On Diverging Concertina Tearing

[+] Author and Article Information
T. Wierzbicki, K. A. Trauth

Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

A. G. Atkins

Department of Engineering, University of Reading, Whiteknights, Reading RG6 6AY, England

J. Appl. Mech 65(4), 990-997 (Dec 01, 1998) (8 pages) doi:10.1115/1.2791943 History: Received April 22, 1997; Revised January 19, 1998; Online October 25, 2007


A simplified theory of the process of concertina tearing of thin plates with two diverging cracks is developed. The cracks initiate from a local cut and propagate away from the initiation site as the loading punch is pushed in the in-plane direction. At the same time the plate strip between the two cracks folds back and forth in much the same way as the “concertina” collapse pattern of circular tubes, studied extensively in the literature. Closed-form solutions are derived for the punch force and the length of the folding wave. Postulating a differential equation for the direction of the crack growth, a path of the tearing fracture is determined. It is shown that the crack trajectories depend on the plate thickness and the size of the initiation cut but, perhaps surprisingly, are independent of the material properties of the plate. This means that the process of concertina tearing would be similar for metal, plastic, paper, leather, etc. A series of experiments on 0.4-mm-thick mild steel plate was performed showing a very good agreement with the theoretical predictions.

Copyright © 1998 by The American Society of Mechanical Engineers
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