Main Article Content
Abstract
Modified Virtual Crack Closure Integral (MVCCI) has become a valuable tool for estimation of mixed-mode fracture parameters in Linear Elastic Fracture Mechanics (LEFM) problems. When finite elements with fewer nodes and using polynomial shape functions are employed at the crack tip for fracture analysis, the expressions for MVCCI can easily be derived and many times also be expressed in closed form. For higher order elements they become unwieldy and so a numerical integration scheme is proposed and this can be used with any type of element. The scheme requires a two-step numerical integration: one to evaluate nodal forces exerted by the solid below the crack extension line on the portion above and the second to evaluate Strain Energy Release Rates. This development makes the post-processing for fracture parameters easy and computationally economical for 3-dimensional fracture problems. The technique is used to estimate fracture parameters in certain practical problems using higher order elements and typical numerical results are presented.
Keywords
Article Details
References
- Broek, D., Elementary Engineering Fracture Mechanics, Martinus Nijhoff Publications, The Hague, 1982.
- Rybicki, E.F and Kanninen, M.F.A., "Finite Element Calculation of Stress Intensity Factors by a Modified Crack Closure Integral", Engineering Fracture Mechanics, Vol. 9, pp. 931-938, 1977.
- Buchholz, F.G., "Improved Formulae for FE-Calculation of the Strain Energy Release Rate by the Modified Crack Closure Integral Method", Proc. 4th Word Congr. and Exhib. in FEM, Interlaken, pp. 650-659, 1984.
- Ramamurthy, T.S., Krishnamurthy, T. , Badarinarayana, K., Dattaguru, B. and Vijayakumar, K., "Modified Crack Closure Integral Method with Quarter Point Elements", Mech. Res. Commun., Vol. 13, pp. 179-186, 1986.
- Raju, I.S., "Calculationof Strain Energy Release rates with Higher Order and Singular Finite Elements", Engineering Fracture Mechanics, Vol. 28, pp. 251- 274, 1987.
- Badari Narayana, K. Dattaguru, B., Ramamurthy, T.S. and Vijay Kumar, K., "A General Procedure for Modified Crack Closure Integral (MCCI) in 3D Problems with Cracks", Engineering Fracture Mechanics, Vol. 48, No. 2, pp. 167-176, 1994.
- Irwin, G.R., Fracture Handbook Phys. Vol. 6, pp. 551-90, 1958.
- Palani, G.S., Nagesh R. Iyer and Dattaguru, B., "Numerically Integrated Modified Virtual Crack Closure Integral Techniques for 2D Crack Problem", Int. J. Structural Engineering and Mechanics, Vol. 18, No. 6, pp. 731-744, 2004.
- Palani, G.S., Nagesh R. Iyer and Dattaguru, B., "A Generalised Technique for Fracture Analysis of Cracked Plates under Combined Tensile, Bending and Shear Loads", Computers and Structures, Vol.84, pp. 2050-2064, 2006.
- Rooke, D.P. and.Cartwright, D.J., "Compendium of Stress Intensity Factors", Her Majestys Stationery Office, London, 1976.
- Palani, G.S., Nagesh R. Iyer and Dattaguru, B., "Fracture Analysis of Cracked Stiffened Plates under Combined Tensile, Bending and Shear Loads", AIAA Journal, Vol. 43, pp. 2039-2051, 2005.
- Timoshenko, S.P. and Gere, J.M. Mechanics of Materials, 3rd Edition, McGraw-Hill Book Company, 1995.
- Kanninen, M.F. and Popelar, C.H., Advanced Fracture Mechanics, Oxford University Press, Oxford, 1985.
- DeGeorges, D.G., Maison, S., Trallero, D. and Petitnito, J.L., "Buckling and Post-Buckling Behavior of a De-lamination in a Carbon-Epoxy Laminated Structure: Experiments and Modeling", Aerospatiale Louis Bleriot Joint Research Center, Institut de Mcanique des fluids de Lille, (ONERA) 59045 Lille cdex, France. De-bonding and De-lamination of Composites, AGARD CP 530, pp. 7-11, 1992.
- Singh, K L., Dattaguru, B. and Ramamurthy, T.S., "Fracture Analysis of Delaminated Composite Panels in Compression Using Numerically Integrated MVCCI", Mechanics of Advanced Materials and Structures, Vol. 13, No. 4, pp. 303-315, 2006.
References
Broek, D., Elementary Engineering Fracture Mechanics, Martinus Nijhoff Publications, The Hague, 1982.
Rybicki, E.F and Kanninen, M.F.A., "Finite Element Calculation of Stress Intensity Factors by a Modified Crack Closure Integral", Engineering Fracture Mechanics, Vol. 9, pp. 931-938, 1977.
Buchholz, F.G., "Improved Formulae for FE-Calculation of the Strain Energy Release Rate by the Modified Crack Closure Integral Method", Proc. 4th Word Congr. and Exhib. in FEM, Interlaken, pp. 650-659, 1984.
Ramamurthy, T.S., Krishnamurthy, T. , Badarinarayana, K., Dattaguru, B. and Vijayakumar, K., "Modified Crack Closure Integral Method with Quarter Point Elements", Mech. Res. Commun., Vol. 13, pp. 179-186, 1986.
Raju, I.S., "Calculationof Strain Energy Release rates with Higher Order and Singular Finite Elements", Engineering Fracture Mechanics, Vol. 28, pp. 251- 274, 1987.
Badari Narayana, K. Dattaguru, B., Ramamurthy, T.S. and Vijay Kumar, K., "A General Procedure for Modified Crack Closure Integral (MCCI) in 3D Problems with Cracks", Engineering Fracture Mechanics, Vol. 48, No. 2, pp. 167-176, 1994.
Irwin, G.R., Fracture Handbook Phys. Vol. 6, pp. 551-90, 1958.
Palani, G.S., Nagesh R. Iyer and Dattaguru, B., "Numerically Integrated Modified Virtual Crack Closure Integral Techniques for 2D Crack Problem", Int. J. Structural Engineering and Mechanics, Vol. 18, No. 6, pp. 731-744, 2004.
Palani, G.S., Nagesh R. Iyer and Dattaguru, B., "A Generalised Technique for Fracture Analysis of Cracked Plates under Combined Tensile, Bending and Shear Loads", Computers and Structures, Vol.84, pp. 2050-2064, 2006.
Rooke, D.P. and.Cartwright, D.J., "Compendium of Stress Intensity Factors", Her Majestys Stationery Office, London, 1976.
Palani, G.S., Nagesh R. Iyer and Dattaguru, B., "Fracture Analysis of Cracked Stiffened Plates under Combined Tensile, Bending and Shear Loads", AIAA Journal, Vol. 43, pp. 2039-2051, 2005.
Timoshenko, S.P. and Gere, J.M. Mechanics of Materials, 3rd Edition, McGraw-Hill Book Company, 1995.
Kanninen, M.F. and Popelar, C.H., Advanced Fracture Mechanics, Oxford University Press, Oxford, 1985.
DeGeorges, D.G., Maison, S., Trallero, D. and Petitnito, J.L., "Buckling and Post-Buckling Behavior of a De-lamination in a Carbon-Epoxy Laminated Structure: Experiments and Modeling", Aerospatiale Louis Bleriot Joint Research Center, Institut de Mcanique des fluids de Lille, (ONERA) 59045 Lille cdex, France. De-bonding and De-lamination of Composites, AGARD CP 530, pp. 7-11, 1992.
Singh, K L., Dattaguru, B. and Ramamurthy, T.S., "Fracture Analysis of Delaminated Composite Panels in Compression Using Numerically Integrated MVCCI", Mechanics of Advanced Materials and Structures, Vol. 13, No. 4, pp. 303-315, 2006.