Description of void coalescence by internal necking/shearing within XFEM via a micromechanical 3D volumetric cohesive zone model (μ-VCZM)

Abstract

This work addresses ductile failure in engineering structures, particularly in aerospace, naval, automotive, and nuclear industries. During accidental overloading or metal forming, materials such as titanium and aluminum alloys experience plastic deformation and ductile damage (by void nucleation, growth, and coalescence) that may eventually lead to crack propagation and fracture. The present study concentrates explicitly on the void coalescence stage. Indeed, building upon a numerical methodology developed by the present authors and detailed in a companion paper, a novel micromechanics-based volumetric cohesive zone model ($\mu$-VCZM) is incorporated within the Extended Finite Element Method (XFEM) to reproduce the process of void coalescence while overcoming the mesh objectivity issues of the numerical results during the softening regime. The Mode I (extension) and Mode II (shear) coalescence onset criteria and evolution laws are derived from micromechanical considerations. Subsequently, the yield surfaces and the integration algorithm necessary to determine the stress state within the coalescence band are established. Finally, the micromechanics-based $\mu$-VCZM is applied within the XFEM-VCZM unified methodology. The numerical model, implemented as user element (UEL) into the computation code Abaqus, demonstrates efficacy in replicating the stages of ductile fracture, highlighting its potential for addressing complex finite strain three-dimensional boundary value problems. Notably, the results obtained with coarse meshes exhibit no mesh dependency below a specific mesh size, reproducing realistic Mode I and II fracture surfaces.