Analytical Solutions of Finite Wedges Coated by an Orthotropic Coating Containing Multiple Cracks and Cavities

Document Type : Research Paper

Author

Department of Mechanical Engineering, Iran University of Science & Technology (IUST), Tehran , Iran

10.22034/jsm.2021.1921133.1673

Abstract

This paper presents a general formulation for an isotropic wedge reinforced by an orthotropic coating involving multiple arbitrarily oriented defects under out of plane deformation. The exact closed form solution of the problem weakened by a screw dislocation in the isotropic wedge is obtained by making use of finite Fourier cosine transform. Also, the closed-form solutions of the out of plane stress and displacement fields are obtained. After that, by making use of a distributed dislocation approach, a set of singular integral equations of the domain involving smooth cavities and cracks subjected to out of plane external loading are achieved. The cracks and cavities are considered to be only in the isotropic wedge. The presented integral equations have Cauchy singularity and must be evaluated numerically. Multiple numerical examples will be presented to show the applicability and efficiency of the presented solution. The geometric and point load singularities of the stress components are obtained and compared with the available data in the literature.                 

Keywords

  1.  Erdogan F., 2000, Fracture mechanics, International Journal of Solids and Structures 37: 171-183.
  2.  Hills D.A., Kelly P., Dai D., Korsunsky A., 2013, Solution of Crack Problems: The Distributed Dislocation Technique, Springer Science & Business Media.
  3.  Matbuly M., Nassar M., 2009, Analysis of multiple interfacial cracks in an orthotropic bi-material subjected to anti-plane shear loading, Engineering Fracture Mechanics 76: 1658-1666.
  4.  Li X-F., Duan X-Y., 2006, An interfacially-cracked orthotropic rectangular bi-material subjected to antiplane shear loading, Applied Mathematics and Computation 174:1060-1079.
  5.  Kargarnovin M., Fariborz S., 2000, Analysis of a dissimilar finite wedge under antiplane deformation, Mechanics Research Communications 27:109-116.
  6.  Kargarnovin M., Shahani A., Fariborz S., 1997, Analysis of an isotropic finite wedge under antiplane deformation, International Journal of Solids and Structures 34:113-128.
  7.  Shahani A., 1999, Analysis of an anisotropic finite wedge under antiplane deformation, Journal of Elasticity 56:17-32.
  8.  Shahani A., 2003, Mode III stress intensity factors for edge-cracked circular shafts, bonded wedges, bonded half planes and DCB’s, International Journal of Solids and Structures 40: 6567-6576.
  9.  Lin R-L., Ma C-C., 2004, Theoretical full-field analysis of dissimilar isotropic composite annular wedges under anti-plane deformations, International Journal of Solids and Structures 41: 6041-6080.
  10.  Chen C-H., Wang C-L., 2009, A solution for an isotropic sector under anti-plane shear loadings, International Journal of Solids and Structures 46: 2444-2452.
  11.  Mkhitaryan S.M., Melkoumian N., Lin B.B., 2001, Stress-strain state of a cracked elastic wedge under anti-plane deformation with mixed boundary conditions on its faces, International Journal of Fracture 108: 291-315.
  12.  Shahani A., Ghadiri M., 2010, Analysis of anisotropic sector with a radial crack under anti-plane shear loading, International Journal of Solids and Structures 47: 1030-1039.
  13.  Lechnickij S.G., Lekhnit͡skiĭG., 1963, Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day.
  14.  Faal R., Fariborz S., Daghyani H., 2007, Stress analysis of a finite wedge weakened by cavities, International Journal of Mechanical Sciences 49: 75-85.
  15.  Faal R.T., Fariborz S.J., Daghyani H.R., 2006, Antiplane deformation of orthotropic strips with multiple defects, Journal of Mechanics of Materials and Structures 1: 1097-1114.
  16.  Pook L.P., 2007, Metal Fatigue What it is, Why it Matters, Dordrecht, Springer.
  17.  Pook L.P., 2003, A finite element analysis of cracked square plates and bars under antiplane loading, Fatigue & Fracture of Engineering Materials & Structures 26: 533-541.
  18.  Chen Y.Z., Lin X.Y., Chen R.S. 1997, Solution of torsion crack problem of an orthotropic rectangular bar by using computing compliance method, Communications in Numerical Methods in Engineering 13: 655-663.
  19.  Gracia L., Doblare M., 1988, Shape optimization of elastic orthotropic shafts under torsion by using boundary elements, Computers & Structures 30: 1281-1291.
  20.  Benveniste Y., Chen T., 2003, The Saint-Venant torsion of a circular bar consisting of a composite cylinder assemblage with cylindrically orthotropic constituents, International Journal of Solids and Structures 40: 7093-7107.
  21.  Rongqiao X., Jiansheng H., Weiqiu C., 2010, Saint-Venant torsion of orthotropic bars with inhomogeneous rectangular cross section, Composite Structures 92: 1449-1457.
  22.  Santoro R., 2010, The line element-less method analysis of orthotropic beam for the De Saint Venant torsion problem, International Journal of Mechanical Sciences 52: 43-55.
  23.  Faal R., Fotuhi A., Fariborz S., Daghyani H., 2004, Antiplane stress analysis of an isotropic wedge with multiple cracks, International Journal of Solids and Structures 41: 4535-4550.
  24.  Faal R., Daliri M., Milani A., 2011, Anti-Plane stress analysis of orthotropic rectangular planes weakened by multiple defects, International Journal of Solids and Structures 48: 661-672.
  25.  Weertman J., Weertman J., 1992, Elementary Dislocation Theory, Oxford University Press, New York.
  26.  Barber J.R., 2002, Elasticity, Springer.
  27.  Hills D.A., Kelly P.A., Dai D.N., Korsunsky A.M., 2013, Solution of Crack Problems: The Distributed Dislocation Technique, Springer Netherlands.