Multiscale modeling of polycrystalline materials: A boundary element approach to material degradation and fracture

Abstract

In this work, a two-scale approach to degradation and failure in polycrystalline materials is proposed. The formulation involves the engineering component level (macro-scale) and the material grain level (micro-scale). The macro-continuum is modelled using a three-dimensional boundary element formulation in which the presence of damage is taken into account employing an initial stress approach for modelling the local softening in the neighborhood of points experiencing degradation at the micro-scale. The microscopic degradation is explicitly modelled by associating Representative Volume Elements (RVEs) to relevant points of the macro continuum, for representing the polycrystalline microstructure in the neighborhood of the selected points. A three-dimensional grain-boundary formulation is used to simulate intergranular degradation and failure in the microstructure, whose morphology is generated using Voronoi tessellations. Intergranular degradation and failure are modelled through cohesive and frictional contact laws. To couple the two scales, macro-strains are transferred to the RVE as periodic boundary conditions, while overall macro-stresses are obtained as volume averages of the micro-stress field. The comparison between effective macro-stresses for the damaged and undamaged RVE allows to define a macroscopic measure of material degradation. To avoid pathological damage localization at the macro-scale, integral non-local counterparts of the strains are employed. The multiscale processing algorithm is described. Some multiscale simulations are performed to investigate the capability of the method.

Modelling intergranular and transgranular micro-cracking in polycrystalline materials

“…To the best of the authors' knowledge, this is the first time a boundary element formulation has been employed to simultaneously address inter and trans-granular cracking within three-dimensional anisotropic crystal aggregates. The boundary element method has been successfully used to study intergranular failure of 2D [37] and 3D [38][39][40][41] polycrystalline materials at the grain scale; the above grain-scale intergranular models have also been successfully employed in a multi-scale framework [42,43] for capturing material degradation initiation and evolution at an engineering component level. A 2D model for inter-and transgranular micro-cracking has been recently presented by Geraci and Aliabadi [28].…”

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis—A Survey

“…Details on localization techniques are presented in [418,421]. Within the surveyed literature, continuum downscaling consists in transferring the displacement and surface force vector fields or stress and strain tensor fields calculated at points inside the spatial domain of LS x as suitable BCs to the boundaries of the RVEs of LS x`1 [422][423][424][425][426].…”

A multiscale modeling of CNT-reinforced cement composites

“…Based on the one dimensional geometry of reinforcing bars, an efficient finite element model was presented to simulate the bond between reinforcing bars and concrete [33]. A multiscale boundary element approach was investigated by which to study material degradation and fracture, which involved the engineering component level at the macroscale and the material grain level at the microscale [34].…”