Wiener–Hopf Method to Solve the Anti-Plane Problem of Moving Semi-Infinite Crack in Orthotropic Composite Materials

Shiv Shankar Das,Anshika Tanwar,Subir Das,Eduard-Marius Craciun

MATHEMATICS AND MECHANICS OF SOLIDS（2024）

Indian Inst Technol BHU | Ovidius Univ Constanta

Cited 0|Views6

Abstract

This paper contains the solution to the problem of a semi-infinite moving crack situated in an orthotropic strip bonded between two identical strips. The crack moves with a constant velocity, and the surface is under shear wave disturbance. We first examine the equations of elasticity, which include equilibrium equations and stress and displacement constitutive relations with the model-specific continuity and boundary conditions. Using the Fourier integral transform, the standard form for the Wiener–Hopf (W-H) equation is obtained, which is solved using the W-H method. The analytical expressions for the considered crack problem have been obtained for stress intensity factor (SIF), normalized stress intensity factor (NSIF), and stress magnification factor (SMF). The behavior of NSIF has been graphically presented for particular cases of composite materials for different crack propagation velocities and various depth ratios of the strips. The novelty of this paper lies in the analytic solutions using the W-H method for the semi-infinite moving crack problem under the influence of anti-plane shear waves. The pictorial presentations of normalized SIF clearly show their dependency on strip depths, crack propagation velocities and elastic constants.

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Key words

Stress intensity factor,anti-plane traction,analytic function,composite materials,Wiener-Hopf method

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【要点】：本文提出了一种利用Wiener-Hopf方法解决正交各向异性复合材料的半无限移动裂纹问题，得到应力强度因子和应力放大因子的解析解，并揭示了这些因子与裂纹传播速度和条带深度的关系。

【方法】：作者通过平衡方程和应力及位移本构关系，结合模型特定的连续性和边界条件，采用傅里叶积分变换导出Wiener-Hopf方程的标准形式，并利用Wiener-Hopf方法求解。

【实验】：通过数值计算和图形展示，研究了不同裂纹传播速度和条带深度比对正交各向异性复合材料的归一化应力强度因子（NSIF）的影响，数据集为特定条件下的复合材料的数值模拟结果。