The hot deformation behavior of Nb–V–Ti microalloyed ultra-high strength steel was investigated by isothermal compression at 900–1200 °C with strain rates from 0.01 to 10 s−1. The microstructure evolution and precipitation behavior were studied using an optical microscope and a transmission electron microscope Results indicate that the peak stress of experimental steel increases with increasing the strain rate and decreasing the deformation temperature. The constitutive equation of hot deformation was developed with the activation energy Q being about 407.29 kJ/mol. The processing maps were also obtained to identify the instable regions of the flow behavior and to evaluate the efficiency of hot deformation. The size of dynamically recrystallized grains increases gradually with a decrease in the strain rate. Three types of carbides were identified, namely M3C, rich-Ti MC, and rich-Nb MC. With the increase of the deformation rate, the amounts of carbides increase, and the average sizes of the carbides decrease gradually.

A series of hot compression tests of medium carbon Cr–Ni–Mo-alloyed steel, 34CrNiMo steel, were conducted on a Gleeble-1500 thermal mechanical simulator, in a wide temperature range of 1173–1423 K and at a strain rate range of 0.002–5 s−1. Three constitutive models, namely the Johnson–Cook (JC) model, strain compensated Arrhenius model, and the physically based constitutive model, were established to describe the hot deformation of 34CrNiMo steel. A comparative study of the three models was investigated by comparing the accuracy of prediction of flow stress behavior. The results imply that the JC model is not able to adequately represent the high-temperature flow behavior with the existance of recovery and recrystallization. The Arrhenius-type model based on mathematics has a good prediction in the flow stress behavior in all strain ranges during the hot deformation. The physically based constitutive model gives a better prediction accuracy of the deformation behavior in both flow stress and deformation mechanism.

The constitutive equation was established based on the consideration of strain compensation to describe the hot deformation behavior of low carbon reduced activation ferritic/martensitic (RAFM) steels at the temperatures of 850–1050 °C and the strain rates of 0.01–10 s−1. The result indicates that the flow stress is increased with the increase of strain rate but decreased with increase of deformation temperature. During the hot deformation process, the increase of temperature is beneficial to attain the complete dynamic recrystallization (DRX). However, excessively high temperature leads to grow up of dynamic recrystallized grain. Higher strain rate leads to finer recrystallized grains. The material constants (α, n, A) and deformation activation energy (Q) are calculated by the regression analysis. The increase of strain caused the decrease of Q, indicating the DRX occurred more easily. In addition, the developed constitutive equation could accurately predict the hot deformation behavior of the low carbon RAFM steel.

Isothermal compression testing of Ti–5.8Al–3Sn–5Zr–0.5Mo–1.0Nb–1.0Ta–0.4Si–0.2Er titanium alloy is performed on a Gleeble-3500 thermal simulator, and the corresponding microstructures are analyzed to clarify the softening mechanism and participates evolution. A constitutive equation compensated by strain has been established to describe the hot deformation behavior of the alloy. The deformation activation energies are calculated to be 369760.93–699310.86 J/mol in α + β two-phase region and 268030.03–325800.41 J/mol in β single-phase region. At a temperature of 880 °C, the main softening mechanism is the continuous dynamic recrystallization of lamellar α colony, controlled by the mechanical rotation of the sub-grain followed by dislocation climbing and annihilation by diffusion. Meanwhile, the dominant softening mechanism is the discontinuous dynamic recrystallization of β phase during the deformation at temperatures of 920 °C–1080 °C. Silicide containing Er with an average diameter of 20 nm is formed during the water quenching.

To study the hot deformation behavior of the Ti–22Al–25Nb alloy, isothermal compression tests were conducted at the temperature range of 930–1080 °C with strain rates of 0.001–1.0 s−1. Both the strain rate and the deformation temperature have a significant influence on the stress–strain behavior of the Ti–22Al–25Nb alloy. A hyperbolic–sine constitutive equation is established to quantitatively demonstrate the relationship between the parameters involved, and the hot deformation activation energy Q is determined as 621 kJ/mol. To optimize the processing window, a hot processing map is established, which is related to the microstructure evolution in hot working. The lamellar globularization as well as the dynamic recrystallization (DRX) would contribute to the stable regions with high power dissipation, while the adiabatic shear bands would lead to unstable regions. Moreover, an Avrami-type kinetics model is applied to examine the evolution of DRX during isothermal deformation process.

The present study was conducted to predict the hot deformation behavior of the as-forged Nitinol 60 shape memory alloy by using the Arrhenius type, multiple-linear, and artificial neural network (ANN) models. The acquired flow stress data from isothermal hot compression tests in a temperature range of 650–850 °C under strain rate range of 0.01–1 s−1 were used to calculate the material constants for establishing the corresponding constitutive equations. Furthermore, a comparative study has been made on the capability of the aforementioned models to predict the high-temperature deformation behavior by comparing the prediction relative errors, average absolute relative error, and correlation coefficient. The results show that multiple-linear model predicts the flow behavior more accurately than the Arrhenius type model. The ANN model is much more efficient and has a better prediction power for the as-forged Nitinol 60 alloy than both the Arrhenius type and multiple-linear models.

A polydisperse case of an entangled linear polymer melts constitutive equation wasstudied. This constitutive equation, proposed by S. Dhole et al. [J. Non-Newtonian FluidMech. 161 (2009) 10–18], based on the reptation theory and the tube model, was tested on apolystyrene in shear (capillary rheometry) and planar extension in a complex flow(fieldwise measurements in a contraction flow) for different level of strain rates. A goodquantitative prediction of all the set of experiments was obtained, using no adjustablenonlinear parameters.