Constitutive modeling for hot deformation behavior of T24 ferritic steel

Hot compression tests of T24 ferritic steel were carried out using Gleeble-3500 thermo mechanical simulator in the temperature range of 1323-1473 K with the strain rate of 0.01-10 s⁻¹ and the height reduction of 60%. The flow behavior of T24 ferritic steel was characterized based on analysis of the true stress-strain curves. Constitutive equations incorporating the effects of temperature, strain rate and strain have been developed to model the hot deformation behavior of T24 ferritic steel. Material constants α, n, ln A and activation energy Q in the constitutive equations were calculated as a function of strain. The flow stress values of T24 ferritic steel predicted by the proposed constitutive equations show a good agreement with experimental results, which indicated that the developed constitutive equations could give an accurate and precise prediction for the flow stress of T24 ferritic steel.     

Constitutive modeling of hot deformation behavior of H62 brass

The hot deformation behaviors of H62 brass are investigated by isothermal compression tests on a Gleeble 1500 thermal-mechanics simulator in the temperature range of 650-800 °C and the strain rate range of 0.01-10 s⁻¹. Most of the stress-strain curves exhibit a single peak stress, indicating a typical dynamic recrystallization (DRX) behavior of the alloy. Further microstructural observation confirms the occurrence of DRX behavior and the β → α phase transformation of H62 brass under the deformation conditions. A new constitutive equation coupling flow stress with strain, strain rate and deformation temperature is developed on the basis of the Arrhenius-type equation, in which the Zener-Hollomon parameter is modified by considering the compensation of the strain rate. In the constitutive equation, the material constants α, n, Q and A are found to be functions of the strain. The flow stress predicted by the constitutive equation shows good agreement with the experimental stress, which validates the efficiency of the constitutive equation in describing the deformation behavior of the material.     

Hot compressive deformation behavior of the as-quenched A357 aluminum alloy

The objective of the present work was to establish an accurate thermal-stress mathematical model of the quenching operation for A357 (Al–7Si–0.6Mg) alloy and to investigate the deformation behavior of this alloy. Isothermal compression tests of as-quenched A357 alloy were performed in the temperature range of 350–500 °C and at the strain rate range of 0.001–1 s⁻¹. Experimental results show that the flow stress of as-quenched A357 alloy decreases with the increase of temperature and the decrease of strain rate. Based on the hyperbolic sine equation, a constitutive equation is a relation between 0.2 pct yield stress and deformation conditions (strain rate and deformation temperature) was established. The corresponding hot deformation activation energy (Q) for as-quenched A357 alloy is 252.095 kJ/mol. Under the different small strains (≤0.01), the constitutive equation parameters of as-quenched A357 alloy were calculated. Values of flow stress calculated by constitutive equation were in a very good agreement with experimental results. Therefore, it can be used as an accurate thermal-stress model to solve the problems of quench distortion of parts.     

Hot working behavior of 2205 austenite-ferrite duplex stainless steel characterized by constitutive equations and processing maps

The hot deformation characteristics of the 2205 duplex stainless steel were analyzed using constitutive equations and processing maps. The hot compression tests were performed at temperature range of 950-1200 °C and strain rate of 0.001-1 s⁻¹. Flow stress was modeled by the constitutive equation of hyperbolic sine function. However, the stress exponent and strain rate sensitivity were different at low and high deformation temperatures where austenite and ferrite are dominant, respectively. It was recognized that strain at the peak point of flow curve increases with the Zener-Hollomon parameter, Z, at low temperature deformation while at high temperature deformation it actually decreases with Z. The power dissipation map, instability map and processing map were developed for the typical strain of 0.3. It was realized that dynamic restoration mechanisms could efficiently hinder the occurrence of flow instability at low and medium strain rates. Otherwise, the increase in strain rate at low and high temperatures could increase the risk of flow instability.     

Hot compressive deformation behavior of a new hot isostatically pressed Ni–Cr–Co based powder metallurgy superalloy

The hot compressive deformation behavior of a new hot isostatically pressed Ni–Cr–Co based powder metallurgy (P/M) superalloy was studied in the temperature range of 950–1150 °C and strain rate range of 0.0003–1 s⁻¹ using Gleeble-1500 thermal simulator. The dynamic recrystallization-time–temperature (RTT) curve was developed and the constitutive equation of flow stress during hot deformation was established. The results show that the flow stress decreases with increasing deformation temperature and decreasing strain rate. The flow stress represents as the characteristic of dynamic crystallization with the increasing of strain at the deformation temperatures lower than 1100 °C and strain rates higher than 0.0003 s⁻¹. The beginning time of dynamic crystallization has no linear relationship with deformation temperature in the condition of strain rate lower than 0.01 s⁻¹. Besides, the experiments verify that the hyperbolic sine model including the variable of strain reflects the changing law of flow stress during the hot deformation process.     

Constitutive analysis of the hot deformation behavior of Fe–23Mn–2Al–0.2C twinning induced plasticity steel in consideration of strain

In this study, constitutive analysis has been carried out on Fe–23Mn–2Al–0.2C twinning induced plasticity (TWIP) steel. For this purpose, hot compression tests were conducted on a Gleeble-3500 thermo-mechanical simulator in the temperature range of 900–1150 °C and the strain rate range of 0.001–20 s⁻¹. The effects of deformation heating and friction on flow stress were analyzed and corrected. On the basis of Sellars–Tegart–Garofalo equation, the strain-dependent constitutive equations of the steel were derived. The results show that deformation heating has a significant influence on the flow stress at lower temperatures and higher strain rates, while the frictional effect is slight even at the highest strain level investigated. Comparison of the calculated flow stress with the experimental data suggests that the developed constitutive equations can adequately describe the relationships between the flow stress, strain rate, temperature and strain of the steel during hot deformation. This is supported by a high correlation coefficient (R = 0.996) and a low average absolute relative error (AARE = 3.31%) for the entire deformation condition range investigated.     

Constitutive equations for high temperature flow stress prediction of Al-14Cu-7Ce alloy

In order to find material parameters of established Zener-Hollomon constitutive equations and predict high-temperature flow stress of Al-14Cu-7Ce alloy, isothermal hot compression tests were conducted using a Gleeble 3500 thermomechanical simulator at constant stain rates of 0.001, 0.01, 0.1 and 1 s⁻¹ and at temperatures ranging from 300 to 550 °C at intervals of 50 °C. The effects of strain rate and temperature on hot deformation behavior were represented by Zener-Hollomon parameter including Arrhenius term. Four material constants α, n, A and activation energy Q in the equations were calculated by compensation of strain. The results show that the proposed constitutive equations give a precise estimate for high temperature flow stress of Al-14Cu-7Ce alloy, which means it can be used for numerical simulation of hot deformation process and for choosing proper deformation parameter in engineering practice accurately.     

Constitutive modeling for flow behavior of GCr15 steel under hot compression experiments

The thermal compressive deformation behavior of GCr15 (AISI-52100), one of the most commonly used bearing steels, was studied on the Gleeble-3500 thermo-simulation system at temperature range of 950–1150 °C and strain rate range of 0.1–10 s⁻¹. According to the experimental results, the stress level decreases with increasing deformation temperature and decreasing strain rate. The peak stresses on the true stress–strain curves suggest that the dynamic softening of GCr15 steel occurs during hot compression tests. To formulate the thermoplastic constitutive equation of GCr15 steel, Arrhenius equation and the Zener–Hollomon parameter in an exponent-type equation were utilized in this paper. In addition, a modified Zener–Hollomon parameter considering the compensation of strain rate during hot compression was employed to improve the prediction accuracy of the developed constitutive equation. Analysis results indicate that the flow stress values predicted by the proposed constitutive model agree well with the experimental values, which confirms the accuracy and reliability of the developed constitutive equation of GCr15 steel.     

Constitutive analysis to predict high temperature flow stress in 20CrMo continuous casting billet

The experimental true strain–true stress data from isothermal hot compression tests on a Gleeble-1500D thermal simulation machine, across a wide range of temperatures (1173–1373 K) and strain rates (1.5 × 10⁻³–1.5 × 10⁻² s⁻¹), were employed to study the deformation behavior and develop constitutive equations of 20CrMo alloy continuous casting billet steel. The objective was to obtain the relational expression for deformation activation energy and material constants as a function of true strain and the constitutive equation for high temperature deformation of 20CrMo based on the hyperbolic sine form model. A correlation coefficient of 0.988 and an average absolute relative error between the experimental and the calculated flow stress of 8.40% have been obtained. This indicates that the constitutive equations can be used to accurately predict the flow behavior of 20CrMo alloy steel continuous casting billet during high temperature deformation.     

Constitutive modeling for hot deformation behavior of ZA27 alloy

The hot deformation behavior of ZA27 alloy was investigated in the temperature range of 473–523 K with the strain rates in the range of 0.01–5 s⁻¹ and the height reduction of 60 % on Gleeble-1500 thermo mechanical simulator. Based on the experimental results, constitutive equations incorporating the effects of temperature, strain rate, and strain have been developed to model the hot deformation behavior of ZA27 alloy. Material constants, α, n, ln A, and activation energy Q in the constitutive equations were calculated as a function of strain. The results showed that the stress–strain curves of ZA27 alloy predicted by the constitutive equations are in good agreement with experimental results, which validates the efficiency of the constitutive equations in describing the hot deformation behavior of the material.     

Prediction of hot deformation behaviour of Fe-25Mn-3Si-3Al TWIP steel

Hot deformation behaviour of Fe-25Mn-3Si-3Al twinning-induced plasticity (TWIP) steel was investigated by hot compression testing on Gleeble 3500 thermo-mechanical simulator in the temperature range from 800 to 1100 °C and at strain rate range from 0.01 to 5 s⁻¹, and the microstructural evolution was studied by metallographic observations. The results show that the true stress-true strain curves exhibit a single peak stress at certain strain, after which the flow stresses decrease monotonically until the end of deformation, showing a dynamic flow softening. The peak stress level decreases with increasing deformation temperature and decreasing strain rate, which can be predicted by the Zener-Hollomon (Z) parameter in the hyperbolic sine equation with the hot deformation activation energy Q of 405.95 kJ/mol. The peak and critical strains can also be predicted by Z parameter in power-law equations, and the ratio of critical strain to peak strain is about 0.7. The dynamic recrystallization (DRX) is the most important softening mechanism for the experimental steel during hot compression. Furthermore, DRX procedure is strongly affected by Z parameter, and the decreasing of Z value leads to more extensive DRX.     

Constitutive base analysis of a 7075 aluminum alloy during hot compression testing

In the field of deformation process modeling, the constitutive equations may properly represent the flow behavior of the materials. In fact, these valuable relationships are used as a calculation basis to simulate the materials flow responses. Accordingly, in the present study a hot working constitutive base analysis has been conducted on a 7075 aluminum alloy. This has been performed using the stress–strain data obtained from isothermal hot compression tests at constant strain rates of 0.004, 0.04 and 0.4 s⁻¹ and deformation temperatures of 450, 500, 520, 550 and 580 °C up to a 40% height reduction of the specimen. A set of constitutive equations for 7075 Al alloy have been proposed employing an exponent-type equation. The related material constants (i.e., A, n and α) as well as the activation energy Q for each temperature regime have been determined. The correlation of flow stress to strain rate and temperature can be deduced from the proposed equations. Furthermore, a change in deformation mechanism has been realized in the semi-solid temperature range. This has been related to the onset of lubricated flow mechanism during processing.     

Application of neural networks to predict the elevated temperature flow behavior of a low alloy steel

In order to study the workability and establish the optimum hot forming processing parameters for 42CrMo steel, the compressive deformation behavior of 42CrMo steel was investigated at the temperatures from 850 °C to 1150 °C and strain rates from 0.01 s⁻¹ to 50 s⁻¹ on Gleeble-1500 thermo-simulation machine. Based on these experimental results, an artificial neural network (ANN) model is developed to predict the constitutive flow behaviors of 42CrMo steel during hot deformation. The inputs of the neural network are deformation temperature, log strain rate and strain whereas flow stress is the output. A three layer feed forward network with 12 neurons in a single hidden layer and back propagation (BP) learning algorithm has been employed. The effect of deformation temperature, strain rate and strain on the flow behavior of 42CrMo steel has been investigated by comparing the experimental and predicted results using the developed ANN model. A very good correlation between experimental and predicted result has been obtained, and the predicted results are consistent with what is expected from fundamental theory of hot compression deformation, which indicates that the excellent capability of the developed ANN model to predict the flow stress level, the strain hardening and flow softening stages is well evidenced.     

Constitutive equations to predict high temperature flow stress in a Ti-modified austenitic stainless steel

The experimental stress–strain data from isothermal hot compression tests, in a wide range of temperatures (1123–1523 K) and strain rates (10⁻³–10² s⁻¹), were employed to develop constitutive equations in a Ti-modified austenitic stainless steel. The effects of temperature and strain rate on deformation behaviors were represented by Zener-Holloman parameter in an exponent type equation. The influence of strain was incorporated in the constitutive analysis by considering the effect of strain on material constants. The constitutive equation (considering the compensation of strain) could precisely predict the flow stress only at 0.1 and 1 s⁻¹ strain rates. A modified constitutive equation (incorporating both the strain and strain rate compensation), on the other hand, could predict the flow stress throughout the entire temperatures and strain rates range except at 1123 K in 10 and 100 s⁻¹. The breakdown of the constitutive equation at these processing conditions is possibly due to adiabatic temperature rise during high strain rate deformation.     

Flow stress and ductility of AA7075-T6 aluminum alloy at low deformation temperatures

The present investigation has been conducted in order to develop a rational approach able to describe the changes in flow stress of AA7075-T6 aluminum alloy with deformation temperature and strain rate, when this material is deformed at temperatures in the range of 123-298 K at strain rates in the range of 4 × 10⁻⁴ to 5 × 10⁻² s⁻¹. The constitutive formulation that has been advanced to accomplish these objectives represents a simplified form of the mechanical threshold stress (flow stress at 0 K) model developed at Los Alamos National Laboratory (Los Alamos, New Mexico, USA). Thus, it is assumed that the current flow stress of the material arises from both athermal and thermal barriers to dislocation motion. In the present case, the effect of three thermal barriers has been considered: solid solution, precipitation hardening and work-hardening. The first two effects do not evolve during plastic deformation, whereas the last one is considered as an evolutionary component of the flow stress. Such an evolution is described by means of the hardening law earlier advanced by Estrin and Mecking (1984) [20]. The law is implemented in differential form and is integrated numerically in order to update the changes in strain rate that occur during tensile tests carried out both at constant and variable crosshead speed. The extrapolation of the hardening components from 0 K to finite temperatures is accomplished by means of the model earlier advanced by Kocks (1976) [19]. The results illustrate that the constitutive formulation developed in this way is able to describe quite accurately both the flow stress and work-hardening rate of the material, as well as temperature and strain rate history effects that are present when deformation conditions change in the course of plastic deformation. The evaluation of the ductility of the alloy indicates that the changes in this property are mainly determined by deformation temperature rather by strain rate. When deformation temperature decreases from 298 to 123 K, ductility also decreases from ∼35 to 24%. However, despite these relatively small variations, significant changes in the fracture morphology could be observed on the fracture surfaces of the examined specimens, with the predominance of a mixed ductile-brittle mechanism at lower temperatures.     

A comparative study on modified Johnson Cook,modified Zerilli–Armstrong and Arrhenius-type constitutive models to predict the hot deformation behavior in 28CrMnMoV steel

The true stress-strain data from isothermal hot compression tests on Gleeble-3500 thermo mechanical simulator, in a wide range of temperatures (1173–1473 K) and strain rates (0.01–10 s⁻¹), were employed to establish the constitutive equations based on modified Johnson Cook, modified Zerilli–Armstrong, and strain-compensated Arrhenius-type models respectively to predict the high-temperature flow stress of 28CrMnMoV steel. Furthermore, a comparative study has been made on the capability of the three models to represent the elevated temperature flow behavior of this steel. Suitability of the three models were evaluated by comparing the accuracy of prediction of deformation behavior, correlation coefficient, average absolute relative error (AARE) and relative errors of prediction, the number of material constants, and the time needed to evaluate these constants. The results showed that the predicted values by the modified Johnson Cook and Zerilli–Armstrong models could agree well with the experimental values except under the strain rate of 0.01 s⁻¹. However, the strain-compensated Arrhenius-type model could track the deformation behavior more accurately throughout the entire temperature and strain rate range.     

The high temperature flow behavior modeling of AZ81 magnesium alloy considering strain effects

In the field of deformation process modeling, constitutive equations are invariably used as a calculation basis to estimate the materials flow responses. Accordingly, in the present study, a constitutive analysis has been conducted on the AZ81 magnesium alloy employing experimental stress–strain data obtained from isothermal hot compression tests. These tests had been done in the temperature range of 250–450 °C under strain rates of 0.003, 0.03 and 0.3 s⁻¹. The effects of the temperature and strain rate on hot deformation behavior have been expressed in terms of an exponent-type Zener–Hollomon equation. Furthermore, the influence of strain has been included in the constitutive equation by considering its effect on different material constants. Consequently, a model to predict the high-temperature flow behavior of AZ81 magnesium alloy has been established. The true stress–true strain curves predicted by the extracted model are in good agreement with the experimental results, thereby confirming the validity of the developed constitutive relation.     

Research on the hot deformation behavior of Ti40 alloy using processing map

The deformation behavior of a Ti40 titanium alloy was investigated with compression tests at different temperatures and strain rates to evaluate the activation energy and to establish the constitutive equation, which reveals the dependence of the flow stress on strain, strain rate and deformation temperature. The tests were carried out in the temperature range between 900 and 1100 °C and at strain rates between 0.01 and 10 s⁻¹. Hot deformation activation energy of the Ti40 alloy was calculated to be about 372.96 kJ/mol. In order to demonstrate the workability of Ti40 alloy further, the processing maps at strain of 0.5 and 0.6 were generated respectively based on the dynamic materials model. It is found that the dynamic recrystallization of Ti40 alloy occurs at the temperatures of 1050-1100 °C and strain rates of 0.01-0.1 s⁻¹, with peak efficiency of power dissipation of 64% occurring at about 1050 °C and 0.01 s⁻¹, indicating that this domain is optimum processing window for hot working. Flow instability domains were noticed at higher stain rate (≥1 s⁻¹) and stain (≥0.6), which located at the upper part of the processing maps. The evidence of deformation in these domains has been identified by the microstructure observations of Ti40 titanium alloy.     

Prediction of the critical conditions for initiation of dynamic recrystallization

Both the critical stress and strain for initiation of dynamic recrystallization (DRX) were determined using: (1) the strain hardening rate versus stress curve, (2) the natural logarithm of strain hardening rate versus strain curve, and (3) the constitutive equations. In order to perform these analyses, the behavior of a 17-4 PH stainless steel during hot compression test was investigated at temperatures of 950–1150 °C and strain rates of 0.001–10 s⁻¹. The first and second methods were found to be the best ones for determining the critical stress and strain, respectively. The Cingara constitutive equation was also used to model the flow curves up to the peak point and subsequently was used for predicting the critical strain. In summary, for 17-4 PH stainless steel, the DRX was found to start when the normalized stress and strain reach to the values of 0.89 and 0.47, respectively.     

A study on the hot workability of wrought NiTi shape memory alloy

The hot workability of a wrought 49.8 Ni-50.2 Ti (at pct) alloy was assessed using the hot compression tests in temperature range of 700-1000 °C, strain rate of 0.001-1 s⁻¹, and the total strain of 0.7. The constitutive equations of Arrhenius-type hyperbolic-sine function was used to describe the flow stress as a function of strain rate and temperature. The preferable regions for hot workability of the alloy were achieved at Z (Zener-Holloman parameter) values of about 10⁹-10¹³ corresponding to the peak efficiency of 20-30% in the processing map. However, a narrow area in the processing map including the deformation temperature of 1000 °C and strain rate of 1 s⁻¹ is inconsistent with the related Z values. A flow instability region was observed at high Z values. Further instability regions were found at low temperature of 700 °C and low strain rates of 0.01-0.001 s⁻¹ as well as at high temperature of 1000 °C and high strain rate of 1 s⁻¹. The apparent feature of flow curves, the low value of peak efficiency, the similarity between the estimated apparent activation energy of deformation and that of the self diffusion of Ti in Ni, and the stress exponent of higher than 5, suggested that dynamic recovery (DRV) is the dominant restoration phenomenon during the hot working of the alloy.