  Coalescence of voids by internal necking is in most cases the last
microscopic event related to ductile fracture and corresponds to a localized
plastic flow between adjacent voids. Macroscopic load associated to the onset
of coalescence is classically estimated based on limit analysis. However, a
rigorous upper-bound mathematical expression for the limitload required for
flat voids coalescence that remains finite for penny-shaped voids/cracks is
still unavailable. Therefore, based on limit analysis, theoretical upper-bound
estimates - both integral expression and closed-form formula - are obtained for
the limit-load of cylindrical flat voids in cylindrical unit-cell subjected to
boundary conditions allowing the assessment of coalescence, for axisymmetric
stress state. These estimates, leading to finite limit-loads for pennyshaped
cracks, are shown to be in very good agreement with numerical limit analysis,
for both cylindrical and spheroidal voids. Approximate formula is also given
for coalescence under combined tension and shear loading. These coalescence
criteria can thus be used to predict onset of coalescence of voids by internal
necking in ductile fracture modelling.
