Fracture strength in randomly perforated plates

Abstract

We have measured the forces that need to be applied quasistatically to randomly perforated rectangular aluminum plates to tear them apart. Concomitantly, for identical geometrical structures, we have carried out numerical simulations of the tearing process. The two results agree quite reasonably, and especially so for perforated area densities (P) that are rather less than the critical percolation densities. A given value of P can be achieved through various different realizations (patterns of perforations), each with a somewhat different fracture (or failure) strength F. Our results predict empirically an “expected F” [F¯(P)] and an expected standard deviation [root variance, S(P)] as functions of P. This enables the risk analysis of failures in plates under tensile stress, which is needed in, e.g., the estimation of the flying safety of a spacecraft subject to multiple perforations.