ELLIPTIC VOID GROWTH IN SHEAR

An approximate upper bound approach is developed to analyse the growth of an elliptical void contained in a finite unit cell undergoing simp le shearing combined with superimposed hydrostatic tension. The matrix is assumed to be an incompressible nonlinear power-law viscous solid. For a void in an infinite linearly viscous matrix material, the prese nt result is in good agreement with Eshelby's solution. For a nonlinea rly viscous matrix material, to calculate the constitutive potential, an accurate numerical method is developed. Comparisons of the upper bo und solution of the potential and its first-order approximation with t he accurate one are made. It is found that the potential values from t he first-order approximation are closer to the accurate values than th ose from the upper bound solution. Therefore, the first-order approxim ation of the upper bound for the constitutive relations is used to giv e the relations of the stress triaxiality and the void growth rate. Fo r both Newtonian materials and perfectly plastic materials, the sugges ted method gives closed forms for the void growth rate as an implicit function of the stress triaxiality, the void volume fraction, the void aspect ratio and the strain rate sensitivity exponent. For other case s, the void growth is investigated numerically.