A coalescence criterion for porous single crystals

Abstract

Voids can be observed at various scales in ductile materials, frequently of sizes lower than the grain size, leading to porous single crystals materials. Two local deformation modes of porous ductile (single crystals) materials have been identified and referred to as void growth and void coalescence, the latter being characterized by strong interactions between neighboring voids. A simple semi-analytical coalescence criterion for porous single crystals with periodic arrangement of voids is proposed using effective isotropic yield stresses associated with a criterion derived for isotropic materials. An extension of the coalescence criterion is also proposed to account for shear with respect to the coalescence plane. Effective yield stresses are defined using Taylor theory of single crystal deformation, and rely ultimately on the computation of average Taylor factors. Arbitrary sets of slip systems can be considered. The coalescence criterion is assessed through comparisons to numerical limit-analysis results performed using a Fast-Fourier-Transform based solver. A good agreement is observed between the proposed criterion and numerical results for various configurations including different sets of slip systems (Face-Centered-Cubic, Hexagonal-Close-Packed), crystal orientations, void shapes and loading conditions. The competition between void growth and void coalescence is described for specific conditions, emphasizing the strong influence of both crystal orientation and void lattice, as well as their interactions.

A size-dependent ductile fracture model: Constitutive equations, numerical implementation and validation

“…However, a strong dependence of the onset of coalescence to this parameter was observed in this study. The effect of void distribution on coalescence stress should be investigated in more details, as for example initiated in [57].…”

“…cell simulations [16,17,18]. Homogenized yield criteria for porous single crystals have been developed to account for the effects of crystal orientation [19,20,21,22,23].Most of these homogenized models for porous materials are size-independent, assuming implicitly that only void volume fraction matters irrespectively of void size, although porous materials with voids ranging from micrometric [13] down to nanometric sizes [24,25] are encountered in industrial applications. Moreover, size effects have been predicted from theoretical and numerical studies.…”

“…cell simulations [16,17,18]. Homogenized yield criteria for porous single crystals have been developed to account for the effects of crystal orientation [19,20,21,22,23].…”

A strain gradient plasticity model of porous single crystal ductile fracture

“…( 54) for porous single crystals is not straightforward, because it was derived in the context of isotropic plasticity. A derivation of the limit load of a porous unit-cell was extended recently to the crystal plasticity framework (Hure, 2019). Yet, for the sake of simplicity, it remains interesting to evaluate the validity of the limit load in Eq.…”

“…Single crystal void growth models were settled by Crépin et al (1996), Han et al (2013), Mbiakop et al (2015), Ling et al (2016), Song and Castañeda (2017) and Paux et al (2018). Even fewer studies deal with void coalescence in single crystals (Yerra et al, 2010;Hure, 2019). A comprehensive model combining void growth and void coalescence criteria in porous single crystals is still lacking.…”