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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.

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.

The problem of proper identification of material model parameters is crucial for simulations of any material forming thermomechanical process and it directly affects the results of computations. Th...

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.

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.

Numerical modeling is an important tool assisting in the designing and optimization of the production technology. The highest predictive capabilities are offered by multiscale modeling. The most important limitation of its wide application is computational cost. One of possible solutions is application of metamodels for fine scale modeling. In this paper, a systematic approach to development of metamodels is presented. All necessary steps, analyzing the model, selecting the metamodel inputs and outputs, gathering the training and testing datasets, choosing a metamodelling technique, training and testing the metamodel are described with a scientific background and practical examples. Development of the exemplary metamodel, replacing thermodynamic modeling of precipitation kinetic is presented.

Two different formulations of the Cahn-Hilliard equations implemented in modern PETIGA library for isogeometric analysis simulations are dealt with. In the first formulation, fourth order strong form resulting in weak second-order formulation with cubic B-splines used for discretization is used. In the second formulation, a system of two-second order equations resulting in a first order weak formulation with quadratic B-splines used for discretization is used. The second formulation requires twofold unknowns but lower order B-splines. The computational costs of iterative solvers from PETSc library, showing that the two-field formulation, even with the larger number of unknowns, can be solved in lower computational cost are tested.

Local variations in chemical composition, i.e., compositional heterogeneities, play an important role in the thermodynamic stability and spatial distribution of phases in multiphase steels. The influence of heterogeneous elemental distribution on the resulting local microstructure and mechanical properties has been investigated in the present work. Two steels, one with dual-phase (DP) and one with complex-phase (CP) microstructure, were fabricated from the same cast but differently heat treated in the intercritical annealing regime to yield variations in local microstructure formation. The heterogenous distribution of C and Mn that exists on different length scales are quantified by a characterization approach correlating local chemistry, microstructure, and hardness by using electron probe microanalysis (EPMA), electron backscattered diffraction (EBSD), and nanoindentation. Mn was alternately enriched and depleted in bands parallel to the rolling direction caused by segregation during continuous casting. The local C content was closely associated with the spatial phase distribution resulting from intercritical annealing. In the DP steel, the heterogeneity of C distribution was more pronounced and martensite inherited from the Mn banding due to the lower intercritical annealing temperature. On the other hand, the CP steel, heat treated at higher intercritical annealing temperature, exhibited a more homogenous C distribution resulting in a homogeneous distribution of martensite. In addition to their varying partitioning into the present phases, C and Mn in large martensite islands tended to concentrate in the vicinity of phase interfaces and deplete in the center. Furthermore, chemical boundaries with the smooth transition in local properties were observed in the CP steel. The Mn segregation bands and their impact on martensite morphology and location is reflected by the local hardness distribution. The correlation between compositional heterogeneity, microstructure formation, and microscopic as well as macroscopic mechanical properties is discussed in detail.

We followed the Genetic Tambourine Man[1] Professor Nirupam Chakraborti since 2003 and tried to respond to his calls for special issues on applications of genetic algorithms in materials science, w...

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.

The objectives of the paper were twofold. The first was exploring possibility of fast and reliable modelling of phase transformations during cooling of steels, accounting for the evolution of the carbon concentration in the austenite. Existing discrete models require long computing times and their application to optimization of industrial processes is limited. Therefore, a model based on the modified JMAK equation was proposed. Control of the carbon concentration in the austenite during ferritic and bainitic transformations allowed to predict incomplete austenite transformation and occurrence of the retained austenite. Moreover, prediction of the onset of pearlitic transformation after the bainitic was possible. The model was validated by comparison the predictions with the results of physical simulations. Numerical simulations for various industrial processes were performed. Problem of the difference in the incubation time between isothermal and constant cooling rate tests was raised.

The paper deals with the problem of identification of microstructure evolution model on the basis of two-step compression test. Classical interpretation of this test assumes uniform fields of strains, stresses and temperatures in the deformation zone and calculates the coefficients in the model on the basis of force measurements in the second step. In the present paper the inverse approach was applied. Finite element (FE) simulations of the compression test were performed and local values of microstructural parameters were determined accounting for the inhomogeneity of deformation. Objective function was formulated as the Euclid norm for the error between measured and calculated forces for various interpass times. Coefficients in the microstructure evolution model were determined by searching for the minimum of the objective function. Optimized model was validated in simulations of plane strain compression tests.

In this paper we propose two formulations of Cahn-Hilliard equations, which have several applications in cancer growth modeling and material science phase-field simulations. The first formulation uses one C4 partial differential equations (PDEs) the second one uses two C2 PDEs. Finally, we compare the computational costs of direct solvers for both formulations, using the refined isogeometric analysis (rIGA) approach.

The domain of the presented work is the design of a computer advisory system which should offer support on general design of production cycle. The idea of functioning of the advisory system is related to the reuse of information gathered from previous processes of production design. The information on the design of entire production cycle is suggested to be split into fragments related to specific production phases in the whole manufacturing chain. The advisory system should provide the possibility of making use of diverse piece of information so as to obtain the full production cycle for a new product similar to others manufactured in the past. The idea of information processing is based on the data mining rules induction methods and is visualized with examples of fasteners manufacturing.

The paper deals with the identification of material model based on the internal variable. The model with one internal variable, which was average dislocation density, was considered. Identification was performed using inverse analysis (IA) of uniaxial compression tests. In this work IA was transformed to an optimization task and the goal function was defined as difference (in Euclid's norm) between measured and calculated parameters: loads in plastometric tests (used to identify flow stress) and stresses in stress relaxation tests (used to identify recrystallization kinetics). Exploring a possibility of making the identification more reliable by application the Sensitivity Analysis (SA) was the main objective of the work. The IA was preceded by SA of the model output with respect to the model parameters to select an efficient optimization algorithm and/or eliminate local minima. Selected results of identification for different materials are presented in the paper, as well.

The development of the best manufacturing technology for fasteners was the subject of this work. Physical and numerical simulations were used to evaluate various technological variants. Possibility of application of new generation bainitic steels was considered, as well. Improvement of exploitation properties was the objective of the optimization having in mind tool wear and manufacturing costs as constraints. Several fasteners were investigated but results for three parts, including Allen screw, screw anchors used to carry concrete plates are presented as a case study. Industrial trials were performed and confirmed correctness of the designed manufacturing technology.

Although Mg alloys possess many attractive properties, the use of Mg alloys has been limited due to their extremely poor corrosion resistance. In the authors' previous study, they have developed a new process for Mg/Al cladding by hot extrusion with a convex die. In the extrusion process, it was found that the thickness uniformity of the Al coating layer can be controlled by changing the die angle. However, the optimal condition of the extrusion and the influences of extrusion parameters on the coating thickness uniformity remain unclear. In this study, therefore, the sensitivity analysis has been performed in order to evaluate the influences of extrusion parameters on the coating thickness uniformity. The sensitivities of the following five parameters were evaluated: (1) initial thickness of the coating material plate, (2) extrusion temperature, (3) ram speed, (4) die angle, and (5) ratio of simulated flow stress to the experimental one for pure Al. In order to perform the sensitivity analysis, the process for Mg/Al cladding was modeled. The results from the extrusion model fairly agree with the experimental results. Thus, it can be said that the present model of Mg/Al cladding process is reliable. From the sensitivity analysis, it was found that the initial thickness of the coating material plate and die angle influence on the uniformity most. The extrusion temperature, ram speed, and flow stress ratio do not have significant influences.

Statistically Similar Representative Volume Element (SSRVE) is used to simplify computational domain for microstructure representation of material in multiscale modelling. The procedure of SSRVE creation is based on optimization loop which allows to find the highest similarity between SSRVE and an original material microstructure. The objective function in this optimization is built upon computationally intensive numerical methods, including simulations of virtual material deformation, which is very time consuming. To avoid such long lasting calcu- lations we propose to use the data farming approach to identification of SSRVE for Advanced High Strength Steels (AHSS) characterized by multiphase microstructure. The optimization method is based on a nature inspired approach which facilitates distribution and parallelization. The concept of SSRVE creation as well as the software architecture of the proposed solution is described in the paper in details. It is followed by examples of the results obtained for the identification of SSRVE parameters for DP steels which are widely exploited in modern automotive industry. Possible directions for further development as well as possible industrial applications are described in the conclusions.

Application of sensitivity analysis in optimization of process parameters of production processes for innovative materials, e.g. dual phase steel, requires deterministic model of thermomechanical processes and large datasets that covers whole surface of results. Difficulties in optimization of process parameters correspond with large number of control variables, which should be considered in the technology design. Furthermore, conduction of such analysis takes the great computational cost. Presented work concerns possibility of application of regression trees, especially CART model, in preliminary analysis for sensitivity analysis. Use of data mining algorithms enables acquiring of preliminary, rough results: relationships among parameters of the hot rolling process of dual phase steel strips and rules of optimization of this process, it also does not require any apriori knowledge about thermomechanical processes.

Product properties for innovative materials, e.g. dual phase steels, require precise control of production processes. Difficulties in optimization of process parameters correspond with large number of control variables, which should be considered in the technology design. Sensitivity analysis allows evaluating the importance of all process inputs on the final properties of material. Information on the most important inputs is crucial for further design of the process. Application of sensitivity analysis requires detailed knowledge of the process phenomena as well as the definition of the mathematical model of the thermomechanical process. Furthermore, some sensitivity analysis algorithms are of the high computational cost. Presented work concerns possibility of the application of data exploration approach in evaluation of the importance of process inputs as the alternative for sensitivity analysis. Use of data mining algorithms eliminates necessity of mathematical model development, it also does not require any apriori knowledge about the process. Authors presents the comparison of sensitivity analysis and data exploration approach in evaluating relationships between inputs and outputs of the hot rolling for dual phase steel strips. The presented approach and the perspectives of the practical application could lead to significant decrease of time necessary for the computations of process design. The theoretical considerations are supplemented with the results of both types of analysis.

The manuscript is about the design of the thermal cycle for heat treatment of rails. Optimization methods were applied with the objective function formulated as the maximum of the wear resistance which was related to the hardness of the rail head running surface. The finite element model of controlled cooling of rails coupled with microstructure evolution model was used to solve direct problem. Microstructure is directly related to the rolling surface hardness. The model predicts temperature field during cooling, kinetics of phase transformations, microstructural parameters, and mechanical properties of the product. Sensitivity analysis was applied to select the process parameters with the largest influence on the objective function. The following parameters were selected as the optimization variables: time of the 1st stage of fast cooling by the rail head immersing in the polymer solution, time of the second stage of cooling in air, depth of the immersion in the polymer solution, and heat transfer coefficient between the rail head and the polymer solution. As a result of the sensitivity analysis, the best thermal cycle was designed.

Manufacturing of dual phase (DP) steels products is a complex process. Application of special thermal cycles during continuous annealing is one of the methods of obtaining DP microstructures. Development and validation of the numerical model for the continuous annealing of DP steels was the objective of the paper. Experimental part include dilatometric tests and physical simulations of various thermal cycles characteristic for the continuous annealing. The former were combined with the inverse analysis and were used for identification of the model. The latter supplied data regarding microstructure and properties after various annealing cycles. Numerical tests of the model confirmed its good predictive capabilities.

Improvement of the efficiency of the inverse analysis (IA) for various material tests was the objective of the paper. Flow stress models and microstructure evolution models of various complexity of mathematical formulation were considered. Different types of experiments were performed and the results were used for the identification of models. Sensitivity analysis was performed for all the models and the importance of parameters in these models was evaluated. Metamodels based on artificial neural network were proposed to simulate experiments in the inverse solution. Performed analysis has shown that significant decrease of the computing times could be achieved when metamodels substitute finite element model in the inverse analysis, which is the case in the identification of flow stress models. Application of metamodels gave good results for flow stress models based on closed form equations accounting for an influence of temperature, strain, and strain rate (4 coefficients) and additionally for softening due to recrystallization (5 coefficients) and for softening and saturation (7 coefficients). Good accuracy and high efficiency of the IA were confirmed. On the contrary, identification of microstructure evolution models, including phase transformation models, did not give noticeable reduction of the computing time.

The paper deals with the problem of identification of microstructure evolution model on the basis of two-step compression test. This test is characterized by non-uniform fields of strains, stresses and temperatures in the deformation zone. Therefore, the inverse approach with finite element model for the experiment – direct problem, was applied to eliminate the influence of these inhomogeneities. Inverse solution for two-step compression test is time consuming. Thus, sensitivity analysis was performed and an influence of the parameters of the microstructure model on the goal function defined in the inverse solution was evaluated. Data generated for sensitivity analysis was reused in the inverse approach to reduce the computation costs of identification.

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 probleme d’efficacite des algorithmes inverses utilises dans l’identification de modele de materiau. On considere l’identification de modeles de contrainte d’eco...

The general objective of the present work was to perform numerical tests for the inverse analysis of various plastometric tests. Uniaxial compression, plane strain compression and ring compression were investigated for different materials. The experimental results, in the form of load vs. displacement measurements carried out in two laboratories for various sample dimensions, were used as input for inverse calculations. As a result, a large number of data was obtained and the comparison of flow stress values determined in various tests and in various laboratories was possible. The capabilities of the inverse analysis as well as the influence of the method of testing on the material properties were examined. It is shown, in general, that when the inverse analysis is applied to the interpretation of the plastometric tests, the properties of the material are insensitive to the method of testing and to the sample dimensions.

As mentioned, searching for a balance between accuracy of modeling and efficiency of metals processing simulations is the overall objective of this book. Majority of the content deals with various aspects and possibilities of increasing the accuracy and at the same time decreasing the computing costs. However, it has to be pointed out that modeling of materials processing requires not only solutions of the family of differential and/or algebraic equations as presented in Chapter 3 but also proper definition of boundary and initial conditions. Boundary conditions in metal forming usually describe friction or the transfer of heat and forces at the contact zone. Initial conditions define the behavior of the workpiece before and during formation. Identification of material models and boundary conditions is usually performed using inverse analysis of experimental tests and also requires long computing times but is of importance from computational accuracy point of view. Possibilities of making inverse analysis more efficient are discussed in the present chapter. Tests performed to identify material models are briefly described in the first part. Testing techniques are discussed with their advantages and disadvantages. Examples of application of inverse analysis to interpretation of these tests are presented in the second part. The results of the tests are examined and empirical and mathematical models presented in Chapter 3 are identified, which allows further use of the data. The particular emphasis is put on presenting possibilities to decrease the computing costs.

The multiscale modeling of phenomena occurring across various length and time scales is becoming more and more important in analysis of material behavior during plastic deformation. It can be even stated that capturing the multiscale nature of deformation is presently one of the major challenges in contemporary computational mechanics of materials. The methods to cope with this challenge are usually classified into two groups: upscaling methods and concurrent multiscale computing.

In the modeling of materials processing definition of the computational domain is crucial for computational costs of the model. On the one hand, this domain should reproduce accurately materials granular microstructure including grains, grain boundaries, and phases. On the other, accounting for all these features causes significant increase of the computing costs.

Computer aided design of materials processing is common now. Beyond one step forming operations, also whole manufacturing chains can be simulated. Conventional optimization problems for the manufacturing cycles are based on simulations of various variants of several processes according to the applied optimization technique. In the industrial problems finite element (FE) simulations are usually used for calculations of the objective function, which usually consists of dimensional accuracy of products and their in use properties, as well as tool life. Thus, solution of the optimization task is costly and there is a continuous search for alternative methods. The generic process models were proposed by Behrens et al. Application of metamodeling is possible, as well (see Section 2.1.2 of this book). These solutions improved the efficiency of optimization but the costs are still high. A new approach to solve optimization problem was proposed based on dynamic analysis of behavior in a group of coexisting agents. Review of the cited publications shows that various modeling techniques can be used, from advanced multiscale numerical models to the artificial neural networks. It is pointed out in the introduction to this book that selection of an adequate model to a particular simulation task is crucial for the efficiency of the optimization procedure. Thus, the selected examples of the case studies showing search for a compromise between predictive capabilities and computing costs of materials processing models are presented in the following sections of the book. The manufacturing chains for automotive part, pearlitic steel rails, and fasteners were considered.