Spherical indentation over multilayered transversely isotropic media with imperfect interfaces

In coating and substrate structures, interface defects and imperfect bonding between the adjacent layers commonly occur due to manufacturing processes. These imperfect interfaces mostly behave like springs, characterized by displacement discontinuity with traction being directly linked to the displacement jump at the interface. This study presents an innovative theoretical solution for a rigid sphere over a multilayered and functionally graded transversely isotropic elastic half-space with such imperfect interfaces. For the given indentation depth, the unknown contact radius and vertical load are obtained through a self-adaptive integral least-square scheme along with the influence function for an annular load over a multilayered and/or functionally graded half-space. The influence function is determined in terms of the Fourier-Bessel series system of vector functions in conjunction with the dual-variable and position method. We first validate the accuracy of our method by comparing it with the established exact solutions for a uniform elastic medium. We then apply the new solution to investigate the effects of imperfect-bonding and layer stiffness on the vertical load and stress field distribution in both layered and functionally graded material systems. Numerical examples show that while the von Mises stress is sensitive to the interface imperfection and Young's modulus ratio in the graded material, the vertical load and normal contact stress distribution are sensitive to the layer stiffness.