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The need for a reliable prediction of the distribution of microstructural parameters in metallic materials during processing was the motivation for this work. The model describing the evolution of dislocation populations, which considers the stochastic aspects of occurring phenomena, was formulated. The validation of the presented model requires the application of proper parameters corresponding to the considered materials. These parameters have to be identified through the inverse analysis, which, on the other hand, uses optimization methods and requires the formulation of the appropriate objective function. In our case, where the model involves the stochastic parameters, it is a crucial task. Therefore, a specific form of the objective function for the inverse analysis was developed using a measure based on histograms. The elaborated original stochastic approach to modeling the phenomena occurring during the thermomechanical treatment of metals was validated on commercially pure copper and selected multiphase steel.

The paper deals with the new approach to the optimization of the pearlitic rail’s head hardening process aimed at balancing the relation between strength and ductility of the head running surface. In the industrial process, efforts have been undertaken so far to maximize the hardness of the rail’s head while maintaining its pearlite structure, resulting in obtaining enhanced wear resistance and resistance to the contact fatigue defects initiation. The new approach, described in this paper, aims at designing the head hardening process enabling achievement of the high hardness of the running surface combined with high ductility expressed in terms of the total elongation. To achieve this aim of the investigation, a computer program was developed capable of predicting the occurrence of the phase transformations during rail head cooling and microstructure features after cooling. The program was linked with dedicated inverse module enabling the adjustment of the cooling conditions to achieve the required state of the pearlitic structure.

Enhancing strength-ductility synergy of materials has been for decades an objective of research on structural metallic materials. It has been shown by many researchers that significant improvement of this synergy can be obtained by tailoring heterogeneous multiphase microstructures. Since large gradients of properties in these microstructures cause a decrease of the local fracture resistance, the objective of research is to obtain smoother gradients of properties by control of the manufacturing process. Advanced material models are needed to design such microstructures with smooth gradients. These models should supply information about distributions of various microstructural features, instead of their average values. Models based on stochastic internal variables meet this requirement. Our objective was to account for the random character of the recrystallization and to transfer this randomness into equations describing the evolution of dislocations and grain size during hot deformation and during interpass times. The idea of this stochastic model is described in the paper. Experiments composed of uniaxial compression tests were performed to supply data for the identification and verification of the model in the hot deformation and static recrystallization parts. Histograms of the grain size were measured after hot deformation and at different times after the end of deformation. Identification and validation of the model were performed. The validated model, which predicts evolution of heterogeneous multiphase microstructure, is the main output of our work. The model was implemented in the finite element program for hot rolling of plates and sheets and simulations of these processes were performed. The model’s capability to compare and evaluate various rolling strategies are demonstrated in the paper.

A novel criterion for microcrack resistance of multi-phase steels based on property gradient maps is proposed. Two industrial sheets of steel were processed to obtain dual-phase and complex-phase microstructures with exactly the same chemical composition. Experimental investigations showed characteristic differences for the tensile tests, hole expansion and the local plastic behavior during deformation. An innovative full-field modeling approach that explicitly predicts mechanical property gradients as a function of microstructural gradients during forming was developed and validated. This allowed to form a new criterion for evaluation of structure–property relationship in nano-structured multi-phase steels and can reveal the formability limitations.

Development of a reliable model of phase transformations in steels presents significant challenges, not only metallurgical but also connected to numerical solutions and implementation. The model proposed in this paper is dedicated to austenitic transformation during heating and ferritic transformation during cooling. The goal was to find a solution which allows for the decreasing of computing time without noticeable decreasing the accuracy and reliability of the model. Proceedings to achieve this goal were twofold. Statistically Similar Representative Volume Element was used as a representation of the microstructure. It allowed for the reducing of the complexity of the computational domain. For the purpose of the model, carbon diffusion was assumed to be the main driving force for both transformations. A coupled finite element–level set method was used to describe growth of a new phase. The model was verified and validated by comparing the results with the experimental data. Numerical tests of the model were performed for the industrial intercritical annealing process.

Major, recent developmental trends in the field of metal forming are presented in the paper both from experimental and numerical point of view. First, progress made in metal forming processes such as: rolling of long flat products, cross wedge rolling, open die forging, die forging, extrusion, drawing, and stamping are addressed. Then, the study provides information on the current trends in the application of numerical modeling in the field of metal forming. Presented discussion of the particular issues, is confronted with the authors’ own, recently elaborated, solutions.

The need for fast mean field models describing phase transformations in varying temperatures was the motivation for the research. The aim was to propose an austenite-ferrite transformation model wh...

Selection of the best model for simulation of manufacturing processes of pearlitic steel rails was the objective of the paper. Achieving a proper balance between its predictive capabilities and computing costs was used as a criterion. Review of the pearlitic transformation models was performed and modification of the JMAK equation was selected for further analysis. Empirical models were developed to describe microstructure and mechanical properties of rails. Dilatometric tests were performed to supply data for identification of the phase transformation model. Physical simulations of various thermal cycles were performed to validate and verify the models. Finite element (FE) simulations of the hot rolling provided distributions of the temperature and the austenite grain size at the cross section of the rail, which were used as an input for modelling of phase transformations during cooling. Accelerated cooling by a cyclic immersion of the rail head in the polymer solution was considered as a case study. Performed simulations confirmed good predictive capabilities of the model.

The objective of the paper was to describe the concept of a virtual, digital equivalent to a physical process. The basic idea of the virtual counterpart for the process called a digital twin is described first. Following this the hybrid computer system dedicated to the design of the optimal manufacturing technology for thin steel strips is presented. The models used in the system and the database are described. Numerical tests showing capabilities of the system recapitulate the work. 1.

Selection and development of distribution functions (descriptors) for the complex phase steels is described in the paper. The objective was to design the multiphase microstructure with smooth gradients of microstructural features, which will prevent deterioration of local ductility of dual phase steels during stretch-forming process. Sensitivity analysis of descriptors with respect to microstructural parameters is described. Identification of descriptors based on experimental data was performed. The descriptors of complex phase microstructure were defined in the form of distribution functions.

Evaluation of the effect of precipitation on mechanical properties of Advanced High Strength Steel strip was the objective of the project. Physical simulations of the multipass rolling were performed in plane strain compression. Different pass schedules were applied to investigate the influence of strain accumulation during the last two deformations on the subsequent microstructure and product properties. Various coiling temperatures were applied and an effect of precipitation in the coil was investigated. VirtRoll computer system, which is a digital twin of the full scale mill, was applied to reproduce investigated hot rolling routes.

The development and identification of the complex microscale austenite to ferrite transformation model during continuous cooling based on the Cellular Automata method and DigiCore library is the main goal of the work. The model is designed to predict phase transformation from a fully austenitic range and involves nucleation of ferrite grains with their further growth. The major driving force for the CA grain growth is based on the carbon concentration differences across the microstructure. The model parameters are identified with the inverse analysis method with the goal function defined on the basis of the dilatometric investigation. The basic assumption of the developed model, experimental procedure, as well as subsequent identification stages, are presented within the work.

The paper describes physical and numerical simulations of a manufacturing process composed of hot forging and controlled cooling, which replace the conventional heat treatment technology. The objective was to investigate possibilities and limitations of the heat treatment with the use of the heat of forging. Three steels used to manufacture automotive parts were investigated. Experiments were composed of two sets of tests. The first were isothermal (TTT) and constant cooling rate (CCT) dilatometric tests, which supplied data for the identification of the numerical phase transformation model. The second was a physical simulation of the sequence forging-cooling on Gleeble 3800, which supplied data for the validation of the models. In the numerical part, a finite element (FE) thermal-mechanical code was combined with metallurgical models describing recrystallization and grain growth during forging and phase transformations during cooling. The FE model predicted distributions of the temperature and the austenite grain size in the forging, which were input data for further simulations of phase transformations during cooling. A modified JMAK equation was used to calculate the kinetics of transformation and volume fraction of microstructural constituents after cooling. Since the dilatometric tests were performed for various austenitization temperatures before cooling, it was possible to include austenite grain size as a variable in the model. An inverse algorithm developed by the authors was applied in the identification procedure. The model with optimal material parameters was used for simulations of hot forging and controlled cooling in one of the forging shops in Poland. Distributions of microstructural constituents in the forging after cooling were calculated. As a consequence, various cooling sequences during heat treatment could be analyzed and compared.

Computer system for the design of technology of the manufacturing of pearlitic and bainitic rails was presented in this paper. The system consists of the FEM simulation module of thermal–mechanical phenomena and microstructure evolution during hot rolling integrated with the module of phase transformation occurring during cooling. Model parameters were identified based on dilatometric tests. Physical simulations, including Gleeble tests, were used for validation and verification of the models. In the case of pearlitic steels, the process of subsequent immersions of the rail head in the polymer solution was numerically simulated. The objective function in the optimization procedure was composed of minimum interlamellar spacing and maximum hardness. Cooling in the air at a cooling bed was simulated for the bainitic steel rails and mechanical properties were predicted. The obtained results allowed us to formulate technological guidelines for the process of accelerated cooling of rails.

The paper demonstrates the capability of the developed phase transformation model to design the cooling conditions in the Stelmor process allowing for obtaining different types of microstructures in wire rod of 32CrB4 steel. The model based on modified JMAK equation was developed using the results of the tests conducted in a DIL 805 A/D/T dilatometer. The model is composed of sub-models of ferritic, pearlitic, bainitic and martensitic transformations. Its predictive capability was confirmed in industrial conditions by performing trials with different settings of fans involved in the cooling process on the Stelmor line of CMC Poland. Excellent performance of the model was achieved through the modification of commonly used equations which allows accurate predictions of the phase transformations start and finish temperatures, as well as volume fraction of microstructural constituents, in a wide range of cooling rates. It was demonstrated that the model can effectively be applied to design the cooling conditions in the Stelmor process, which will result in the required microstructural composition of the wire rod.

Accuracy of phase transformation models depends on the correctness of coefficients evaluation, adequate to the investigated material. Dilatometric tests combined with the inverse analysis are used to perform identification. Since the problem is nonlinear, analytical approach is not possible and the inverse solution is transferred into the optimization task. It leads to difficulties typical for optimization of multivariable function such as local minima and lack of proof of the uniqueness. The problem of the effectiveness and uniqueness of the inverse algorithms used for identification of phase transformation models for steels was investigated for two models. The first was a modified JMAK (Johnson–Mehl–Avrami–Kolmogorov) equation. The second was an upgrade of the Leblond equation, in which second-order derivative of the volume fraction with respect to time was introduced. In classical identification, the result for one transformation depends on the coefficients for the remaining transformations and optimization has to be performed several times until the compatibility between transformations is reached. To avoid encountered problems, complex optimization simultaneously for all coefficients in the models was performed. This approach was based on nature-inspired optimization techniques. Models with identified coefficients for various steels were validated in simulations of industrial processes of laminar cooling and continuous annealing of strips.

Evaluation of the possibility of substitution of steel part in the car body by the one made of AZ31 alloy was the main objective of the whole project. The objective of this paper was to determine the flow stress model, which accounts for the difference in the behavior of magnesium alloys during tension and compression. Tension tests on Zwick machine and compression tests on Gleeble 3800 were performed. Inverse analysis was applied to interpretation of the results of the tests. Separate numerical models for tension and compression were implemented into Abaqus software and simulations of the stamping were performed. Sensitivity of the results to the flow stress model was evaluated.

The analysis of the heat transfer in the magnesium coil in the radial direction by laboratory tests using a deformation simulator Bahr BTA 800 was proposed. Based on the obtained results, the equivalent thermal conductivity as the radial heat transfer was determined as a function of thickness, temperature and pressure, which was further integrated into the developed coil model. The validation of the model was carried out by the comparison of the calculated and measured temperatures during coil cooling. The results showed a good agreement between predicted and experimental data.

The approach based on solution of diffusion equation and multiple Level Set Method was proposed to model phase transformation phenomena occurring in Dual Phase (DP) steels during continuous annealing. Coupled solutions of the Second Fick Law and level set equations were used to create framework for dealing with a moving boundary problems. Diffusion and level set partial differential equations were solved using Finite Element (FE) method with local mesh refinement. Velocity function depended on the curvature of the interface and the carbon concentration gradient, was proposed to simulate grain growth. Statistically Similar Representative Volume Element with DP microstructure was generated. This element was subjected to plastic deformation in tension, compression and shear. Finally, homogenized properties of the DP steel were determine.