engleski

An Analytical Elastic-Plastic Solution of Crack Tip Opening Displacement

A thin plate with a straight crack is considered. It is assumed that the plate material is ductile and that plastic zones around crack tips will occur under loading. This means that in these zones the material yields and the phenomenon of crack opening is started. The crack is loaded with two pairs of co-linear, concentrated compressive forces which act on the surface of the crack and open it, while the edges of the plate are free of loading. Two parameters of elastic-plastic fracture mechanics, i.e. the magnitude of the plastic zone around the crack tip r_p in dependence on the exterior loading on the plate and the crack tip opening displacement &#948 ; ; _t in dependence on the increment of loading, are analyzed in this paper. The increment in the magnitude of the plastic zone around the crack tip, as well as the increment in the displacement on the crack surface in dependence on the increment of loading is observed. By changing the position of concentrated forces F, we investigate how the position influences the magnitude of the two parameters of elastic-plastic fracture mechanics. Analytical methods of the theory of functions with complex variables are used in the analysis of these two parameters. Westergaard's complex function Z(z) is derived for the analyzed problem. By using this function and the known, but transformed, equations of mathematical theory of elasticity, we determine stresses and displacements on the whole plate with a straight crack. The Dugdale-Barenblat plasticity model is used for modelling narrow plastic zones around the crack tips. It is assumed that cohesive stresses &#963 ; ; _Y in the yielded zone are constant. Both conditions of plasticity, i.e. Tresca's and Mises', have been used in determining the shape and magnitude of the plastic zone around the crack tip, in determining the stresses and displacements in the zone of plastification, and in the analysis of the crack tip opening displacement.

Elastic-Plastic Fracture Mechanics; Dugdale Strip Yield Model; Plastic Zone; Crack Tip Opening Displacement; Analytical Methods of the Complex Variable

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