Original Article J Strain Analysis 1–13 Ó IMechE 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0309324714555384 sdj.sagepub.com A new approach for the correction of stress–strain curves after necking in metals Gholam-Hossain Majzoobi 1 , Farzad Fariba 2 , Mohammad K Pipelzadeh 3 and Stephen J Hardy 3 Abstract The true stress–strain curve has a significant role in the analysis of deformation in theoretical plasticity and numerical simulations. Because of the triaxial state of stress in the neck zone, the relationship that is normally obtained from the engineering stress–strain curve is no longer valid and must be corrected. Various correction techniques have been pro- posed and can be found in the literature. In this study, a new semi analytical approach for the correction of the stress– strain curve for circular cross-section specimens (axisymmetric) is introduced and a relation for a correction factor is derived based on the theory of plasticity. The relation requires only a few experimental surface strain measurements which caneasily be made using an image processing technique. In the new method, the neck zone is divided into a num- berof thin walled toroidal elements. The algorithm for the correction factor is obtained in terms of the initial specimen radius, the neck radius and the z-strain on the neck surface. In this work, the true stress–strain curve, that is obtained using the image processing, follows a power law trend before the onset of necking and a linear trend after necking. However, the method is not limited by the trend of the stress–strain curve and can accommodate any trend describing the stress–strain relationship. The proposed approach is compared with methods proposed by Bridgman–Leroy, Bridgman, Davidenkov and Spiridonova, Siebel and Schwaigere and also numerical simulations. The number of simplifying assumptions in the present work is less than that of the Bridgman approach and some of the other methods. Keywords Stress–strain curve, correction factor, material model, image processing, numerical simulation Date received: 26 October 2013; accepted: 2 September 2014 Introduction The true stress–strain (TSS) curve represents the yield surface of materials and is an essential requirement in the theory of plasticity particularly in the simulation of large non-linear plastic deformation. It defines the strain hardening of a material and determines the gen- eral stress–strain relation when the plastic deformation is taking place. Thus, measuring the uniaxial TSS rela- tionship is the most fundamental task before any plas- tic analysis can be performed. Unfortunately, experimental determination of uniax- ial TSS relationships by uniaxial tensile testing is com- plicated because of the necking phenomenon. Also, in the numerical modelling of large deformation and impact problems, this curve represents the material model or the constants that will influence the result of modelling. The TSS curve is obtained from the engi- neering stress–strain (ESS) curve which in turn is computed from the load–displacement history normally obtained from tensile or compressive tests. The conver- sion of ESS to TSS, however, applies only up to the onset of necking where the state of stress becomes triaxial and the resulting curve should be corrected to take account of this stress triaxiality. The correction of stress–strain curves after necking has been the subject of many investigations over the past decades. Some of the methods are complicated and not applicable in 1 Mechanical Engineering Department, Bu-Ali Sina University, Hamedan, Iran 2 Mechanical Engineering Department, Takestan Azad University, Takestan, Iran 3 College of Engineering, Swansea University, Swansea, UK Corresponding author: Mohammad K Pipelzadeh, College of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP, UK. Email: m.k.pipelzadeh@swansea.ac.uk