Different theoretical and numerical aspects of the polycrystalline problem using the boundary element method are investigated: first, being the formulation based on a integral representation of the governing equations, a novel and more compact expression of the integration kernels capable of representing the multi-field behaviour of generally anisotropic materials is presented second, the sources of the high computational cost of polycrystalline analyses are identified and suitably treated by means of different strategies including an ad-hoc grain boundary meshing technique developed to tackle the large statistical variability of polycrystalline micro-morphologies third, non-linear deformation and failure mechanisms such as inter-granular and trans-granular cracking and generally anisotropic crystal plasticity are studied and the numerical results presented throughout the thesis demonstrate the potential of the developed framework. The computational framework developed in this thesis is based on a non-linear multi-domain BEM approach for generally anisotropic materials and is devoted to the analysis of three-dimensional polycrystalline microstructures. Among the others, the Boundary Element Method (BEM) represents a viable alternative to FEM approaches as it allows to express the problem in terms of boundary values only, thus reducing the total number of degrees of freedom. However, finite element formulations usually lead to an extremely high number of degrees of freedom of the considered micro-structures, thus making alternative formulations of great engineering interest. Micro-mechanics studies are commonly performed using the Finite Element Method (FEM) for its versatility and robustness. In the present thesis, a computational framework for the analysis of the deformation and damage phenomena occurring at the micro-scale of polycrystalline materials is presented. A review of the current literature hypothesis and different modeling constitutive equations for modeling the corrosion of magnesium alloys along with a summary of the supplementary experimental methods is provided in this paper. Due to the complexity of the degradation process and the various factors that can be involved, several hypotheses were introduced to provide a realistic simulation of the corrosion behavior in vitro and in vivo. Furthermore, considerable research was done to develop numerical models towards an inexpensive and fast designing tools capable of simulating the degradation/corrosion behavior of magnesium-based implants.
Most of the research effort in the literature has been focused on assuring the biocompatibility, improving mechanical properties, and tailoring the corrosion rate of magnesium-based implants. In this scope, magnesium and its alloys were widely investigated due to their superior biocompatibility over other metals. This work concerns simulations in 3D and extends the previous work limited to 2D simulations.īiodegradable metals have been under significant research as promising alternatives to the currently in-use nonbiodegradable materials in the field of supportive medical implants.
A strong correlation is established between the roughness evolution, the metal crystalline properties and the corrosion mechanism of metal dissolution. A complex surface structure appears with a high geometrical roughness when defects are not too dense. The corrosion probability for grain boundary is set to a value higher than it is for the grain core. The parameters of the model, taking into account the polycrystalline aspect of corrosion, are the domain density and the corrosion probabilities of metal grain core and grain boundary sites. Either, a periodic pattern or randomly generated domains of Voronoï tessellation are used to represent the polycrystalline structure. The domains represent the monocrystalline cores while their boundaries represent the intergranular defects. The corroding polycrystalline material consists of domains and their boundaries.
A simple model for the effect of intergranular corrosion on overall corrosion processes is investigated using a cellular automata approach.