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.     

Deformation behavior and constitutive model for high temperature compression of a newly type of Ni3Al‐based superalloy

In order to investigate the hot deformation mechanism of a newly development Ni₃Al‐based superalloy, hot compression tests at temperatures between 1100 °C–1250 °C and the strain rates of 0.001 s^?1–1.0 s^?1 were conducted. The results show that the curves of true stress‐strain indicate the thermal deformation is a typical dynamic recrystallization process, which the peak stresses and steady‐state stresses increase with decreasing temperatures and increasing strain rates. The softening mechanism is mainly dynamic recrystallization. The experimental data of peak stresses and steady‐state stresses is employed to calculate the constants in the Arrhenius equation. The steady‐state stresses are considered more reasonable for solving the parameters in the Arrhenius equation. Based on the constitutive equation obtained, the calculated values of steady‐state stresses match well with the experimental values at the strain rates of 0.001 s^?1, 0.01 s^?1 and 0.1 s^?1, whereas there exists much deviation at 1.0 s^?1. For the sake of accuracy of predicted results at 1.0 s^?1 strain rate, a modified Zener‐Hollomon parameter Z’ is introduced. The results show that the modified constitutive equations established in this study could well predict the value of steady‐state stress in hot deformation of the newly development Ni₃Al‐based alloy.     

Hot tensile deformation behaviors and constitutive model of 42CrMo steel

The hot tensile deformation behaviors of 42CrMo steel are studied by uniaxial tensile tests with the temperature range of 850–1100 °C and strain rate range of 0.1–0.0001 s⁻¹. The effects of hot forming process parameters (strain rate and deformation temperature) on the elongation to fracture, strain rate sensitivity and fracture characteristics are analyzed. The constitutive equation is established to predict the peak stress under elevated temperatures. It is found that the flow stress firstly increases to a peak value and then decreases, showing a dynamic flow softening. This is mainly attributed to the dynamic recrystallization and material damage during the hot tensile deformation. The deformation temperature corresponding to the maximum elongation to fracture increases with the increase of strain rate within the studied strain rate range. Under the strain rate range of 0.1–0.001 s⁻¹, the localized necking causes the final fracture of specimens. While when the strain rate is 0.0001 s⁻¹, the gage segment of specimens maintains the uniform macroscopic deformation. The damage degree induced by cavities becomes more and more serious with the increase of the deformation temperature. Additionally, the peak stresses predicted by the proposed model well agree with the measured results.     

Constitutive modeling for flow stress of 55SiMnMo bainite steel at hot working conditions

The hot deformation behavior of 55SiMnMo bainite steel was studied through isothermal hot compression tests conducted using a Gleeble 3500 at 950–1100 °C, with strain rates of 0.01 s⁻¹ to 10 s⁻¹. A constitutive equation was established using the experimental results to describe the stress–strain relationship based on the dislocation density variation, considering the influence of the dynamic softening mechanism. When dynamic recovery is the only softening mechanism, a constitutive equation for flow stress was obtained from the variation of the dislocation density during hot deformation based on work hardening and dynamic recovery. When dynamic recrystallization occurs, the relationship between the dislocation density and the volume fraction of dynamic recrystallization was used to predict the flow stress after the peak. The reliability of the model was verified through a comparison between the predicted flow stress curves from the model and the experimental data.     

Effect of processing parameters on the hot deformation behavior of as-cast TC21 titanium alloy

Isothermal compression tests of as-cast Ti–6A1–2Zr–2Sn–3Mo–1Cr–2Nb (TC21) titanium alloy are conducted in the deformation temperature ranging from 1000 to 1150 °C with an interval of 50 °C, strain rate ranging from 0.01 to 10.0 s⁻¹ and height reductions of 30%, 45%, 60% and 75% on a computer controlled Gleeble 3500 simulator. The true stress–strain curves under different deformation conditions are obtained. Based on the experimental data, the effects of deformation parameters on the hot deformation behavior of as-cast TC21 alloy were studied. The deformation mechanisms of the alloy in the whole regimes are predicted by the power dissipation efficiency and instability parameter and further investigated through the microstructure observation. It is found that at the height reductions of 30%, 45% and 60%, the softening of stress–strain curves at high strain rate (>1.0 s⁻¹) is mainly associated with flow localization, which is caused by local temperature rise, whereas at low strain rate, the softening is associated with dynamic recrystallization (DRX). However, the instability showed in flow localization occurs at low strain rate of 0.01 s⁻¹ when the height reduction reaches 75%. In addition, the effects of strain rate, deformation temperature and height reduction on microstructure evolution are discussed in detail, respectively.     

Quantitative Analysis of Work Hardening and Dynamic Softening Behavior of low carbon alloy Steel Based on the Flow Stress

In this study, the constitutive equation and DRX(Dynamic recrystallization) model of Nuclear Pressure Vessel Material 20MnNiMo steel were established to study the work hardening and dynamic softening behavior based on the flow behavior, which was investigated by hot compression experiment at temperature of 950 °C, 1050 °C, 1150 °C and 1250 °C with strain rate of 0.01 s⁻¹, 0.1 s⁻¹ and 10 s⁻¹ on a thermo-mechanical simulator THE RMECMASTOR-Z. The critical conditions for the occurence of dynamic recrystallization were determined based on the strain hardening rate curves of 20MnNiMo steel. Then the model of volume fraction of DRX was established to analyze the DRX behavior based on flow curves. At last, the strain rate sensitivity and activation volume V^* of 20MnNiMo steel were calculated to discuss the mechanisms of work hardening and dynamic softening during the hot forming process. The results show that the volume fraction of DRX is lower with the higher value of Z (Zener–Hollomon parameter), which indicated that the DRX fraction curves can accurately predicte the DRX behavior of 20MnNiMo steel. The storage and annihilation of dislocation at off-equilibrium saturation situation is the main reason that the strain has significant effects on SRS(Strain rate sensitivity) at the low strain rate of 0.01 s⁻¹ and 0.1 s⁻¹. While, the effects of temperature on the SRS are caused by the uniformity of microstructure distribution. And the cross-slip caused by dislocation piled up which beyond the grain boundaries or obstacles is related to the low activation volume under the high Z deformation conditions. Otherwise, the coarsening of DRX grains is the main reason for the high activation volume at low Z under the same strain conditions.     

Microstructure characteristic for high temperature deformation of powder metallurgy Ti–47Al–2Cr–0.2Mo alloy

Hot compression tests of a powder metallurgy (P/M) Ti–47Al–2Cr–0.2Mo (at. pct) alloy were carried out on a Gleeble-3500 simulator at the temperatures ranging from 1000 °C to 1150 °C with low strain rates ranging from 1 × 10⁻³ s⁻¹ to 1 s⁻¹. Electron back scattered diffraction (EBSD), scanning electron microscope (SEM) and transmission electron microscope (TEM) were employed to investigate the microstructure characteristic and nucleation mechanisms of dynamic recrystallization. The stress–strain curves show the typical characteristic of working hardening and flow softening. The working hardening is attributed to the dislocation movement. The flow softening is attributed to the dynamic recrystallization (DRX). The number of β phase decreases with increasing of deformation temperature and decreasing of strain rate. The ratio of dynamic recrystallization grain increases with the increasing of temperature and decreasing of strain rate. High temperature deformation mechanism of powder metallurgy Ti–47Al–2Cr–0.2Mo alloy mainly refers to twinning, dislocations motion, bending and reorientation of lamellae.     

A characterization for the flow behavior of 42CrMo steel

In order to evaluate the flow stress and the dynamic softening characteristics of casting 42CrMo steel, isothermal upsetting experiments with height reduction 60% were performed at the temperatures of 1123 K, 1198 K, 1273 K and 1348 K, and the strain rates of 0.01 s⁻¹, 0.1 s⁻¹, 1 s⁻¹ and 10 s⁻¹ on thermal physics simulator Gleeble 1500. The flow behavior of the applied stress as a function of strain, strain rate and temperature exhibits a more pronounced effect of temperature than strain rate, and a typical characteristic of dynamic recrystallization softening. To characterize the flow behavior more factually and accurately, the traditional Fields–Backofen equation was amended, and an innovative mathematical model containing a softening item s, n-value and m-value variable functions was brought forth. The stress–strain curves calculated by the derived flow stress equation are fit with the experimental results well not only at the hardening stage but also at softening stage.     

Hot deformation and processing map of an as-extruded Mg–Zn–Mn–Y alloy containing I and W phases

The hot deformation characteristics of an as-extruded ZM31 (Mg–Zn–Mn) magnesium alloy with an addition of 3.2 wt.% Y, namely ZM31 + 3.2Y, have been studied via isothermal compression testing in a temperature range of 300–400 °C and a strain rate range of 0.001–1 s^− 1. A constitutive model based on hyperbolic-sine equation along with processing maps was used to describe the dependence of flow stress on the strain, strain rate, and deformation temperature. The flow stress was observed to decrease with increasing deformation temperature and decreasing strain rate. The deformation activation energy of this alloy was obtained to be 241 kJ/mol. The processing maps at true strains of 0.1, 0.2, 0.3 and 0.4 were generated to determine the region of hot workability of the alloy, with the optimum hot working parameters being identified as deformation temperatures of 340–500 °C and strain rates of 0.001–0.03 s^− 1. EBSD examinations revealed that the dynamic recrystallization occurred more extensively and the volume fraction of dynamic recrystallization increased with increasing deformation temperature. The role of element Y and second-phase particles (I- and W-phases) during hot compressive deformation was discussed.     

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.     

Dynamic recrystallization behavior of an as-cast TiAl alloy during hot compression

High temperature compressive deformation behaviors of as-cast Ti–43Al–4Nb–1.4W–0.6B alloy were investigated at temperatures ranging from 1050 °C to 1200 °C, and strain rates from 0.001 s^− 1 to 1 s^− 1. Electron back scattered diffraction technique, scanning electron microscopy and transmission electron microscopy were employed to investigate the microstructural evolutions and nucleation mechanisms of the dynamic recrystallization. The results indicated that the true stress–true strain curves show a dynamic flow softening behavior. The dependence of the peak stress on the deformation temperature and the strain rate can well be expressed by a hyperbolic-sine type equation. The activation energy decreases with increasing the strain. The size of the dynamically recrystallized β grains decreases with increasing the value of the Zener–Hollomon parameter (Z). When the flow stress reaches a steady state, the size of β grains almost remains constant with increasing the deformation strain. The continuous dynamic recrystallization plays a dominant role in the deformation. In order to characterize the evolution of dynamic recrystallization volume fraction, the dynamic recrystallization kinetics was studied by Avrami-type equation. Besides, the role of β phase and the softening mechanism during the hot deformation was also discussed in details.     

Constitutive models for high-temperature flow behaviors of a Ni-based superalloy

The high-temperature deformation behaviors of a typical Ni-based superalloy are investigated by hot compression tests under the strain rate of 0.001–1 s⁻¹and temperature of 920–1040 °C. The experimental results show that the deformation behaviors of the studied superalloy are significantly affected by the deformation temperature, strain rate and strain. The flow stress increases with the increase of strain rate or the decrease of deformation temperature. The flow stress firstly increases with the strain to a peak value, showing the obvious work hardening behaviors. Then, the stress decreases with the further straining, indicating the dynamic flow softening behaviors. Considering the coupled effects of deformation temperature, strain rate and strain on the hot deformation behaviors of the studied Ni-based superalloy, the phenomenological constitutive models are established to describe the work hardening-dynamic recovery and dynamic softening behaviors. In the established models, the material constants are expressed as functions of the Zener–Hollomon parameter. The established constitutive models can give good correlations with the experimental results, which confirm an accurate and precise estimation of the flow stress for the studied Ni-based superalloy.     

Hot deformation behavior of the new Al–Mg–Si–Cu aluminum alloy during compression at elevated temperatures

The hot deformation behavior of the new Al–Mg–Si–Cu aluminum alloy was investigated by compression tests in the temperature range 350 °C–550 °C and strain rate range 0.005 s^− 1–5 s^− 1 using Gleeble-1500 system, and the associated structural changes were studied by observations of metallographic and TEM. The results show that the true stress–true strain curves exhibit a peak stress at a small strain (< 0.15), after which the flow stresses decrease monotonically until high strains, showing a dynamic flow softening. The stress level decreases with increasing deformation temperature and decreasing strain rate, which can be represented by a Zener-Hollomon parameter in an exponent-type equation with the hot deformation activation energy Q of 236 kJ/mol. The substructure in the deformed specimens consists of very small amount and fine precipitates with equaixed polygonized subgrains in the elongated grains and developed serrations in the grain boundaries, indicating that the dynamic flow softening is mainly as the result of dynamic recovery (DR) and recrystallization (RDX).     

Constitutive modeling for the hot deformation behavior of Mg–3.06Zn–0.58Zr–1.07Y alloy

In order to improve the understanding flow behaviors of hot compressive deformation as‐homogenized of Mg–3.06Zn–0.58Zr–1.07Y alloy, carried out a series of isothermal compressive tests with 60% height reduction of specimens were performed at constant temperature of 523 K, 573 K, 623 K, 673 K, and 723 K, and strain rates of 0.001, 0.01, 0.1, and 1 s^?1 on Gleeble‐1500 thermo‐mechanical simulator. The results of the true stress–strain curves show that the flow stress increases with the increasing strain rate and decreasing deformation temperature. The flow behavior at constant strain rate was characterized by the dynamic recrystallization and dynamic recovery softening mechanisms occur simultaneously. The number of the dynamic recrystallization curve increases with increasing strain rate. A nonlinear flow model and its constitutive equation, based on the Arrhenius‐type equation, were employed for studying the deformation behavior and relationships between the deformation temperature, strain rate, and flow stress. Finally, the processing map of Mg–3.06Zn–0.58Zr–1.07Y alloy at the strain of 0.3 was obtained through the dynamic materials modeling. The optimal processing temperature and strain rate, using the microstructure and constitutive modeling, were found to be in the rage 623–723 K and 0.1–1 s^?1, respectively.     

Kinetics of low-temperature discontinuous deformation of metals

Kinetic characteristics of discontinuous yielding at a temperature of 4 K as functions of a number of factors are obtained using numerical simulation and experimental data for austenitic steel and aluminum alloy. During the development of a strain jump, the deformation rate and acceleration are 19 s⁻¹ and 5000 s⁻², respectively, for steel specimens and are much lower for aluminum alloy. The jump duration is mainly determined by the characteristics of the loading system. An equation relating the strain jump and the critical stress for low-temperature ductile materials is derived. The energy balance and the mechanism of low-temperature discontinuous yielding of metals are discussed. Its dynamic and thermally activated components are estimated taking into account the strain hardening of the material.     

Effect of Nb and C on the hot flow behavior of Nb microalloyed steels

The compressive deformation behaviors of a C–Mn steel (0.36C–1.42Mn) and two Nb microalloyed steels (0.35C–1.41Mn–0.044Nb and 0.055C–1.42Mn–0.036Nb) were investigated at the temperatures from 900 °C to 1100 °C and strain rates from 0.005 s⁻¹ to 10 s⁻¹ on Gleeble-1500 thermo-mechanical simulator. It was found that the flow stress of the C–Mn steel is the lowest among the experimental steels, indicating that Nb microalloying in HSLA steels can effectively increase the hot deformation flow stress, and the 0.055C–1.42Mn–0.036Nb steel has a higher flow stress than that of the 0.35C–1.41Mn–0.044Nb steel, indicating that C addition generates a softening effect. The flow stress constitutive equations of hot deformation were developed for the experimental steels, the activation energy Q about 360 kJ/mol for the 0.055C–1.42Mn–0.036Nb steel was higher than that for the 0.35C–1.41Mn–0.044Nb steel (347 kJ/mol) and the C–Mn steel (278 kJ/mol). Characteristic points of flow stress for the three steels were analyzed. The results showed that Nb addition can effectively increase the peak strain and the steady state strain of steels, thus delay distinctly the occurrence of dynamic recrystallization, while C addition can reduce the peak strain and the steady state strain of Nb microalloyed steels, thus promote the occurrence of dynamic recrystallization.     

Strain rate effects on tensile deformation behavior of Fe-3.5Mn-0.3C-5Al ferritic based lightweight steel

Tensile deformation behavior of Fe-3.5Mn-0.3C-5Al ferritic based lightweight steel was studied in a large range of strain rate (0.001 s⁻¹–1200 s⁻¹). Microstructures of the steel before and after tension were observed. The results show that Fe-3.5Mn-0.3C-5Al lightweight steel has a good strength (820 MPa) and plasticity (40 %) and exhibits excellent combinations of specific strength and ductility (>32000 MPa %) at the strain-rate of 0.001 s⁻¹ after annealing at 850 °C for 5 minutes then directly quenching into water. The austenite in the steel tested was transformed into α′-martensite during the tensile deformation process. With an increase in strain rate from 0.001 s⁻¹ to 1200 s⁻¹, tensile strength of the steel investigated increased from 820 MPa to 932 MPa, while its elongation first decreased from 40 % to 15 %, and then increased from 15 % to 29 %. At the strain rate of 1200 s⁻¹, adiabatic heating resulted in temperature rising in matrix, suppressed the transformation of austenite to α′-martensite. Comparing with transformation induced plasticity steel, the austenite in 3.5Mn lightweight steel is obviously unstable and cannot provide progressive phase transition.     

Hot deformation characteristics and strain-dependent constitutive analysis of Inconel 600 superalloy

The hot deformation characteristics and constitutive analysis of Inconel (IN) 600 superalloy were investigated at elevated temperatures. Hot compressive tests were carried out in the temperature and strain rate ranging from 900 to 1150 °C and 1 × 10⁻³–10 s⁻¹, respectively. The flow behavior analyses and microstructural observations indicate that the softening mechanisms were related to dynamic recrystallization (DRX) and grain growth. DRX played a dominant role in the microstructural evolution at low temperatures (or high strain rates). DRX was the dominant softening effect at low strains on testing at high temperatures with low strain rates, whereas growth of the dynamically recrystallized grains was responsible for softening at high strains. The flow stress of IN 600 was fitted well by the constitutive equation of the hyperbolic sine function under the deformation conditions performed in this study. A constitutive equation as a function of strain was established through a simple extension of the hyperbolic sine constitutive relation.     

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.     

Modeling the constitutive relationship of powder metallurgy Al–W alloy at elevated temperature

The deformation behavior of Al–W alloy was researched with isothermal compression tests at various deformation temperatures and strain rates to evaluate the deformation activation energy and to develop the constitutive relationship equation, which is in pursuit of revealing the dependence of the flow stress on the strain, strain rate and deformation temperature. The compression tests were conducted in the temperature range between 420 and 570 °C and at strain rates between 0.001 and 5.0 s⁻¹. With the help of determination of related material constants (such as A, β and α) and activation energy Q (451.15 kJ mol⁻¹), the Arrhenius-type constitutive relationship equation of Al–W alloy is developed. It was found that the correlation coefficient R and the AARE is 0.997% and 4.08%, respectively. The results show that the Arrhenius-type model, which considers the combined influence of strain rate and deformation temperature, is able to provide the accurate prediction of high temperature flow stress for the researched alloy.