Cavity growth from crack-like defects in soft materials

Abstract

We study the growth and failure of small crack-like defects in elastomers under hydrostatic tension. Since the elastic modulus of elastomers are typically very small in comparison with the cohesive strength, crack-like defects can grow into spherical-like cavities before failure. The condition of crack growth or cavity failure is determined using Griffith's fracture criterion, that is, failure of the cavity or crack growth occurs when the energy release rate of the crack-like defect exceeds the surface energy. Three different material behaviors are considered. In the first, we use a power law material model where the strain energy density function w is \displaystylew=\fracμ2nβ([1+β(I ₁−3)]ⁿ−1), where I ₁ is the sum of squares of the principal stretches, μ is the infinitesimal shear modulus, β and n≠0 are material constants. In the second case, we consider a Mooney-Rivlin material, which describes the deformation of pressure sensitive adhesives. In the final case, we consider a material model proposed by Gent (1996), which takes into account the condition that a molecular network will fail at some critical stretch ratio. The dependence of the energy release rate on the applied hydrostatic tension is determined using a large strain finite element method. Comparisons are made between our analysis and a previous result of Gent and Wang (GW) (1991), as well as a result of Williams and Schapery or WS (1965). The role of strain hardening in determining the critical applied hydrostatic tension to fail a cavity is examined by comparing the numerical results using the above three constitutive models.