Crack-Tip Stress and Deformation Fields in Strain-Softening Nonlinearly Viscoelastic Materials

In some polymers, stress-induced changes in molecular mobility give rise to a strain-softening effect. The influence of this effect on the stress and deformation fields near a crack tip are examined using the finite element method. A phenomenological nonlinearly viscoelastic constitutive model (based on the concept of free volume) is used in the calculations. When a load is suddenly applied to a cracked specimen, the instantaneous response of the material is linearly elastic. However, strain-induced softening in the crack-tip region leads to a relaxation in the stress and time variation of the region over which the singular field prevails. For realistic material parameters, this region may become extremely small. In addition, a zone of strain-softened material emanantes from the crack tip and extends along the crack line. This process zone can promote conditions which are favorable for the nucleation and growth of microvoids and the formation of crazes.