Simulation of cyclic plastic deformation response in SA333 C–Mn steel by a kinematic hardening model Surajit Kumar Paul a,b, * , S. Sivaprasad a , S. Dhar b , M. Tarafder a , S. Tarafder a a Materials Science & Technology Division, National Metallurgical Laboratory (Council of Scientific & Industrial Research), Jamshedpur 831 007, India b Department of Mechanical Engineering, Jadavpur University, Kolkata 700 032, India article info Article history: Received 14 December 2009 Received in revised form 19 February 2010 Accepted 25 February 2010 Available online xxxx Keywords: Cyclic plasticity Low cycle fatigue Ratcheting Kinematic hardening model abstract Cyclic plasticity deals with non-linear stress–strain response of materials subjected to external repetitive loading. An effort has been made to describe cyclic plastic deformation behavior of the SA333 C–Mn steel by finite element based plasticity model. The model has been developed on the framework using a yield surface together with Armstrong–Frederick type kinematic hardening model. No isotropic hardening is considered and yield stress is assumed to be a constant in the material. Kinematic hardening coefficient and kinematic hardening exponent reduces exponentially with plastic strain in the proposed model. The proposed model has been validated through experimental results. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Plasticity models or constitutive equations are the mathemati- cal relations describing non-linear stress–strain response of a material subjected to external loading. Finite element based cyclic plasticity models are nowadays frequently used for design optimi- zation and stress analysis of engineering structures. Especially, there is an increasing demand for ‘easy-to-apply’ cyclic plasticity models for structural design in nuclear power plants. For example, ratcheting effect has already been included in the American ITER design code and ASME NB 32xx code for nuclear pipes. Most of the finite element based theories at macroscopic scale share a com- mon basic framework by using a combination of a yield surface in the deviatoric stress space and normality flow rule. Kinematic hardening in all these models is considered through translation of the yield surface, and isotropic hardening is often modeled through the expansion and contraction of the yield surface. The only difference among various models is in the specification of yield surface translation, which is often referred to as hardening model. Kinematic hardening models are commonly used to simulate cyclic plastic deformation behavior of a material such as low cycle fatigue and ratcheting. Ratcheting can be defined as the directional progressive accumulation of plastic strain in a component due to imposition of asymmetric stress cycling. Ratcheting is considered as one of the most critical structural problems to be addressed. A number of kinematic hardening models have been developed to predict the ratcheting response of materials to a reasonable accu- racy. Basically, kinematic hardening models can be classified into two broad categories: coupled models and uncoupled models [1,2]. In coupled models, the plastic modulus calculation is coupled with its kinematic hardening model through a yield surface consis- tency condition as in the classical model proposed by Prager [3]. In the second category of models, the plastic modulus may be indi- rectly influenced by kinematic hardening model, however, its cal- culation is not coupled to kinematic hardening model through consistency condition [4,5]. Coupled kinematic hardening models can further be classified into two sub categories: multilinear and non-linear kinematic hardening models. Examples of multilinear kinematic hardening models are those proposed by Besseling [6] without any notion of surfaces and by Ohno and Wang (I) [7,8] that employs a piecewise linear kinematic hardening model. All these models under uniaxial loading essentially divide the stress–strain curve into many linear segments. These models have the capability to predict the stress–strain hysteresis loops accurately when suffi- cient numbers of segments are chosen [1,2]. However similar to the Prager linear kinematic hardening model [3], multilinear mod- els fail to predict uniaxial ratcheting strain [1,2]. By introducing a slight non-linearity into the Ohno and Wang (I) [7,8] multilinear model, reasonable correlation of ratcheting responses [1] has been shown. All non-linear kinematic hardening models are able to envisage ratcheting response. For example, the Armstrong and Frederick (AF) model [9] is capable of predicting the ratcheting 0927-0256/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2010.02.037 * Corresponding author. Address: Materials Science & Technology Division, National Metallurgical Laboratory (Council of Scientific & Industrial Research), Jamshedpur 831 007, India. Tel.: +91 6572345190; fax: +91 6572345153. E-mail addresses: paulsurajit@yahoo.co.in, surajit@nmlindia.org (S.K. Paul). Computational Materials Science xxx (2010) xxx–xxx Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci ARTICLE IN PRESS Please cite this article in press as: S.K. Paul et al., Comput. Mater. Sci. (2010), doi:10.1016/j.commatsci.2010.02.037