Remarks on the Woodthorpe–Pearce “anomalous” behavior in sheet metals

Abstract

The capability to accommodate the “Woodthorpe–Pearce ‘anomalous’ behavior” has often been used as a criterion to judge the flexibility of yield functions for sheet metals. For metals which exhibit neither sharp yield points nor perfectly plastic behavior, the meaning of this term becomes ambiguous in common usage; instead, we employ it to refer to what Woodthorpe and Pearce [3] observed and failed to predict in their study on aluminum sheets with average r-value <1, namely: in tension tests the balanced biaxial flow curve always lies above the average uniaxial flow curve in a common figure where the horizontal axis denotes the balanced biaxial true-strain and the uniaxial true-strain for the two curves, respectively. In this paper, using the generalized Hershey–Hosford yield function with isotropic strain hardening, we show that the balanced biaxial flow curves in Woodthorpe and Pearce׳s experiments can be predicted from their corresponding average uniaxial flow curves. Moreover, our analysis and other examples suggest that the aforementioned “anomaly” coined by Woodthorpe and Pearce should be quite common.