New stress intensity factor solutions for an elliptical crack in a plate

Crack assessment in engineering structures relies first on accurate evaluation of the stress intensity factors. In recent years, a large work was conducted in France by the Atomic Energy Commission to develop influence coefficients for surface cracks in pipes. However, the problem of embedded cracks in plates (and pipes), which is also of practical importance, has not received so much attention. Presently, solutions for elliptical cracks are available either in infinite solid with a polynomial distribution of normal loading or in plate, but restricted to constant or linearly varying tension. This paper presents the work conducted at EDF R and D to obtain influence coefficients for plates containing an elliptical crack with a wide range of the parameters: relative size (2a/t ratio), shape (a/c ratio) and free surface proximity (a/d ratio, where d is the distance from the center of the ellipse to the closest free surface). These coefficients were developed through extensive 3D finite element calculations: 200 geometrical configurations were modeled, each containing from 18,000 to 26,000 nodes. The limiting case of the tunnel crack (a/c = 0) was also analyzed with 2D finite element calculation (50 geometrical configurations). The accuracy of the results was checked by comparison with analytical solutions for infinite solids and, when possible, with solutions for finite-thickness plates (generally loaded in constant tension). These solutions have been introduced in the RSE-M Code that provides rules and requirements for in-service inspection of French PWR components