Numerical Simulation of Semi-Elliptical Axial Crack in Pipe Bend Using XFEM
الموضوعات :
K Sharma
1
(Reactor Structures Section, Reactor Safety Division, BARC, Mumbai, India)
I.V Singh
2
(Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee)
B.K Mishra
3
(Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee)
S.K Maurya
4
(Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee)
الکلمات المفتاحية: Elliptical cracks, Pipe bend, SIFs, XFEM,
ملخص المقالة :
In this work, XFEM is employed to obtain the stress intensity factors (SIFs) of a semi elliptical part through thickness axial crack. In XFEM, additional functions are employed to enrich the displacement approximation using partition of unity approach. Level set functions are approximated using higher order shape functions in the crack front elements to ensure the accurate modeling of the crack. The axial crack is placed either on the inner or the outer surface in an internally pressurized pipe bend. The SIFs are extracted from XFEM solution by domain type interaction integral approach for a wide range of geometry parameters like bend radius ratio, cross sectional radius ratio and relative crack length. The results obtained by XFEM approach are compared with those obtained by FEM. These simulations show that the orientation and type of crack in pipe bend has a significant effect on the SIF.
[1] Atluri S.N., Kathiresan K., 1979, 3D Analyses of surface flaws in thick-walled reactor pressure-vessels using displacement-hybrid finite element method, Nuclear Engineering Design 51: 163-176.
[2] Tan C.L., Fenner R.T., 1980, Stress intensity factors for semi-elliptical surface cracks in pressurized cylinders using the boundary integral equation method, International Journal of Fracture 16: 233-245.
[3] Pu S.L., Hussain M.A., 1981, Residual stress redistribution caused by notches and cracks in a partially autofrettaged tube, ASME Journal of Pressure Vessel Technology 103: 302-306.
[4] Tan C.L., Shim M.L., 1986, Stress intensity factor influence coefficients for internal surface cracks in thick-walled cylinders, International Journal of Pressure Vessels and Piping 24: 49-72.
[5] Perl M., Levy C., Wang J., 1997, Interaction effects on the 3D stress intensity factor of combined arrays of radial and longitudinal coplanar cracks in an internally pressurized thick-walled cylinder, ASME Journal of Pressure Vessel Technology 119:167-174.
[6] Parker A.P., Tan C.L., 2006, Stress intensity factors for straight and curved-fronted cracks in thick cylinders, ASME Journal of Pressure Vessel Technology 128: 227-232.
[7] Ma Q., Levy C., Perl M., 2008, The bauschinger effect on 3D SIF’s for networks of radial and longitudinal coplanar semi-elliptical internal surface cracks in autofrettaged pressurized thick-walled cylinders, Computer Modelling in Engineering and Science 5: 95-110.
[8] Chattopadhyay J., Dutta B.K., Kushwaha H.S., Mahajan S.C., Kakodkar A., 1994, A database to evaluate stress intensity factors of elbows with through-wall flaws under combined internal pressure and bending moment, International Journal of Pressure Vessels and Piping 60: 71-83.
[9] Chattopadhyay J., Dutta B.K., Kushwaha H.S., Mahajan S.C., Kakodkar A., 1995, Limit load analysis and safety assessment of an elbow with a circumferential crack under a bending moment, International Journal of Pressure Vessels and Piping 62: 109-116.
[10] Yahiaoui K., Moreton D.N., Moffat D.G., 2002, Evaluation of limit load data for cracked pipe bends under opening moment and comparisons with existing solutions, International Journal of Pressure Vessels and Piping 79:27-36.
[11] Saxena S., Ramakrishnan N., 2007, Characterizing the crack initiation load in circumferentially through-wall cracked elbows under bending load, International Journal of Pressure Vessels and Piping 84: 493-501.
[12] Henshell R.D., Shaw K.G., 1975, Crack tip finite elements are unnecessary, International Journal for Numerical Methods in Engineering 9: 495-507.
[13] Akin J.E., 1976, The generation of elements with singularities, International Journal for Numerical Methods in Engineering 10: 1249-1259.
[14] Barsoum R.S., 1977, Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements, International Journal for Numerical Methods in Engineering 11: 85-98.
[15] Nikishkov G. P. , Alturi S. N., 1987, Calculation of fracture mechanics parameters for an arbitrary three-dimensional crack by the equivalent domain integral method, International Journal for Numerical Methods in Engineering 24: 1801-1821.
[16] Rhee H. C., Salama M. M., 1987, Mixed-mode stress intensity factor solutions of a warped surface flaw by three-dimensional finite element analysis, Engineering Fracture Mechanics 28: 203-209.
[17] Portela A., Aliabadi M., Rooke D., 1991, The dual boundary element method: effective implementation for crack problem, International Journal for Numerical Methods in Engineering 33: 1269-1287.
[18] Yan A. M., Nguyen-Dang H., 1995, Multiple-cracked fatigue crack growth by BEM, Computational Mechanics 16: 273-280.
[19] Belytschko T., Gu L., Lu Y.Y., 1994, Fracture and crack growth by element-free Galerkin methods, Modelling Simulation for Materials Science and Engineering 2: 519-534.
[20] Belytschko T., Lu Y.Y., Gu L., 1995, Crack propagation by element-free Galerkin methods, Engineering Fracture Mechanics 51: 295-315.
[21] Belytschko T., Black T., 1999, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering 45: 601-620.
[22] Dolbow J., 1999, An extended finite element method with discontinuous enrichment for applied mechanics, Theoretical and Applied Mechanics Department, Northwestern University.
[23] Moës N., Dolbow J., Belytchsko T., 1999, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering 46: 131-150.
[24] Daux C., Moës N., Dolbow J., Sukumar N., Belytschko T., 2000, Arbitrary branched and intersecting cracks with the extended finite element method, International Journal for Numerical Methods in Engineering 48: 1741-1760.
[25] Sukumar N., Chopp D.L., Moës N., Belytschko T., 2001, Modeling holes and inclusions by level sets in the extended finite-element method, Computer Methods in Applied Mechanics and Engineering 190: 6183-6200.
[26] Sukumar N., Moës N., Moran B., Belytschko T., 2000, Extended finite element method for three-dimensional crack modelling, International Journal for Numerical Methods in Engineering 48: 1549-1570.
[27] Moës N., Gravouil A., Belytschko T., 2002, Non-planar 3D crack growth by the extended finite element and level sets-Part I: Mechanical model, International Journal for Numerical Methods in Engineering 53: 2549-2568.
[28] Gravouil A., Moës N., Belytschko T., 2002, Non-planar 3D crack growth by the extended finite element and level sets-Part II: Level set update, International Journal for Numerical Methods in Engineering 53: 2569-2586.
[29] Sharma K., Bhasin V., Singh I.V., Mishra B.K., Vaze K.K., X-FEM simulation of 2-D fracture mechanics problems, SMiRT-21, New Delhi, India.
[30] Pathak H., Singh A., Singh I.V., Yadav S. K., 2013, A simple and efficient XFEM approach for 3-D cracks siluations, Internationa Journal of Fracture 181: 189-208.
[31] Melenk J., Babuska I., 1996, The partition of unity finite element method: basic theory and applications, Computer Methods in Applied Mechanics and Engineering 139: 289-314.
[32] Zi G., Belytschko T., 2003, New crack-tip elements for XFEM and applications to cohesive cracks, International Journal for Numerical Methods in Engineering 57: 2221-2240.
[33] Sukumar N., Chopp D.L., Moran B., 2003, Extended finite element method and fast marching method for three-dimensional fatigue crack propagation, Engineering Fracture Mechanics 70: 29-48.
[34] Moran B., Shih C., 1987, A general treatment of crack tip contour integrals, International Journal of Fracture 35: 295-310.
[35] Shih C.F., Asaro R.J., 1988, Elastic-plastic analysis of cracks on bimaterial interfaces: Part I-small scale yielding, Journal of Applied Mechanics 55: 299-316.
[36] Gosz M., Dolbow J., Moran B., 1998, Domain integral formulation for stress intensity factor computation along curved three-dimensional interface cracks, International Journal of Solids and Structures 35: 1763-1783.
[37] Gosz M., Moran B., 2002, An interaction energy integral method for computation of mixed-mode stress intensity factors along non-planar crack fronts in three dimensions, Engineering Fracture Mechanics 69: 299-319.
