scholarly journals Stress Intensity Factors for a Non-Circular Hole with Inclusion Layer Embedded in a Cracked Matrix

Aerospace ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 17
Author(s):  
Chenchun Chiu ◽  
Shaochen Tseng ◽  
Chingkong Chao ◽  
Jheyuan Guo

The failure analysis of a non-circular hole with an inclusion layer embedded in an infinite cracked matrix under a remote in-plane uniform load is presented. In this study, a series solution of stress functions for both the matrix and inclusion layer is obtained using the complex variable theory in conjunction with the method of conformal mapping. The stress intensity factor (SIF) can then be determined numerically by solving the singular integral equation (SIE) for the interaction among different crack sites, material properties, and geometries of irregular holes with an inclusion layer. In particular, the failure behavior of composite structures associated with an approximately triangular hole and an approximately square hole with inclusion layers, such as those of oxides, nitrides, and sulfides, is examined in detail. The results demonstrate that a softer layer would enhance the SIF and a stiffer layer would restrain the SIF when a crack is near the inclusion layer. It can be concluded that crack propagation would be suppressed by a stiffer layer even when a micro-defect such as a hole resides in the inclusion layer.

2021 ◽  
Vol 37 ◽  
pp. 327-332
Author(s):  
F M Chen ◽  
C K Chao ◽  
C C Chiu ◽  
N A Noda

Abstract The general solutions of the stress intensity factors (SIFs) for a cusp-type crack problem under remote uniform mechanical and thermal loads are presented in this work. According to the complex variable theory and the method of conformal mapping, a symmetric airfoil crack is mapped onto a unit circle, and both the temperature and stress potentials are used to solve the relevant boundary-value problems. By introducing the auxiliary function and applying the analytical continuation theorem, the SIFs at the cusp-type crack tip can be analytically determined. The obtained SIF results are dependent on the geometric configurations of the cusp-type crack components and the magnitudes of the mechanical and thermal loads. For some combinations of combined loads, the SIF is maximized, and the system has a high risk of damage.


2002 ◽  
Vol 18 (3) ◽  
pp. 145-151
Author(s):  
Y. C. Shiah ◽  
Jiunn Fang ◽  
Chin-Yi Wei ◽  
Y.C. Liang

AbstractIn this paper, the crack problem of a large beam-like strip weakened by a circular arc crack with in-plane bending moments applied at both ends is approximately solved using the complex variable technique. Complex stress functions corresponding to the applied bending moments are superposed with those due to the disturbance of the crack to satisfy the governing boundary equation. The conformal mapping function devised to transform the contour surface of a circular arc crack to a unit circle is then substituted in the boundary equation to facilitate the evaluation of Cauchy integrals. In this way, the complex stress functions due to the crack disturbance are determined and the stress intensity factors are calculated through a limiting process to give their explicit forms. Eventually, the geometric functions for the variation of the stress intensity factors on account of the crack shape are plotted as a function of the curvature of a circular-arc crack.


2007 ◽  
Vol 353-358 ◽  
pp. 3100-3103
Author(s):  
Naoaki Noda ◽  
Yasushi Takase ◽  
Ryohji Shirao ◽  
Jun Li ◽  
Jun Suke Sugimoto

In this study, singular stress fields at the ends of fibers are discussed by the use of models of rectangular and cylindrical inclusions in a semi-infinite body under pull-out force.The body force method is used to formulate those problems as a system of singular integral equations where the unknown functions are densities of the body forces distributed in a semi-infinite body having the same elastic constants as those of the matrix and inclusions.Then generalized stress intensity factors at the corner of rectangular and cylindrical inclusions are systematically calculated with varying the elastic ratio, length, and spacing of the location from edge to inner of the body. The effects of elastic modulus ratio and aspect ratio of inclusion upon the stress intensity factors are discussed.


2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Xiangqiao Yan

This note deals with the stress intensity factors (SIFs) for double edge half-circular-hole cracks in a rectangular sheet in tension by means of the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author. Moreover, an empirical formula of the SIFs of the crack problem is presented and examined. It is found that the empirical formula is simple, yet accurate for evaluating the SIFs of the crack problem.


1987 ◽  
Vol 109 (1) ◽  
pp. 36-39
Author(s):  
C. A. Bigelow

Stress-intensity factors are determined for an infinite cracked orthotropic sheet adhesively bonded to an orthotropic stringer. Since the stringer is modeled as a semi-infinite sheet, the solution is most appropriate for a crack tip located near a stringer edge. Both adherends are treated as homogeneous, orthotropic media which are representative of many fiber-reinforced composite materials. The complex variable theory of elasticity was used to obtain a set of integral equations describing the problem. The integral equations are replaced by an equivalent set of algebraic equations, which are solved to obtain the shear stress distribution in the adhesive layer. From these adhesive stresses, the stress-intensity factors are found. A parametric study is conducted to determine the sensitivity of the system to material properties and specimen configuration. Unless the crack tip is very close to or under the stringer, the stress-intensity factor is approximately that of the unstiffened sheet. However, as the crack propagates beneath the stringer, the stress-intensity factor decreases significantly. Increasing the stringer stiffness or the adhesive stiffness also decreases the stress-intensity factor.


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