ANALYSIS OF A LONG STRIP CONTAINING AN INTERNAL OR EDGE CRACK USING FEM

This paper presents the elastostatic plane problem of a long strip containing an internal or edge crack perpendicular to its boundaries. The plane problem consists of an infinitely long strip of thickness h. The infinitely long strip is loaded by uniformly distributed load and rests on two simple supports. It is assumed that the effect of gravity is neglected. The finite element model of the problem is constituted using ANSYS software and the two dimensional analysis of the problem is carried out. Normalized stress-intensity factors for the cases with internal and edge crack, and normal stress (x) for uncracked layer case are obtained for various dimensionless quantities. Finally, the results obtained from the finite element analysis are verified by comparing with analytical ones and it is seen that the results from finite element analysis indicate a good agreement with the analytical solution.

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  • [1] Birinci, A. and Erdöl, R., (2004) A Layered Composite Containing a Crack in its Lower Layer Loaded by a Rigid Stamp, European Journal of Mechanics A/Solids 23, 909–924.
  • [2] Lowengrub, M., (1966) A Two-Dimensional Crack Problem, International Journal of Engineering Science 4, 289–299.
  • [3] Gupta, G. D. and Erdogan, F., (1974) The Problem of Edge Cracks in an Infinite Strip, Journal of Applied Mechanics 41, 1001-1006.
  • [4] Bakioglu, M. and Erdogan, F., (1977) The Crack-Contact and the Free-End Problem for a Strip under Residual Stress, Journal of Applied Mechanics 44, 41-46.
  • [5] Nied, H. F. and Erdogan, F., (1983) The elasticity problem for a thick-walled cylinder containing a circumferential crack, International Journal of Fracture 22, 277-301.
  • [6] Hong, H. and Chen, J., (1988) Derivations of Integral Equations of Elasticity, Journal of Engineering Mechanics 114(6), 1028–1044.
  • [7] Chen, Y.Z., (1995) A Survey of New Integral Equations in Plane Elasticity Crack Problem, Engineering Fracture Mechanics 51, 97–134.
  • [8] Beghini, M. and Bertini, L., (1996) Effective Stress Intensity Factor and Contact Stress for a Partially Closed Griffith Crack in Bending, Engineering Fracture Mechanics 54, 667-678.
  • [9] Kadioğlu, S., Dag, S. and Yahsi, S., (1998) Crack Problem for a Functionally Graded Layer on an Elastic Foundation, International Journal of Fracture 94, 63–77.
  • [10] Shbeeb, N.I. and Binienda, W.K., (1999) Analysis of an Interface Crack for a Functionally Graded Strip Sandwiched between Two Homogeneous Layers of Finite Thickness, Engineering Fracture Mechanics 64, 693-720.
  • [11] Chen, Y.Z., (1999) A Contact Crack Problem in an Infinite Plate, International Journal of Engineering Science 37, 621–630.
  • [12] Chen, J.T. and Hong, H.-K., (1999) Review of Dual Boundary Element Methods with Emphasis on Hypersingular Integrals and Divergent Series, Applied Mechanics Reviews 52(1), 17-33.
  • [13] Choi, H. J., (2001) The Problem for Bonded Half-Planes Containing a Crack at an Arbitrary Angle to the Graded Interfacial Zone, International Journal of Solids and Structures 38, 6559-6588.
  • [14] Dag, S. and Erdogan, F., (2002) A Surface Crack in a Graded Medium Loaded by a Sliding Rigid Stamp, Engineering Fracture Mechanics 69, 1729–1751.
  • [15] Chen, J., Liu, Z. and Zou, Z., (2002) Transient Internal Crack Problem for a Nonhomogeneous Orthotropic Strip (Mode I), International Journal of Engineering Science 40, 1761–1774.
  • [16] Yue, Z.Q., Xiao, H.T. and Tham, L.G., (2003) Boundary Element Analysis of Crack Problems in Functionally Graded Materials, International Journal of Solids and Structures 40, 3273–3291.
  • [17] Guo, L. C., Wu, L. Z., Ma, L. and Zeng, T., (2004) Fracture Analysis of a Functionally Graded Coating-Substrate Structure with a Crack Perpendicular to the Interface - Part I: Static Problem, International Journal of Fracture 127, 21–38.
  • [18] Xiao, H.T., Yue, Z.Q. and Tham, L.G., (2005) Analysis of an Elliptical Crack Parallel to Graded Interfacial Zone of Bonded Bi-Materials, Mechanics of Materials 37, 785–799.
  • [19] Kahya, V., Birinci, A., Ozsahin, T. S. and Erdol, R., (2006) Partial Closure of a Crack Located in an Anisotropic Infinite Elastic Layer, European Journal of Mechanics A/Solids 25, 819–833.
  • [20] Caimmi, F. and Pavan, A., (2008) A Mode II Crack Problem with Sliding Contact in an Orthotropic Strip, International Journal of Fracture 153, 93-104.
  • [21] Dag, S., Apatay, T., Guler, M. A. and Gulgeç, M., (2012) A Surface Crack in a Graded Coating Subjected to Sliding Frictional Contact, Engineering Fracture Mechanics 80, 72–91.
  • [22] Zozulya, V. V., (2013) Comparative Study of Time and Frequency Domain BEM Approaches in Frictional Contact Problem for Antiplane Crack under Harmonic Loading, Engineering Analysis with Boundary Elements 37, 1499–1513.
  • [23] Yong, H. D., Jing, Z. and Zhou, Y. H., (2014) Crack Problem for Superconducting Strip with Finite Thickness, International Journal of Solids and Structures 51, 886–893.
  • [24] Xie, G., Zhang, J., Huang, C., Lu, C. and Li, G., (2014) A Direct Traction Boundary Integral Equation Method for Three-Dimension Crack Problems in Infinite and Finite Domains, Computational Mechanics 53, 575–586.
  • [25] Erdöl, R., (1982) A long strip problem containing a through crack perpendicular to the sides (In Turkish), Karadeniz University Engineering Architecture Faculty Civil Eng. Department Journal 1, 65-74.
  • [26] ANSYS 13 [Computer software]. Houston, PA, Swanson Analysis Systems.