相场法与Armstrong-Frederick模型耦合模拟循环载荷下的延性损伤
Coupling of the phase field approach to the Armstrong-Frederick model for the simulation of ductile damage under cyclic load
摘要：
本文提出了一个韧性损伤的数值模拟模型。该模型将断裂的相场法耦合到具有随动硬化的Armstrong-Frederick塑性模型。后者特别适合于模拟循环载荷下的材料行为。该模型依赖于耗散势的最小原理。然而，这种方法的应用是具有挑战性的，因为耦合方法的潜力是在不同的空间中定义的：相场模型的耗散潜力表示在内部变量的速率方面，而阿姆斯特朗-弗雷德里克模型提出了一个配方取决于热力学力。因此，独特的公式需要对其中一个势进行勒让德变换。本文对Armstrong-Frederick势进行了变换，使得最终的公式只在内部变量的速率空间中表示。在假设自由能和联合耗散势的情况下，演化方程的推导是简单的。该模型的应用说明了选定的数值例子研究不同的负载星座和样品的几何形状的材料响应。本文还提供了与实验结果的比较。
英文摘要：
The present contribution proposes a thermodynamically consistent model for the simulation of the ductile damage. The model couples the phase field method of fracture to the Armstrong-Frederick plasticity model with kinematic hardening. The latter is particularly suitable for simulating the material behavior under a cyclic load. The model relies on the minimum principle of the dissipation potential. However, the application of this approach is challenging since potentials of coupled methods are defined in different spaces: The dissipation potential of the phase field model is expressed in terms of rates of internal variables, whereas the Armstrong-Frederick model proposes a formulation depending on thermodynamic forces. For this reason, a unique formulation requires the Legendre transformation of one of the potentials. The present work performs the transformation of the Armstrong-Frederick potential, such that final formulation is only expressed in the space of rates of internal variables. With the assumption for the free energy and the joint dissipation potential at hand, the derivation of evolution equations is straightforward. The application of the model is illustrated by selected numerical examples studying the material response for different load constellations and sample geometries. The paper provides a comparison with the experimental results as well.
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