The calculation of crack opening area and crack opening volume from stress intensity factors

Abstract

This report describes a method which permits the calculation, directly from the elastic stress-intensity factors of the crack opening area of a two-dimensional crack or the crack opening volume of a penny-shaped crack when subjected to uniform or non-uniform stress distributions. Although stress intensity factors are well documented, especially for two-dimensional cracks (see e.g. [1-3]), it is sometimes necessary to obtain additional information pertaining to particular crack configurations or non-uniform loading systems. A quantity which can be calculated directly from the stress intensity factor is the crack opening area, as shown recently by M't)ller and Harris [4] for uniformly loaded two-dimensional crack configurations. The crack opening area may be of interest, e.g. in estimating leakage rates from cracks in fluid-containing components, such as thin-walled tubes in cooling circuits or chemical plant. Miiller and Harris [4] used the interrelation between the energy release rate and the stress intensity factor to derive an equation for the crack opening area of a two dimensional crack subjected to a uniform applied stress in terms of the corresponding stress intensity factor. In the present paper, starting from the weight function fomaulation, we derive a more general equation for computing the crack opening area of arbitrarily non-uniform loaded two-dimensional crack configurations from stress intensity factors. An analogous relationship for the crack opening volume of a penny-shaped crack subjected to radially symmetric stress distributions is also derived. Application of the results is demonstrated by selected examples. Two-dimensional cracks: Consider first a centre-synametric crack of length 2a in a finite sheet subjected to a non-uniform crack face pressure p(x)=-cy(x) corresponding to the centre-symmetric applied normal stress distribution ~(x) = cy(-x) at the prospective crack site. The coordinate x coincides with the crack line with its origin at the crack centre. Then the stress intensity factors Kin(a) and Kc2~(a) of the same cracked body subjected to two different load cases oo~(x) and ~2~(x), respectively, are interrelated according to Betti's reciprocal theorem and the superposition principle by (cf. e.g. [3])