Nonlinear elastic constants of solids with cracks

Abstract

Experimental data on a cracked medium exhibiting high acoustic nonlinearity is a commonly observed phenomenon. Here a physical model of a medium with cracks is suggested to explain the observed phenomena. The model is based on the assumption of uniform stress that is valid for a low concentration of cracks. The crack behavior is described using the model in which a crack is represented as an elastic contact of two rough surfaces, pressed one to the other under the action of internal stresses in the surrounding solid. Linear and nonlinear acoustic constants of the fractured medium are calculated. It is shown that, in this medium, negative values of the Poisson’s ratio and anomalously high values of the nonlinear constants are possible.

Quantitative assessment of fatigue damage accumulation in wavy slip metals from acoustic harmonic generation

“…Theoretical β versus percent total fatigue life curves for polycrystalline nickel and AA2024-T4 calculated from the model are given in Section 5. The results for AA2024-T4 are compared to the experimental measurements (Cantrell and Yost 4 1994, Na et al 1996, Nazarov and Sutin 1997, and Frouin et al 1999 indicate that each stage of the fatigue process may be characterized by a unique nonlinear relationship between an impressed stress perturbation (e.g., a sound wave) and a microelastic-plastic straining of the material. The straining is quantified by an experimentally determined nonlinearity parameter β that increases monotonically by several hundred percent over the fatigue life.…”

“…Nazarov and Sutin (1997) derived an expression for the contribution to the nonlinearity parameter of non-interacting penny-shaped cracks in bulk material.…”

“…crack propagation is applied in the present study to the Nazarov-Sutin (1997) crack nonlinearity equation to assess the change in β as a function of crack growth during the fatigue process. The resulting expression is combined with the Cantrell (2004) substructural nonlinearity model to assess the value of β at each stage of the fatigue process from the virgin state to fracture.…”

“…In Section 3 the contribution to β via the Cantrell (2004) model resulting from such substructures is considered. In Section 4 the Paris-Erdogan (1963) equation is applied to the Nazarov-Sutin (1997) crack nonlinearity equation to assess the effects of crack growth during fatigue on the value of β. Theoretical β versus percent total fatigue life curves for polycrystalline nickel and AA2024-T4 calculated from the model are given in Section 5.…”

“…Nazarov and Sutin (1997) have shown that the appearance of macrocracks in the material also produces large increases in β. The Paris-Erdogan (1963) …”