<p>The present article presents a numerical model for analyzing interfacial fracture in ductile materials exhibiting perfectly elastoplastic behavior, taking into account the ductility induced by the increase in tension at the crack tip. The analysis of structures with cracked interfaces requires the satisfaction of interface continuity conditions—namely, the continuity of displacement and the continuity of the stress vector. To address this, a mixed finite element, designated RMQ-7, is employed to determine the size of the plastic zone (PZ) around the crack tip under both mode I and mixed-mode (I + II) loading conditions. The calculations are performed according to the Von Mises plasticity criterion, implemented within the mixed finite element framework, which incorporates the elastoplastic constitutive law of the material. The results obtained using the RMQ-7 element show good agreement with both numerical and analytical results, as verified by the maximum crack opening displacement and the classical Irwin formula. In addition, this paper addresses the problem of slant and kinking cracks. The proposed special mixed finite element, combined with the virtual crack extension technique, has been developed to evaluate the energy release rate within a single finite-element analysis. The element is defined from a parent element in the natural coordinate plane (ξ, η), which simplifies the numerical computation within each element of the simulation. Finally, an example problem involving slant cracks in a homogeneous material, drawn from the literature, is presented to assess the computational accuracy of the proposed approach.</p>

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Estimation of the Plastic Area Around the Crack Tip Using a New Mixed Finite Element Approach

  • Ahmed Bougueroua,
  • Hamoudi Bouzerd,
  • Mohamed Kezzar

摘要

The present article presents a numerical model for analyzing interfacial fracture in ductile materials exhibiting perfectly elastoplastic behavior, taking into account the ductility induced by the increase in tension at the crack tip. The analysis of structures with cracked interfaces requires the satisfaction of interface continuity conditions—namely, the continuity of displacement and the continuity of the stress vector. To address this, a mixed finite element, designated RMQ-7, is employed to determine the size of the plastic zone (PZ) around the crack tip under both mode I and mixed-mode (I + II) loading conditions. The calculations are performed according to the Von Mises plasticity criterion, implemented within the mixed finite element framework, which incorporates the elastoplastic constitutive law of the material. The results obtained using the RMQ-7 element show good agreement with both numerical and analytical results, as verified by the maximum crack opening displacement and the classical Irwin formula. In addition, this paper addresses the problem of slant and kinking cracks. The proposed special mixed finite element, combined with the virtual crack extension technique, has been developed to evaluate the energy release rate within a single finite-element analysis. The element is defined from a parent element in the natural coordinate plane (ξ, η), which simplifies the numerical computation within each element of the simulation. Finally, an example problem involving slant cracks in a homogeneous material, drawn from the literature, is presented to assess the computational accuracy of the proposed approach.