Luis A. Varela Department of Mechanical Engineering, The University of Texas at El Paso, El Paso, TX 79968 e-mail: Lavarela@miners.utep.edu Calvin M. Stewart Assistant Professor Department of Mechanical Engineering, The University of Texas at El Paso, El Paso, TX 79968 Modeling the Creep of Hastelloy X and the Fatigue of 304 Stainless Steel Using the Miller and Walker Unified Viscoplastic Constitutive Models Hastelloy X (HX) and 304 stainless steel (304SS) are widely used in the pressure vessel and piping industries, specifically in nuclear and chemical reactors, pipe, and valve applications. Both alloys are favored for their resistance to extreme environments, although the materials exhibit a rate-dependent mechanical behavior. Numerous unified viscoplastic models proposed in literature claim to have the ability to describe the inelas- tic behavior of these alloys subjected to a variety of boundary conditions; however, typi- cally limited experimental data are used to validate these claims. In this paper, two unified viscoplastic models (Miller and Walker) are experimentally validated for HX sub- jected to creep and 304SS subjected to strain-controlled low cycle fatigue (LCF). Both constitutive models are coded into ANSYS Mechanical as user-programmable features. Creep and fatigue behavior are simulated at a broad range of stress levels. The results are compared to an exhaustive database of experimental data to fully validate the capa- bilities and performance of these models. Material constants are calculated using the recently developed Material Constant Heuristic Optimizer (MACHO) software. This soft- ware uses the simulated annealing algorithm to determine the optimal material constants through the comparison of simulations to a database of experimental data. A qualitative and quantitative discussion is presented to determine the most suitable model to predict the behavior of HX and 304SS. [DOI: 10.1115/1.4032319] Keywords: unified viscoplastic model, Miller, Walker, inelastic behavior, Hastelloy X, 304 stainless steel, constant optimizer, creep, low cycle fatigue 1 Introduction Nuclear and chemical reactors can be used to generate electric- ity while minimizing greenhouse gas emissions [1]. The efficiency of these reactors is related to the high temperature at which they operate. High-operating temperatures are desired for better effi- ciency. The reactors require cooling systems to keep them within safe operating temperature. The coolant system is the intermediate heat exchanger (IHX) which exchanges heat between the primary heated coolant that comes directly from the reactor at a tempera- ture of around 950  C and the secondary working fluid which cools down the primary coolant [1–3]. IHX performance is crucial for a safe operation and a high efficiency. Therefore, accurate IHX component design is pivot to achieve high-quality reactors. It is essential to have a deep understanding of the mechanical behav- ior of the constituent material under servicelike conditions [4]. Since the IHX operates at elevated temperature and extreme conditions, a material resistant to high temperature, thermal and mechanical stresses, corrosion, and oxidation is required. The nickel-base superalloy HX is an attractive candidate material. It is favored for piping applications because of its high nickel content, which provides excellent mechanical properties at high tempera- ture, including high resistance to creep, oxidation, and corrosion [5–10]. A second candidate material for this piping application is 304SS. In order to optimize the design of IHX components, a detailed modeling of the material’s behavior under any loading condition is essential. On the other hand, a better understanding of the mate- rial behavior leads to less conservative designs that in return reduce the cost of hardware and components [11]. There has been considerable effort to develop unified constitutive models capable of describing the inelastic behavior of HX and 304SS. These “unified” models are designed to model the multiple deformation mechanisms present during various loading cases, such as stress relaxation, monotonic tension, creep, and fatigue. Historically, numerous viscoplastic models have been proposed in literature, such as Chaboche, Bodner, Hart, Miller, Walker, Bodner–Partom among many others [12–17]. However, few researchers have vali- dated these models for HX under creep and for 304SS under LCF conditions. The response of viscoplastic constitutive model is driven by the material constants, where the constants are charac- teristic of each material type. Material constants are typically cal- culated using specific types of experimental data that activate the deformation mechanisms of interest. The complexity of the con- stitutive equations and the considered temperature ranges dictate the total number of material constants required to model the me- chanical behavior. The process to determine these material con- stants is not well documented for most viscoplastic constitutive models; therefore, there exist gaps in the calculation process that lead to the “unsystematic” calculation of material constants. This unsystematic calculation of constants might result in improper usage of the viscoplastic models. In the present work, Miller [18] and Walker [19] unified visco- plastic constitutive models are exercised and analyzed to deter- mine the most accurate model describing the inelastic deformation of HX under creep and 304SS under fatigue. To ensure a systematic calculation of material constants, a numerical optimization software is used for both constitutive models. HX Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received June 4, 2015; final manuscript received December 13, 2015; published online January 29, 2016. Assoc. Editor: Vadim V. Silberschmidt. Journal of Engineering Materials and Technology APRIL 2016, Vol. 138 / 021006-1 Copyright V C 2016 by ASME Downloaded From: https://materialstechnology.asmedigitalcollection.asme.org on 07/13/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use