Skip to main content
Log in

The conservative M-integral for thermal-elastic problems

  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

In this investigation, the conservative M-integral is extended to treat thermal-elastic, mixed mode problems. With it, stress intensity factors are obtained for cracks in homogeneous, isotropic materials, as well as isotropic and anisotropic, bimaterials. Excellent agreement is found between results determined in this study and those found in the literature. In addition, new results are obtained for interface cracks for a wide range of material properties and for a delamination in a composite material.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ashkenazi, D. (1999). Determination of Critical Interface Energy Release Rates for Bonded Elastic Materials. Ph.D. Thesis (in Hebrew), Tel Aviv University.

  • Atkinson, C. (1977). On quasistatic problems of cracks in a non-homogeneous elastic layer. Acta Mechanica 26, 103–113.

    Article  Google Scholar 

  • Banks-Sills, L. and Sherman, D. (1992). On the computation of stress intensity factors for three-dimensional geometries by means of the stiffness derivative and J-integral methods. International Journal of Fracture 53, 1–20.

    Google Scholar 

  • Banks-Sills, L., Travitzky, N., Ashkenazi, D. and Eliasi, R. (1999). A methodology for measuring interface fracture toughness of composite materials. International Journal of Fracture 99, 143–161.

    Google Scholar 

  • Banks-Sills, L. and Boniface, V. (2000). Fracture mechanics for an interface crack between a special pair of transversely isotropic materials. In: Multiscale Deformation and Fracture in Materials and Structures-The James R. Rice 60th Anniversary Volume. (Edited by T.-J. Chuang and J.W. Rudnicki). pp. 183–204. Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Banks-Sills, L., Boniface, V. and Eliasi, R. (2003). Effect of residual stresses on delaminations in fiber reinforced composites. Interface Science 11, 339–348.

    Article  Google Scholar 

  • Banks-Sills, L. and Ishbir, C. (2004). A conservative integral for bimaterial notches subjected to thermal stresses. International Journal for Numerical Methods in Engineeering, to appear.

  • Bathe, K.J. (2001). ADINA-Automatic Dynamic Incremental Nonlinear Analysis System, Version 7.5, Adina Engineering, Inc. USA.

    Google Scholar 

  • Brown, E.J. and Erdogan, F. (1968). Thermal stresses in bonded materials containing cuts on the interface. International Journal of Engineering Science 6, 517–529.

    Google Scholar 

  • Brust, F.W., Nakagaki, M. and Springfield, C. (1989). Integral parameters for thermal fracture. Engineering Fracture Mechanics 33, 561–579.

    Google Scholar 

  • Deng, X. (1993). General crack-tip fields for stationary and steadily growing interface cracks in anisotropic bimaterials. Journal of Applied Mechanics 60, 183–189.

    Google Scholar 

  • Doroguy, A. and Banks-Sills, L. (2004). Shear loaded interface crack under the influence of friction-a finite difference solution. International Journal for Numerical Methods in Engineering, to appear.

  • Dundurs, J. (1969). Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading. Journal of Applied Mechanics 36, 650–652.

    Google Scholar 

  • Erdogan, F. (1965). Stress distribution in bonded dissimilar materials with cracks. Journals of Applied Mechanics 32, 403–410.

    Google Scholar 

  • Fung, Y.C. (1965). Foundation of Solid Mechanics. Prentice Hall, New Jersey, 354–355.

    Google Scholar 

  • Hellen, T.K. and Cesari, F. (1979). On the solution of the centre cracked plate with a quadratic thermal gradient. Engineering Fracture Mechanics 12, 469–478.

    Google Scholar 

  • Hutchinson, J.W., Mear, M.E. and Rice, J.R. (1987). Crack paralleling an interface between dissimilar materials. Journal of Applied Mechanics 54, 828–832.

    Google Scholar 

  • Hutchinson, J.W. (1990). Mixed-mode fracture mechanics of interfaces. In: Metal-Ceramic Interfaces. (Edited by M. Rühle, A.G. Evans, M.F. Ashby and J.P. Hirth). pp. 295–301. Pergamon Press, Oxford.

    Google Scholar 

  • Ikeda, T. and Sun, C.T. (2001). Stress intensity factor analysis for an interface crack between dissimilar isotropic materials under thermal stress. International Journal of Fracture 111, 229–249.

    Google Scholar 

  • Ishikawa, H., Kitagawa, H. and Okamura, H. (1979). J integral of a mixed mode crack and its application. In Mechanical Behavior of Materials, Vol. 3, ICM-3, Cambridge, England, 447–455.

    Google Scholar 

  • Kou, A.-Y. and Riccardella, P.D. (1987) Path-independent line integrals for steady-state, two-dimensional thermoelasticity. International Journal of Fracture 35, 71–79.

    Google Scholar 

  • Lee, K.Y. and Shul, C.W. (1991). Determination of thermal stress intensity factor for an interface crack under vertical uniform heat flow. Engineering Fracture Mechanics 40, 1067–1074.

    Google Scholar 

  • Li, F.Z., Shih, C.F. and Needleman, A. (1985). A comparison of methods for calculating energy release rates. Engineering Fracture Mechanics 21, 405–421.

    Google Scholar 

  • O’Dowd, N.P., Shih, F.C. and Stout, M.G. (1992). Test geometries for measureing interfacial fracture toughness. International Journal of Solids and Structures 29, 571–589.

    Google Scholar 

  • Paley, M. and Aboudi, J. (1992). Micromechanical analysis of composites by the generalized cells model. Mechanics of Materials 14, 127–139.

    Article  Google Scholar 

  • Qian, Z.Q. and Akisanya, A.R. (1998). Analysis of free-edge stress and displacement fields in scarf joints subjected to a uniform change in temperature. Fatigue and Fracture of Engineering Materials and Structures 21, 687–703.

    Google Scholar 

  • Rice, J.R. (1968). A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics 35, 379–386.

    Google Scholar 

  • Rice, J.R. (1988). Elastic fracture mechanics concepts for interfacial cracks. Journal of Applied Mechanics 55, 98–103.

    Google Scholar 

  • Rice, J.R., Suo, Z. and Wang, J.-S. (1990). Mechanics and thermodynamics of brittle interface failure in bimaterial systems. In: Metal-Ceramic Interfaces. (Edited by M. Rühle, A.G. Evans, M.F. Ashby and J.P. Hirth), pp. 269–294. Pergamon Press, Oxford.

    Google Scholar 

  • Shih, C.F., Moran, B. and Nakamura, T. (1986). Energy release rate along a three-dimensional crack front in a thermally stressed body. International Journal of Fracture 30, 79–102.

    Google Scholar 

  • Suga, T., Elssner, G. and Schmauder, S. (1988). Composite parameters and mechanical compatibility of material joints. Journal of Composite Materials 22, 917–934.

    Google Scholar 

  • Ting, T.C.T. (1996). Anisotropic Elasticity-Theory and Applications. Oxford University Press, Oxford.

    Google Scholar 

  • Wilson, W.K. and Yu, I.-W. (1979). The use of the J-integral in thermal stress crack problems. International Journal of Fracture 15, 377–387.

    Google Scholar 

  • Wilson, R.I. and Meguid, S.A. (1995). On the determination of mixed mode stress intensity factors of an angled crack in a disc using FEM. Finite Elements in Analysis and Design 18, 433–438.

    Google Scholar 

  • Yau, J.F., Wang, S.S. and Corten, H.T. (1980). A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. Journal of Applied Mechanics 47, 335–341.

    Google Scholar 

  • Yau, J.F. and Wang, S.S. (1984). An analysis of interface cracks between dissimilar isotropic materials using conservation integrals in elasticity. Enginering Fracture Mechanics 20, 423–432.

    Article  Google Scholar 

  • Yosibash, Z. (1998). Thermal generalized stress intensity factors in 2-D domains. Computer Methods in Applied Mechanics and Engineering 157, 365–385.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Banks-Sills, L., Dolev, O. The conservative M-integral for thermal-elastic problems. Int J Fract 125, 149–170 (2004). https://doi.org/10.1023/B:FRAC.0000021065.46630.4d

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:FRAC.0000021065.46630.4d

Navigation