Analysis of cracks perpendicular to bimaterial interfaces using a novel finite element

Abstract

Inverse square root, 1/√γ, singularity characterizes the stress field at the crack tip of homogeneous isotropic elastic media. This 1/√γ singularity does not, however, hold for cracks present in inhomogeneous solids; such as, a crack terminating at a right angle to bimaterial interface, which is the subject of the current paper. A few attempts have been made to treat this problem analytically. However, in view of the complexity of the resulting equations and the numerical difficulties associated with these attempts, only a very limited number of approximate solutions exist. It is therefore the objective of this study to: (i) provide a comprehensive theoretical treatment of the current boundary value problem using the eigenfunction expansion method, and (ii) to utilize the results of the eigenfunction method to develop a novel singular finite element which is capable of treating cracks terminating perpendicularly to interfaces accurately and efficiently. To establish the validity of the method, a number of test cases are examined and compared with existing simplified solutions. Furthermore, numerical examples are provided to show the effect of the elastic mismatch and crack length upon the resulting stress intensity factors and the associated stress fields.