Johannes Lohmar

Influence of Different Interpolation Techniques on the Determination of the Critical Conditions for the Onset of Dynamic Recrystallisation

Accurate modeling of dynamic recrystallization (DRX) is highly important for forming processes like hot rolling and forging. To correctly predict the overall level of dynamic recrystallization reached, it is vital to determine and model the critical conditions that mark the start of DRX. For the determination of the critical conditions, a criterion has been proposed by Poliak and Jonas. It states that the onset of DRX can be detected from an inflection point in the work hardening rate as a function of flow stress. The work hardening rate is the derivative of the flow stress with respect to strain. Flow curves are in general measured at a certain sampling rate, yielding tabular stress-strain data, which are per se not continuously differentiable. In addition, inevitable jitter occurs in measured flow curves. Hence, flow curves need to be interpolated and smoothed before the work hardening rate and further derivatives necessary for evaluating the criterion by Poliak and Jonas can be computed. In this paper, the polynomial interpolation originally proposed by Poliak and Jonas is compared to a new approach based on radial basis functions using a thin plate spline kernel, which combines surface interpolation of various flow curves and smoothing in a single step. It is shown for different steel grades that the interpolation method used has a crucial influence on the resulting critical conditions for DRX, and that a simultaneous evaluation by surface interpolation might yield consistent critical conditions over a range of testing temperatures.

Recent developments in modeling of hot rolling processes: Part I - Fundamentals

The numerical simulation of industrial rolling processes has gained substantial relevance over the past decades. A large variety of models have been put forward to simulate single and multiple rolling passes taking various interactions between the process, the microstructure evolution and the rolling mill into account. On the one hand, these include sophisticated approaches which couple models on all scales from the products microstructure level up to the elastic behavior of the roll stand. On the other hand, simplified but fast models are used for on-line process control and automatic pass schedule optimization. This publication gives a short overview of the fundamental equations used in modeling of hot rolling of metals. Part II of this paper will present selected applications of hot rolling simulations.

Assessment of flat rolling theories for the use in a model-based controller for high-precision rolling applications

© 2017 Author(s). In the electrical and medical industries the trend towards further miniaturization of devices is accompanied by the demand for smaller manufacturing tolerances. Such industries use a plentitude of small and narrow cold rolled metal strips with high thickness accuracy. Conventional rolling mills can hardly achieve further improvement of these tolerances. However, a model-based controller in combination with an additional piezoelectric actuator for high dynamic roll adjustment is expected to enable the production of the required metal strips with a thickness tolerance of +/-1 μm. The model-based controller has to be based on a rolling theory which can describe the rolling process very accurately. Additionally, the required computing time has to be low in order to predict the rolling process in real-time. In this work, four rolling theories from literature with different levels of complexity are tested for their suitability for the predictive controller. Rolling theories of von Karman, Siebel, Bland & Ford and Alexander are implemented in Matlab and afterwards transferred to the real-time computer used for the controller. The prediction accuracy of these theories is validated using rolling trials with different thickness reduction and a comparison to the calculated results. Furthermore, the required computing time on the real-time computer is measured. Adequate results according the prediction accuracy can be achieved with the rolling theories developed by Bland & Ford and Alexander. A comparison of the computing time of those two theories reveals that Alexanders theory exceeds the sample rate of 1 kHz of the real-time computer.

A new FE-model for the investigation of bond formation and failure in roll bonding processes

Roll bonding is a process to join two or more different materials permanently in a rolling process. A typical industrial application is the manufacturing of aluminum sheets for heat exchangers in cars where the solder is joined onto a base layer by roll bonding. From a modelling point of view the challenge is to describe the bond formation and failure of the different material layers within a FE-process model. Most methods established today either tie the different layers together or treat them as completely separate. The problem for both assumptions is that they are not applicable to describe the influence of tangential stresses that can cause layer shifting and occur in addition to the normal stresses within the roll gap. To overcome these restrictions in this paper a 2D FE-model is presented that integrates an adapted contact formulation being able to join two bodies that are completely separated at the start of the simulation. The contact formulation is contained in a user subroutine that models bond formation by adhesion in dependence of material flow and load. Additionally if the deformation conditions are detrimental already established bonds can fail. This FE-model is then used to investigate the process boundaries of the first passes of a typical rolling schedule in terms of achievable height reductions. The results show that passes with unfavorable height reduction introduce tensile and shear stresses that can lead to incomplete bonding or can even destroy the bond entirely. It is expected that, with adequate calibration, the developed FE-model can be used to identify conditions that are profitable for bond formation in roll bonding prior to production and hence can lead to shorter rolling schedules with higher robustness.

Investigation on Hardening and Softening Behavior of Steel after Rapid Strain Rate Changes

The design of industrial hot metal forming processes nowadays is mostly carried out using commercial Finite Element (FE) software codes. For precise FE simulations, reliable material properties are a crucial factor. In bulk metal forming, the most important material property is the materials flow stress, which determines the form filling and the necessary forming forces. At elevated temperatures, the flow stress of steels is determined by strain hardening, dynamic recovery and partly by dynamic recrystallization, which is dependent on strain rate and temperature. To simulate hot forming processes, which are often characterized by rapidly changing strain rates and temperatures, the flow stress is typically derived from flow curves, determined at arbitrary constant temperatures and strain rates only via linear interpolation. Hence, the materials instant reaction and relaxation behavior caused by rapid strain rate changes is not captured during simulation. To investigate the relevance of the relaxation behavior for FE simulations, trails with abrupt strain rate change are laid out and the effect on the material flow stress is analyzed in this paper. Additionally, the microstructure evolution due to the strain rate change is investigated. For this purpose, cylinder compression tests of an industrial case hardening steel are conducted at elevated temperatures and different strain rates. To analyze the influence of rapid strain rate changes, changes by one power of ten are performed at a strain of 0.3. As a reference, flow curves of the same material are determined at the initial and final constant strain rate. To investigate the microstructure evolution, compression samples are quenched at different stages, before and after the strain rate change. The results show that the flow curves after the strain rate change tend to approximate the flow curves measured for the final strain rate. However, directly after the strain rate change significant differences between the assumed instant flow stress and the real material behavior can be observed. Furthermore, it can be shown that the state of dynamic recrystallization at the time of the strain rate change influences the material response and relaxation behavior resulting in different slopes of the investigated flow curves after the strain rate change.

Extended Conical Tube-Upsetting Test to Investigate the Evolution of Friction Conditions

Friction has a significant influence on almost all metal forming processes. An in situ measurement of the friction stress within the forming process is in general difficult. Therefore, different experimental setups based on the indirect measurement of a friction dependent value are used to determine the friction conditions in laboratory experiments. For example the ring compression test and the conical tube-upsetting test are using the change of the geometrical shape of a specimen to investigate an averaged friction coefficient within the process. The essential advantages of conical tubes are the prevention of sticking friction and a homogeneous displacement and relative velocity along the contact surface depending on the friction conditions and the used cone angle. However, in both methods the development of the friction conditions during the upsetting process and the relative velocity between tool and workpiece are unknown. In this paper an extended setup of the conical tube-upsetting test is presented. The development of the specimen profile is detected by a laser sensor during the process at elevated temperatures. Experiments are conducted for different cone angles and the measured data is compared to FE-simulations. The time-dependent geometric data is used for the calculation of the relative displacement and relative velocity between tool and workpiece at the edge of the contact zone. A comparison with classical nomograms indicates a change of the friction conditions during the upsetting process. Finally, simulations are fitted to the experimental results by using a variable friction coefficient.

Model for texture evolution in cold rolling of 2.4 wt.-% Si non-oriented electrical steel

Iron loss and limited magnetic flux density are constraints for NGO electrical steel used in highly efficient electrical machinery cores. The most important factors that affect these properties are the final microstructure and the texture of the NGO steel. Reviewing the whole process chain, cold rolling plays an important role because the recrystallization and grain growth during the final heat treatment can be strongly affected by the stored energy and microstructure of cold rolling, and some texture characteristics can be inherited as well. Therefore, texture evolution during cold rolling of NGO steel is worth a detailed investigation. In this paper, texture evolution in cold rolling of non-oriented (NGO) electrical steel is simulated with a crystal plasticity finite element method (CPFEM) model. In previous work, a CPFEM model has been implemented for simulating the texture evolution with periodic boundary conditions and a phenomenological constitutive law. In a first step the microstructure in the cor...

Influence of transient strain rates on material flow stress and microstructure evolution

A comprehensive knowledge about the material flow stress is a key parameter for a reliable design of hot forming processes using Finite Element (FE) software codes. Due to the microstructure evolution caused by the interaction of hardening and softening phenomena that take place during hot forming operations, the material flow stress is influenced by strain rate and temperature. While transient strain rates and temperatures typically characterize the industrial forming processes, the flow curves used in FE simulations are normally determined at arbitrary constant temperatures and strain rates. To calculate the flow stress evolution in between the measured strain rates, FE programs use linear interpolation. Hence, the material relaxation behavior caused by the microstructure evolution during transient strain rates is not considered. Previous investigations by various authors have shown that for a rapid strain rate change by one order of magnitude significant deviations between measured flow stress and line...

Using Data Sampling and Inverse Optimization for the Reduction of the Experimental Effort in the Characterization of Hot Working Behaviour for a Case Hardening Steel

For the full characterization of the hot working behaviour of a given material a large number of laboratory experiments have to be performed. The experiments themselves are time consuming and the required specimen material can be quite expensive. With the increasing versatility of the testing machines, like dilatometry with easily variable temperatures, overthinking the classical approaches for materials characterization becomes expedient.In this paper a new technique for the reduction of the experimental effort is presented at the example of a 25MoCrS4 case hardening steel. To analyse the potential for the reduction of the experimental effort the classical approach of a full experimental test matrix is chosen. Here 55 flow curves with temperatures between 700 and 1200°C and strain rates from 0.01 to 100/s are experimentally determined. Then a semi-empirical model for strain hardening and dynamic recrystallization is fitted using an automated routine for parameter determination, taking all available flow curves into account. Subsequently, the number of flow curves used to fit the model parameters is gradually reduced. The model accuracy obtained with the reduced experimental data is compared to the initial fit. The natural decrease in accuracy with the use of less data compared to the gain due to the reduction of experimental effort is analysed. In addition optimal distribution of the sampling points in the experimental matrix for a reduced number of experiments is discussed. It is shown that less than a quarter of the full matrix is sufficient to reach accuracies comparable to using the full matrix. Using the vertices and symmetrical distribution of the data within the full experimental matrix allows a drastic reduction of experimental effort while maintaining the initial accuracy. The results suggest that it might be possible to reduce the costs and effort for material characterization by 50-80%.

Recent developments in modeling of hot rolling processes: Part II - Applications

This publication gives a short overview of current developments in modeling and simulation of hot rolling processes of metals at the Institute of Metal Forming of RWTH Aachen University. It is based on the fundamentals treated in Part I also contained in this conference issue. It features applications in the field of fast on-line models, where a fast multi-stage rolling model and an analytical approach for predicting the through-thickness shear distribution are presented. In addition, a new concept for sensitivity analysis by automatic differentiation is introduced and discussed. Finally, applications of rolling simulations in the field of integrated computational materials engineering are presented with a focus on TWIP and linepipe steels as well as aluminum.