Interaction of a turnpike crack with nonideal bimaterial interfaces in a composite laminate

Abstract

1. A turnpike crack at distances greater than the thickness of the nearest band recognizes the interface as “ideal.” However, starting at some distance d(τ*) (depending significantly on the dimensionless parameter (τ* = μ0τh2−1), the interface is recognized as “free.” The value of d(τ*) depends only slightly on the ratio of the elastic moduli of the layer and matrix. 2. Parameter τ* has its greatest effect in the frequently encountered case in which the shear modulus of the matrix is less than the geometric mean modulus of the layer. A small transverse interphase crack may arise in this case, which corresponds to the mechanism for inhibition of a turnpike crack proposed by Cherepanov [10]. 3. When the layer is an order of magnitude less than the matrix, the effect of the nonideal nature of the contact even on the nearest interface may be neglected. 4. The stress distribution already at the next bimaterial interface depends only very slightly on τ*. Thus, the effect of the nonideal nature of the contacts along the other layers of the composite on local stresses near the crack tip may be neglected. This significantly distinguishes this problem from the problem of determining the effective properties of composite laminates. 5. The anisotropy of the layer closest to the crack plays an important role only when the elastic modulus\(\mu _l = \sqrt {{{\mu _x } \mathord{\left/ {\vphantom {{\mu _x } {\mu _y }}} \right. \kern-\nulldelimiterspace} {\mu _y }}} \) is an order of magnitude less than the shear modulus of the matrix. 6. The specific type of stresses along the crack sides (in the case of a fixed major vector) has greatest effect on the SIF in the case of ideal contact (τ = 0). In the case of nonideal contact, this permits us to use approximation (3) for calculating the SIF.