Mode Stresses for the Interaction between Straight and Curved Cracks Problem in Plane Elasticity

DOI: 10.4236/jamp.2014.25028   PDF   HTML     3,543 Downloads   4,365 Views   Citations

Abstract

In this paper, the complex variable function method is used to obtain the hypersingular integral equations for the interaction between straight and curved cracks problem in plane elasticity. The curved length coordinate method and suitable quadrature rule are used to solve the integrals for the unknown function, which are later used to evaluate the stress intensity factor, SIF. Three types of stress modes are presented for the numerical results.

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Aridi, M. , Long, N. and Eshkuvatov, Z. (2014) Mode Stresses for the Interaction between Straight and Curved Cracks Problem in Plane Elasticity. Journal of Applied Mathematics and Physics, 2, 225-234. doi: 10.4236/jamp.2014.25028.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Helsing, J. (2011) A Fast and Stable Solver for Singular Integral Equations on Piecewise Smooth Curved. SIAM Journal on Scientific Computing, 33, 153-174. http://dx.doi.org/10.1137/090779218
[2] Helsing, J. and Peters, G. (1999) Integral Equation Methods and Numerical Solutions of Crack and Inclusion Problems in Planar Elastostatics. SIAM Journal on Applied Mathematics, 59, 965-982.
[3] Chen, Y.Z., Hasebe, N. and Lee, K.Y. (2003) Multiple Crack Problems in Elasticity. WIT Press, Southampton.
[4] Johnson, J. and Qu, J. (2007) An Interaction Integral Method for Computing Mixed Mode Stress Intensity Factors for Curved Biomaterial Interface Cracks in Non-Uniform Temperature Fields. Engineering Fracture Mechanics, 74, 2282- 2291. http://dx.doi.org/10.1016/j.engfracmech.2006.10.008
[5] Chen, Y.Z. and Lin, X.Y. (2010) Numerical Solution of Singular Integral Equation for Multiple Curved Branch-Cracks. Structural Engineering and Mechanics, 34, 85-95. http://dx.doi.org/10.12989/sem.2010.34.1.085
[6] Chen, Y.Z. and Hasebe, N. (1997) Fredholm Integral Equation for the Multiple Circular Arc Crack Problem in Plane Elasticity. Archieve of Applied Mechanics, 67, 433-446. http://dx.doi.org/10.1007/s004190050129
[7] Nik Long, N.M.A. and Eshkuvatov, Z.K. (2009) Hypersingular Integral Equation for Multiple Curved Crack Problem in Antiplane Elasticity. International Journal of Solids and Structures, 46, 2611-2617. http://dx.doi.org/10.1016/j.ijsolstr.2009.02.008
[8] Chen, Y.Z., Gross, D. and Huang, Y.J. (1991) Numerical Solution of the Curved Crack Problem by Means of Polynomial Approximation of the Dislocation Distribution. Engineering Fracture Mechanics, 39, 791-797. http://dx.doi.org/10.1016/0013-7944(91)90184-3
[9] Muskhelishvili, N.I. (1957) Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff International Publishing, Leyden.
[10] Cotterell, B. and Rice, J.R. (1980) Slightly Curved or Kinked Cracks. International Journal of Fracture, 6, 155-169. http://dx.doi.org/10.1007/BF00012619
[11] Mayrhofer, K. and Fischer, F.D. (1992) Derivation of a New Analytical Solution for a General Two Dimensional Finite-Part Integral Applicable in Fracture Mechanics. International Journal of Numerical Method in Engineering, 33, 1027-1047. http://dx.doi.org/10.1002/nme.1620330509

  
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