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.