An effective spring stiffness approximation is proposed for a hexagonal array of coplanar penny shaped cracks located at the interface between two dissimilar solids. The approximation is based on the factorization of the solution on the material dissimilarity factor, the crack interaction factor and the effective spring stiffness solution for non-interacting cracks in a homogeneous material. Such factorization is exact and was validated for 2D collinear cracks between two dissimilar solids. The crack interaction factor is obtained using a recently developed model for stress intensity factors for an array of coplanar penny shaped cracks in a homogeneous material; also the material dissimilarity function recently obtained for non-interacting penny shaped crack at the interface between two dissimilar materials is employed. The obtained solution is useful for an assessment by ultrasonic measurements of the interface stiffness in bonded structures for monitoring the interfacial microdamage growth due to mechanical loading and environmental factors.

中文翻译：

---

两种不同的各向同性材料之间的界面处相互作用的共面便士形裂纹的周期性阵列的有效弹簧刚度

对于位于两个不同固体之间的界面处的共面便士形裂纹的六边形阵列，提出了一种有效的弹簧刚度近似值。该近似值基于材料相异因子的解的因式分解、裂纹相互作用因子和均质材料中非相互作用裂纹的有效弹簧刚度解。这种分解是准确的，并且已针对两个不同固体之间的 2D 共线裂纹进行了验证。裂纹相互作用因子是使用最近开发的应力强度因子模型获得的，该模型用于均质材料中的一组共面的硬币形裂纹；还采用了最近为两种不同材料之间的界面处的非相互作用便士形裂纹获得的材料相异函数。