Failure criterion for highly stretchable elastomers under triaxial loading

Abstract

A failure criterion is introduced for highly stretchable hyper-elastic materials under tensile-dominated triaxial loading. It is based on energy balance using Griffith approach but is presented by the critical state of load as in traditional size independent strength theories. The basic argument is made of the recent assessment about the cavity nucleation in soft materials: the volumetric energy dissipation in the growth of defect and size-insensibility of the critical load in soft materials when the defect is smaller than the material characteristic length. Thus, using the energy approach as in fracture mechanics, we are able to estimate the critical state of load using only one material parameter, which is subsequently replaced by the critical stress under one specific loading, e.g., the strength of uniaxial loading. This leads us to the failure surface in the normalized principal stress space. The predictions of the present theory agree well with the experimental results collected from the literature, including an order of magnitude difference between the strengths of the uniaxial loading and hydrostatic loading. This addresses a variety of difficulties in the previous failure analyses. For the easiness of practical application, we further analyze the data and obtain a criterion using mean stress and the first invariant of Cauchy–Green deformation tensor, I1. We are able to obtain the widely mentioned maximum I1 criterion, and also find its limitation: only applicable when one of the principal stresses is zero. For general triaxial loadings, the material can fail at any allowable I1 and the critical mean stress monotonically increases with I1; and under a constant mean stress that is above the hydrostatic strength, the material is only safe when I1 is above a mean stress-dependent lower bound but below an unknown up-bound.