Numerical Investigation of the Mixed-Mode Stress Intensity Factors in FGMs Considering the Effect of Graded Poisson’s Ratio

Journal of Solid Mechanics

مقاله 13، دوره 9، شماره 1، خرداد 2017، صفحه 172-185   

نوع مقاله: Research Paper

نویسندگان

R Ghajar^{* 1}؛ S Peyman¹؛ J Sheikhi²؛ M Poorjamshidian³

¹Department of Mechanical Engineering, K.N. Toosi University ,Tehran, Iran

²Department of Civil Engineering ,Razi University , Kermanshah, Iran

³Department of Mechanical Engineering, Kashan University ,Kashan, Iran

چکیده

In this paper, the interface crack of two non-homogenous functionally graded materials is studied. Subsequently, with employing the displacement method for fracture of mixed-mode stress intensity factors, the continuous variation of material properties are calculated. In this investigation, the displacements are derived with employing of the functional graded material programming and analysis of isoparametric finite element; then, with using of displacement fields near crack tip, the mixed-mode stress intensity factors are defined. In this present study, the problems are divided into homogenous and non-homogenous materials categories; and in order to verify the accuracy of results, the analytical and numerical methods are employed. Moreover, the effect of Poisson's ratio variation on mixed-mode stress intensity factors for interface crack be examined and is shown in this study. Unlike the homogenous material, the effect of Poisson’s ratio variations on mixed-mode stress intensity factors at interface crack between two nonhomogenous is considerable.

کلیدواژه‌ها

Interface crack؛ Displacement method؛ Nonhomogeneous materials

مراجع

[1] Williams M.L., 1959, The stresses around a fault or crack in dissimilar media, Bulletin of the Seismological Society of America 49 (2): 199-204.
[2] England A.H., 1965, A crack between dissimilar media, Journal of Applied Mechanics 32: 400-402.
[3] Erdogan F., 1965, Stress distribution in bonded dissimilar materials with cracks, Journal of Applied Mechanics 32: 403- 410.
[4] Rice J.R., Sih G.C., 1965, Plane problems of cracks in dissimilar media, Journal of Applied Mechanics 32: 418-423.
[5] Rice J.R., 1988, Elastic fracture mechanics concepts for interfacial cracks, Journal of Applied Mechanics 55: 98-103.
[6] Hutchinson J.W., Mear M.E., Rice J.R., 1987, Crack paralleling an interface between dissimilar materials, Journal of Applied Mechanics 54: 828-832.
[7] Hutchinson J.W., Suo Z., 1992, Mixed mode cracking in layered materials, Advances in Applied Mechanics 29: 63-191.
[8] Rice J.R., 1968, A path independent integral and the approximate analysis of strain concentration by notches and cracks, Journal of Applied Mechanics 35: 379-386.
[9] Smelser R.E., Gurtin M.E., 1977, On the J-integral for bi-material bodies, International Journal of Fracture 13: 382-384.
[10] Nagashima T., Omoto Y., Tani S., 2003, Stress intensity factor analysis of interface cracks using X-FEM, International Journal for Numerical Methods in Engineering 56: 1151-1173.
[11] Sukumar N., Huang Z.Y., Prévost J.H., Suo Z., 2004, Partition of unity enrichment for bimaterial interface cracks, International Journal for Numerical Methods in Engineering 59: 1075-1102.
[12] Matsumto T., Tanaka M., Obara R., 2000, Computation of stress intensity factors of interface cracks based on interaction energy release rates and BEM sensitivity analysis, Engineering Fracture Mechanics 65: 683-702.
[13] Cisilino A.P., Ortiz J.E., 2005, Three-dimensional boundary element assessment of a fibre/matrix interface crack under transverse loading, Computers and Structures 83: 856-869.
[14] Ortiz J.E., Cisilino A.P., 2005, Boundary element method for J-integral and stress intensity factor computations in three-dimensional interface cracks, International Journal of Fracture 133: 197-222.
[15] Johnson J., Qu J.M., 2007, An interaction integral method for computing mixed mode stress intensity factors for curved bimaterial interface cracks in nonuniform temperature fields, Engineering Fracture Mechanics 74: 2282-2291.
[16] Merzbacher M.J., Horst P., 2009, A model for interface cracks in layered orthotropic solids: convergence of modal decomposition using the interaction integral method, International Journal for Numerical Methods in Engineering 77: 1052-1071.
[17] Eischen J.W., 1987, Fracture of nonhomogeneous materials, International Journal of Fracture 34: 3-22.
[18] Erdogan F., 1995, Fracture mechanics of functionally graded materials, Composites Engineering 5 (7): 753-770.
[19] Chen Y.F., Erdogan F., 1996, The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate, Journal of the Mechanics and Physics of Solids 44: 771-787.
[20] Noda N., 1999, Thermal stresses in functionally graded materials, Journal of Thermal Stresses 22 (4-5):477-512.
[21] Guler M.A., Erdogan F., 2006, Contact mechanics of two deformable elastic solids with graded coatings, Mechanics of Materials 38 (7): 633-647.
[22] Guo L.C., Noda N., 2007, Modeling method for a crack problem of functionally graded materials with arbitrary properties – piece wise exponential model, International Journal of Solids and Structures 44(21): 6768-6790.
[23] Guo L.C., Noda N., 2008, Fracture mechanics analysis of functionally graded layered structures with a crack crossing the interface, Mechanics of Materials 40 (3):81-99.
[24] 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: 2557-2574.
[25] Paulino G.H., Kim J.H., 2004, A new approach to compute T-stress in functionally graded materials by means of the interaction integral method, Engineering Fracture Mechanics 71: 1907-1950.
[26] Kim J.H., Paulino G.H., 2003, T-stress, mixed-mode stress intensity factors, and crack initiation angles in functionally graded materials: a unified approach using the interaction integral method, Computer Methods in Applied Mechanics and Engineering 192: 1463-1494.
[27] Kim J.H., Paulino G.H., 2005, Consistent formulations of the interaction integral method for fracture of functionally graded materials, Journal of Applied Mechanics 72: 351-364.
[28] Hongjun Yu., Linzhi Wu ., Licheng Guo., Qilin He., Shanyi Du., 2009, Interaction integral method for the interfacial fracture problems of two nonhomogeneous materials, Journal of Applied Mechanics of Materials 42: 435 -450.
[29] Yildrim B., Dag S., Erdogan F., 2005, Three dimensional fracture analysis of FGM coatings under thermomechanical loading, International Journal of Fracture 132: 369-395.
[30] Ghajar R., Moghaddam A.S., 2010, Numerical investigation of the mode III stress intensity factors in FGMs consideringthe effect of graded Poisson’s ratio, Engineering Fracture Mechanics 78: 1478-1486.
[31] Paulino G.H., Kim J.H., 2004, On the poisson's ratio effect on mixed-mode stress intensity factors and T-stress in
functionally graded materials, International Journal of Computational Engineering Science 5: 833-861.
[32] Malyshev B.M., Salganik R.L., 1965, The strength of adhesive joints using the theory of cracks, International Journal of Fracture 1: 114-128.
[33] Suo Z., 1989, Mechanics of Interface Fracture, Ph.D. Thesis, Division of Applied Sciences, Harvard University,
Cambridge, MA, U.S.A.
[34] Dundurs J., 1969, Edge-bonded dissimilar orthogonal elastic wedges, Journal of Applied Mechanics 36:
650-652.
[35] Walters M. C., Paulino G. H., Dodds R. H., 2006, Computation of mixed-mode stress intensity factors for cracks in three-dimensional functionally graded solids, Journal of Engineering Mechanics 132: 1-15.
[36] Kim J.H., Paulino G.H.,2002, Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials, Journal of Applied Mechanics 69: 502-514.
[37] Hughes T. J. R., 1987, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ.