Revisiting classical concepts of Linear Elastic Fracture Mechanics - Part III: The stress field in a double-edge notched finite strip by means of the “stress-neutralization” technique

Abstract

This is the third part of a short series of paper, revisiting some classical concepts of Linear Elastic Fracture Mechanics. Based on the solution for the single edge notched strip, discussed in Part-II, the present study deals with the stress field developed in a stretched finite strip, weakened by two symmetric edge notches. The notches are of parabolic shape, approximating the configuration of a rounded V-notch, varying from almost semicircular edge cavities to “mathematical” edge cracks of zero distance between their lips. The solution is obtained combining Muskhelishvili’s complex potentials technique with a procedure for “stress-neutralization” of specific areas of the loaded strip. To simplify the procedure, the notches are assumed to be “shallow” (short) so that they do not affect each other. Once the complex potentials are obtained, the stress field variations are plotted along strategic loci of the strip and along the periphery of the notches. Attention is paid to the stress field developed around the bases (tips or crowns) of the two notches, providing relatively simple formulae for the critical tensile stress. In addition, the respective stress concentration factor k is obtained for blunt notches, while in the case the edge discontinuities become “mathematical” cracks, a simple expression is given for the mode-I stress intensity factor K_I at the tip of the crack. It is revealed that the assumption of “shallow” notches suffices a quite efficient solution for the overall stress field in finite strips.