Prediction of the formability of metastable low nickel austenitic stainless steel sheets A. Kanni Raj, K.A. Padmanabhan * Metal Forming Laboratory, Department of Metallurgical Engineering, Indian Institute of Technology, Chennai 600 036, India Received 11 March 1998 Abstract The formability of metastable low nickel austenitic stainless steel sheets is predicted by extending an earlier analysis due to one of the authors and his co-worker. As in the earlier analysis, the size of the imperfection in the thickness direction is associated with surface roughness. Two concurrent modes of ¯ow localisation, viz., geometric instability (thickness strain, surface roughening and void growth) and bulk shear band formation, are assumed to contribute equally and additively to the limiting strain. In this modi®ed method, void growth is described by a re®ned Avrami relation that takes into account the effect of the strain (stress) state. Also, the  parameter in the analysis that was assumed as unity in the earlier analysis is presented now as a function of the stress (strain) ratio, the material properties and the initial sheet thickness. A reasonably good correlation with experimental results is demonstrated. # 1999 Elsevier Science S.A. All rights reserved. Keywords: Forming-limit diagrams (FLDs); Low nickel metastable stainless steel sheets; AISI 304 stainless steel; Formability modelling; Instability; Flow localisation 1. Introduction This paper is concerned with the prediction of the form- ability of metastable stainless steel sheets, and is an exten- sion of an earlier model [1]. Diffuse necking under plane-stress conditions was ana- lysed by Swift [2], whilst Hill [3] examined discontinuous plastic states in thin sheets with reference to localised necking. Following the pioneering work of Keeler and Backofen [4], various experimental and theoretical investi- gations have been completed on the estimation of limit strains in sheet metal forming. Unlike in uniaxial tension, failure in sheet metals subjected to biaxial straining does not involve a well-de®ned region of non-uniform deformation. Marciniak et al. [5,6] proposed an analysis (the M±K analysis) that is somewhat different from those of Swift and Hill, which was nevertheless based on geometric instability. The M±K hypothesis was extended by Sowerby and Duncan [7] and Azrin and Backofen [8] to cover all cases of biaxial stressing. It was shown [9] that the expected form of the M± K curves was not in agreement with experimental results. The major strain calculated on the basis of the M±K theory was too low under conditions of plane strain. To explain this anomaly, it was proposed [10,11] that the inhomogeneity did not become critical until diffuse necking commenced. Yamaguchi and Mellor [11] stated that ¯ow localisation was due to Swift diffuse instability, which could then be handled by the M±K analysis. It was shown by Tvergaard [12] that the forming-limit diagram predicted by the kine- matic hardening rule was in much better agreement with the experimental results than the curves predicted using stan- dard ¯ow theory. Based on the M±K hypothesis, another model was presented by Lee and Zaverl [13] to evaluate the entire forming-limit diagram. Chan et al. [14] examined localised necking for negative strain ratios. Venter and Kharshafdjian [15], in contrast, modi®ed the analysis of Parmar and Mellor [16,17] by introducing a  parameter (see later) and obtained closer ®ts with experimental results. A different instability theory was proposed by Storen and Rice [18], which postulated that localised necking was due to the development of a corner or vertex on the yield surface due to a velocity discontinuity along the slip lines. The vertex was conceptualised as the intersection of smooth yield surfaces. A vertex on the yield surface was found to Journal of Materials Processing Technology 94 (1999) 201±207 *Corresponding author. Indian Institute of Technology, Kanpur 208 016, India. Fax: +91-512-590-260/590-007 E-mail address: kap@iitk.ac.in (K.A. Padmanabhan) 0924-0136/99/$ ± see front matter # 1999 Elsevier Science S.A. All rights reserved. PII:S0924-0136(99)00106-5