Theoretical Analysis of Large Deformation Simultaneous Tearing and Peeling of Elastoplastic Materials

Abstract

Simultaneous tearing and peeling of multiple strips is theoretically investigated using the large deflection theory of cantilevers made of elastoplastic material with linear strain hardening. The relationship between the fracture toughness and the curvature at the fracture propagation front is obtained for general cases. It is shown that for the moment loading case, the non-dimensional external moment, m1, during tearing and peeling along straight paths, is a constant and is independent of the initial beam length Lo. With concentrated force loading, the non-dimensional force f will reach a constant value f=fm during propagation. It is shown that fm is almost the same for both initially straight and pre-bent beams, and decreases with an increase in the external force loading angle φ. For initially straight beams, when the non-dimensional fracture toughness, D, is small, fm may be less than the initiation force f1 for fracture. Fm/H does not increase linearly with an increase in the beam width B0 and decreases at large B0 after it passes through a peak value. Comparison is made with experimental results for the tearing of ductile metal sheets along straight paths and the tearing fracture toughness value is found, including a method that uses propagation crack front curvature alone, without additional reference to the tearing force. However, the accuracy of the curvature at the crack propagation front has a large effect on the estimation of fracture toughness. High work-hardening and/or low toughness materials have no rapid change of curvature away from the crack front so that good estimates are possible and vice versa for low work-hardening solids.