, transgranular cracking in a crystal plasticity framework, by Weinzapfel et al 68 , who presented a finite element model for analyzing subsurface stresses in an elastic half-space subjected to a general Hertzian contact load, with explicit consideration of the material microstructure topology, by Bomidi et al 21 , who developed a 3D finite element model to investigate intergranular fatigue damage of micro-electromechanical systems (MEMS) devices and to account for the effects of topological randomness of material microstructure on fatigue lives and by Benedetti and Aliabadi 69,70 , who studied the evolution of intergranular damage and cracking through cohesive-frictional boundary elements. It is worth noting that Voronoi tessellations are also frequently taken as initial microstructures in many thermodynamics-based models (phase field, level-set, .…”

“…The authors observed that their model could be suitable to analyze inelastic deformation and fracture of materials with little or no transgranular plasticity, such as ceramics and rock-like materials, where the pseudo-plasticity and non-linear stressstrain curves arise primarily from grain boundary separation and sliding. The damage and cracking behavior of polycrystalline specimens subjected to quasi static loads has been investigated by Luther and Könke 66 , who focused on the development of a modified Voronoi algorithm to improve the approximation of grain size distribution in artificially generated microstructures. The intergranular interfaces were represented with a cohesive zone model, to simulate crack propagation along grain boundaries.…”

Numerical modelling of intergranular fracture in polycrystalline materials and grain size effects

“…The parameters of the average Mode I traction-separation curve, corresponding to an average value of l2=0.15 μm, were selected in order to obtain an average Mode I fracture energy of 0.18 N/mm and a peak stress of 500 N/mm 2 , as suggested in [6] for polycrystalline interfaces (see the corresponding curve in Fig. 8 with solid 110 10 E   N/mm 2 were set for the grains, and the parameter α was selected as 0.0035.…”

“…In order to simplify the real material microstructure by considering a finite element discretization with zero-thickness interfaces, a suitable interface constitutive law has to be used (see [5][6][7][8][9][10][11][12][13][14][15][16] for a wide range of problems modelled using CZMs). Here, we consider the nonlocal CZM recently proposed in [2] for finite thickness interfaces.…”

3d vs. 2d Modelling of Cracking and Plasticity in Polycrystalline Materials

“…So far, the limitation of using 2D models over more realistic 3D simulations has not yet been fully quantified, although it is an information of primary importance from the engineering point of view. In case of intergranular crack growth, for instance, only qualitative statements regarding the crack pattern, much more tortuous in 3D than in 2D, are available [7].…”