Boundary element methods for cohesive thermo-mechanical damage and micro-cracking evolution

Abstract

In this thesis, Boundary Element Methods (BEM) are developed for micro-mechanic cohesive non linear problems. Modelling of intergranular and transgranular damage and micro-cracking evolution in polycrystalline materials is presented for different physical engineering problems and loading conditions: mechanical and thermo-mechanical applications are considered in the context of micromechanics. Throughout the thesis the different models are based on a multi-region boundary element approach combined with the dual boundary element formulation. The polycrystalline microstructures are generated with Voronoi tessellations, which well represent statistically the morphology of multi-grain materials; the formulation is able to consider the stochastic effect of each grain’s crystal anisotropy within the whole aggregate. Linear cohesive laws are used for assessing initiation and propagation of damage on intergranular and transgranular surfaces; moreover different physical assumptions on the cohesive models are investigated in order to guarantee energetic independence between mode I and II of fracture as well as inter- and trans-granular damage. Transgranular surfaces are introduced during the numerical simulation, so that the benefits of BEM are maintained and any internal damage propagation is not affected by initial discretization: the nucleation is based on a stress criterion. Upon cohesive failure, non linear frictional contact analysis is introduced. The effect of thermal loading is then introduced to model stress generation and damage propagation due to steady state and transient thermal loading. The cohesive model is updated to take into account the new thermal fields. Damage dependent Fourier’s law is implemented to model cohesive surfaces as heat barriers. Investigations on the effect of grain size, critical fracture energies and loading conditions are done. The presented formulations are shown to provide efficient modelling of the aforementioned engineering applications and their accuracy is compared throughout the thesis with analytical, numerical and experimental findings, where available.