Separation at a circular interface under biaxial load

On the nucleation of cavities in planar elasticity

“…Thus, transition occurs when the interface force reaches its maximum value. Furthermore, because the pre-bifurcated state under equibiaxial loading is rotationally symmetric (and therefore describable by a single uniform mode), the results obtained are exact and consistent with Levy (1994Levy ( , 1995.…”

“…Thus, bifurcation under remote equibiaxial loading first occurs when the interface force law attains its maximum value. (Symmetric and non-symmetric bifurcations of (2.15) have been studied in detail in Levy (1994) and Levy (1995), respectively.) Unfortunately, when the remote loading is other then equibiaxial a simple bifurcation condition (analogous to D u0 f = 0) no longer exists, in part because D u f is no longer uniform.…”

The cohesive law for the particle/matrix interfaces in high explosives

“…Needleman (1987) used the cohesive zone model to simulate the process of void nucleation from particle/matrix interfaces, from initial to complete debonding. Using Ferrante et al's (1982) cohesive law that is primarily for bimetallic interfaces, Levy (1994) studied the debonding of a circular fiber in an infinite matrix subject to equibiaxial load. There are also analytical studies of interface debonding based on cohesive zone models and these studies focus on the effect of interface debonding on the macroscopic behavior of composite materials.…”

Numerical modeling of crack growth under dynamic loading conditions

“…This cohesive surface formulation, Needleman (1987), differs from the classical cohesive zone models of Barenblatt (1962) and Dugdale (1960) in several respects; for example, an initial crack is not required to be present so that issues of nucleation of defects can be addressed and the length of a cohesive zone is not a parameter of the model. This framework has been used to address issues regarding void nucleation (Needleman 1987;Tvergaard 1990;Xu and Needleman 1993), quasi-static crack growth (Needleman 1990;Tvergaard andHutchinson 1992, 1993), stability of the separation process (Suo et al 1992;Levy 1994), reinforcement cracking in metal-matrix composites (Finot et al 1994), dynamic crack growth (Xu and Needleman 1994;Siegmund andNeedleman 1996, 1997), and interface fracture (Tvergaard and Hutchinson 1993;Needleman 1995, 1996).…”