Void growth and coalescence in sigmoidal hardening porous plastic solids under tensile and shear loading

This work examines the void growth and coalescence in isotropic porous elastoplastic solids with sigmoidal material hardening via finite element three-dimensional unit cell calculations. The investigations are carried out for various combinations of stress triaxiality ratio (\({\mathcal {T}}\)) and Lode parameter (\({\mathcal {L}}\)) and consider a wide range of sigmoidal hardening behaviors with nominal hardening rates spanning two decades. The effect of \({\mathcal {L}}\) is considered in the presence and in the absence of imposed shear stress. Our findings reveal that depending on the nature of sigmoidal hardening the cell stress-strain responses may exhibit two distinct transitions with increasing stress triaxiality (\({\mathcal {T}}\)). Below a certain lower threshold triaxiality the stress-strain responses are sigmoidal, while above a certain higher triaxiality they exhibit softening immediately following the yield. Between these threshold levels, the responses exhibit an apparent classical rather than sigmoidal strain hardening. The sigmoidal hardening characteristics also influence porosity evolution, which may stagnate before a runaway growth up to final failure. For a given \({\mathcal {L}}\), an imposed shear stress adversely affects the material ductility at moderate \({\mathcal {T}}\) whereas at high \({\mathcal {T}}\) it improves the ductility. Finally, we discuss the role of material hardening and stress state on the residual cell ductility defined as strain to final failure beyond the onset of coalescence.