A damage accumulation model for complex strain paths: Prediction of ductile failure in metals Rimma Lapovok a,Ã , D. Hodgson b a ARC CoE in Design of Light Metals, Department of Materials Engineering, Monash University, Vic. 3800, Australia b Centre for Material and Fibre Innovation, Deakin University, Geelong, Vic. 3217, Australia article info Article history: Received 19 May 2009 Received in revised form 9 July 2009 Accepted 30 July 2009 Keywords: Damage tensor Strain path Low-bound ductility Metal forming operations abstract The characterisation of strain path with respect to the directionality of defect formation is discussed. The criterion of non-monotonic strain path is used in the scalar and tensor models for damage accumulation and recovery. Comparable analysis of models and their verification has been obtained by simulation of crack initiation in a two-stage metal forming operation consisting of wire drawing followed by constrained upsetting. & 2009 Elsevier Ltd. All rights reserved. 1. Introduction During the sequence of metal forming operations, metals are subjected to multi-axial loading along complex strain paths. The effect of strain path on the constitutive behaviour of materials during plastic deformation has been widely studied (Hill, 2000; Peng and Ponter, 1993; Wu, 2003; Petryk and Thermann, 2000) and a number of plasticity models have been developed to incorporate the manifestation of pre-strain on inelastic behaviour, such as the change in yield surface, the transient stage after reloading to yield stress, Baushinger effect, etc. Several time-independent constitutive models to describe kinematic hardening in non-monotonic loading have been proposed (Chaboche, 1986). Another important aspect of the strain-path influence is its effect on accumulation of damage, which can be used for prediction of fracture of the metal during plastic deformation. Regardless of the choice of damage measure, e.g. macroscopic damage variable proposed by Kachanov (1986) or tensor damage characteristics proposed by Murakami (1988), Lubarda and Krajcinovic (1993), Kachanov (1992), Karihaloo and Fu (1990) and others, the kinetics of damage development and recovery depends on the characteristics of the loading path. However, the characteristics of strain path such as length of strain trajectory, curvature of strain trajectory, delay angle (Ohashi and Tanaka, 1981; Cobbold and Barbotin, 1988; Ohashi et al., 1983) and Schmitt parameter Schmitt et al. (1994) cannot be used in conjunction with damage criterion without consideration of directionality of defect accumulation during deformation. In this paper we discuss the means for characterisation of strain path with respect to the directionality of defect formation and formulate a criterion of non-monotonic strain path used in the model for damage accumulation and recovery. The model is then verified for the prediction of crack initiation in a two-stage metal forming operation consisting of wire drawing followed by constrained upsetting. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jmps Journal of the Mechanics and Physics of Solids ARTICLE IN PRESS 0022-5096/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jmps.2009.07.008 Ã Corresponding author. Tel.: +613 9905 9294; fax: +613 9905 4940. E-mail address: rimma.lapovok@eng.monash.edu.au (R. Lapovok). Journal of the Mechanics and Physics of Solids 57 (2009) 1851–1864