Vol.:(0123456789) 1 3 Metals and Materials International https://doi.org/10.1007/s12540-018-00225-8 Neural Network Approach to Construct a Processing Map from a Non‑linear Stress–Temperature Relationship Chan Hee Park 1  · Dojin Cha 2  · Minsoo Kim 2  · N. S. Reddy 3  · Jong‑Taek Yeom 1 Received: 24 October 2018 / Accepted: 20 November 2018 © The Korean Institute of Metals and Materials 2018 Abstract An accurate processing map for a metal provides a means of attaining a desired microstructure and required shape through thermo-mechanical processing. To construct such a map, the isothermal fow stress, σ iso , is required. Conventionally, the non-isothermal fow stress measured by experiment is corrected to σ iso using whole-temperature-range linear interpolation (WRLI) or partial-temperature-range linear interpolation (PRLI). However, these approaches could incur signifcant errors if the non-isothermal fow stress exhibits a non-linear relationship with the temperature. In this study, an artifcial neural network (ANN) model was applied to correct the non-isothermal fow stress in 10 wt% Cr steel, which exhibits a non-linear tempera- ture dependence within a target temperature range of 750–1250 °C. Processing maps were constructed using σ iso corrected by applying the WRLI, PRLI, and ANN approaches, respectively, and were then compared with the actual microstructures. The WRLI approach produced the highest minimum error of σ iso (17.2%) and over-predicted the shear-band formation. The PRLI approach reasonably predicted the microstructural changes, but the minimum error for σ iso (8.9%) was somewhat high. The ANN approach not only realized the lowest minimum error of σ iso (~ 0%), but also efectively predicted the microstructural changes. Keywords Metallic alloys · Thermomechanical · Processing · Microstructure · Stress–strain measurements · Computer modelling 1 Introduction A processing map is constructed by superimposing an instability map [1–3] or fow localization map [4] onto a power dissipation map [5]. The resulting processing map can be employed to predict the microstructure evolution and to optimize the thermo-mechanical processing of various metals. Application of these theories requires a database of isothermal fow stress σ iso as functions of strain, strain rate, and target temperature T target . In most experiments, however, the non-isothermal fow stress σ non-iso is obtained because the instantaneous temperature T instant of the specimen dif- fers from T target , especially in the case of high strain rates in which deformation heating occurs. Thus, σ non-iso should be corrected to σ iso prior to the construction of the processing map. There are many constitutive equations for determining σ iso . These can be classifed into phenomenological models and physically based models. The phenomenological mod- els such as the Johnson–Cook (JC) [6], Khan–Huang–Liang (KHL) [7, 8], and their modifcations [9, 10] always require fow stress data at a low strain rate, at which deformation heating does not occur, to identify material constants. Mean- while, the physically based models, such as the mechanical threshold stress (MTS) model [11, 12] and its modifca- tions [13, 14], require fow stress values at either low or very high temperatures to determine the threshold stress or * Chan Hee Park chpark@kims.re.kr Dojin Cha dojin.cha@doosan.com Minsoo Kim min-soo.kim@doosan.com N. S. Reddy nsreddy@gnu.ac.kr Jong-Taek Yeom yjt96@kims.re.kr 1 Advanced Metals Division, Korea Institute of Materials Science, Changwon 51508, Republic of Korea 2 Corporate R&D Institute, Doosan Heavy Industries and Construction, Changwon 51711, Republic of Korea 3 School of Materials Science and Engineering, Gyeongsang National University, Jinju 52828, Republic of Korea