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.     

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.     

Effect of hot working on flow behavior of Ti–6Al–4V alloy in single phase and two phase regions

Hot deformation behavior of the alloy Ti–6Al–4V was investigated via conducting hot compression tests at temperatures of 800–1150 °C and at strain rates, ranging from 0.001 s⁻¹ to 1 s⁻¹, at an interval of an order of magnitude. The apparent differences of flow stress curves obtained in dual phase α + β and single phase β regions were analyzed in term of different dependence of flow stress to temperature and strain rate and different microstructural evolutions. The values of strain rate sensitivity and apparent activation energy were obtained respectively as 0.20 and 530 kJ/mol for two phase microstructure. However, for single phase β microstructure they were approximated as 0.19 and 376 kJ/mol, respectively. It was found that in two phase region the values of strains corresponding to peak point, ε_p, and the highest rate of flow softening, ε^*, are almost independent to Zenner–Hollomon parameter. In single phase region, ε_p and ε^* exhibited a direct relationship to Z parameter and the corresponding empirical equations were proposed.     

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.     

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.     

Constitutive modeling for the dynamic recrystallization evolution of AZ80 magnesium alloy based on stress-strain data

In order to improve the understanding of the dynamic recrystallization (DRX) behaviors of as-cast AZ80 magnesium alloy, a series of isothermal upsetting experiments with height reduction 60% were performed at the temperatures of 523 K, 573 K, 623 K and 673 K, and the strain rates of 0.01 s⁻¹, 0.1 s⁻¹, 1 s⁻¹ and 10 s⁻¹ on a Gleeble 1500 thermo-mechanical simulator. Dependence of the flow stress on temperature and strain rate is described by means of the conventional hyperbolic sine equation. By regression analysis, the activation energy of DRX in the whole range of deformation temperature was determined to be Q = 215.82 kJ mol⁻¹. Based on dσ/d? versus σ curves and their processing results, the ?ow stress curves for AZ80 magnesium alloy were evaluated that they have some characteristic points including the critical strain for DRX initiation (?_c), the strain for peak stress (?_p), and the strain for maximum softening rate (?*), which means that the evolution of DRX can be expressed by the process variables. In order to characterize the evolution of DRX volume fraction, the modified Avrami type equation including ?_c and ?* as a function of the dimensionless parameter controlling the stored energy, Z/A, was evaluated and the effect of deformation conditions was described in detail. Finally, the theoretical prediction on the relationships between the DRX volume fractions and the deformation conditions were validated by the microstructure graphs.     

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 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.     

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.     

Recrystallization of 30Cr2Ni4MoV ultra-super-critical rotor steel during hot deformation. Part I: Dynamic recrystallization

This paper presents an investigation that characterizes the evolution of the dynamically recrystallized structure of 30Cr2Ni4MoV ultra-super-critical rotor steel during hot deformation, as a starting point for studies of the static recrystallization (SRX) and the metadynamic recrystallization (MDRX) behaviors, by hot compression tests which are performed at the temperatures from 1243 K to 1543 K and strain rates from 0.001 s⁻¹ to 0.1 s⁻¹ on Gleeble-3500 thermo-mechanical simulator, and the corresponding flow curves are obtained. A third-order polynomial is then fitted to the work hardening region of each curve. The critical stress for initiation of dynamic recrystallization (DRX) can be calculated by setting the second derivative of the third order polynomial. By regression analysis, the activation energy in whole range of deformation temperature is determined to be Q = 368.45 kJ/mol. The complete DRX grain size (D_drx) of the test steel is a function of Zener-Hollomon parameter (Z) and is independent of the true strain. The relationship of D_drx and Z is found to be described in a form of power law function with an exponent of −0.24.     

Hot deformation behavior and microstructural evolution of Ag-containing 2519 aluminum alloy

The hot deformation behaviors of Ag-containing 2519 aluminum alloy were studied by isothermal compression at 300–500 °C with strain rates from 0.01 s⁻¹ to 10 s⁻¹. The microstructural evolution of the alloy was investigated using Polyvar-MET optical microscope and Tecnai G² 20 transmission electron microscope (TEM). It has been shown that the flow stress of the alloy increases with increasing the strain rate and decreasing the deformation temperature. When the strain rate is lower than 10 s⁻¹, the flow stress increases with increasing strain until the stress reached the peak value, after which the flow stress remains almost constant. This result indicates that dynamic recovery happens during deformation. When the strain rate is 10 s⁻¹ and the temperature is higher than 300 °C, serrated flow behavior is generally observed with the stress decreasing with increasing strain, a typical phenomenon of dynamic recrystallization.     

Effect of powder preparation technology on the hot deformation behavior of HIPed P/M nickel-base superalloy FGH96

In this paper, the hot deformation characteristics of P/M nickel-base superalloy FGH96 prepared by different powder preparation technologies were studied in the deformation temperature range from 1000 °C to 1100 °C and the strain rate range from 0.001 s⁻¹ to 1 s⁻¹ using hot compression tests. The peak stress vs. deformation temperature curves and the peak stress vs. strain rate curves were established, respectively. The results show that the specimens prepared by plasma rotation electric pole (PREP) powder were more sensitive to deformation temperature and strain rate. On the basis of the dynamic material model, the processing maps for hot working were developed. The activation energies and Zener-Hollomon parameters were obtained by linear statistical regression method. For the specimens prepared by PREP powder, the peaks of power dissipation mainly located in lower temperature domain (1000-1030 °C), and the efficiencies of power dissipation (EPD) obtained in the strain range from 0.1 to 0.7 were essentially similar. This indicated that strain had a slight influence on processing maps. For the specimens prepared by argon atomization (AA) powder, the effects of strain on EPD and instability domains were significant. The lower activation energies and Z values indicated that the workability of the specimens prepared by AA powder is better than that prepared by PREP powder. Moreover, it was found that effects of the heat treatment time on activation energy and Zener-Hollomon parameter were significant. With the increase of heat treatment time, the dislocation density and the volume fraction of precipitation phase gradually decreased. Microstructural observation demonstrated that the phenomenon of recrystallized grains coarsening existed in the specimens prepared by longer heat treatment time. The heat treatment time of the specimens prepared by AA powder should be appropriately shortened in order to prevent recrystallized grains coarsening.     

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.     

Forming behavior and workability of 6061/B4CP composite during hot deformation

Compression tests of 6061/B₄C_P composite have been performed in the compression temperature range from 300 °C to 500 °C and the strain rate range from 0.001 s⁻¹ to 1 s⁻¹. The flow behavior and processing map have been investigated using the corrected data to elimination of effect of friction. The processing maps exhibited two deterministic domains, one was situated at the temperature between 300 °C and 400 °C with strain rate between 0.003 s⁻¹ and 0.18 s⁻¹ and the other was situated at the temperature between 425 °C and 500 °C with strain rate between 0.003 s⁻¹ and 0.18 s⁻¹.The estimated apparent activation energies of these two domains, were 129 kJ/mol and 149 kJ/mol, which suggested that the deformation mechanisms were controlled by cross-slip and lattice self-diffusion respectively. The optimum parameters of hot working for the experimental composite were 350 °C - 0.01 s⁻¹ and 500 °C - 0.01 s⁻¹. In order to exactly predict dangerous damaging mechanism under different deformation conditions exactly, Gegel’s criterion was applied to obtain processing map in the paper. The result showed that the processing map used Gegel’s criterion can be effectively to predict the material behavior of the experimental composite.     

Deformation behavior in isothermal compression of the TC11 titanium alloy

Isothermal compression of the TC11 titanium alloy has been conducted on Gleebe-1500 hot-simulator at the deformation temperatures ranging from 1023 K to 1323 K, the strain rates ranging from 0.001 s⁻¹ to 10.0 s⁻¹, and the height reductions ranging from 50% to 70%. The effect of deformation temperature, strain rate and strain on the flow stress and the apparent activation energy for deformation is in depth analyzed. The experimental results show that the apparent activation energy for deformation in isothermal compression of the TC11 titanium alloy decreases with the increasing of strain. Moreover, the apparent activation energy for deformation in α + β two-phase region of the TC11 titanium alloy increases with the increasing of deformation temperature and decreases with the increasing of strain rate. A power dissipation efficiency map in isothermal compression of the TC11 titanium alloy is constructed at a strain of 0.6, in which three domains with higher power dissipation efficiency are observed, and deformation characteristics of the above-mentioned domains are analyzed. Finally, optical micrographs of the TC11 titanium alloy obtained on a Leica DMLP microscope showed the evidence of deformation in three domains.     

Prediction of flow stress in isothermal compression of Ti–6Al–4V alloy using fuzzy neural network

Isothermal compression of Ti–6Al–4V alloy at the deformation temperatures ranging from 1093 K to 1303 K with an interval 20 K, the strain rates ranging from 0.001 s⁻¹ to 10.0 s⁻¹ and the height reductions ranging from 20% to 60% with an interval 10% were carried out on a Thermecmaster-Z simulator. Based on the experimental results, a model for the flow stress in isothermal compression of Ti–6Al–4V alloy was established in terms of the fuzzy neural network (FNN) with a back-propagation learning algorithm using strain, strain rate and deformation temperature as inputs. The maximum difference and the average difference between the predicted and the experimental flow stress are 18.7% and 4.76%, respectively. The comparison between the predicted results based on the FNN model for flow stress and those using the regression method has illustrated that the FNN model is more efficient in predicting the flow stress of Ti–6Al–4V alloy.     

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.     

The influence of dynamic strain aging on resistance to strain reversal as assessed through the Bauschinger effect

The Bauschinger effect of three commercially produced medium carbon bar steels representing different microstructural classes with similar tensile strengths and substantially different yielding and work-hardening behaviors at low-strain was evaluated at room temperature and in situ at temperatures up to 361 °C. The influence of deformation at dynamic strain aging temperatures as a means to produce a more stable dislocation structure was evaluated by measuring the resistance to strain reversal during in situ Bauschinger effect tests. It was shown that the three medium carbon steels exhibited substantial increases in strength at dynamic strain aging temperatures with the peak in flow stress occurring at a test temperature of 260 °C for an engineering strain rate of 10⁻⁴ s⁻¹. Compressive flow stress data following tensile plastic prestrain levels of 0.01, 0.02 and 0.03 increased with an increase in temperature to a range between 260 °C and 309 °C, the temperature range where dynamic strain aging was shown to be most effective. The increased resistance to flow on strain reversal at elevated temperature was attributed to the generation of more stable dislocation structures during prestrain. It is suggested that Bauschinger effect measurements can be used to assess the potential performance of materials in fatigue loading conditions and to identify temperature ranges for processing in applications that utilize non-uniform plastic deformation (e.g. shot peening, deep rolling, etc.) to induce controlled residual stress fields stabilized by the processing at temperatures where dynamic strain aging is active.     

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.     

Post-welding formability of AZ31 magnesium alloy

The plastic flow behaviour and formability of friction stir welded AZ31 magnesium alloys were widely investigated. Flow curves were obtained in extended ranges of temperature (250–350 °C) and strain rate (0.001–0.1 s⁻¹) by means of uniaxial tensile tests; furthermore, forming limit curves were determined using the hemispherical punch method in the same range of temperature but with a constant crosshead speed of 0.1 mm/s. The results were compared with those obtained, under the same experimental conditions, on the base material. The flow stress levels of joint and base material are very similar up the peak of the flow curve although the equivalent strains at the peak and to failure are usually lower than those of base material. However, at the highest temperature and lowest strain rate investigated (350 °C and 0.001 s⁻¹), the flow behaviour of the welded joint tends to be similar to the one of the base alloy. Finally, formability of the friction stir welded material, evaluated in terms of forming limit curves, is usually lower than the one of the base material.