Abstract
A new law has been proposed to describe the distribution of the cohesive forces present within the internally structured nonlinear zone that precedes the leading edge of a moving crack contained within a nonelastic solid. The nonlinear effects are modeled by the narrow strips emanating from the crack front and endowed with a certain internal structure (unlike the classic models of Barenblatt and Dugdale). The bulk of the material, though, is assumed to behave as linear elastic solid. Mathematical form the law resembles somewhat the Planck's formula used to explain radiation given off by a perfectly black body at very short wavelength of the visible light spectrum. With Sneddon's integral transformations employed and properly modified, the quantities essential in the Nonlinear Mechanics of Fracture have been quantified. In particular another so-called `ubiquitous eta factor' is discussed and related to the material microstructure by means of a certain transcendental equation. The eta-factor enters the formula for the specific work of fracture measured with specimens of various geometrical and loading configurations, and so far is known only empirically. Both the stationary and quasi-static crack problems are discussed. It has been shown that the variations in the microstructural parameters strongly affect the process zone along with the associated work of separation. The other important factors that influence the cohesive stress distribution and all the resulting fracture parameters, specifically those that are responsible for a ductile-to-brittle transition of fracture mode, are the characteristics of the state of stress induced in the vicinity of the crack front. These 3D effects are best represented by the triaxiality parameter, defined as the ratio of the mean stress to the von Mises effective stress
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Wnuk, M.P., Legat, J. Work of fracture and cohesive stress distribution resulting from triaxiality dependent cohesive zone model. International Journal of Fracture 114, 29–46 (2002). https://doi.org/10.1023/A:1014880921017
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DOI: https://doi.org/10.1023/A:1014880921017