VELOCITY, STRAIN-RATE AND STRESS-FIELDS AROUND A SPHEROIDAL CAVITY INA LINEARLY VISCOUS MATERIAL

The exact velocity, stress and strain rate fields around a spheroidal cavity in an infinite linearly viscoplastic matrix are derived analyti cally by the 'Three Function Approach'. The spheroidal coordinate syst em adopted here depends on the void mean radius and eccentricity and t herefore allows large inelastic strains to be dealt with. The perturba tion of the velocity field due to the presence of the cavity is the su perposition of three independent velocity modes. The two first are ass ociated with homothetic growth and pure distortion of the void, respec tively, whereas the third one produces both volume and shape changes. It is shown that the increase of the cavity volume is significantly de layed when its eccentricity is non zero, and thus the void shape shoul d be taken into account in order to model damage growth accurately. Si milarly, the calculated distributions of equivalent strain rate and me an stress within the matrix exhibit large concentrations near the pole or the equator of the cavity. The occurrence of induced secondary dam age is thus likely to be sensitive to the shape of the void. Finally, the analytical expression of the velocity field derived in this paper can be used to build approximate solutions for modelling cavity growth in nonlinear viscoplastic or strain-hardening materials.