Variational phase-field formulation of non-linear ductile fracture
Variational phase-field formulation of non-linear ductile fracture
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DOI：
10.1016/j.cma.2018.07.029
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发表时间：
2018-07
影响因子：
7.2
通讯作者：
M. Dittmann;F. Aldakheel;J. Schulte;P. Wriggers;C. Hesch
中科院分区：
文献类型：
--
作者：
M. Dittmann;F. Aldakheel;J. Schulte;P. Wriggers;C. Hesch
变分一致相场方法是近十年来发展起来的。脆性和韧性断裂问题的广泛应用已经证明了预测三维几何形状中复杂裂纹图案的能力。然而，目前的相场模型韧性断裂没有制定，材料和几何非线性。在这方面的贡献，我们提出了一个计算框架来考虑三维断裂韧性固体经历大的弹性和塑性变形。该模型是基于变形梯度的三重乘法分解和时间离散设置中的返回映射的指数更新方案。这提高了延性材料行为（包括弹塑性、硬化、颈缩、裂纹萌生和扩展）的整个范围的精度。高阶相场正则化和梯度增强塑性模型的应用进一步提高了精度和收敛性。为了解释断裂时的韧性行为，提出了一个依赖于等效塑性应变的临界断裂能密度模型，并通过实验数据进行了验证。
Variationally consistent phase-field methods have been well established in the recent decade. A wide range of applications to brittle and ductile fracture problems could already demonstrate the ability to predict complex crack patterns in three-dimensional geometries. However, current phase-field models to ductile fracture are not formulated for both, material and geometrical non-linearities. In this contribution we present a computational framework to account for three-dimensional fracture in ductile solids undergoing large elastic and plastic deformations. The proposed model is based on a triple multiplicative decomposition of the deformation gradient and an exponential update scheme for the return map in the time discrete setting. This increases the accuracy on the entire range of the ductile material behavior encompassing elastoplasticity, hardening, necking, crack initiation and propagation. The accuracy and convergence properties are further improved by the application of a higher order phase-field regularization and a gradient enhanced plasticity model. To account for the ductile behavior at fracture, a model of the critical fracture energy density depending on the equivalent plastic strain is proposed and validated by experimental data.