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

计划项目的目的是能够使用相场法模拟疲劳裂纹扩展，并研究应变硬化对金属材料的萌生和进展的影响。为了实现这一目标，理论，实验和数值步骤是必要的。理论方面首先建立了一个弹塑性材料模型，然后用相场理论的方法对该模型进行了扩展。模型中的硬化机制包括屈服函数中的各向同性硬化和随动硬化，以及成形硬化和旋转硬化。整个模型是以热力学一致的方式制定的，即热力学第二定律以经典的克劳修斯-杜亨不等式的形式满足所有允许的过程。循环塑性的影响是由各自的方法模拟。这些方法有很大的影响的能力，该模型来描述实验观察到的材料行为在循环加载过程中。计划为本项目进行一系列实验。随后，材料模型将通过相场变量进行扩展。对于自由能函数中的退化函数的形式，将使用各向同性损伤力学的一种已建立的方法。本项目开发的裂纹扩展相场模型将通过实验进行验证。将在薄壁圆柱形样品中引入缺口。样本将受到比例和非比例循环加载历史和裂纹萌生和扩展将通过数字图像相关测量。的数值实现的开发的整体模型进行迭代与“交错”算法的帮助下。在第一步中，固定相场问题的变量并求解变形问题。在第二步中，变形是固定的，并且解决了纯相场问题。重复这两个步骤，直到达到规定的收敛误差。为了有效地计算大量的循环，需要开发一种外推法。

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.