An Explicit Weight Function for Semi-Elliptical Surface Cracks

Abstract

An explicit weight function which allows determination of the stress intensity factor for a semi-elliptical surface crack under arbitrary loading is proposed. It was derived by the approximate solution valid for an embedded elliptical crack in infinite body, and a suitable corrective function to account for the free surface effect was obtained on the basis of several accurate stress intensity factor solutions found in literature. By this weight function and a simple numerical quadrature, the SIF at any point of the crack front can be calculated for any loading condition. The method requires negligible time for model preparation and elaboration and little computing resources. It was tested for many crack shapes and loading conditions, and an accuracy of a few percent in the stress intensity factor evaluation was observed. This suggests using the proposed weight function in many practical problems, typical for pressure vessel technology, in which several fracture mechanics analyses are required.

Sharp evaluation of the Oore–Burns integral for cracks subjected to arbitrary normal stress field

“…[14] and the Oore-Burns weight functions, 15 defined for mode I loadings, respect these general proprieties. [15][16][17][18] It is well known that the Oore-Burns weight function is correct for a penny-shaped crack. However, the authors showed that when an elliptical crack is assumed under remote uniform tensile loading, the Oore-Burns integral gives a first-order approximation of SIF, 19 in terms of the eccentricity of the ellipse.…”

An approximation in closed form for the integral of Oore–Burns for cracks similar to a star domain

“…The Oore‐Burns weight function displays a simple analytic form and gives an exact result in the special cases of penny‐shaped cracks or tunnel cracks. Furthermore, this weight function can be used for surface cracks after the introduction of proper coefficients inferred from classical analysis of a surface elliptical crack such as Normal‐Rauj equations (see for instance refinements) . Obviously, the effect of vertex singularities is not taken into account because accurate studies are needed .…”

“…Obviously, the effect of vertex singularities is not taken into account because accurate studies are needed . By means of the Oore–Burns weight, an engineering answer will be given without being too time consuming . In this way, for example, the stress can be evaluated along the front crack for the estimation of the fatigue safety factor …”

“…Furthermore, this weight function can be used for surface cracks after the introduction of proper coefficients inferred from classical analysis of a surface elliptical crack such as Normal-Rauj equations (see for instance refinements). 17,18 Obviously, the effect of vertex singularities is not taken into account because accurate studies are needed. 19,20 By means of the Oore-Burns weight, an engineering answer will be given without being too time consuming.…”

“…19,20 By means of the Oore-Burns weight, an engineering answer will be given without being too time consuming. 17,18 In this way, for example, the stress can be evaluated along the front crack for the estimation of the fatigue safety factor. [21][22][23] Despite its very compact analytical expression, the numerical evaluation of the Oore-Burns integral (hereinafter, OB integral) is very difficult, due to the singular nature of the weight function, and special integration techniques are required as indicated by Desjardins et al 24 and S. R. Montenegro et al 25 For the special case of ellipse cracks, the authors obtained a careful closed-form representation of the OB integral along elliptic cracks under general pressure from previous papers.…”