scholarly journals Complete Williams Asymptotic Expansion Near The Crack Tips of Collinear Cracks of Equal Lengths in an Infinite Plane Medium

2016 ◽  
Vol 2 ◽  
pp. 1789-1796 ◽  
Author(s):  
Larisa Stepanova ◽  
Pavel Roslyakov
Keyword(s):  
Asymptotic Expansion ◽  
Infinite Plane ◽  
Collinear Cracks ◽  
Plane Medium ◽  
Crack Tips

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 mutual effects between two unequal collinear cracks under compression

2016 ◽  
Vol 22 (5) ◽  
pp. 1205-1218 ◽  
Author(s):  
Yong Fan ◽  
Zheming Zhu ◽  
Jiming Kang ◽  
Yangcheng Fu
Keyword(s):  
Crack Surface ◽  
Analytical Formula ◽  
Surface Friction ◽  
Complex Stress ◽  
Infinite Plane ◽  
Collinear Cracks ◽  
Interval Distance ◽  
Crack Tips ◽  
Analytical Result ◽  
Abaqus Code

For two unequal collinear cracks under compression, which crack would propagate first, the longer one or the shorter one, and how they affected each other was studied. By using complex stress function theory and considering crack surface friction, the analytical formula of stress intensity factors (SIFs) for an infinite plane containing two unequal collinear cracks was obtained and the analytical results have been validated through numerical simulation by employing ABAQUS code, photoelastic experiments, and compressive tests. The results show that the numerical, photoelastic, and compressive test results agree well with the analytical result. Finally, the effects of crack length, crack surface friction, and crack interval distance between two crack tips on SIFs were analyzed, and the results show that the SIF values at the longer crack tips are always higher than those at the shorter crack tips; for each crack, the SIF value at the internal tip is always larger than that at the external tip.

The solution of heat transfer problems by the Wiener-Hopf technique. I. Leading edge of a hot film

1973 ◽  
Vol 333 (1594) ◽  
pp. 347-362 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Asymptotic Expansion ◽  
Half Plane ◽  
Leading Edge ◽  
Infinite Plane ◽  
Longitudinal Diffusion ◽  
Boundary Layer Equations ◽  
Leading Term ◽  
Hot Film

An incompressible fluid of constant thermal diffusivity flows with velocity Sy in the x -direction over the infinite plane wall y = 0. The half-plane y = 0, x > 0 is maintained at a uniform temperature T 1 greater than the temperature T 0 of the oncoming fluid. The adiabatic boundary condition T y = 0 is imposed on the half-plane y = 0, x < 0. An exact solution for the dimensionless heat transfer from the heated half-plane x > 0, incorporating longitudinal diffusion, is obtained by the Wiener-Hopf technique, and is reduced to a single convergent real integral which is evaluated numerically. An asymptotic expansion is made in inverse powers of x , whose leading term is Lévêque’s (1928) boundary-layer solution. Subsequent terms in the expansion lead to a determination of the coefficients of the eigenfunctions of the boundary-layer equations which would remain arbitrary in a direct asymptotic expansion of the governing equation.

scholarly journals MULTIPARAMETRIC ANALYSIS OF THE STRESS FIELD NEAR THE CRACK TIP

2017 ◽  
Vol 21 (10) ◽  
pp. 52-76
Author(s):  
L.V. Stepanova ◽  
P.S. Roslyakov
Keyword(s):  
Asymptotic Expansion ◽  
Stress Field ◽  
Mixed Mode ◽  
Infinite Plate ◽  
Higher Order ◽  
Analytical Determination ◽  
Mixed Mode Loading ◽  
Complete Asymptotic Expansion ◽  
Higher Order Terms ◽  
Crack Tips

The paper is devoted to analytical determination of coefficients of the Williams asymptotic expansion of the stress field in the neighborhood of two collinear crack tips in an infinite plate under mixed mode loading. On the basis of the Kolosof-Muskhelishvili approach the complete asymptotic expansion of the stress field in the vicinity of the crack tips of two collinear cracks of equal lengths under mixed mode loading is derived. The analysis of the higher order terms in the asymptotic expansion series is performed. It is clear that it is necessary to take into account the higher order terms.

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