scholarly journals Analytical determination of coefficients in crack-tip stress expansions for a finite crack in an infinite plane medium

2012 ◽  
Vol 49 (3-4) ◽  
pp. 556-566 ◽  
Author(s):  
Gaëtan Hello ◽  
Mabrouk Ben Tahar ◽  
Jean-Marc Roelandt
Keyword(s):  
Crack Tip ◽  
Analytical Determination ◽  
Infinite Plane ◽  
Plane Medium ◽  
Finite Crack ◽  
Crack Tip Stress

Complete Williams Asymptotic Expansion near the Crack Tips of Collinear Cracks of Equal Lengths in an Infinite Plane

2016 ◽  
Vol 258 ◽  
pp. 209-212 ◽  
Author(s):  
Larisa Stepanova ◽  
Pavel Roslyakov ◽  
Tatjana Gerasimova
Keyword(s):  
Plane Elasticity ◽  
Analytical Determination ◽  
Geometrical Parameters ◽  
Infinite Plane ◽  
Variable Theory ◽  
Complex Variable Theory ◽  
Plane Medium ◽  
Crack Tips ◽  
Plane Elasticity Theory

The present study is aimed at analytical determination of coefficients in crack tip expansion for two collinear finite cracks of equal lengths in an infinite plane medium. The study is based on the solutions of the complex variable theory in plane elasticity theory. The analytical dependence of the coefficients on the geometrical parameters and the applied loads for two finite cracks in an infinite plane medium is given. It is shown that the effect of the higher order terms of the Williams series expansion becomes more considerable at large distances from the crack tips. The knowledge of more terms of the stress asymptotic expansions allows us to approximate the stress field near the crack tips with high accuracy.

The Crack Problem for Bonded Nonhomogeneous Materials Under Antiplane Shear Loading

1985 ◽  
Vol 52 (4) ◽  
pp. 823-828 ◽  
Author(s):  
F. Erdogan
Keyword(s):  
Stress Field ◽  
Shear Modulus ◽  
Crack Problem ◽  
Crack Tip ◽  
Shear Loading ◽  
Antiplane Shear ◽  
Intensity Factors ◽  
Finite Crack ◽  
Square Root Singularity ◽  
Crack Tip Stress

The main objective of this paper is the investigation of the singular nature of the crack-tip stress field in a nonhomogeneous medium having a shear modulus with a discontinuous derivative. The problem is considered for the simplest possible loading and geometry, namely the antiplane shear loading of two bonded half spaces in which the crack is perpendicular to the interface. It is shown that the square-root singularity of the crack-tip stress field is unaffected by the discontinuity in the derivative of the shear modulus. The problem is solved for a finite crack and extensive results are given for the stress intensity factors.

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