Microstructure analysis on IN 718 alloy round rod by FEM in the hot continuous rolling process

Based on physical metallurgy rules and experiential equations, models for microstructure analysis on IN 718 alloy in the round rod hot continuous rolling process has been developed using the finite element method (FEM) on the software ANSYS/LS-DYNA. The dynamic and metadynamic recrystallization models in and after deformation, the grain growth models in the compensated reheating process for IN 718 alloy are regressed, and corresponding processes are involved in these models. For a real rolling practice, the calculated central grain sizes were examined and are in good agreement with the measured ones. The element in the center of the workpiece is a typical one possessing the maximum of the effective strain, the temperature and the grain size in the rolling process. In the hot continuous rolling process, the relationship between the final grain size of the typical element and the inlet velocity of the first stand has been regressed by FE analysis, and the lower rolling speed is beneficial to the grain refinement.     

FEM analysis for residual stress prediction in hot rolled steel strip during the run-out table cooling

With the increasing demand of higher quality hot rolled strips, flatness defects occurred on the strips during the cooling process on the run-out table have received significant attention and should be considered in the online shape control model. Non-uniform temperature distribution and cooling across the strip width are the main reasons why the strip becomes unflatten after cooling process although the strip is rolled flat at the finishing mill. A thermal, microstructural and mechanical coupling analysis model for predicting flatness change of steel strip during the run-out table cooling process was established using ABAQUS Finite Element Software. In this model, Esaka phase transformation kinetics model was employed to calculate the phase transformation, and coupled with temperature calculation by means of the user subroutine program HETVAL. An elasto-plasticity constitutive model of the material, in which conventional elastic and plastic strains, thermal strain, phase transformation strain and transformation induced plastic strain were taken into account, was derived and realized using the user subroutine program UMAT. The conclusion that the flatness of the steel strip will develop to edge wave defect under the functions of the different thermal and microstructural behaviors across strip width direction during the run-out table cooling procedure was acquired through the analysis results of this model. The calculation results of this analysis model agree with the actual measurements and observation, therefore this model has a high accuracy. To better control the flatness quality of hot rolled steel strip, the shape compensation control strategy of slight center wave rolling is proposed based on the analysis result. This control strategy has been verified by actual measurements, and applied in actual production.     

Using a Facility Location Algorithm to Determine Optimum Cast Bloom Lengths

The dimensions of a bloom, which is a rectangular piece of steel, are critical for efficiently and effectively rolling the bloom into a finished structural shape (I-beam) for sale to the customer. To achieve maximum productivity and yield, the bloom size (thickness, width and length) to be rolled on a finishing mill into a structural shape must be determined by steel deformation experts. Suppose, for a particular finishing mill, these ‘rolled' blooms are all produced from a ‘cast' bloom of the same cross-section but with many different lengths. It is necessary to consolidate the many ‘cast' bloom length-metallurgical grade combinations to a number that can be managed by the casting operation and bloom stockyard without significantly impacting productivity and yield. An uncapacitated facility location problem formulation and algorithm were used to solve this problem. The way in which this approach was used to solve a real-world application is discussed.     

Optimization model of recrystallization hot rolling of titanium-vanadium steels

An optimization model was built based on the data of a pilot-scale (4.5 MN load, 225 KW power capacity) rolling mill to minimize the austenite grain sizes of Ti–V steels, which prevail at the instant of completion of the static recrystallization during hot rolling. A computer program developed for this optimization model was run for the rolling schedule, which is designed according to the complete recrystallization case. An energy optimization model developed previously was applied to different rolling schedules. The grain size optimization results demonstrate the effectiveness of these modelling approaches in terms of final grain size, final plate thickness, measured and computed roll force and torque values for both the design of the thermomechanical schedules which produce plate with fine-grained microstructures, high strength, and notch toughness and the temperature-reduction schedules of conventional controlled rolling.     

Microstructure evolution during rolling and annealing of mild steels

The process chain for components made of sheet metals consists of different forming techniques like hot rolling, cold rolling, and deep drawing as well as heat treatment operations like annealing. For the design and optimization of the whole manufacturing process and the final component behavior, a correct representation of the material behavior and the application of appropriate numerical simulation techniques are required. For our first investigations, a ferritic mild steel DC04, which is a typical steel grade for automotive applications, is analyzed. Therefore, specimens are taken out of a real manufacturing process after hot and cold rolling and after annealing. These specimens are intensively investigated in order to study the texture evolution and the development of other material properties, like yield function during the process chain. In this paper different homogenization methods are used to simulate the texture evolution during cold rolling. The results are compared concerning accuracy and efficiency of the considered models. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of mathematical model for microstructure and mechanical property of hot rolled wire rods

A set of integrated mathematical models for predicting microstructures evolution during hot rolling and controlled cooling of high carbon wire rods has been developed through laboratory research work and industrial validation experiments. It consists of many sub-models such as critical strain, static and dynamic recrystallization of austenite, fraction of transformed austenite, interlamellar spacing of pearlite, microstructure–property relations. Based on the models, a simulating software is programmed which can run on PC computers. The physical metallurgy process during hot rolling and controlled cooling including the temperature distribution, the evolution of austenite grains, fraction of transformation austenite, final microstructure and mechanical properties were predicted. The predicted results are agree well with measured of the industrial tests.     

Modeling steel rolling processes by fluid-like differential equations

We derive a fluid-dynamics model to describe high-volume steel rolling processes. We model steel rolling as a particle game where each particle corresponds to a piece of steel at a certain production stage. Based on a stochastic interpretation of the particle game we derive a kinetic equation as well as fluid-like limiting equations under suitable scaling of time. Numerical results on the fluid-like equation are presented.     

Optimization of elastic material parameters of sheet metal with FEMU and DIC

In this paper a deep-drawing sheet steel is characterized through tensile tests with samples taken in different angles to the rolling direction. The displacement field is recorded with an optical full-field measurement system and the deformation field is calculated by Digital Image Correlation (DIC). The orthotropic elastic material parameters are identified through an iterative parameter optimization via Finite Element Model Updating (FEMU). In this procedure the material parameters are modified in every iteration so that the numerically computed deformation field and forces match the measured values as well as possible. Depending on the objective function and the input values used in the optimization routine, global or only local minima exist. To show the convergence of the applied technique, two different optimization algorithms, one gradient-based and one gradient-free with different initial starting points were used. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of strain induced austenite-martensite transformation

Grain refinement due to phase transformation is an effective method for improving the mechanical properties of steel. An approach is proposed in the present work based on the FEM, for numerical simulation of the microstructure evolution as a result of hot rolling and subsequent cold torsion. Grain refinement in 304 stainless steel at four different technological schedules is considered. Results of numerical simulation are compared with experimental data. Coupling of the thermoplastic deformation with microstructure evolution is realized. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

LP modelling of the finishing hot rolling programme for low carbon steel coils

In this paper a mathematical model was developed to optimize the finishing rolling of hot rolled coils by increasing the productivity of the rolling programme, to help achieve the required level of quality assurance and to facilitate production planning and control in the hot rolling mill. A brief account of the technological and planning aspects of the hot rolling processes and mills relevant to strip steel is given. Linear (mixed integer) programming is used to formulate the objective function and the various types of constraints of the model. The model takes into consideration, the general aspects pertinent to hot rolling of low carbon steel and the characteristics of the hot rolling mills as stipulated by the operational codes and guidelines of the relevant establishments. Owing to the flexibility offered by linear programming the model can incorporate any modifications and/or additional requirements, if any, in case of other types of steel and/or other types of mills. The full modelling of the problem required the incorporation of some zero/one variable constraints. Owing to the complexity involved and the need to keep the model as simple as possible, it was decided to exclude these constraints and deal with them externally. HYPER LINDO PC was used to solve the programme. Using available data, in the case under consideration the model showed astonishing results in achieving the objectives. Taking into account the effect on the overall productivity as well as quality improvement, the investigation showed that a net improvement in conforming output to the effect of around 43%, could have been obtained had the model been used in the case under consideration.     

Modelling of heat affected zone in cylindrical steel elements surfaced by welding

Computational models of a temperature field in cylindrical steel elements surfaced by the following methods: controlled pitch, spiral welding sequence and spiral welding sequence with swinging motion of the welding head are presented in the paper. The lateral surface of regenerated cylindrical object, subjected to the welding heat source, has been treated as a plane rolled on cylinder and temperature field of repeatedly surfaced plain massive body was solved. Temperature rises, caused by overlaying consecutive welding sequences and self-cooling of areas previously heated, were taken into consideration in the solution. The computations of the temperature field for continuous casting steel machine roll made of 13CrMo4 steel were carried out.     

A Nonlinear Control Concept for Rolling Mills

This contribution is concerned with the nonlinear control of a temper rolling mill based on the exact input/output linearization method. The considered subsystem of the temper rolling plant consists of a four‐high mill stand with a hydraulic adjustment system, and bridle rolls in the entry and the exit section. The demand on the temper rolling process is to establish a certain elongation of the steel strip under the action of the roll force and certain predefined backward and forward strip tensions in order to achieve the desired material characteristics and surface properties of the rolled product. The nonlinear control concept to be presented is characterized by the fact that the torques of the bridle rolls are intended as control inputs for the elongation and master speed control, whereas the hydraulic adjustment system and the main mill drive are used to take effect on the strip tensions. After a brief review of the mathematical model of the mill we will focus on the multi‐input nonlinear tension control.     

Numerical investigation of microstructure evolution in metal forming processes

Grain size evolution and phase transformation during metal forming processes is investigated numerically by means of the Finite element method. Appropriate microstructure models are involved into the FEM code MSC.MARC. Material characteristics obtained by means of own experiments are used. Hot closed die forging and rod rolling are considered. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Variational Approach to Dynamic Recrystallization Using Probability Distributions

We investigate a model of dynamic recrystallization in polycrystalline materials. A probability distribution function is introduced to characterize the state of individual grains by grain size and dislocation density. Specifying free energy and dissipation within the polycrystalline aggregate we are able to derive an evolution equation for the probability density function via a thermodynamic extremum principle. Once the distribution function is known macroscopic quantities like average strain and stress can be calculated. For distribution functions which are constant in time, describing a state of dynamic equilibrium, we obtain a partial differential equation in parameter space which we solve using a marching algorithm. Numerical results are presented and their physical interpretation is given. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

提高优质碳素结构钢(20#)钢板质量的研究

本文运用正交试验方法 ,确定优质碳素结构钢 (2 0 # )钢板热轧工艺参数 ,实现控制 ,提高2 0 #钢板的综合机械性能和冷弯工艺性能 ,提高产品质量     

Solvability of a quasi-steady rolling problem for porous materials

A quasi-steady rolling problem with nonlocal friction, for porous rigid-plastic, strain-rate-sensitive and strain hardening materials, is considered. A variational formulation is derived, consisting of a variational inequality and two evolution equations, coupling the velocity, strain hardening and relative density variables. The convergence of a variable stiffness parameters method is proved, and existence and uniqueness results are obtained. An algorithm, combining this method with the finite element method, is proposed and used for solving an illustrative rolling problem.     

Simulation of Size Effects in Ferroelectric Materials using a Phase Field Model

An electro-mechanically coupled phase field model for domain evolution in ferroelectric materials is presented. The inner length scale introduced by the model gives rise to size effects, especially in the context of the poling behavior of polycrystals. Such size effects are investigated by 2D numerical simulations for barium titanate polycrystals. Ferroelectric hysteresis curves and coercive fields are calculated for two different transition conditions for the order parameter at the grain boundaries. The results show that there is a significant size effect for the investigated polycrystal systems. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The numerical analysis of the trapezoidal thread rolling process

The thread rolling is difficult technological process. Improve quality and contemporary reduce manufacture cost of the trapezoidal thread requires acquaintances of physical phenomena observed in the contact zone between rolls and deform work-pieces. Therefore, in this paper the physical and mathematical models of deformations (displacements and strains) and stress in the cold process of trapezoidal thread rolling, were developed. The process is considered as a geometrical and physical non-linear, initial as well as boundary value problem. The phenomena on a typical incremental step were described using a step-by-step incremental procedure, with an updated Lagrangian formulation. The state of strains was described by Green-Lagrange's tensor, while the state of stress by the second symmetrical Pioli-Kirchhoff's tensor. The object was treated as an elastic (in the reversible zone) and visco-plastic body (in non-reversible zone) with mixed hardening. The variational equation of motion in three dimensions for this case was proposed. Then, the finite elements methods (FEM) and dynamic explicit method (DEM) were used to obtain the solution. The application developed for in the ANSYS programme, which provides a complex time analysis for displacement, strains and stresses occurring in the object. The recommendations concern modeling the trapezoidal thread rolling process, where reduce degrees of freedom in numerical model is very important and provide convergence calculated results for maximum stress and strain values in the thread surface layer, were elaborated. The influence a various process conditions on the states deformation and stress for examples calculations, were presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Prediction of temperature distribution and phase transformation on the run-out table in the process of hot strip rolling

In this paper a mathematical model based on the finite element method and the Scheil additivity rule is presented for predicting the temperature distribution and phase transformation behavior on the run-out table during the hot strip rolling of a low carbon steel. The model considers the austenite to ferrite and pearlite transformations, the temperature-dependent material properties of the cooling austenite as well as the austenite work hardening effect on the kinetics of austenite transformation. To determine the validity of the model predictions, the time-temperature histories of a low carbon steel rod in different cooling media were measured and also hot rolling experiments were performed. Good agreement between the predictions and the experimental results indicates the reliability of the model.     

Error estimation,adaptivity and data transfer in enriched plasticity continua to analysis of shear band localization

In this paper, an adaptive FE analysis is presented based on error estimation, adaptive mesh refinement and data transfer for enriched plasticity continua in the modelling of strain localization. As the classical continuum models suffer from pathological mesh-dependence in the strain softening models, the governing equations are regularized by adding rotational degrees-of-freedom to the conventional degrees-of-freedom. Adaptive strategy using element elongation is applied to compute the distribution of required element size using the estimated error distribution. Once a new mesh is generated, state variables and history-dependent variables are mapped from the old finite element mesh to the new one. In order to transfer the history-dependent variables from the old to new mesh, the values of internal variables available at Gauss point are first projected at nodes of old mesh, then the values of the old nodes are transferred to the nodes of new mesh and finally, the values at Gauss points of new elements are determined with respect to nodal values of the new mesh. Finally, the efficiency of the proposed model and computational algorithms is demonstrated by several numerical examples.