Thermoelastic Fracture Parameters for Anisotropic Plates

Document Type: Research Paper

Authors

1 Laboratoire de Mécanique Appliquée , Université des Sciences et de la Technologie d’Oran , Alegria

2 Laboratoire de Mécanique Appliquée , Université des Sciences et de la Technologie d’Oran , Alegria---- Laboratoire de Recherche des Technologies Industrielles , Université Ibn Khaldoun de Tiaret , Alegria

3 Laboratoire de Recherche des Technologies Industrielles , Université Ibn Khaldoun de Tiaret , Alegria

Abstract

This paper deals with the determination of the effect of varying material properties on the value of the stress intensity factors, KI and KII, for anisotropic plates containing cracks and subjected to a temperature change. Problems involving cracks and body forces, as well as thermal loads are analysed. The quadratic isoperimetric element formulation is utilized, and SIFs may be directly obtained using the ‘traction formula’ and the ‘displacement formula’. Three cracked plate geometries are considered in this study, namely: (1) a plate with an edge-crack; (2) a plate with a double edge-crack; (3) a plate with symmetric cracks emanating from a central hole. Where appropriate, finite element method (FEM) analyses are also performed in order to validate the results of the BEM analysis. The results of this study show that, for all crack geometries, the mode-I stress intensity factor, KI decreases as the anisotropy of the material properties is increased. Additionally, for all these cases, KI decreases as the angle of orientation of the material properties, , increases with respect to the horizontal axis. The results also show that BEM is an accurate and efficient method for two-dimensional thermoelastic fracture mechanics analysis of cracked anisotropic bodies.

Keywords

Sih G.C., Paris P.C., Irwin G.R., 1965, On cracks in rectilinearly anisotropic bodies, International Journal of Fracture Mechanics 1: 189-203.
[2] Bowie O.L., Freese C.E., 1972, Central crack in plane orthotropic rectangular sheet, Journal of Fracture Mechanics 1: 49-58.
[3] Ghandi K.R., 1972, Analysis of an inclined crack centrally placed in an orthotropic rectangular plate, Journal of Strain Analysis 7: 157-162.
[4] Rizzo F.J., Shippy D.J., 1970, A method for stress determination in plane anisotropic elastic bodies, Journal of Composite Materials 4: 36-61.
[5] Snyder M.D., Cruse T.A., 1975, Boundary-integral equation analysis of cracked anisotropic plates, International Journal of Fracture 11: 315-328.
[6] Sollero P., Alliabadi M.H., 1995, Anisotropic analysis of cracks in composite laminates using the dual boundary element method, Composite Structures 31: 229-237.
[7] Pan E., 1997, A general boundary element analysis of 2-D linear elastic fracture mechanics, International Journal of Fracture 88: 41-59.
[8] Haj-Ali R., Wei B. S., Johnson S., El-Hajjar R., 2008, Thermoelastic and infrared-thermography methods for surface strains in cracked orthotropic composite materials, Engineering Fracture Mechanics 75(1): 58-75.
[9] Shiah Y. C., Tan C. L., 2000, Fracture mechanics analysis in 2-D anisotropic thermoelasticity using BEM, Computer Modeling in Engineering & Sciences 1(3): 91-99.
[10] Pasternak I., 2012, Boundary integral equations and the boundary element method for fracture mechanics analysis in 2D anisotropic thermoelasticity, Engineering Analysis with Boundary Elements 36(12): 1931-1941.
[11] Ju S. H., Rowlands R. E., 2003, Thermoelastic determination of and in an orthotropic graphite–epoxy composite, Journal of Composite Materials 37(22): 2011-2025.
[12] Dag S., 2006, Thermal fracture analysis of orthotropic functionally graded materials using an equivalent domain integral approach, Engineering Fracture Mechanics 73(18): 2802-2828.
[13] Tan C.L., Gao Y.L., 1992, Boundary element analysis of plane anisotropic bodies with stress concentrations and cracks, Composite Structures 20: 17-28.
[14] Portela A., Aliabadi M.H., Rooke D.P., 1991, Efficient boundary element analysis of sharp notched plates, International Journal for Numerical Methods in Engineering 32: 445-470.
[15] Sollero P., Alliabadi M.H., 1993, Fracture mechanics analysis of anisotropic plates by the boundary element method, International Journal of Fracture 64: 269-284.
[16] Aliabadi M.H., Cartwright D.J., Rooke D.P., 1989, Fracture-mechanics weight functions by the removal of singular fields using boundary element analysis, International Journal of Fracture 40: 271-284.
[17] Portela A., Aliabadi M.H., Rooke D.P., 1991, Efficient boundary element analysis of sharp notched plates, International Journal for Numerical Methods in Engineering 32: 445-470.
[18] Solkonikoff I.S., 1956, Mathematical Theory of Elasticity, McGraw-Hill, New York.
[19] Zhang J.J., Tan C.L., Afagh F.F., 1996, A general exact transformation of body- force volume integral in BEM for 2D anisotropic elasticity, Computational Mechanics 19: 1-10.
[20] Zhang J.J., Tan C.L., Afagh F.F., 1997, Treatment of body-force volume integrals in BEM by exact transformation for 2-D anisotropic elasticity, International Journal for Numerical Methods in Engineering 40: 89-109.
[21] Pape D.A., Banerjee P.K., 1987, Treatment of body forces in 2D electrostatic BEM using particular integrals, Transactions of the ASME 54: 866-871.
[22] Shiah Y.C., Tan C.L., 1997, BEM treatment of two-dimensional anisotropic field problems by direct domain mapping, Engineering Analysis with Boundary Elements 20: 347-351.
[23] Shiah Y.C., Tan C.L., 1999, Exact boundary integral transformation of the thermoelastic domain integral in BEM for general 2D anisotropic elasticity, Computational Mechanics 23: 87-96.
[24] Shiah Y.C., Tan C.L., 2000, Determination of interior point stresses in two dimensional BEM thermoelastic analysis of anisotropic bodies, International Journal of Solids and Structures 37: 809-829.
[25] Shiah Y .C., Tan C.L., 2000, Fracture mechanics analysis in 2-D anisotropic thermoelasticity using BEM, Computer Modeling in Engineering & Sciences 3: 91-99.
[26] Deb A., Banerjee P.K., Wilson R.B., 1991, Alternate BEM formulations for 2- and 3-D anisotropic thermoelasticity, International Journal of Solids and Structures 27: 1721-1738.
[27] Deb A., Banerjee P.K., 1991, Multi-domain two- and three-dimensional thermoelasticity by BEM, International Journal for Numerical Methods in Engineering 32: 991-1008.
[28] De Saxce G., Kang C.H., 1992, Application of the hybrid mongrel displacement finite method to the computation of stress intensity factors in anisotropic material, Engineering Fracture Mechanics 41: 71-83.
[29] Zhang J.J., Tan C.L., Afagh F.F., 1996, An argument redefinition procedure in the BEM for 2D anisotropic electrostatics with body forces, Processing Symposium on Mechanics in Design, Toronto, Meguid.