Hypersingular integral equations for the solution of penny-shaped interface crack problems

Abstract

Based on the theory of elasticity, previous analytical solutions concerning a penny-shaped interface crack employ the derivative of the crack surface opening displacements as the primary unknowns, thus leading to singular integral equations with Cauchy-type singularity. The solutions to the resulting integral equations permit only the determination of stress intensity factors and energy release rate, and do not directly provide crack opening and sliding displacements. However, the crack opening and sliding displacements are physically more meaningful and readily validated against the finite element analysis predictions and experimental measurements. Therefore, the present study employs crack opening and sliding as primary unknowns, rather than their derivatives, and the resulting integral equations include logarithmic-, Cauchy-, and Hadamard-type singularities. The solution to these singular integral equations permits the determination of not only the complex stress intensity factors but also the crack opening displacements.

Elastodynamic Problem for Two Penny-Shaped Cracks: The Effect of Cracks’ Closure

“…Due to the presence of non-integrable singularities in the integral kernels ) , , ( 33 k F ω y x , Eq. (11), whose rank exceeds the dimension of the integration region, the appropriate integrals in the system (12) are hypersingular and should be treated in the sense of the Hadamard finite part, see, for instance, Martin et al (1989), Kilic and Madenci (2007), Men'shikov et al (2007), . The structure of integrals depends on the types of the weight and trial functions.…”

Elastic interaction of interfacial spherical-cap cracks in hollow particle filled composites

“…This study is applicable to syntactic foams with low particle volume fraction as it neglects particle-to-particle interactions and focuses on a single inclusion embedded in an infinite matrix. Results are verified through finite element analysis (FEA) and compared with findings for penny-shaped cracks (see for example Gorbatikh, 2004;Kilic and Madenci, 2007), which enables understanding the effect of the interfacial crack curvature on the ERR.…”

Boundary integral equations in the frequency domain for interface linear cracks under impact loading

“…Penny-shaped interface crack under unit pressure was considered in [17], where the study employs crack opening and sliding as primary unknowns, that allows the determination of crack opening and sliding displacement as well as complex stress intensity factors. Harmonic loading of penny-shaped crack in multi-layered composite was studied by Yu and Cooper [18].…”