Calculation of mode III stress intensity factors for two interacting cracks in elastic spaces

• Main Author: Wong, Daryl Wai Mun
• Other Authors: Ang Whye Teong
• Format: Final Year Project
• Language: English
• Published: 2015
• Subjects: DRNTU::Engineering::Mechanical engineering
• Online Access: http://hdl.handle.net/10356/62118
• Institution: Nanyang Technological University

Fracture mechanics studies the propagation of cracks in materials. In the framework of linear elasticity, the stresses at the crack tips are singular. The stress intensity factors which are coefficients of the singular stress at the crack tips are used as criteria for determining the stability of cracks. They depend on the geometry of the sample, size and locations of the cracks as well as the magnitude and distribution of loads on the sample. In this report, we formulated a Mode III crack problem in terms of a system of hypersingular integral equations. Concepts such as boundary integral equation, Green’s functions and conformal mapping were used in the formulation of the problem. The displacements across opposite crack faces are determined and from there, the Mode III crack tip stress intensity factors can be easily obtained. MATLAB (R2012b) is the programming software used for the computation of the solution. The code in this dissertation can be used to obtain stress intensity factors of two cracks in an idealized geometry of a half space, an infinite wedge sector of angle π/n and a semi-circle. The program was run several times with similar crack coordinates to note the difference in stress intensity factors of the different idealized geometries. The results can be easily compared with each other to check for consistency. As the boundaries of the other geometries are stretched and the cracks are placed far from each other, the stress intensity factors tend to unity. Similarly, the cracks can be placed far from the all of the other boundaries except the y = 0 boundary to emulate a half space problem.