Abstract
Crack growths processes of various types are widely covered by power laws. Especially, both creep deformation of creep-resistant bulk materials and creep crack growth in such materials can be covered by power laws and possess close exponents in many cases [1]. This paper focuses on the microscopic thermodynamic mechanisms of the correspondence and the power law itself. In this paper, it is shown that the power laws can be considered as certain homogenous kinetic rate laws of local or microscopic internal variables within the thermodynamic framework of Rice [2, 3] and correspond to a certain macroscopic requirement of maximum dissipation. It is revealed that nonlinear phenomenological equations and Onsager reciprocal relations emerge naturally from the framework if each rate is a monotonic increasing and homogeneous function of the same degree in its conjugate force. The homogeneity property transfers exactly from local internal variables to global internal variables. On the basis of the remarkable properties, it is shown that the power laws of crack growth directly lead to the refined Griffith criterion by Rice [4], and both exponents of creep deformation and creep crack growth can be related by a simple linear relation.
References
1 Riedel, H., Fracture at High Temperatures, Springer-Verlag, Berlin, 1987.10.1007/978-3-642-82961-1Search in Google Scholar
2 Rice, J.R., Inelastic constitutive relations for solids: An integral variable theory and its application to metal plasticity, J. Mech. Phys. Solids, 19 (1971), 433–455.10.1016/0022-5096(71)90010-XSearch in Google Scholar
3 Rice, J.R., Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms, in: Constitutive Equations in Plasticity, Ed. A.S. Argon, pp. 23–79, MIT Press, Cambridge, MA, 1975.Search in Google Scholar
4 Rice, J.R., Thermodynamics of quasi-static growth of Griffith cracks, J. Mech. Phys. Solids, 26 (1978), 61–78.10.1016/0022-5096(78)90014-5Search in Google Scholar
5 Carranza, F.L., Haber, R.B., A numerical study of intergranular fracture and oxygen embrittlement in an elastic-viscoplastic solid, J. Mech. Phys. Solids, 47 (1999), 27–58.10.1016/S0022-5096(98)00085-4Search in Google Scholar
6 Delph, T.J., A simple model for crack growth in creep resistant alloys, Int. J. Fracture, 98 (1999), 77–86.10.1023/A:1018717808350Search in Google Scholar
7 Sih, G.C., Current approaches to material damage at different size and time scales – Foreword, Theor. Appl. Fract. Mech., 41 (2004), XIII–XVI.10.1016/j.tafmec.2004.03.001Search in Google Scholar
8 Yang, Q., Tham, L.G., Swoboda, G., Micromechanical basis of non-linear phenomenological equations as damage evolution laws, Mech. Res. Commun., 29 (2002), 131–136.10.1016/S0093-6413(02)00235-5Search in Google Scholar
9 Yang, Q., Tham, L.G., Swoboda, G., Relationship between refined Griffith criterion and power laws for cracking, Mech. Res. Commun., 31 (2004), 429–434.10.1016/j.mechrescom.2004.02.002Search in Google Scholar
10 Yang, Q., Tham, L.G., Swoboda, G., Normality structures with homogeneous kinetic rate laws. J. Appl. Mech.-T. ASME, 2004 (in press).10.1115/1.1867991Search in Google Scholar
11 Onsager, L., Reciprocal relations in irreversible processes, I, II, Phys. Rev., 37 (1931), 405–406; 38 (1931), 2265–2279.Search in Google Scholar
12 de Groot, S.R., Mazur, P., Non-Equlibrium Thermodynamics, North-Holland, Amsterdam, 1962.Search in Google Scholar
13 Ziegler, H., An Introduction to Thermomechanics, North-Holland, Amsterdam, 1977.Search in Google Scholar
14 Maugin, G.A., The Thermodynamics of Nonlinear Irreversible Behaviors, World Scientific, Singapore, 1999.10.1142/3700Search in Google Scholar
15 Ritchie, R.O., Gilbert, C.J., McNaney, J.M., Mechanics and mechanisms of fatigue damage and crack growth in advanced materials, Int. J. Solids Struct., 37 (2000), 311–329.10.1016/S0020-7683(99)00096-7Search in Google Scholar
16 Broek, D., Elementary Engineering Fracture Mechanics, Martinus Nijho Publishers, Boston, 1982, 3rd rev. ed.10.1007/978-94-011-9055-8Search in Google Scholar
17 Edelen, D.G.B., A nonlinear Onsager theory of irreversibility, Int. J. Eng. Sci., 10 (1972), 481–490.10.1016/0020-7225(72)90091-2Search in Google Scholar
18 Riedel, H., Wagner, W., Creep crack growth in nimonic 80A and in a 1 Cr-½Mo steel, in: Advances in Fracture Research '84 – Proceedings of ICF6, Eds. S. Valluri et al., pp. 2199–2206, Pergammon Press, Oxford, 1985.Search in Google Scholar
19 Yang, Q., Zhou, W.Y., Swoboda, G., Micromechanical identification of anisotropic damage evolution laws, Int. J. Fracture, 68 (1999), 740–750.Search in Google Scholar
Walter de Gruyter GmbH & Co. KG