Stress intensity factors for cracks emanating from a circular hole in an infinite quasi‐orthotropic plane

Abstract

An infinite quasi‐orthotropic plane with a cracked circular hole under tensile loading at infinity is studied analytically. To this end, complex variable theory of Muskhelishvili is used. In addition, to obtain analytical functions, a new conformal mapping is proposed and expanded to series expressions. Stress intensity factors (SIFs) for two unequal cracks emanating from a circular hole are obtained. To validate the analytical SIFs in a quasi‐orthotropic plane, the results are compared with FEM and the results of isotropic plane. The SIFs for small cracks in a quasi‐orthotropic and an isotropic plane are different, because of difference between stress concentrations in points which cracks emanate from the hole. However, the results of quasi‐orthotropic plane converge to isotropic plane for the large cracks. Therefore, the SIFs of the large cracks in a quasi‐orthotropic plane can be replaced by the results of the center crack with equivalent length in an isotropic plane.

Analytical calculation of stress intensity factors for orthotropic plates containing cracks emanating from a circular hole using Schwarz integration

“…The difference between the present research and other researches in this field is in the presentation of the mapping function in such a way that the potential functions can be easily calculated through the Schwartz integration method. for this purpose, Equation ( 1) is used to map the area outside the unit circle of an isotropic plate to the area outside the circle with cracks of length 𝑎 𝑅 and 𝑎 𝐿 on its right and left sides, respectively 𝑎 𝑅 and 𝑎 𝐿 [23].…”

“…The above integrals are calculated on the unite circle. The contour surface is free from external forces and due to the infinite plate is loaded at distances far from the hole edge, the potential functions 𝜑(𝜁) and 𝜓(𝜁) are presented as the following relationship [23]:…”

“…Qajar and HajiMohammadi [22] presented a new mapping function for solving the SIF in an infinite plate with a square hole with two unequal cracks. In another article, they analyzed an infinite quasi-orthotropic plate with a cracked circular hole under tensile load at infinity by using the Mushkhlishvili's complex variable method [23]. Using the weight function method, Xu et al [24] presented the SIF and the displacement of circular hole with edge cracks in an infinite plate, under different loads.…”

Thermomechanical analysis of riveted carbon fiber laminates for aerospace applications

“…Useful review papers 1–3 introduce the reader to a better comprehension of the phenomena involved in determining mechanical behavior of fastened joints. Nevertheless, its complexity, stress field around a pin‐loaded hole has been largely studied considering the effect of friction, clearance, contact, and geometrical parameters 4–12 . Static behavior of mechanically fastened joints could be well determined through an experimental test campaign following, for example, ASTM standards 13,14 .…”

“…Nevertheless, its complexity, stress field around a pin-loaded hole has been largely studied considering the effect of friction, clearance, contact, and geometrical parameters. [4][5][6][7][8][9][10][11][12] Static behavior of mechanically fastened joints could be well determined through an experimental test campaign following, for example, ASTM standards. 13,14 The application of a fatigue load changes significantly this behavior.…”