On the energy release rate and the J-integral for 3-D crack configurations

Abstract

In this paper an analytical expression for the energy release rate has been derived and put in a form suitable for a numerical analysis of an arbitrary 3-D crack configuration. The virtual crack extension method can most conveniently be used for such a derivation. This method was originally developed from finite element considerations and the resulting expressions were, therefore, based on the finite element matrix formulation [1][2][3][4][5]. In this paper the derivation of the energy release rate leads to an expression which is independent of any specific numerical procedure. The formulation is valid for general fracture behavior including nonplanar fracture and shear lips and applies to elastic materials as well as materials following the deformation theory of plasticity. The body force effect is also included. For 3-D fracture problems it is of advantage to use both an average and a local form of the energy release rate and definitions for both forms are suggested. For certain restrictions on the crack geometry it is shown that the energy release rate reduces to the 3-D form of the J-integral.

A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes

“…(2) is cumbersome in the FE scheme as the contour is preferably selected to pass through Gauss points where stresses are expected to be the most accurate. To circumvent this difficulty, the line-integral form of J can be recast as a domain integral (DeLorenzi, 1982;Li et al, 1985). Let us assume q is a sufficiently smooth scalar function in the region enclosed by Γ c = Γ 0 + Γ + + Γ − − Γ, holding unity on Γ and vanishing on Γ 0 .…”

“…It has been shown that the domain version of the J-integral has superior path independence than does the line integral, yielding much more accurate results for the crack field parameters (Nikishkov and Atluri, 1987a;Raju and Shivakumar, 1990). The domain integral method corresponds to a continuum formulation of the finite-element virtual crack extension technique (DeLorenzi, 1982). One can refer to Moran and Shih (1987a,b) for a general discussion on crack-tip contour integrals and their associated domain integral representation.…”

“…For a 3D crack configuration, the J-integral generalizes to a surface integral where two definitions of J-integral have been proposed: (i) the average value which gives the average of the energy release rate per unit crack advance at the whole crack front; and (ii) the pointwise value which gives the energy release rate due the extension of the crack front locally at a given point on the crack front (Budiansky and Rice, 1973;DeLorenzi, 1982;Li et al, 1985). The pointwise J-integral reveals the variation of the strength of the energy release rate along the crack front, and can be used to compute the SIFs at any point on the crack front.…”

A geometry-dependent generalized shape function for calculation of stress intensity factor for axially cracked thin-walled tubes

“…For evaluating the SIF, the analysis is carried out for the applied displacement of 0.01 mm in each specimen and the corresponding compliance values are calculated for each value of a/W. Many approaches exist in the literature (Paris and Sih 1965;Ingraffea and Manu 1980;Raju and Newman 1977;De Lorenzi 1982;Parks 1974) to determine the SIF values. If all approaches are broadly categorized, there are two different methods with which SIF can be derived from the compliance data.…”

“…The extrapolation techniques are based on asymptotic displacement and stress fields near the crack-front (Paris and Sih 1965): by the displacement-field approach (Ingraffea and Manu 1980) and by nodal-force approach (Raju and Newman 1977). The indirect method on the other hand is one where K is determined via its relation with other quantities such as the compliance, the elastic energy (G), or the J integral (De Lorenzi 1982;Parks 1974). For indirect methods, it is possible to calculate the compliance for a range of different crack sizes; from the data using numerical differentiation with respect to crack size SIF can be evaluated.…”