Stress softening of elastomers in hydrostatic tension

This study is concerned with inelastic effects of non-reinforcing carbon-black filled elastomers when subjected to periodic hydrostatic loading-unloading cycles in tension. During cyclic testing of sufficient magnitude, a critical state may be reached where microcavities suddenly grow inside the rubber, possibly initiated at sites of internal imperfections. As a result of cavitation damage the tensile bulk modulus in the natural configuration is reduced. A series of hydrostatic tension tests are performed at room temperature to provide new insight into the progressive deterioration of the bulk stiffness. We define dilatational stress softening as a phenomenon where the hydrostatic stress on unloading and subsequent submaximal reloading is significantly less than that on primary loading for the same volumetric strain. Dilatational stress softening during initial loading cycles and the permanent volumetric change upon unloading are not accounted for when the mechanical properties are represented in terms of a strain-energy function, i.e. if the material is modelled as hyperelastic. In this paper a constitutive model is derived to include the progressive reduction of the bulk stiffness and the permanent volumetric change of carbon-black filled elastomers subjected to quasi-static loading. The basis of the model is the theory of pseudo-elasticity, which including a softening variable modifies the dilatational strain energy function. An acceptable correspondence between the theory and the data is obtained.