PSI - Issue 42

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Toru Yagi et al. / Procedia Structural Integrity 42 (2022) 702–713 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 3.6 New pop-in criterion

4. FEM Model Incorporating Energy Dissipation 4.1. Energy Dissipation In this section, the idea of energy dissipation during the brittle fracture is incorporated to the FEM analysis to explain the pop-in fracture mechanism. The energy balance during brittle fracture can be written as the equation (7). The potential strain energy is made up by the kinetic energy of crack and the energy dissipation. The crack likely arrests as the energy dissipation gets bigger. To apply this idea to the FEM analysis, the model explained below is used. The energy dissipation c is defined to reproduce the brittle fracture in FEM analysis. The stress between adjacent nodes increased proportional to the crack tip opening displacement. When the stress approaches the critical condition, the stress between adjacent nodes gradually decreases and then the nodes are divided. The energy dissipation is modelled as how the stress decreases. d d − d d = d d + d k d (7) The energy dissipation during the brittle fracture consists by a lot of elements such as heat and sound wave. However, the main element of energy dissipation is the fracture surface energy which is consumed to create the fracture surface area. This surface energy depends pm the fracture surface roughness. As Sharon and Fineberg in 1996 said, the fracture surface roughness considered to be proportional to the crack velocity. Nakamura in 2020 conducted further research and found out that the loading mode is another parameter for the fracture surface roughness. He also found that the fracture roughness of tensile mode is bigger compared to the bending mode when the crack velocity is more than 500m/s. To apply the idea of energy dissipation to the FEM analysis, a dynamic explicit analysis with cohesive surface is conducted. The cohesive surface is one of the surface interaction properties. There are basically two parameters in the cohesive behavior. One is the damage initiation which defines the initiation of damage and the other is the damage evolution which is the modelling of the progressive failure for cohesive surface. In this analysis, the damage initiation is the replacement of critical fracture stress f and the damage evolution is the replacement of the energy dissipation