Mixed-Mode Stress Intensity Factors for Surface Cracks in Functionally Graded Materials Using Enriched Finite Elements

Subject Areas : Engineering

J Sheikhi ¹ , M Poorjamshidian ² , S Peyman ³

1 - Civil Engineering, Imam Hossein University
2 - Department of Mechanical Engineering, Imam Hossein University
3 - Instructor, Department of Mechanical Engineering, Imam Hossein University

Received: 2014-10-15 Accepted : 2014-12-29 Published : 2015-03-30

Keywords: Mixed-mode, Surface crack, Enriched finite elements,

Abstract :

Three-dimensional enriched finite elements are used to compute mixed-mode stress intensity factors (SIFs) for three-dimensional cracks in elastic functionally graded materials (FGMs) that are subject to general mixed-mode loading. The method, which advantageously does not require special mesh configuration/modifications and post-processing of finite element results, is an enhancement of previous developments applied so far on isotropic homogeneous and isotropic interface cracks. The spatial variation of FGM material properties is taken into account at the level of element integration points. To validate the developed method, two- and three-dimensional mixed-mode fracture problems are selected from the literature for comparison. Two-dimensional cases include: inclined central crack in a large FGM medium under uniform tensile strain loading and an edge crack in a finite-size plate under shear traction load. The three-dimensional example models a deflected surface crack in a finite-size FGM plate under uniform tensile stress loading. Comparisons between current results and those from analytical and other numerical methods yield good agreement. Thus, it is concluded that the developed three-dimensional enriched finite elements are capable of accurately computing mixed-mode fracture parameters for cracks in FGMs.

References:

[1] Ozturk M., Erdogan F., 1996, Axisymmetric crack problem in bonded materials with a graded interfacial region, International Journal of Solids and Structures 33(2):193-219.
[2] Delale F., Erdogan F., 1983, The crack problem for a nonhomogeneous plane, Journal of Applied Mechanics 50(3): 609-614.
[3] Eischen j.w., 1987, Fracture of nonhomogeneous materials, International Journal of Fracture 34: 3-22.
[4] Konda N., Erdogan F., 1994, The mixed-mode crack problem in a nonhomogeneous elastic medium, Engineering Fracture Mechanics 47(3): 533-545.
[5] Erdogan F., Wu B.H., 1997, The surface crack problem for a plate with functionally graded properties, Journal of Applied Mechanics 64(1): 449-456.
[6] Honein T., Herrmann G., 1997, Conservation laws in nonhomogeneous plane elastostatics, Journal of Mechanics and Physics of Solids 45(5): 789-805.
[7] Gu P., Dao M., Asaro R.J., 1999, A simplified method for calculating the crack-tip field of functionally graded materials using the domain integral, Journal of Applied Mechanics 66(1): 101-108.
[8] Santare M.H., Lambros J., 2000, Use of graded finite elements to model the behavior of nonhomogeneous materials, Journal of Applied Mechanics 67(4): 819-822.
[9] Kim J.H., Paulino G.H., 2002, Finite element evaluation of mixed mode stress intensity factors in functionally graded materials, International Journal for Numerical Methods in Engineering 53(6): 1903-1935.
[10] Dolbow J.E., Gosz M., 2002, On the computation of mixed-mode stress intensity factors in functionally graded materials, International Journal of Solids and Structures 39(2): 2557-2574.
[11] Kim J.H., Paulino G.H., 2002, Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials, Journal of Applied Mechanics 69(4): 502-514.
[12] Anlas G., Lambros J., Santare M.H., 2002, Dominance of asymptotic crack tip fields in elastic functionally graded materials, International Journal of Fracture 115(4): 193-204.
[13] Shim D.J., Paulino G.H., Dodds R.H., 2006, Effect of material gradation on K-dominance of fracture specimens, Engineering Fracture Mechanics 73(4): 643-648.
[14] Walters M.C., Paulino G.H., Dodds R.H., 2004, Stress-intensity factors for surface cracks in functionally graded materials under mode-I thermomechanical loading, International Journal of Solids and Structures 41(5): 1081-1118.
[15] Yildirim B., Dag S., Erdogan F., 2005, Three-dimensional fracture analysis of FGM coatings under thermomechanical loading, International Journal of Fracture 132 (4): 369-395.
[16] Walters M.C., Paulino G.H., Dodds R.H., 2004, Computation of mixed-mode stress intensity factors for cracks in three-dimensional functionally graded solids, Journal of Engineering Mechanics 132 (1): 1-15.
[17] Ayhan A.O., 2007, Mixed-mode stress intensity factors for deflected and inclined surface cracks in finite-thickness plates, Engineering Fracture Mechanics 71 (7):1059-1079.
[18] Ayhan A.O., Nied H.F., 2002, Stress intensity factors for three-dimensional surface cracks using enriched finite elements, International Journal for Numerical Methods in Engineering 54 (6): 899-921.
[19] Hartranft R.J., Sih G.C., 1969, The use of eigenfunction expansions in the general solution of three-dimensional crack problems, Journal of Mathematics and Mechanics 19:123-138.