Analysis of Mode III Fraction in Functionally Graded Plate with Linearly Varying Properties

Journal of Solid Mechanics

مقاله 6، دوره 6، شماره 3، آذر 2014، صفحه 299-309   

نوع مقاله: Research Paper

نویسنده

M.R Torshizian^*

Mechanical Engineering Department, Mashhad Branch, Islamic Azad University

چکیده

A model is provided for crack problem in a functionally graded semi-infinite plate under an anti-plane load. The characteristic of material behavior is assumed to change in a linear manner along the plate length. Also the embedded crack is placed in the direction of the material change. The problem is solved using two separate techniques. Primary, by applying Laplace and Fourier transformation, the governing equation for the crack problem is converted to the solution of a singular integral equation system. Then, finite element technique is employed to analyze this problem by considering quadrilateral eight nodded singular element near the crack tips. The effects of material non-homogeneity and crack length on the stress intensity factor are studied and the results of two methods are judged against each other.

کلیدواژه‌ها

Functionally graded material؛ Stress intensity factor؛ Linear material properties

مراجع

[1] Erdogan F., Kaya A.C., Joseph P.F., 1991, The crack problem in bonded nonhomogeneous materials, Journal of Applied Mechanics 58: 410-418.
[2] Erdogan F., Ozturk M., 1992, Diffusion problems in bonded nonhomogenous materials with an interface cut, International Journal of Solids and Structures 30: 1507-1523.
[3] Wang B., Mai Y., 2003, Anti-plane fracture of a functionally graded material strip, European Journal of Mechanics - A/Solids 22: 357-368.
[4] Chue C., Ou Y.L., 2005, Mode III crack problems for two bonded functionally graded piezoelectric materials, International Journal of Solids and Structures 42: 3321-3237.
[5] Hu K.Q., Zhong Z., Jin B., 2005, Anti-plane shear crack in a functionally gradient piezoelectric layer bonded to dissimilar half spaces, International Journal of Mechanical Sciences 47: 82-93.
[6] Ou Y., Chue C., 2006, Mode III eccentric crack in a functionally graded piezoelectric strip, International Journal of Solids and Structures 43: 6148-6164.
[7] Ma L., Li J., Abdelmoula R., Wu L.Z., 2007, Mode III crack problem in a functionally graded magneto-electro-elastic strip, International Journal of Solids and Structures 44: 5518-5537.
[8] Ma L., Wu L.Z., 2007, Mode III crack problem in a functionally graded coating-homogeneous substrate structure, Mechanical Engineering Science 222: 329-337.
[9] Yong H.D., Zhou Y.H., 2007, A mode 3 crack in a functionally graded piezoelectric strip bonded to two dissimilar piezoelectric half-planes, Composite Structures 79:404-410.
[10] Li Y.D., Lee K.Y., 2007, An anti-plane crack perpendicular to the weak micro discontinuous interface in a bi-FGM structure with exponential and linear non-homogeneities, International Journal of Fracture 146: 203-211.
[11] Li Y.D., Tan W., Lee K.Y., 2008, Stress intensity factor of an anti-plane crack parallel to the weak micro discontinuous interface in a bi-FGM composite, Acta Mechanica Solida Sinica 21: 34-43.
[12] Hsu W.H., Chue C.H., 2009, Mode III fracture problem of an arbitrarily oriented crack in an FGPM strip bonded to a homogeneous piezoelectric half-plane, Meccanica 44: 519-534.
[13] Torshizian M.R., Kargarnovin M.H., 2010, Anti-plane shear of an arbitrarily oriented crack in a functionally graded strip bonded with two dissimilar half-plane, Theoretical and Applied Fracture Mechanics 54: 180-188.
[14] Torshizian M.R., Kargarnovin M.H., Nasirai C., 2011, Mode III fracture of an arbitrarily oriented crack in two dimensional functionally graded material, Mechanics Research Communications 38: 164-169.
[15] Kargarnovin M.H., Nasirai C., Torshizian M.R., 2011, Anti-plane stress intensity, energy release and energy density at crack tips in a functionally graded strip with linearly varying properties, Theoretical and Applied Fracture Mechanics 56: 42-48.
[16] Polyanin A.D., 2002, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman and Hall/CRC.
[17] Jefrey A., Dai H.H, 2008, Handbook of Mathematical Formulas and Integrals, Elsevier Academic Press.
[18] Chan Y.S., Fannjiang A.C., Paulino G.H., 2003, Integral equation with hypersingular kernels theory and applications to fracture mechanics, International Journal of Engineering Science 41: 683-720.
[19] Kronrod A.S., 1965, Nodes and Weights of Quadrature Formulas, Consultants Bureau, New York.