Behaviour of porous ductile solids at low stress triaxiality in different modes of deformation - Tvergaard, Viggo (International journal of solids and structures, 2015)
•Ductile material subject to stress states in the vicinity of pure shear.•Cell model analyses for periodic array of voids.•Voids close up to form micro-cracks, which remain closed.•Different initial void sizes are considered.•No failure mode is indicated for the low stress triaxialities. The effect of low stress triaxiality on ductile failure is investigated for a material subject to pure shear or to stress states in the vicinity of pure shear. Many recent studies of ductile failure under low hydrostatic tension have focused on shear with superposed tension, which can result in simple shear or in stress states near that. A material with a periodic array of voids is subjected to tensile stresses in one direction and compressive stresses in the transverse direction. Numerical solutions for a plane strain unit cell model are obtained numerically. For stress states in the vicinity of pure shear it is found that the voids close up to micro-cracks, and these cracks remain closed during continued deformation, with large compressive stresses acting between crack surfaces. The same type of behaviour is found for different initial sizes of the voids and for cases where the two types of voids in the unit cell have very different initial size. The analyses do not indicate a final failure mode where the stress carrying capacity of the material drops off to zero. In previous analyses for stress states in the vicinity of simple shear such final failure has been predicted, so it appears that the behaviour of a porous ductile material at low stress triaxiality depends a great deal on the mode of deformation.