Initiation and propagation of fatigue cracks in plastic materials with deformation-induced anisotropy.

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The aim of the planned project is to be able to simulate fatigue crack propagation using the phase field method and to investigate the influence of strain hardening on initiation and progress for metallic materials. To achieve this goal, theoretical, experimental and numerical steps are necessary. The theoretical aspects include first the formulation of a material model of elastoplasticity, and then the extension of this model with the approaches of phase field theory. The hardening mechanisms of the model to be considered include isotropic and kinematic hardening, as well as formative and rotational hardening in the yield function. The entire model is formulated in a thermodynamically consistent manner, i.e. the second law of thermodynamics is fulfilled in the form of the classical Clausius-Duhem inequality for all permissible processes. Effects of cyclic plasticity are modeled by the respective approaches. These approaches have a great influence on the ability of the model to describe experimentally observed material behaviour during cyclic loading processes. A series of experiments is planned for the present project. Subsequently, the material model will be extended by a phase field variable. For the form of the degradation function in the free energy function one of the established approaches of isotropic damage mechanics will be used. The phase field model for crack propagation developed within the project will be validated by experiments. Notches will be introduced into thin-walled, cylindrical samples. The samples will be subjected to proportional and non-proportional cyclic loading histories and crack initiation and propagation will be measured by digital image correlation. The numerical implementation of the developed overall model is performed iteratively with the help of a "staggered" algorithm. In the first step the variables of the phase field problem are fixed and the deformation problem is solved. In a second step the deformation is fixed and a pure phase field problem is solved. The two steps are repeated until a prescribed convergence error is undershot. For an effective calculation of large numbers of cycles an extrapolation method is to be developed.