Strain-compensated Constitutive Equation Research Articles

High-temperature hot deformation behavior and processing map of Ti-22Al-25Nb alloy

The high-temperature deformation behavior of the Ti-22Al-25Nb alloy was investigated by conducting hot compression experiments. A constitutive equation predicting the flow behavior of the Ti-22Al-25Nb alloy was established by analyzing its stress–strain curves. The strain-compensated constitutive equation effectively predicted the flow stress of the alloy with a correlation coefficient of 0.992 between the measured and predicted values and an average absolute relative error of 6.548 %. A hot processing map was obtained based on a dynamic material model. It demonstrated that the optimal processing region corresponded to the deformation temperatures of 1273–1353 K and strain rates of 0.001–0.01 s−1. Using electron backscatter diffraction data, thermal deformation mechanisms were elucidated under different deformation conditions within the safe region. The obtained results revealed that under the low temperature (T ≤ 1323 K) and low strain rate (ε̇ ≤ 1 s−1) conditions, continuous dynamic recrystallization and dynamic recovery (DRV) were the main thermal deformation mechanisms. Under the medium-to-high temperature (T ≥ 1323 K) and low strain rate (ε̇ ≤ 1 s−1) conditions, the main thermal deformation mechanisms were discontinuous dynamic recrystallization and DRV. At high strain rates (ε̇ ≥ 1 s−1), the primary thermaldeformation mechanism was DRV. The occurrence of discontinuous yielding in the alloy at high strain rates was related to the proliferation of mobile dislocations at grain boundaries.

High-Temperature Deformation Behavior of M50 Steel

The hot deformation characteristics of M50 steel in the temperature range of 900–1150 °C and strain-rate range of 0.01–10 s−1 was investigated in this study using a Gleeble-3800 thermal simulation testing machine. The true stress–strain curves showed that the deformation resistance increased with decreasing deformation temperature, and increasing strain rate before the peak stress was reached. After the peak stress, dynamic reversion occurred, and consequently, the deformation stress decreased. The softening phenomenon was more obvious when the strain rate was low. The calculated values of the thermal deformation-activation energy Q and stress index n were 233,684.2 J/mol and 5.025568, respectively. On this basis, the Arrhenius-type constitutive equation was established, and in addition, a polynomial fit based on strain was performed to obtain the 9th-order strain-compensated constitutive equation with high fitting accuracy. By processing the flow stress curves, the processing maps of M50 steel were constructed, and the optimal processing range was predicted to be in the range of 1070–1150 °C and 0.01–1 s−1. The recrystallization behavior of M50 steel was also studied by constructing a dynamic recrystallization kinetic model and combining optical microscope (OM) and electron backscatter diffraction (EBSD) observation. The results show that with the increase of deformation temperature, the degree of recrystallization transformation increased accordingly, and the original grains were gradually replaced by recrystallized grains. Besides, in the optimal process zone for thermal processing, the recrystallized grains grew with decreasing strain rate and increasing temperature.

Hot Deformation Behavior of a High-Mn TWIP Steel and Establishment of Strain-Compensated Constitutive Equation

Hot Deformation Behavior of a High-Mn TWIP Steel and Establishment of Strain-Compensated Constitutive Equation

Hot-deformation-induced structural and mechanical properties of Ce-modified SAF 2507 super duplex stainless steel

A typical rare-earth element modified Ce-SAF 2507 super duplex stainless steel was isothermally hot-compressed to reach superior mechanic properties over its pristine and peers. Mechanical, macro- and micro-structural evolutions subjected to hot-modification were studied in detail toward an optimal hot working for the Ce-SAF2507. A dynamic softening phenomenon shows that the increase of hot deformation temperature and decrease of the strain rate were dominated by the dynamic recovery of ferrite at a high strain rate and low deformation temperature. The same phenomenon at a low strain rate but high deformation temperature was ruled by the dynamic recrystallization of austenite. These two processes determined significant phase transformations from austenite to ferrite under higher deformation temperature and strain rate. A hot deformation activation energy Q ∼406kJmol−1 was obtained through a unified strain-compensated constitutive equation for Ce-SAF2507. Quantitative grain size refinements further proved the above mechanisms deduced from mechanical and microscopic observations, while structure induced changes of mechanical properties were crosschecked with the microhardness. Insights of microstructure also demonstrated the existences of the Cr2N in both phases, grain boundaries, and α/γ interface. The overall deformation dynamics was explicated based on the structural and quantitative results.

Hot compression deformation behavior and processing maps of ATI 718Plus superalloy

Abstract In this work, hot compression deformation behavior and processing maps of ATI 718Plus superalloy were studied by isothermal compression test on Gleeble-3800 thermal simulation testing machine. The results showed that under the present conditions (with deformation temperature range of 1030–1180 °C, strain rate of 0.01–10 s−1 and deformation amount of 50%), flow stress decreased with the increasing of deformation temperature and decreasing of strain rates. Meanwhile, simplified and strain-compensated classical Arrhenius constitutive equation models were established respectively, and strain-compensated constitutive equation improves the accuracy of flow stress prediction. In addition, processing maps showed that the optimal hot processing parameter ranges were 1140–1180 °C with strain rate of 0.01–0.1 s−1 respectively. The effects of strain rate and deformation temperature on microstructure evolution was investigated and low strain rate and high deformation temperature are conductive to DRX.

Hot Deformation Behavior and Strain-Compensated Constitutive Equation of Nano-Sized SiC Particle-Reinforced Al-Si Matrix Composites.

The hot deformation behavior of nano-SiCp/Al-Si composites was studied by isothermal compression tests at 470–530 °C and strain rates of 0.01–5 s−1. A strain-compensation constitutive model was developed with a Z parameter and an Arrhenius function, and its accuracy was verified by error analysis. The results show that the flow stress of the composites decreased with the increase in deformation temperature and the decrease in strain rate. The average activation energy for nano-SiC particle-reinforced Al-Si matrix composites was 277 kJ/mol, which was larger than the activation energy for self-diffusion of pure aluminum. The average relative error was calculated as 2.88%, indicating the strain-compensated constitutive equation could accurately predict the hot deformation behavior of nano-SiCp/Al-Si composites.

Hot deformation behavior and processing map of Zr-4 alloy

The hot deformation behavior of Zr-4 alloy at the deformation temperature range of 750–1000 °C and the strain rate range of 0.001–10 s−1 was studied on a Gleeble-3500 thermal simulator. The results show that the flow stress increases with the increasing strain rates or the decreasing deformation temperature. Based on the experimental data, the strain-compensated constitutive equation was established to predict flow stress during different strains, strain rates and temperatures. Meanwhile, the hot deformation activation energy of Zr-4 alloy was respectively calculated to be 224.31 kJ/mol, 593.50 kJ/mol and 345.71 kJ/mol in α single-phase region, α+β two-phase region and β single-phase region, which are obviously much higher than the activation energy of pure zirconium (113 kJ/mol). It indicates that the main deformation mechanism is not the dynamic recovery but other deformation mechanisms. According to the dynamic material model and Murty instability criterion, Murty processing maps have been constructed at the true strain of 0.6 and 1.2. Moreover, by combining microstructural observations, the areas of 750–880 °C/0.01–0.32 s−1 and 900–1000 °C/0.03–1 s−1 are identified to be the optimum hot working parameters.

High temperature behavior of severely deformed AA 5083 through equal channel lateral extrusion

Describing the high temperature behavior of a fine-grained AA 5083 aluminum alloy using an improved constitutive model is the focus of this paper. Dual Equal Channel Lateral Extrusion (DECLE) was utilized to create fine-grain microstructure in AA 5083 aluminum alloy. EBSD confirmed the formation of fine-grain microstructure after 5 passes of DECLE. The hot deformation behavior of the DECLEd alloy was assessed by hot compression tests at temperatures of 200–275 °C and strain rates of 10−4-10−1 s−1. The material constants, A, n and Q, in the hyperbolic-sine constitutive equation were calculated at peak stresses. The results suggested that the grain size affects the values of α and n, while the activation energy (Q) is more or less independent of the grain size. The values of α and n for the fine-grain material were obtained as 0.004357 (MPa−1) and 9.97, respectively. These calculated values (α and n) are respectively lower and higher than those reported for a coarse-grain one in the literature. This result was related to the high flow stress of the refined microstructure. The value of Q showed that the dislocation-dispersoid interactions are the rate-controlling mechanism during hot deformation. By iterating the calculation of constants at various strains, a strain-compensated constitutive equation was proposed for the prediction of flow stress over a wide range of strain. Finally, the processing maps were developed for the AA 5083 alloy at various strains.

Deformation characteristics and strain-compensated constitutive equation for AA5083 aluminum alloy under hot compression

Abstract The hot deformation behavior of AA5083 aluminum alloy was studied using isothermal compression tests with a Gleeble–3500 thermal simulator at strain rate of 0.01–10 s−1 and at temperature of 300–500 °C. The experimental results indicate that dynamic recrystallization (DRX) tends to occur at high strain rates and temperatures, and therefore the flow stress is decreased. To predict the flow behavior under different deformation conditions, a strain-compensated constitutive equation based on Arrhenius-type equation and Zener–Hollomon parameters was proposed. The flow stresses obtained from the constitutive equation are consistent with the experimental results. The average absolute relative error is only 4.52% over the entire experimental range, indicating that the proposed constitutive equation exhibits high prediction precision for the hot deformation behavior of AA5083 aluminum alloy.

On the High Temperature Deformation Behaviour of 2507 Super Duplex Stainless Steel

High temperature deformation behaviour of 2507 super duplex stainless steel was investigated by conducting isothermal hot compression tests. The dominant restoration processes in ferrite and austenite phases present in the material were found to be distinct. The possible causes for these differences are discussed. Based on the dynamic materials model, processing map was developed to identify the optimum processing parameters. The microstructural mechanisms operating in the material were identified. A unified strain-compensated constitutive equation was established to describe the high temperature deformation behaviour of the material under the identified processing conditions. Standard statistical parameter such as correlation coefficient has been used to validate the established equation.

Characterization of Hot Deformation Behavior of a New Near-β Titanium Alloy: Ti555211

AbstractThe deformation behavior of an isothermally compressed Ti555211 titanium alloy was examined by an Arrhenius-type constitutive model using experimental data obtained from hot compression tests; these tests were performed at temperatures and strain rates of 750–950°C and 0.001–1 s−1, respectively. Activation energies of hot deformation were calculated in 0.05 intervals for strains ranging from 0.1 to 0.7. The respective values of were obtained for the (α+β) and β region. In addition, the predictive capability of the model was described by the average absolute relative error (AARE) and the correlation coefficient (R). The simulated values were compared with the experimental values, and R and AARE of 0.99084 and 6.914%, respectively, were obtained for the Arrhenius-type constitutive model. These values were indicative of the good predictive capabilities of the developed strain-compensated constitutive equation. Moreover, in this work isothermal compression tests, scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and transmission electron microscopy (TEM) were used to systematically investigate the high-temperature deformation behavior of Ti555211 alloy under different processing conditions. EBSD and TEM were used to reveal the substructure and grain orientation of samples of the hot-deformed Ti555211 alloy. The phenomenon of discontinuous yielding was also discussed.

The Strain-Compensated Constitutive Equation for High Temperature Flow Behavior of an Al-Zn-Mg-Cu Alloy

In order to study flow stress behavior for hot working of a typical Al-Zn-Mg-Cu alloy, experimental stress-strain data obtained from isothermal hot compression tests at strain rates of 0.004, 0.04, and 0.4 s−1 and deformation temperatures of 400, 450, 500, and 520 °C were used to develop the constitutive equation. The peak stress decreased with increasing deformation temperature and decreasing strain rate. The effects of temperature and strain rate on deformation behavior were represented by Zener-Hollomon parameter in an exponent-type equation. Employing an Arrhenius-type constitutive equation, the influence of strain has been incorporated by considering the related material constants as functions of strain. The accuracy of the developed constitutive equations has been evaluated using standard statistical parameters such as correlation coefficient and average absolute relative error. The results indicate that the proposed strain-dependent constitutive equation gives an accurate and precise estimate of the flow stress in the relevant temperature range.