Elastodynamic parameters for dynamic interface fracture mechanics

Abstract

Dynamic extension of cracks running along curvilinear interfaces of brittle bimaterials subjected to mechanical crack surface loads and superimposed thermal strains acting along the ligament is considered. This paper especially addresses the provision and discussion of elastodynamic interface parameters in order to assess quantitatively the bimaterial fracture in view of the governing physical features: applied mechanical and thermal strain loading, existence of an interface, crack-tip velocity and curvature of the interface contour. By utilizing the linear theory of thermoelasticity and adopting Stroh's method of generalized complex potentials, from the corresponding boundary and continuity conditions vectorial Hilbert problems are derived. It is shown that the parameters of the eigenvalues and of the eigenvectors of the Hilbert problems can be interpreted as elastodynamic interface mechanics parameters reading (β,vp, β Hf , μ Hf ). Generalized Dundurs parameters of dynamics (α, β) and consequently an associated generalized Dundurs diagram of dynamics are proposed. While the aforementioned elastodynamic interface parameters (α, β,vp, β Hf , μ Hf ) do not assume the interface to be damaged, interfaces with running interface cracks generally cause two additional interface parameters, denoted as bimaterial constants (e, α Hf ), where the latter is specific to the curvature of the interface in conjunction with the velocity of the interface crack. However, the bimaterial constants (e, α Hf ) can be traced back to interface parameters for an uncracked bimaterial, namely to (β, β Hf ).