Chapter 7 - Heuristic Approach for Approximating Energy Release Rates of Small Cracks Under Finite Strain, Multiaxial Loading

Abstract

In this chapter, a parameter is presented that attempts approximately to describe the energy release rate of a small crack of arbitrary orientation under multiaxial loading. The parameter, herein called the cracking energy density, specifically attempts to address several aspects common to the analysis of fatigue in rubber: finite straining, nonlinear elasticity, and the possibility of crack closure under compressive loading. As motivation, the connection between the strain energy density and the energy release rate for small cracks under uniaxial loading is first discussed. Small strain and finite strain definitions of the cracking energy density are then presented. The accuracy of the cracking energy density as an approximation of the energy release rate at small strains is assessed via comparison with results from linear elastic fracture mechanics (LEFM). The cracking energy density is shown to exhibit dependence on crack orientation and stretch biaxiality that resembles that predicted via LEFM. Since the cracking energy density is evaluated at a material point in the uncracked material, this parameter is particularly useful for the analysis of crack nucleation from initially unobserved flaws, a common task in the design of rubber components. In such applications, it is possible to predict not only a fatigue crack nucleation life, but also specific planes on which cracks would be expected to appear.