An Analytical Solution for the Periodically Spaced Two Collinear and Symmetric Cracks Under Remote Tension

• Published in: Journal of elasticity Vol. 157; no. 1
• Main Authors: Hu, Jiayao, Jin, Fan, Xia, Fan, Li, Jicheng
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2025; Springer Nature B.V
• Subjects: Biomechanics; Boundary conditions; Classical and Continuum Physics; Classical Mechanics; Complex variables; Contact stresses; Crack initiation; Engineering; Exact solutions; Finite element method; Integral equations; Materials Science; Mathematical analysis; Mathematical Applications in the Physical Sciences; Normal stress; Plastic zones; Stress distribution; Stress intensity factors; Theoretical and Applied Mechanics; Fracture mechanics; Stress intensity factor; Singular integral equations; Collinear cracks; 74R10; Periodic cracks; 74
• ISSN: 0374-3535; 1573-2681
• DOI: 10.1007/s10659-024-10093-6

The present paper provides an analytical solution for a periodic array of two collinear and symmetric cracks (P-TCSC) under remote tension. This is achieved by representing the multiple collinear cracks problem as the contact problem with discrete ligament regions, and the governing equations are obtained as integral equations with Cauchy-type kernel. Closed-form expressions are derived for the crack opening profile, normal stress distribution and mode I stress intensity factors (SIFs), which can reduce to the classical solutions of two collinear and symmetric cracks (TCSC) or a periodic row of collinear cracks with equal length and equal spacing (PCEE) under special conditions. Finite element analysis is also performed to validate the analytical solutions obtained. Different from the TCSC case, results show that crack initiation for P-TCSC seems more complicated depending on a combination of two nondimensional parameters, and a SIFs map for P-TCSC is further constructed to give a more precise evaluation. The proposed method relies solely on solving the integral equations with Cauchy-type kernel combined with the corresponding boundary conditions without a prior knowledge of the complex potential function in traditional complex variable method of plane elasticity, and it may find application in plastic zone evaluation and fracture criteria of collinear cracks.