Three-Dimensional Finite Element Analysis of Stress Intensity Factors in a Spherical Pressure Vessel with Functionally Graded Coating

Document Type : Research Paper


Abadan Institute of Technology, Petroleum University of Technology, Abadan, Iran


This research pertains to the three-dimensional (3D) finite element analysis (FEA) of the stress intensity factors (SIFs) along the crack front in a spherical pressure vessel coated with functionally graded material (FGM). The vessel is subjected to internal pressure and thermal gradient. The exponential function is adopted for property of FGMs. SIFs are obtained for a wide variety of crack shapes and layer thickness. The reported results clearly show that the material gradation of coating and the crack configuration can significantly affect the variation of SIFs along the crack front. The results are given which are applicable   for fatigue life assessment and fracture endurance of FGM coating spherical pressure vessel and can be used in design purposes. 


[1] Akis T., 2009, Elastoplastic analysis of functionally graded spherical pressure vessels, Computational Materials Science 46: 545-554.
[2] Perl M., Bernshtein V., 2012, Three-dimensional stress intensity factors for ring cracks and arrays of coplanar cracks emanating from the inner surface of a spherical pressure vessel, Engineering Fracture Mechanics 94: 71-84.
[3] Perl M., Bernshtein V., 2011, 3-D stress intensity factors for arrays of inner radial lunular or crescentic cracks in thin and thick spherical pressure vessels, Engineering Fracture Mechanics 78: 1466-1477.
[4] Hakimi A.E., Le Grognec P., Hariri S., 2008, Numerical and analytical study of severity of cracks in cylindrical and spherical shells, Engineering Fracture Mechanics 75: 1027-1044.
[5] Perl M., Bernshtein V., 2010, 3-D stress intensity factors for arrays of inner radial lunular or crescentic cracks in a typical spherical pressure vessels, Engineering Fracture Mechanics 77: 535-548.
[6] You L.H., Zhang J.J., You X.Y., 2005, Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials, International Journal of Pressure Vessels and Piping 82(5): 347-354.
[7] Chen Y.Z., Lin X.Y., 2008, Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials, Computational Materials Science 44: 581-587.
[8] Choules B.D., Kokini K., Taylor T.A., 2001, Thermal fracture of ceramic thermal barrier coatings under high heat flux with time dependent behavior – Part I: Experimental results, Materials Science and Engineering: A 299:296-304.
[9] Rangaraj S., Kokini K., 2004, A study of thermal fracture in functionally graded thermal barrier coatings using a cohesive zone model, Journal of Engineering Materials and Technology 126: 103-115.
[10] Eischen J.W., 1987, Fracture of non-homogeneous materials, International Journal of Fracture 34: 3-22.
[11] Zhang C., Cui M., Wang J., Gao X.W., Sladek J., Sladek V., 2011, 3D crack analysis in functionally graded materials, Engineering Fracture Mechanics 78: 585-604.
[12] 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.
[13] Mohammadi M., Dryden J.R., 2009, Influence of the spatial variation of Poisson’s ratio upon the elastic field in non-homogeneous axisymmetric bodies, International Journal of Solids and Structures 46:788-795.
[14] Moghaddam A.S., Alfano M., Ghajar R., 2013, Determining the mixed mode stress intensity factors of surface cracks in functionally graded hollow cylinders, Materials & Design 43: 475-484
[15] Raju I.S., Newman Jr. J.C., 1980, Stress intensity factors for internal surface cracks in cylindrical pressure vessel, ASME Journal of Pressure Vessel Technology 102: 342-356.