Variation of elastic T-stresses along slightly wavy 3D crack fronts

Abstract

The non-singular terms in the series expansion of the elastic crack-tip stress field, commonly referred to as the elastic T-stresses, play an important role in fracture mechanics in areas such as the stability of a crack path and the two-parameter characterization of elastic-plastic crack-tip deformation. In this paper, a first order perturbation analysis is performed to study some basic properties of the T-stress variation along a slightly wavy 3D crack front. The analysis employs important properties of Bueckner-Rice 3D weight function fields. Using the Boussinesq-Papkovitch potential representation for the mode I weight function field, it is shown that, for coplanar cracks in an infinite isotropic and homogeneous linear elastic body, the mean T-stress along an arbitrary crack front is independent of the shape and size of the crack. Further, a universal relation is discovered between the mean T-stress and the stress field at the same crack front location under the same loading but in the absence of a crack. First-order-accurate solutions are given for the T-stress variation along a slightly wavy crack front with nearly circular or straight configurations. Specifically, cosine wave functions are adopted to describe smooth polygonal and slightly undulating planar crack shapes. The results indicate that T 11, the 2D T-stress component acting normal to the crack front, increases with the curvature of the crack front as it bows out but T33, acting parallel to the crack front, decreases with the crack front curvature.

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“…Equation 101 implies in particular that the average variation δσ x x + δσ zz is zero whatever the perturbation of the crack front; this means that at a given point of the broken region of the crack plane, the average 2D trace of the stress tensor, σ x x + σ zz , is independent of the position and shape of the crack front. This remarkable property is noted here in the special case of a semi-infinite crack, but was shown by Gao [1992] to in fact hold for any planar crack of arbitrary contour in some infinite body.…”

“…In physical terms, even though σ x x + σ zz , at a given, fixed point of the broken region of the crack plane, is independent of the position and shape of the crack front, evaluating the variation of T 11 + T 33 implies following the point of observation of σ x x + σ zz as the front moves, which inevitably entails a variation of this quantity. Gao. Gao [1992] did not consider only the case of an initially straight crack front as in the present work, but also that of a circular one.…”

“…in the physical space are interesting in themselves, and getting them from those of [Gao 1992] through inverse Fourier transform is not a completely straightforward operation.…”

“…The calculation of the SIF was carried out in [Rice 1985] and [Gao and Rice 1986], with definitive results. That of the nonsingular stresses was carried out in [Gao 1992], but with restrictive hypotheses and incomplete results, making the completion of the task an indispensable prerequisite.…”

Three-dimensional fracture mechanics analyses of single edge cracked plate specimens

“…It also presented that the material's Poisson's ratio and the specimen's thickness affect the three-dimensional evaluation of the biaxiality factor. Gao (1992) analyzed the variation of T n and T 33 along a slightly wavy three-dimensional crack front. The results indicated that the Tn increased with the curvature of the crack front but 7*33 decreased with the crack front curvature.…”