Critical Damage Evolution model for spall failure of ductile metals

Numerical simulation of ductile fracture based on mean field homogenization method: Modeling and implementation

“…The second mode of void coalescence consists in shear localisation between large primary voids [61]. As void coalescence starts, the damage evolution rate is greatly accelerated during the coalescence process [51]. The P-R model is adopted in the present work to describe acceleration of damage softening effect.…”

“…where λ = 0.4 is a constant given by the percolation theory [51], β c is the critical damage for the onset of void coalescence, and β f is the damage at which the coalescence of void is completed and a catastrophic fracture occurs. β f is determined by the failure condition,…”

“…The effective energy density [4] is adopted for evolution of the damage variable. And the acceleration of damage softening due to void coalescence is taken into account based on the percolation theory [51].…”

Molecular dynamic simulation of edge dislocation-void interaction in pure Al and Al-Mg alloy

“…Therefore, improving the mechanical behavior requires a fundamental understanding of the deformation mechanisms at different length scales, from the atomic structure to the continuum level. There have been many studies [1][2][3][4][5][6][7] on mechanical behavior of materials at the atomistic level using molecular dynamics simulations. Studies at the atomistic level can help to elucidate important aspects of dislocation motion and dislocation-defect interaction.…”

Molecular dynamics studies of the roles of microstructure and thermal effects in spallation of aluminum

“…These models, which are mainly used to describe classical spallation behavior on macro-scale are essentially empirical and largely rely on unknown parameters established in experiments. On macro-scales, spallation is computationally studied by finite element and meshfree methods with constitutive models related to cumulative damage and fracture criteria (Fahrenthold and Horban, 1999;Benzerga and Leblond, 2010;Ren et al, 2011;Wright and Ramesh, 2008;Czarnota et al, 2008;Campagne et al, 2005;Wang et al, 2013). The response of materials under shock loading is very complex and involves damage creation and propagation, phase transformation, heat generation, heat transfer, etc.…”