Abstract

The presentation is aimed to cover areas related to modeling of material behaviour using different numerical schemes. Special emphasis is laid on homogenization procedures and multi- scale approaches that include inelastic microstructural deformations and development of inter- face cracks. In detail the inelastic responses of polycrystals is investigated including induced anisotropy and nonlinear hardening. The necessary numerical procedures will be discussed and examples from different areas are introduced. 

Included in this presentation is the design of macroscopic constitutive equations with only few parameters that are obtained from homogenization of polycrystal assemblies. The results are validated at micro and macro scale by means of experiments. These include as well results from microstructural observation as from classical pullout tests. Typical and important industrial applications range from ceramic to ductile materials.

Abstract

The influence of the microstructural heterogeneities is an important topic in the study of materials. In the context of computational mechanics, it is therefore necessary to generate virtual materials that are statistically equivalent to the microstructure under study, and to connect that geometrical description to the different numerical methods. Herein, the authors present a procedure to model continuous solid polycrystalline materials, such as rocks and metals, preserving their representative statistical grain size distribution. The first phase of the procedure consists of segmenting an image of the material into adjacent polyhedral grains representing the individual crystals. This segmentation allows estimating the grain size distribution, which is used as the input for an advancing front sphere packing algorithm. Finally, Laguerre diagrams are calculated from the obtained sphere packings. The centers of the spheres give the centers of the Laguerre cells, and their radii determine the cells’ weights. The cell sizes in the obtained Laguerre diagrams have a distribution similar to that of the grains obtained from the image segmentation. That is why those diagrams are a convenient model of the original crystalline structure. The above-outlined procedure has been used to model real polycrystalline metallic materials. The main difference with previously existing methods lies in the use of a better particle packing algorithm.

Abstract

We present a phase-field model to simulate intergranular and transgranular crack propagation in ferroelectric polycrystals. The proposed model couples three phase-fields describing (1) the polycrystalline structure, (2) the location of the cracks, and (3) the ferroelectric domain microstructure. Different polycrystalline microstructures are obtained from computer simulations of grain growth. Then, a phase-field model for fracture in ferroelectric single-crystals is extended to polycrystals by incorporating the differential fracture toughness of the bulk and the grain boundaries, and the different crystal orientations of the grains. Our simulation results show intergranular crack propagation in fine-grain microstructures, while transgranular crack propagation is observed in coarse grains. Crack deflection is shown as the main toughening mechanism in the fine-grain structure. Due to the ferroelectric domain switching mechanism, noticeable fracture toughness enhancement is also obtained for transgranular crack propagation. These observations agree with experiment.

Abstract

We simulate the fracture processes of ferroelectric polycrystals in three dimensions using a phase-field model. In this model, the grain boundaries, cracks and ferroelectric domain walls are represented in a diffuse way by three phase-fields. We thereby avoid the difficulty of tracking the interfaces in three dimensions. The resulting model can capture complex interactions between the crack and the polycrystalline and ferroelectric domain microstructures. The simulation results show the effect of the microstructures on the fracture response of the material. Crack deflection, crack bridging, crack branching and ferroelastic domain switching are observed to act as the main fracture toughening mechanisms in ferroelectric polycrystals. Our fully 3-D simulations illustrate how the combination of these mechanisms enhances the fracture toughness of the material, and pave the way for further systematic studies, including fracture homogenization.