In this project, the influence of the development of geometrically-necessary dislocations (GNDs) at a crack tip in single crystals on the hardening and crack propagation behaviour is investigated. In particular we are interested in examining the effect of such additional hardening on the development of glide and kink bands at the crack tip as well as on the process of crack opening. To this end, following Nye and many other, local deformation incompatibility in the material is adopted as a measure of the density of GNDs. Their development results in additional energy being stored in the material, leading to additional kinematic-like hardening. A thermodynamic formulation of the model in the context of the dissipation principle facilitates the derivation of the corresponding hardening relation. Results suggest that this additional hardening retards kink-band development, but has little or no influence on glide-band development.

The numerical analysis of ductile damage and failure in engineering materials is often based on the micromechanical model of Gurson [1]. Numerical studies in the context of the finite-element method demonstrate that, as with other such types of local damage models, the numerical simulation of the initiation and propagation of damage zones is not reliable and strongly mesh-dependent. The numerical problems concern the global load-displacement response as well as the onset, size, and orientation of damage zones and thus to the reliability of the obtained results. From a mathematical point of view, this problem is caused by the loss of ellipticity of the set of partial differential equations determining (the rate of) the deformation field. Physically it has to do with the fact that the effect of interaction in the microstructure on the material behaviour has not been taken into account.

In metal matrix composites, e.g. made of aluminium A6061T6 and 20 vol% SiC particles, ductile crack extension occurs only in the ductile Al phase, whereas cracks of the rigid SiC inclusions and decohesion of the Al/SiC interfaces are commonly not observed experimentally. The SiC particles lead to locally different constraints on the micro scale, resulting in a zigzag shaped crack path. The application of continuum damage models can predict the crack growth inside the ductile matrix.

The growth of cracks in metal matrix composites is very often accompanied by the formation of localized deformation and damage fields. Standard local continuum approaches for the simulation of such phenomena suffer of a strong mesh dependence of the obtained results. The application of so-called non-local damage models can help to cope with such problems and significantly improve the quality of results obtained with the finite element method.

The purpose of this work is the comparison of damage and failure modeling on the basis of unit-cell calculations and homogenisation methods. To this end such behaviour in particle-reinforced metal matrix composites (PRMMC), promising materials used in many engineering applications, is investigated. The mechanical properties of such composites depend on the microstructural morphological features such as volume fraction and distribution of reinforced particles embedded to the metal matrix. Therefore, the investigation of the structural response and the damage evolution of real and artificial microstructures are considered.

The accurate description of the damage and failure in heterogeneous materials very often requires the consideration of a possible interface damage between the different material layers. Hence, the development of an appropriate description of the underlying damage mechanics at the interface has to be established. To utilize such a behaviour cohesive elements can be used in the framework of a finite element analysis allowing to adapt a wide range of different interface behaviours to interface layers of small thickness.

This work demonstrates the simulation of the damage and failure behaviour of MMC materials within a finite element framework using damage models for the description of ductile damage in the matrix material and the enrichment of the damage behaviour of the composite with help of cohesive elements in order to describe the failure behaviour at the interface between embedded particles and the ductile matrix. The influence of the interface properties (constitutive behaviour, material parameter) on the damage characteristic of the MMC is investigated.

The growth of cracks in metal matrix composites are very often accompanied by the formation of localized deformation and damage fields. Standard local continuum approaches for the simulation of such phenomena suffer of a strong mesh dependence of the obtained results. The application of so-called non-local damage models can help to cope with such problems and significantly improve the quality of results obtained with the finite element method.

This overview briefly demonstrates the use of a framework of adaptive mesh refinement and model adaptivity towards the simulation of ductile damage in a metal matrix composite (MMC). An artificial microstructure detail of a MMC is discretized with a coarse initial mesh of triangular elements. To maintain a high mesh quality an adaptive mesh refinement procedure is used to refine the finite element mesh at regions where damage localization in the ductile matrix occurs. This mesh is controlled with the help of a refinement criterion based on the evolution of porosity in the matrix material.

This work is concerned with the analysis of stability, loss of stability, and the associated bifurcation phenomena in the context of local and non-local simulation of ductile damage in metallic materials at the structural level of finite elements and the material level of observation.

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