REGULAR ARTICLE Sensitivity analysis, identification and validation of the dislocation density-based model for metallic materials Danuta Szeliga 1 , Natalia Czyżewska 2 , Konrad Klimczak 1 , Jan Kusiak 1 , Paweł Morkisz 2 , Piotr Oprocha 2 , Maciej Pietrzyk 1,* , and Paweł Przybyłowicz 2 1 Faculty of Metals Engineering and Industrial Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland 2 Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland Received: 27 January 2021 / Accepted: 26 April 2021 Abstract. Microstructure evolution model based on the differential equation describing evolution of dislocations was proposed. Sensitivity analysis was performed and parameters with the strongest influence on the output of the model were revealed. Identification of the model coefficients was performed for various metallic materials using inverse analysis for experimental data. The model was implemented in the finite element code and simulations of various hot forming processes were performed. Keywords: dislocation density / flow stress / identification / sensitivity analysis / finite element method 1 Introduction Continuous development of various branches of the industry, in particular transport industries, is associated with the search for new construction materials that combine high strength with good plastic properties and which exhibit high strength-to-density ratio. Intensive research during the last few decades have shown that there is still a huge potential for improvement of properties of various metallic materials. Great progress was made for steels. New grades called Advanced High Strength Steels (AHSS) with multiphase microstructures were developed and widely used mainly in the automotive industry [1,2]. Aluminium [3] and magnesium [4] alloys, although to less extent, are also used. Copper alloys are considered when high heat and electric conductivity is additionally required [5,6]. The high strength and elongation of new metallic materials are usually due to combination of soft matrix with hard constituents in steels and due to precipitation in Al, Mg and Cu alloys. These structures, however, are often characterised by large gradients of properties, which cause tendency to local fracture [7]. It is well seen when dual phase (DP) and complex phase (CP) steels are considered. Compared to DP steels, CP steels with even greater microstructure heterogeneity but with smoother transitions between the phases offer superior stretch-flangeability. It is expected that materials with smoother microstructure gradients will have superior formability [8]. More advanced material models are needed to design microstructures with enhanced local fracture resistance. Properties of steels after hot forming are shaped by control of phase transformations during cooling [8]. On the other hand, kinetics of transformations depends strongly on the state of the austenite after forming. If recrystalliza- tion is not completed, an increased dislocation density accelerates austenite decomposition. Therefore, the com- plete model of the manufacturing process has to compose hot forming stage. Numerous models of microstructure evolution in metallic materials during hot forming have been developed during last half of the century. Majority of these models use external variables as independent ones, see review in [9]. The main drawback of this approach is that it does not account for the history of the considered process. The metallic materials in general show some delay in the response to the change in processing conditions and accounting for the history of the process is important. Therefore, the models, which include internal variables as independent parameters, were proposed in the literature. The internal variables remember the state of the material and account for the history of the process. Evolution of the independent variables is described by differential equation, a solution of which presents some difficulties, in particular when dynamic recrystallization or other than slip defor- mation mechanisms have to be considered. Thus, the possibility of using solutions of the evolution equation for the internal variable in modelling materials processing was investigated by many researchers. Dislocation density is the most common internal variable for metallic materials. * e-mail: mpietrz@agh.edu.pl Metall. Res. Technol. 118, 317 (2021) © EDP Sciences, 2021 https://doi.org/10.1051/metal/2021037 Metallurgical Research Technology & Available online at: www.metallurgical-research.org