Actual three-dimensional stresses in notches, crack tips and lamination planes

Abstract

A strange dichotomy exists in the analysis of stresses in local effects and in adhesively bonded parts. It has been known in aeronautical engineering for at least 60 years that the stresses in plates with notches or cracks, or in plates subjected to localized loads, are strongly three-dimensional. Nevertheless, it has been common to invoke the notion of the so-called generalized plane stress state , and to consider the two-dimensional treatment of the stress states in regions of notches, cracks or lamination planes to be completely satisfactory. As a result, many analytical solutions in stress analysis are not testable—the errors are both in the magnitude, up to 30%, and even in the sign. Two problems have developed, one practical, the other aesthetic. First, for obvious reasons, modern technology needs analytical solutions, or computer programs, which simulate reliably the actual physical occurrence. Second, any analytical solution which ignores one or more basic features of the real behavior of materials and bodies under consideration, or is incompatible with some underlying assumptions, or violates some principles of mechanics, is not only insufficiently reliable but cannot be considered elegant. Using Popper's terminology, such a solution is not in the category of a physical theory but is rather in the category of a metaphysical theory. The paper presents selected examples of empirical evidence on the actual, mostly three-dimensional, stresses in notches, cracks, beams with local effects, and in components of adhesively bonded joints . The usefulness of the renormalization procedures for singular solutions is discussed, and more comprehensive and realistic notions of the stress concentration factor in plates are suggested.