Revisiting classical concepts of Linear Elastic Fracture Mechanics - Part II: Stretching finite strips weakened by single edge parabolically-shaped notches

Abstract

This is the second part of a short three-paper series, aiming to revisit some classical concepts of Linear Elastic Fracture Mechanics. Being the intermediate step of the analysis between infinite domains (discussed in Part-I) and finite bodies (that will be discussed analytically in the third part of the series), the present part offers an alternative theoretical approach for the confrontation of problems dealing with both infinite and finite bodies with geometrical discontinuities. The method is here applied to a stretched, single-edge notched strip. Assuming that the strip is made of a linearly elastic and isotropic material, the complex potentials technique is used. The solution is achieved by extending Mushkelishvili’s procedure, for the confrontation of the prob­lem of an infinite perforated plane. Closed form, full-field formulae are obtained for the stresses all over the notched strip. Using these formulae, the stress concentration factor at the base (tip) of the notch is quantified and studied in terms of the geometrical features of the notch and its dimensions relatively to the respective ones of the strip. The stress distributions plotted along characteristic loci, resemble closely, from a qualitative point of view, the respective ones provided by well-established analytical solutions. Preliminary numerical analyses in progress provide results in very good agreement with those of the present analysis.