Thermodynamics of translational crack layer propagation

Abstract

Recognizing that fracture in many materials propagates as a crack preceded by intensive damage, a theory is presented to model the crack and the preceding damage as a single thermodynamic entity, i.e., a crack layer (CL). The active zone of the CL may propagate by translational, rotational, expansional and/or distortional movements. Concepts of irreversible thermodynamics are employed to derive the law of CL propagation by translational mode as:

$$\dot l = \frac{{\beta J_1 \left\langle d \right\rangle }}{{\gamma ^ * R_1 - J_1 }}$$

wherei is the rate of CL translation,β is a dissipative coefficient,J ₁ is the energy release rate, 〈d〉 is a characteristic size of the active zone, γ* is the specific enthalpy of damage andR ₁ is the translational resistance moment. This expression describes the entire history of CL propagation. Experimental results on fatigue crack propagation in polystryrene are in good agreement with the proposed formalism.