Energy release rate and J integral for cracks propagating in nonhomogeneous media Part I - Problem formulation
Keywords:
inactive mechanics, energy release rate, J integral, nonhomogenous medianAbstract
In this paper the energy release rate (or the j integral) is calculated for cracks propagating in media with spatially varying material characteristics. Without any assumption on the direction of such a variation with respect to the crack axis at it was made in a similar approach [ ATK 75], an analytical expression for the energy release rate under genera/loading conditions is derived and put in a form suitable for numerical analysis of an arbitrary 3D crack configuration. For cracks in nonhomogeneous media, it is shown that the equivalent J integral should contain, in the 2D deformation field, an additional surface integral (volume integral in the 3D case) to keep its we/known independence property when computed with different integration paths.
Downloads
References
[ATK 75) ATKINSOI> C., Some results on aack propagation with spatially varying elastic
moduli, Int. Journal ofFradure, Vol. II. N°. 4, pp. 619-628, 1975.
[BRO 91) BROCHARI> J., Suo X.Z. and HoRoWITZ H., Thermal shock experiment analysis
by means of the theta-method, 11 1h confert!nce of S.M.l.R.T., Tokyo, Vol. G, 1991.
[CHE 62] CHEREI'ANNOV G.P., The stress stale in a heterogeneous plate with slits, in
Russian, Izvestia AN SSSR, OTN, Mekhan. i Mashin .. Vol. I, pp. 131-137, 1962.
[DEL 88) DEU.I..E F. and ERDO<;AN F., On the mcdutnical modeling of the interfac.ial
region in bonded half-planes, J. of Appl. Med1. Vol. 55, pp. 317-324, 1988.
[DEL 82) DE LORENZI H.G., On the cn.::rgy rd.::ase rate and the J integral for 3D crack
configurations, Int. Journ. of Fra.::ture, 19, pp. 183-193, 1982.
[DER 88) DERBAUAN G. and LAN<"iE C., J integral estimation with the etiffness gradient
method for power law hardening materials, J. of Pressure Vessel Technology, Vol. 110,
pp. 343-347, 1988.
[DES 811 DES'll.!Yl'DER P. and DJAOUA M., Sur une interpretation mathematique de
l'integrale de Rice en Thcorie d.: Ia rupture fragile, Math. Meth. in the Appl. Sc.i. Vol. 3,
pp. 70-87, 1981.
[DES 831 Dl~'>llfYl'DER P., DJAOtlA M. and LES('IlRE S., Quelques remarques sur Ia
mecaniqu.:: de Ia rupture clastiqu.::, Jour. Me.·a. Then. Appl.. Vol. 2, No I, pp. 113-115,
[GRI 21] GRIFJ:olTH A.A., The phenomena of rupture and tlow in solids, Phil. Trans. Roy.
Soc .. London A 221, 1921, pp. 163-197.
[IRW 58) IRWIN G.R., Fracture, Handbuch dcr Physik VI, pp. 551-590, Flugge, Ed.
Springer, 1958.
[ODE 76] ODEN J.T. and REDDY J.T., Variational methods in theoretical mechanics,
Springer Verlag, Heidelberg, 1976.
[OHT 81] OHTSlJKA K., Generalized J integral and three dimensional fracture mechanics I,
Hiroshma Math. J., 21-52, H, 1981.
[PAR 74] PARKS D.M., A stiffness derivative linile element thechnique for determination of
crack tip stress inknsity fal'lnrs, Int. J. of Fracture, Vol. 10, n° 4, December 1974,
pp. 487-502.
[RIC 68) RICE J.R .. A path independent integral and the approximate analysis of strain
concentrations by notc.hes and •·racks, J. Appl. Med1., 1968, pp. 379-386.
[SUO 92) Suo X.Z. and COMIIl~'>CUIW A., On the application of G(e) method and its
comparison with De Lorenzi's approad1, Al•ccpted for publication in the special issue of
inter. J. of Nuclear Engineering and Des gin, 1992.
[WAS 68] WASHIZII K., Variational Methods in Elasticity and Plasticity, Pergamon Press,
Oxti.)rd, 1968.
[WIL 59] WtLUAMS M.L., The stresses around a Iindt or crack in dissimilar media, Bull.
seismol. Sol•. America, Vol. 49, pp. 199-204, 1959.