Abstract
The paper deals with the three-dimensional nature and the multi-parametric representation of the stress field ahead of cracks and notches of different shape. Finite thickness plates are considered, under different loading conditions. Under certain hypotheses, the three-dimensional governing equations of elasticity can be reduced to a system where a bi-harmonic equation and a harmonic equation have to be simultaneously satisfied. The former provides the solution of the corresponding plane notch problem, the latter provides the solution of the corresponding out-of-plane shear notch problem. The analytical frame is applied to some notched and cracked geometries and its degree of accuracy is discussed comparing theoretical results and numerical data from 3D FE models.
Highlights
INTRODUCTIONA pioneering analytical framework was proposed by Dougall [1] to evaluate the three-dimensional stress fields in plates; Dougall’s method was later applied by Green [2] to the stress analysis of a thick isotropic elastic plate weakened by a cylindrical hole
The former provides the solution of the corresponding plane notch problem, the latter provides the solution of the corresponding out-of-plane shear notch problem
A pioneering analytical framework was proposed by Dougall [1] to evaluate the three-dimensional stress fields in plates; Dougall’s method was later applied by Green [2] to the stress analysis of a thick isotropic elastic plate weakened by a cylindrical hole
Summary
A pioneering analytical framework was proposed by Dougall [1] to evaluate the three-dimensional stress fields in plates; Dougall’s method was later applied by Green [2] to the stress analysis of a thick isotropic elastic plate weakened by a cylindrical hole. In parallel, discussing results from 3D finite element analyses on thin cracked elastic plates remotely subjected to mode II anti-symmetrical loading, Nakamura and Parks [15] found that the asymptotic stress fields were characterized by a combination of plane strain mode II and antiplane mode III singular fields. Their analyses put into light, for the first time, the existence of “local induced modes” due to three-dimensional effects. Two forces are applied to generate Mode III loading conditions on the plate and the automatically generated coupled Mode II is investigated paying attention to the scale effect governing the induced mode
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