Phase field modeling of general imperfect interfaces

• Applicant: Professor Dr.-Ing. Jörn Mosler
• Subject Area: Mechanics
• Term: since 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 401344875

Interfaces are playing an increasingly important role in engineering and materials science - particularly due to the proportion of interfaces in relation to volume on smaller length scales. For example, the positive and seemingly contradictory properties of nanocrystalline materials can be attributed to the high proportion of interfaces and their interaction with the surrounding bulk phases (high strength combined with high ductility). Another example is high-strength dual-phase steel, in which the mechanical properties as well as the distribution of grain boundaries and the interaction with microcracks in the brittle martesite phase can be used to develop damage-tolerant materials. Due to the high relevance of interfaces, it is not surprising that interest in work on interface models has risen sharply. In this project, the focus is on mechanical interfaces. If the geometry and the position of the interfaces to be modeled are known a priori (e.g. in the case of grain boundaries), they can be modeled directly as sharp interfaces - i.e. as two-dimensional objects. However, this is not always the case. For example, the position and geometry of cracks are initially unknown and follow from the boundary value problem to be solved. Phase field models are a promising way of solving these so-called free boundary problems (FBPs). It is precisely such descriptions of propagating interfaces that form the focus of the project. At the beginning of the first project, these models were still based on highly simplified assumptions (Griffith models) and were only significantly expanded in the following years. Currently, phase field models of coherent interfaces (surface elasticity) and phase field models of isotropic cohesive zone models can be regarded as state-of-the-art research. In most cases, however, a simplified geometrically linearized framework is assumed. Even though isotropic cohesive zone models can already describe some relevant mechanical properties, many other phenomena require an anisotropic description. For example, most materials exhibit different fracture energies under mode-I, mode-II and mode-III failure, e.g. concrete. A simple isotropic model cannot represent such effects - especially not for finite deformations. With respect to sharp interfaces, general imperfect interfaces represent a thermodynamically consistent anisotropic extension of cohesive zone models that can be used to describe such effects. A phase field approximation of these anisotropic interface models is the declared aim of the project. The microcrack-closure-reopening effect (MCR) is to be included and at the same time special attention is to be paid to the numerical efficiency within the finite element method.

• DFG Programme: Research Grants