A coalescence criterion for porous single crytals
Résumé
Voids can be observed at various scales in ductile materials, frequently of sizes lower than the grain size, leading to either microscopicallyor macroscopically porous single crystals materials. Under mechanical loading, two local deformation modes ofporous ductile (single crystals) materials have been identified and referred to as void growth and void coalescence, the latter beingcharacterized by strong interactions between adjacent voids. A simple semi-analytical coalescence criterion for porous singlecrystals with periodic arrangement of voids is proposed using eective isotropic yield stresses associated with a criterion derivedfor isotropic materials. The potential influence of shear stress with respect to the coalescence plane is also accounted for in anextended coalescence criterion. Eective yield stresses are defined using Taylor theory of single crystal deformation, and rely ultimatelyon the computation of average Taylor factors. Arbitrary sets of slip systems can be considered. The coalescence criterion isassessed through comparisons to numerical limit-analysis results performed using a Fast-Fourier-Transform based solver. A goodagreement is observed between semi-analytical predictions and numerical results for various configurations including dierent setsof slip systems (Face-Centered-Cubic, Hexagonal-Close-Packed), crystal orientations, void shapes and loading conditions. Thecompetition between void growth and void coalescence is described for specific conditions, emphasizing the strong influence ofboth crystal orientation and void lattice, as well as their interactions.