Maciej Pietrzyk

Analysis of work hardening and recrystallization during the hot working of steel using a statistically based internal variable model

A mathematical model has been developed which describes the hot deformation and recrystallization behavior of austenite using a single internal variable: dislocation density. The dislocation density is incorporated into equations describing the rate of recovery and recrystallization. In each case no distinction is made between static and dynamic events, and the model is able to simulate multideformation processes. The model is statistically based and tracks individual populations of the dislocation density during the work-hardening and softening phases. After tuning using available data the model gave an accurate prediction of the stress–strain behavior and the static recrystallization kinetics for C–Mn steels. The model correctly predicted the sensitivity of the post deformation recrystallization behavior to process variables such as strain, strain rate and temperature, even though data for this were not explicitly incorporated in the tuning data set. In particular, the post dynamic recrystallization (generally termed metadynamic recrystallization) was shown to be largely independent of strain and temperature, but a strong function of strain rate, as observed in published experimental work.

Multiscale modelling of microstructure evolution during laminar cooling of hot rolled DP steels

Accelerated cooling of DP steel strips after hot rolling is considered in the paper. The work is focused on the multi scale model based on the Cellular Automata method as well as on conventional models. Dilatometric tests were performed to identify the coefficients in the models for a DP steel. These models are implemented in the computer system, which simulates controlled cooling of products after hot rolling. This system is described briefly in the paper. Results of numerical tests, which show an influence of the cooling parameters on the structure of the DP steels, are presented in the paper, as well. Arbitrary laminar cooling system, composed of n1 boxes in the first section and n2 boxes in the second section, is considered. Such parameters as strip thickness and velocity, the number of active boxes in the first section of the laminar cooling, the time interval between the two sections and water flux in the sections were independent variables in the analysis. The optimal cooling schedule is the main result of the work.

A study of the effect of the thermomechanical history on the mechanical properties of a high niobium steel

A methodology for including the thermomechanical history in hot forming analyses is presented. A finite element formulation is employed for analysis of the inhomogeneous microstructural development. An earlier model, describing the development of the microstructure in niobium steels, is expanded to predict the final properties of the product and is integrated into the complete model of the hot compression process. Mechanical properties are obtained from a macroscopic description based on the Hall-Petch formulae. The results show that the model calculates correctly the influence of microstructure on the mechanical inhomogeneity. The analyses indicate that when all of the strengthening mechanisms are employed, the root of the sum of the squares summation method gives better agreement with experimental data than linear summation, of importance especially when the last deformation occurs in the two-phase or ferrite region. The proposed model can be used to investigate the complex behavior of a large range of microalloyed steels in hot rolling or forging processes.

Optimization of Cellular Automata Model for the Heating of Dual-Phase Steel by Genetic Algorithm and Genetic Programming

This study considers a common metallurgical problem associated with the phase transformation of steel during heating where austenite grain tends to grow in size with time and results in poor mechanical properties in the final stages. This investigation was performed using a Cellular Automata model for dual-phase steel developed in house. Data-driven metamodels for a biobjective optimization problem involving minimizing average austenite grain size along with the maximizing of time of heating were constructed using Evolutionary Neural Network (EvoNN) and Biobjective Genetic Programming (BioGP). The input variables selected for this task were (i) heating rate, (ii) pearlite percentage, (iii) nucleation density of austenite, and (iv) the finish temperature of austenite formation. The analyses of the results led to the fact that heating rate is the most influencing factor and it needs to be large during transformation to obtain a refined microstructure. The comparison of Pareto front between EvoNN and BioGP reveals a better performance of the latter. Limited experimental confirmation was also carried out.

From High Accuracy to High Efficiency in Simulations of Processing of Dual-Phase Steels

Searching for a compromise between computing costs and predictive capabilities of metal processing models is the objective of this work. The justification of using multiscale and simplified models in simulations of manufacturing of DP steel products is discussed. Multiscale techniques are described and their applications to modeling annealing and stamping are shown. This approach is costly and should be used in specific applications only. Models based on the JMAK equation are an alternative. Physical simulations of the continuous annealing were conducted for validation of the models. An analysis of the computing time and predictive capabilities of the models allowed to conclude that the modified JMAK equation gives good results as far as prediction of volume fractions after annealing is needed. Contrary, a multiscale model is needed to analyze the distributions of strains in the ferritic-martensitic microstructure. The idea of simplification of multiscale models is presented, as well.

Conventional and Multiscale Modeling of Microstructure Evolution During Laminar Cooling of DP Steel Strips

Physical and numerical simulations of the hot rolling and laminar cooling of DP steel strips are presented in the paper. The objectives of the paper were twofold. Physical simulations of hot plastic deformation were used to identify and validate numerical models. Validated models were applied to simulate the manufacturing of DP steel strips. Conventional flow stress model and microstructure evolution model were used in the hot deformation part. The approach to the complex systems analysis based on global thermodynamic characterization and detailed microstructure characterization was applied to determine equilibrium state at various temperatures. Finally, two numerical models were used to simulate kinetics of austenite decomposition at varying temperatures: the first, conventional model based on the Avrami equation, and the second, the discrete Cellular Automata approach. Plastometric tests and stress relaxation tests were used for identification of the hot rolling model for the DP steel. Dilatometric tests were performed to identify the phase transformation models. Verification confirmed good accuracy of all models. Validated models were applied to simulate the manufacturing of DP steel strips. Influence of technological parameters (e.g., strip thickness and velocity, active sections in the laminar cooling, and water flux in the sections) on the DP microstructure was analyzed. The cooling schedules, which give required microstructures were proposed. The numerical tool, which simulates manufacturing chain for DP steel strips is the main output of the paper.

Identification of rheological models and boundary conditions in metal forming

Identification of rheological models and boundary conditions in metal forming is performed. Various rheological models, from classical closed-form equations to advanced multiscale models, are investigated. Capabilities and limitations of models are discussed. Inverse method is applied to identification of the models on the basis of plastometric tests. Ability of this technique to eliminate the effect of inhomogeneity of deformation is demonstrated. Importance of rheological parameters is evaluated using parameter sensitivity analysis. Finally, sensitivity of the inverse approach with respect to assumptions is performed and accuracy of this approach is evaluated. Good practice guide for identification of rheological model is proposed.

Three-dimensional interdiffusion under stress field in Fe-Ni-Cu alloys

We present the method of solving the mechanochemical transport problem in multicomponent solid solutions, namely, the method of quantitative description of the interdiffusion (ID) under the stress field. We postulate that the velocities appearing in the momentum balance equation should be the drift and diffusion velocity. The energy, momentum, and mass transport are diffusion controlled, and the diffusion fluxes of the components are given by the Nernst-Planck formulas. The diffusion depends on the chemical potential gradient and on the stress that can be induced solely by the diffusion as well as by the boundary conditions. The key results lie in the interpretation of the Navier-Lamé equation for the deformed regular crystal, where the concentrations are not uniform and ID occurs. The presented coupling of the Darken and CALPHAD methods with the momentum balance equation allows for quantitative analysis of the transport processes occurring on entirely different time scales. It is shown that the proposed method is effective for modeling transport processes in Fe-Ni-Cu alloys. We demonstrate the case of ID in a planar plate, and predict slower penetration and accumulation. The experimental results confirm theoretical predictions.

Effective strategies of metamodelling of industrial metallurgical processes

The main objective of the metamodelling is replacing the model of analysed process by its simple (with respect to the computation time) approximation. Metamodel gives a significant reduction of computation time of considered process simulation, as well as its further analysis (sensitivity analysis, optimization, etc.). The paper discusses the idea of metamodelling and compares the effectiveness of three techniques: Response Surface Methodology (RSM), Kriging method and Artificial Neural Network (ANN) applied to the benchmark functions. An example of the use of the considered metamodelling techniques in optimization of the problem of laminar cooling of rolled Dual Phase (DP) steel strips is presented. Metamodelling and optimization of a real industrial metal forming problems seems a novel approach in the field of research on Artificial Intelligence and Optimization practical applications.

Application of inverse analysis with metamodelling for identification of metal flow stress

Abstract The problem of effectiveness of the inverse algorithms used for identification of material model is investigated in the paper. Identification of flow stress models in metal forming processes is considered. This identification is usually performed by coupling the Finite element (FE) model with optimisation techniques which leads to long computing times. A proposition of application of the metamodel in the inverse analysis is presented in the paper. Metamodel is an alternative for the FE model. Artificial neural network was used as a metamodel of the axisymmetrical compression test. Experiments were performed on the Gleeble 3800 simulator for various materials and inverse calculations with the metamodel were performed. Validation of the results confirmed with higher degree of accuracy of the proposed approach. Dans cet article, on examine le problème d’efficacité des algorithmes inverses utilisés dans l’identification de modèle de matériau. On considère l’identification de modèles de contrainte d’écoulement dans les procédés de traitement du métal. Cette identification est habituellement effectuée en couplant le modèle d’EF à des techniques d’optimisation, ce qui mène à de longues durées de calculs. Dans cet article, on propose l’application du métamodèle dans l’analyse inverse. Le métamodèle est une substitution du modèle d’EF. On a utilisé le réseau neuronal artificiel comme métamodèle de l’essai de compression axisymétrique. On a effectué des expériences avec le simulateur Gleeble 3800 pour des matériaux variés et l’on a effectué des calculs inverses à l’aide du métamodèle. La validation des résultats a confirmé le très bon degré d’exactitude de cette approche.