Transient Deformation Conditions Research Articles

An Incremental Physically-Based Model of P91 Steel Flow Behaviour for the Numerical Analysis of Hot-Working Processes

This paper is aimed at modelling the flow behaviour of P91 steel at high temperature and a wide range of strain rates for constant and also variable strain-rate deformation conditions, such as those in real hot-working processes. For this purpose, an incremental physically-based model is proposed for the P91 steel flow behavior. This formulation considers the effects of dynamic recovery (DRV) and dynamic recrystallization (DRX) on the mechanical properties of the material, using only the flow stress, strain rate and temperature as state variables and not the accumulated strain. Therefore, it reproduces accurately the flow stress, work hardening and work softening not only under constant, but also under transient deformation conditions. To accomplish this study, the material is characterised experimentally by means of uniaxial compression tests, conducted at a temperature range of 900–1270 °C and at strain rates in the range of 0.005–10 s−1. Finally, the proposed model is implemented in commercial finite element (FE) software to provide evidence of the performance of the proposed formulation. The experimental compression tests are simulated using the novel model and the well-known Hansel–Spittel formulation. In conclusion, the incremental physically-based model shows accurate results when work softening is present, especially under variable strain-rate deformation conditions. Hence, the present formulation is appropriate for the simulation of the hot-working processes typically conducted at industrial scale.

Incremental constitutive description of SAE 5120 steel deformed under hot-working conditions

The present communication describes the development of a novel incremental formulation for the determination of the flow stress of austenite, as a function of microstructure and deformation conditions. The proposed constitutive description is validated by employing the flow stress curves derived from axisymmetric compression tests performed with samples of a SAE 5120 steel, both under constant and transient deformation conditions. The hot-working response of this structural steel grade has been analyzed in the temperature range of 850 °C to 1200 °C, at strain rates in the range of 0.01 to 10 s−1. Under most deformation conditions dynamic recrystallization occurs and the evolution of the volume fraction recrystallized has been determined by an appropriate incremental form of the Johnson-Mehl-Avrami-Kolmogorov equation. The work-hardening rate of the material in the work-hardening and dynamic recovery transient has been described by an equivalent incremental form of the original differential equation advanced by Estrin and Mecking. It has been shown that this novel approach allows a very precise description of the experimental values of the flow stress of the material during deformation under constant deformation conditions, as well as the trend followed by this parameter under transient loading conditions. The latter analysis is conducted on the basis of the H parameter indicated by Abbod and co-workers. It has been determined that hot working of this steel grade at low temperatures in the austenitic range, followed by cooling to room temperature at moderate rates, leads to a significant refinement of the ferrite-pearlite microstructure, with ferrite grain sizes of less than 10 µm.

A New Constitutive Model for the High-Temperature Flow Behavior of 95CrMo Steel

The compressive deformation behavior of 95CrMo steel, one of the worldwide used hollow steels, was investigated on a Gleeble-3500 thermo-simulation machine within temperature range of 1073-1323 K and strain rate range of 0.1-10 s−1. Considering the influence of work-hardening, dynamic recovery and dynamic recrystallization, a new constitutive model for high-temperature flow stress was established in this paper. The calculated values predicted by the new constitutive model lie fairly close to the experimental values with a correlation coefficient (R) of generally above 0.99 and an average absolute relative error of 3.00%, proving a good predictability of the new constitutive model. Also, a modified Sellars-Tegart-Garofalo model (STG model) was introduced to verify the precision of the new constitutive model. Compared to the modified STG model, the new constitutive model has a higher accuracy, which implies it is a reliable tool for predicting flow stress at high temperatures not only under equilibrium state, but also under transient deformation conditions. Besides, the new constitutive model was proved still viable in the initial stage of plastic deformation where plastic strain is lower than 0.05.

A novel approach for modeling the flow stress curves of austenite under transient deformation conditions

A novel differential form of the integrated constitutive description earlier advanced by Jonas et al., for modeling the flow stress of austenite, is developed. The temperature and strain rate dependencies are introduced in the formalism through the temperature-dependent shear modulus of the material, the yield, saturation and steady-state stresses, as well as the time to achieve 50% dynamic recrystallization. The correlation between each of the above stresses and the Zener-Hollomon parameter is carried out by means of the Sellars-Tegart-Garofalo model employing the activation energy for the self-diffusion of Fe in austenite (Q=284kJmol−1). The proposed formalism involves the determination of the flow stress of the material by means of the numerical integration of three differential equations. In this way, it is possible to compute the flow stress both during the work-hardening and dynamic recovery stage, as well as from the onset of dynamic recrystallization up to the work softening transient and final achievement of the steady-state stress. Therefore, it is possible to predict the flow stress curves of austenite under both sharp and ramped transient loading conditions leading to the occurrence of dynamic recrystallization, a novel feature that cannot be accomplished by means of the early advanced model.

Constitutive description of Fe–Mn23–C0.6 steel deformed under hot-working conditions

As observed from the current literature, the vast majority of the constitutive models that have been proposed for the description of the changes in the high-temperature flow stress of high-Mn austenitic steels, in the course of plastic deformation as a function of deformation conditions, have been expressed in terms of the total applied strain to the material (ε), which, as indicated by Follansbee and Kocks, is not a valid state parameter. In order to overcome this disadvantage, which hinders the prediction of the changes in flow stress under transient deformation conditions, commonly found during industrial hot-working processes, a different constitutive description is proposed. The advanced approach is based on the temperature and strain rate description of three important parameters: yield stress, hypothetical saturation stress and actual steady-state stress, which is considered equal to the critical stress for the onset of dynamic recrystallization, as proposed by Jonas et al. This description is accomplished by means of the well established Sellars–Tegart–Garofalo model, employing a unique value of the apparent activation energy for hot-working determined from the analysis of the peak stress values, as proposed earlier by Glover and Sellars. The model also requires a description of the time for achieving 50% dynamic recrystallization, which is expressed as a function of deformation conditions by means of the simple parametric relationship also proposed by Jonas et al. This information is subsequently input into two evolution equations, which describe the change in the work-hardening and work-softening rates of the material, as a function of deformation conditions, either when the work-hardening is counterbalanced only by dynamic recovery or when it is counterbalanced by both dynamic recovery and dynamic recrystallization. The results reported in the present communication indicate that the proposed constitutive description is able to provide an accurate reproduction of the experimental flow stress values determined under constant deformation conditions, obtained by Wietbrock et al. However, the analysis of a hypothetical deformation schedule conducted under transient deformation conditions suggests that a second internal state variable, other than dislocation density, might be required for the improvement in the prediction of the corresponding stress–strain curves.

Physically based and neuro-fuzzy hybrid modelling of thermomechanical processing of aluminium alloys

Modelling of the microstructural evolution of aluminium alloys during thermomechanical processing is a desirable method for predicting the alloy's properties and designing the process variables to achieve the desired goals. A dynamic model has been developed in terms of the internal states variables of the process comprising the dislocation density, the subgrain size, and the misorientation between the subgrains. The developed model is based on a hybrid modelling technique known as grey-box modelling where intelligent models and physical equations are merged to predict the material properties with respect to the deformation conditions. The model predicts the evolution of the internal states variables under transient deformation conditions, as well as the static subsequent recrystallisation behaviour, nucleation of recrystallisation based on experimental results and quantitative metallurgical observations. In the model, the flow stress and recrystallisation behaviour are predicted with respect to temperature, strain rate and strain for different aluminium alloys providing a reasonable agreement with experimental data.

Microstructural modelling of aluminium alloys during thermomechanical processing

Abstract It is well-accepted that modelling of microstructural evolution of aluminium alloys during thermomechanical processing is highly desirable to predict product properties and/or to design process variables based on requirements for the properties. To do so, having soundly based physical models is of interest for both academic research and industrial practice. In the present paper, models for predicting the evolution of internal state variables such as internal dislocation density, subgrain size and misorientation between subgrains, and subsequent recrystallisation behaviour are developed for both constant and transient deformation conditions. In predicting the evolution of the internal state variables under transient deformation conditions, the internal ‘geometrically necessary’ dislocation density is related to the subgrain boundary dislocation density. In the model to predict static recrystallisation behaviour, nucleation of recrystallisation is initially discussed based on experimental results and quantitative metallographic observations. In the calculation of recrystallisation nucleation density, distribution of subgrain size and misorientation between subgrains are key parameters. The predicted evolution of internal state variables and subsequent recrystallisation kinetics and recrystallised grain size using the developed model are in reasonable agreement with experimental data.

The influence of transient deformation conditions on recrystallization during thermomechanical processing of an Al–1% Mg alloy

The recrystallization behaviour of an Al–1% Mg alloy has been investigated following hot deformation under varying strain-rate conditions. Significant differences in recrystallized grain size and recrystallization kinetics are observed following a decreasing strain rate, as compared with constant strain-rate tests. These differences reflect the microstructural transients, which are presented in an accompanying paper. It is shown that the data are reasonably consistent with a physically based internal state variable model for recrystallization. A feature of the modelling is the sensitivity analysis conducted, which indicates the degree of uncertainty in predicting recrystallization behaviour, and identifies the critical areas in which experimental effort should be concentrated.

The Influence of Transient Deformation Conditions on Strength, Microstructure and Recrystallisation during Thermomechanical Processing of an Aluminium Alloy Al-1% Mg

The Influence of Transient Deformation Conditions on Strength, Microstructure and Recrystallisation during Thermomechanical Processing of an Aluminium Alloy Al-1% Mg