Phase field fracture in elasto-plastic solids: Incorporating phenomenological failure criteria for ductile materials

• Published in: Computer methods in applied mechanics and engineering Vol. 391; p. 114580
• Main Authors: Li, Cunyi, Fang, Jianguang, Wu, Chi, Sun, Guangyong, Steven, Grant, Li, Qing
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.2022; Elsevier BV
• Subjects: Axial stress; Crack driving force; Crack initiation; Crack propagation; Criteria; Damage; Ductile fracture; Elastic deformation; Failure analysis; Fracture criteria; Fracture mechanics; Mathematical models; Phase field model; Plastic anisotropy; Stress state; Variational principles; Phase field model; Plastic anisotropy; Crack driving force; Stress state; Ductile fracture; Fracture criteria
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2022.114580

Phase field approaches have been developed to analyze the failure behavior of ductile materials. In the previous phase field models, a constant critical energy or strain threshold is commonly introduced to the formulation of the driving force, aiming to avoid damage initiation at a low level of elastic and plastic deformations. However, it may not suffice to describe complex ductile fracture behavior of materials subject to various stress states. In this study, a new phase field approach is proposed to consider the effects of stress triaxiality and Lode angle, by incorporating phenomenological ductile fracture criteria. The proposed models are formulated using variational principles and implemented numerically in the finite element framework. Analytical homogeneous solutions for uniaxial tension, simple shear, and equibiaxial tension loads are derived to demonstrate the effectiveness of the proposed models. Three groups of numerical examples, covering a wide range of stress states, are utilized to further examine the proposed models. The results show that the models can reproduce the experimental response of the specimen in terms of force versus displacement curve, crack initiation, and crack propagation under various loading conditions. The proposed models are able to capture the stress-state dependence of fracture behavior of ductile materials. •A new phase field model is proposed to predict ductile fracture behavior.•Stress state dependent damage thresholds are introduced via the MMC criterion.•Analytical solutions demonstrate the effectiveness of the proposed models.•Crack initiation and propagation can be reproduced in various benchmark examples.•The proposed models can capture the stress-state dependence of ductile fracture.