Analysis of stress intensity factor in orthotropic bi-material mixed interface crack

• DOI: 10.1007/s10483-014-1864-9
• Publication Date: 2014-07-18T11:54:01Z
• Authors: Wen-bin Zhao; Xue-xia Zhang; Xiao-chao Cui; Wei-yang Yang
• Keywords: Orthotropic material; Shear modulus

Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With consideration of the boundary conditions, a new stress function is introduced to transform the problem of bi-material interface crack into a boundary value problem of partial differential equations. Two sets of non-homogeneous linear equations with 16 unknowns are constructed. By solving the equations, the expressions for the real bi-material elastic constant ɛ t and the real stress singularity exponents λ t are obtained with the bi-material engineering parameters satisfying certain conditions. By the uniqueness theorem of limit, undetermined coefficients are determined, and thus the bi-material stress intensity factor in mixed cracks is obtained. The bi-material stress intensity factor characterizes features of mixed cracks. When orthotropic bi-materials are of the same material, the degenerate solution to the stress intensity factor in mixed bi-material interface cracks is in complete agreement with the present classic conclusion. The relationship between the bi-material stress intensity factor and the ratio of bi-material shear modulus and the relationship between the bi-material stress intensity factor and the ratio of bi-material Young’s modulus are given in the numerical analysis.