Modeling of Ductile Fracture at Engineering Scales: A Mechanism-Based Approach
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Modeling of Ductile Fracture at Engineering Scales: A Mechanism-Based Approach Xiaosheng Gao, Jun Zhou and Jinyuan Zhai Department of Mechanical Engineering, University of Akron, Akron, OH 44325, U.S.A. ABSTRACT This paper summarizes the work we conducted in recent years on modeling plastic response of metallic alloys and ductile fracture of engineering components, with the emphasis on the effect of the stress state. It is shown that the classical J2 plasticity theory cannot correctly describe the plasticity behavior of many materials. The experimental and numerical studies of a variety of structural alloys result in a general form of plasticity model for isotropic materials, where the yield function and the flow potential are expressed as functions of the first invariant of the stress tensor and the second and third invariants of the deviatoric stress tensor. Several mechanism-based models have been developed to capture the ductile fracture process of metallic alloys. Two of such models are described in this paper. The first one is a cumulative strain damage model where the damage parameter is dependent on the stress triaxiality and the Lode parameter. The second one is a modification to the Gurson-type porous plasticity models, where two damage parameters, representing void damage and shear damage respectively, are coupled into the yield function and flow potential. These models are shown to be able to predict fracture initiation and propagation in various specimens experiencing a wide range of stress states. INTRODUCTION Existing approaches to predict fracture are generally of two types. Bottom-up approaches predict material failure by modeling the motion of the basic particles that constitute the material and the interaction among them. As such, they rely on limited, if any, experimental input. However, due to the complexity of the engineering materials and the large difference between the atomistic length scales and the dimensions of the structural components, as illustrated in Fig. 1, bottom-up approaches are unlikely to be developed with adequate accuracy in the near future. On the other hand, top-down approaches, which couple continuum mechanics descriptions to phenomenology and experimental calibration, provide a viable alternative and have shown great promising over the past few decades. In top-down approaches, mechanism-based concepts provide key insights for development of fracture models and experiments are used to provide calibration of these models at the smallest scale of relevance.
nano (~10-10 m)
micro (~10-6 m)
macro (~ m)
Fig. 1. The length scales from atomistic level to structural component level.
In structural analysis, the classical J2 flow plasticity theory [1] has been overwhelming adopted to describe the plastic response of metallic alloys. This theory assumes the hydrostatic stress and the third invariant of the stress deviator do not affect the yield stress and the plastic flow. However, increasing experimental evidences show that these assumptions are invalid for many materials. Ou
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