Jérémy Hure

The aim of this work is to study theoretically and numerically the effect of the inhomogeneity of the yield stress on void coalescence for isotropic porous ductile materials. Such inhomogeneities may arise due to strain hardening prior to void coalescence. Sequential limit analysis is applied to a cylindrical unit cell containing a coaxial cylindrical void in a von Mises matrix material with a radially dependent yield stress. An estimate of the coalescence criterion is obtained for combined tensile and shear loading. The criterion relies on 1D integrals, but two approximations are also provided to obtain analytical expressions. Numerical limit analysis based on FFT simulations is performed to get exact, up to numerical errors, coalescence stresses, and to assess the theoretical expressions. A good agreement is found between the analytical coalescence criterion and the numerical results for a large set of void shape, porosities and yield stress distributions. The coalescence criterion is finally used to assess the effect of strain-hardening on the orientation of void coalescence plane, as well as to describe the full yield locus — accounting for both void growth and coalescence — of porous isotropic materials, for axisymmetric loading conditions.

An experimental methodology is developed to evaluate size effects in nanovoids deformation under macroscopic uniaxial stress loading conditions. Quantitative evaluation of voids deformation as a function of voids size shows both a crystallographic effect, albeit small compared to the scatter, and no evidence of size effects for voids diameter larger than 10 nm, while a slight effect is present for smaller voids. Critical assessment of the data in light of theoretical models indicates that these results may be compatible with the presence of a hardened layer at the void/matrix interface, which is illustrated through finite element simulations accounting for surface tension.

Void coalescence is known to be the last microscopic event of ductile fracture in metal alloys and corresponds to the localization of plastic flow in between voids. Limit-analysis has been used to provide coalescence criteria that have been subsequently recast into effective macroscopic yield criteria, leading to models for porous materials valid for high porosities. Such coalescence models have remained up to now restricted to cubic or hexagonal lattices of spheroidal voids. Based on the limit-analysis kinematic approach, a methodology is first proposed to get upper-bound estimates of coalescence stress for arbitrary void shapes and lattices. Semi-analytical coalescence criteria are derived for elliptic cylinder voids in elliptic cylinder unit cells for an isotropic matrix material, and validated through comparisons to numerical limit-analysis simulations. The physical application of these criteria for realistic void shapes and lattices is finally assessed numerically.