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

doi:10.1007/s10483-014-1864-9

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (10): 1271-1292.doi: https://doi.org/10.1007/s10483-014-1864-9

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

赵文彬, 张雪霞, 崔小朝, 杨维阳

School of Applied Sciences, Taiyuan University of Science and Technology, Taiyuan 030024, P. R. China

收稿日期:2013-03-27 修回日期:2013-09-16 出版日期:2014-10-01 发布日期:2014-10-01
通讯作者: Xue-xia ZHANG, zwbhappy@aliyun.com E-mail:zwbhappy@aliyun.com
基金资助:
Project supported by the National Key Basic Research Program of China (973 Program) (No. 2009CB724201), the Science and Technology Major Project of the Ministry of Education of China (No. 208022), the Postgraduate Scientific and Technological Innovation Project of Taiyuan University of Science and Technology (No. 20125027), and the Scientific Research Funds for Doctoral Students of Taiyuan University of Science and Technology (No. 20122005)

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

Wen-bin ZHAO, Xue-xia ZHANG, Xiao-chao CUI, Wei-yang YANG

School of Applied Sciences, Taiyuan University of Science and Technology, Taiyuan 030024, P. R. China

Received:2013-03-27 Revised:2013-09-16 Online:2014-10-01 Published:2014-10-01
Supported by:
Project supported by the National Key Basic Research Program of China (973 Program) (No. 2009CB724201), the Science and Technology Major Project of the Ministry of Education of China (No. 208022), the Postgraduate Scientific and Technological Innovation Project of Taiyuan University of Science and Technology (No. 20125027), and the Scientific Research Funds for Doctoral Students of Taiyuan University of Science and Technology (No. 20122005)

摘要/Abstract

摘要： Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With con- sideration 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 dif- ferential 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 λ_t and the real stress singularity exponents ε_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 be- tween the bi-material stress intensity factor and the ratio of bi-material Young's modulus are given in the numerical analysis.

关键词: bi-material, complex variable method, orthotropic, interface crack, stress intensity factor

Abstract: Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With con- sideration 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 dif- ferential 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 λ_t and the real stress singularity exponents ε_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 be- tween the bi-material stress intensity factor and the ratio of bi-material Young's modulus are given in the numerical analysis.

Key words: bi-material, interface crack, stress intensity factor, complex variable method, orthotropic

中图分类号:

O346
O174

赵文彬;张雪霞;崔小朝;杨维阳. Analysis of stress intensity factor in orthotropic bi-material mixed interface crack[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(10): 1271-1292.

Wen-bin ZHAO;Xue-xia ZHANG;Xiao-chao CUI;Wei-yang YANG. Analysis of stress intensity factor in orthotropic bi-material mixed interface crack[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(10): 1271-1292.

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

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

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