Out-of-plane stress and displacement for through-the-thickness cracks in plates of finite thickness

Abstract

The out-of-plane stress and displacement fields are investigated analytically for mode I through-thethickness cracks in an infinite plate of finite thickness within the first-order plate theory. The developed method is based on the distributed dislocation approach and an earlier derived three-dimensional solution for an edge dislocation. Numerical results are obtained through application of Gauss-Chebyshev quadrature for both finite length and semiinfinite crack cases. The calculated stress and displacement fields are found to be in good agreement with already published experimental and finite element studies. Further results for the averaged through-the-thickness stress intensity factor are given and again found to be in good agreement with previous finite element values. The developed solutions can therefore be used in experimental techniques for the assessment of the stress intensity factor using the out-of-plane displacement measurements, for example by the interferometry method.

Effect of plate thickness on stress state at sharp notches and the strength paradox of thick plates

“…Numerical (e.g., Nakamura and Parks, 1989a,b;Nevalainen and Dodds, 1995;Leung and Su, 1995;Kwon and Sun, 2000;She and Guo, 2007;Harding et al, in press), analytical (e.g., Hartranft and Sih, 1970;Yang and Freund, 1985;Kotousov, 2007;Codrington et al, 2008;Kotousov et al, in press) and experimental (e.g., Humbert et al, 2000;Heyder et al, 2005) studies have suggested that the three-dimensional effects at sharp notches and cracks are confined within a close proximity to the notch tip and propagate to approximately one-half of the plate thickness from the notch tip in the plane directions. Consider a plane problem of a sharp notch in a plate of thickness 2 h when the zone of the three-dimensional stress state is fully encapsulated by the K-dominance zone, in which the classical plane stress solution is expected to be accurate.…”

Fracture toughness analysis of a ductile steel by means of 3D surface displacements

“…Most of the existing studies concerning the measurement of surface out-of-plane displacements near the crack tip in facture tests are only devoted to cases of small scale yielding in which the experimental data is correlated to analytical solutions based in the K dominant field and/or 3D FEM results [4,5,[9][10][11]. Moreover, almost all of the geometries of the specimens tested are not standard.…”