The flow behavior and constitutive equation in isothermal compression of FGH4096-GH4133B dual alloy

The electron beam welding of superalloy FGH4096 and GH4133B was conducted, and the cylindrical compression specimens were machined from the central part of the electron beam weldments. Isothermal compression tests were carried out on electron beam weldments FGH4096-GH4133B alloy at the temperatures of 1020–11140 °C (the nominal γ′-transus temperature is about 1080 °C) and the strain rates of 0.001–1.0 s⁻¹ with the height reduction of 50%. True stress–true strain curves are sensitive to the deformation temperature and strain rate, and the flow stress decreases with the increasing deformation temperature and the decreasing strain rate. The true stress–true strain curves can indicate the intrinsic relationship between the flow stress and the thermal-dynamic behavior. The apparent activation energy of deformation at the strain of 0.6 was calculated to be 550 kJ/mol, and the apparent activation energy has a great effect on the microstructure. The constitutive equation that describes the flow stress as a function of strain rate and deformation temperature was proposed for modeling the hot deformation process of FGH4096-GH4133B electron beam weldments. The constitutive equation at the strain of 0.6 was established using the hyperbolic law. The relationship between the strain and the values of parameters was studied, and the cubic functions were built. The constitutive equation during the whole process can be obtained based on the parameters under different strains. Comparing the experimental flow stress and the calculated flow stress, the constitutive equation obtained in this paper can be very good to predict the flow stress under the deformation temperature range of 1020–1140 °C and the strain rate range of 1.0–0.001 s⁻¹.     

Effects of initial grain size on hot deformation behavior of commercial pure aluminum

The effects of initial grain size of commercial pure aluminum on hot deformation behavior were investigated using hot compression tests. The hot compression tests were carried out on the pure aluminum samples with the initial grain sizes of 50, 150 and 450 μm using various strains, strain rates and different deformation temperatures. It was found that the hot deformation behavior of used material was sensitive to deformation conditions and initial microstructure. Results indicate that the initial grain size has significant effect on the flow stress. Flow stress decreases when the grain size decreases from 450 to 50 μm and when strain rate is lower than 0.05 s⁻¹. This procedure is reversed at strain rate of 0.5 s⁻¹. Furthermore, effects of other parameters like the strain rates and deformation temperatures on the flow stresses and hardening rates were investigated. It was also found that the inhomogeneity of microstructure distribution at different positions of the deformed specimens depended on the amount of deformation concentration at particular points and other processing parameters such as initial grain sizes, strain rates and deformation temperatures. In addition the geometric dynamic recrystallization (GDRX) was observed in the specimens highly strained (0.7) at elevated temperature (500 °C) using polarized light microscope and sensitive tint (PLM + ST).     

Hot deformation behavior of an antibacterial Co–29Cr–6Mo–1.8Cu alloy and its effect on mechanical property and corrosion resistance

In order to optimize the deformation processing, the hot deformation behavior of Co–Cr–Mo–Cu(hereafter named as Co–Cu) alloy was studied in this paper at a deformation temperature range of 950–1150°C and a strain rate range of 0.008–5 s~(-1). Based on the true stress–true strain curves, a constitutive equation in hyperbolic sin function was established and a hot processing map was drawn. It was found that the flow stress of the Co–Cu alloy increased with the increase of the strain rate and decreased with the increase of the deforming temperature. The hot processing map indicated that there were two unstable regions and one well-processing region. The microstructure, the hardness distribution and the electrochemical properties of the hot deformed sample were investigated in order to reveal the influence of the hot deformation. Microstructure observation indicated that the grain size increased with the increase of the deformation temperature but decreased with the increase of the strain rate. High temperature and low strain rate promoted the crystallization process but increased the grain size, which results in a reduction in the hardness. The hot deformation at high temperature(1100–1150°C) would reduce the corrosion resistance slightly. The final optimized deformation process was: a deformation temperature from 1050 to 1100°C, and a strain rate from 0.008 to 0.2 s~(-1), where a completely recrystallized and homogeneously distributed microstructure would be obtained.     

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.     

Workability characteristics and mechanical behavior modeling of severely deformed pure titanium at high temperatures

In the present study, compression tests were performed at temperatures of 600–900 °C and at strain rates of 0.001–0.1 s⁻¹ to study the deformation and workability characteristics of commercially pure titanium after severe plastic deformation (SPD). It was found that the effects of temperature and strain rate are significant in dictating the steady state flow stress levels and the strain values corresponding to peak flow stress. The strain rate sensitivity (m) during hot compression of severely deformed Ti was shown to be strongly temperature dependent, where m increased with the increase in deformation temperature up to 800 °C. High temperature workability was analyzed based on the flow localization parameter (FLP). According to the FLP values, deformation at and below 700 °C is prone to flow localization. The flow behavior was predicted using Arrhenius type and dislocation density based models. The validities of the models were demonstrated with reasonable agreement in comparison to the experimental stress–strain responses.     

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 equation and model validation for a 31 vol.% B4Cp/6061Al composite during hot compression

An accurate constitutive equation is essential to understanding the flow behavior of B₄C/Al composites during the hot deformation. However, the constitutive equations developed previously in literature are generally for low strain rate deformation. In the present work, we modified the general constitutive equation and take the high strain rate correction into account. The constitutive equation for a 31 vol.% B₄Cp/6061Al composite was constructed based on the flow stresses measured during isothermal hot compression at temperatures ranging from 375 to 525 °C and strain rates from 0.01 to 10 s^?1. The experimental flow stresses were corrected by considering temperature-dependent Arrhenius factor. The modified equation was then verified by using DEFORM-3D finite element analysis to simulate the experimental hot compression process. The results show that the modified equation successfully predicts flow stress, load–displacement, and the temperature rise. This helps to optimize the hot deformation process, and to obtain desirable properties, such as reduced porosity and homogenous particle distribution in B₄C/Al composites.     

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 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 workability of 00Cr13Ni5Mo2 supermartensitic stainless steel

The hot workability of 00Cr13Ni5Mo2 supermartensitic stainless steel was investigated by hot compression and hot tension tests conducted over the temperature range of 950–1200 °C and strain rates varying between 0.1 and 50 s^?1. The processing map technique was applied on the basis of dynamic materials model and Prasad instability criterion. Microstructure evolutions, Zener–Hollomon parameter as well as hot tensile ductility were examined. The results show that, as for the hot working of 00Cr13Ni5Mo2 supermartensitic stainless steel in the industrial production, the large strain deformation should be carried out in the temperature range 1140–1200 °C and strain rate range 0.1–50 s^?1, where the corresponding Zener–Hollomon parameters exhibit low values. Moreover, when deformed under high strain rate range (above 15 s^?1), the deformation temperature can be reduced reasonably.     

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.     

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.     

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 modeling of powder metallurgy processed Al–4%Cu preforms during compression at elevated temperature

In this study, a hot deformation constitutive base analysis has been conducted on powder metallurgy (P/M) processed Al–4%Cu preforms. The main objective is to evaluate the effect of initial relative density on the hot deformation behaviour and to establish the constitutive equation which considers the effect of initial relative density during hot compression test. This has been carried out by using the true stress–true strain curve data obtained from hot compression test of P/M processed Al–4%Cu preforms with different initial relative density of 0.84, 0.87 and 0.9 for various range of temperature 300–500 °C and strain rate range of 0.1–0.4 s⁻¹. It has been found that the flow stress is notably influenced by initial relative density, temperature and strain rate. The results show that the flow stress exhibits peak value at certain strain value, and then decreases showing flow softening until the flow stress remains constant at higher strain values. A constitutive equation that predicts the flow stress in hot compression of P/M processed Al–4%Cu preforms has been developed. The predicted flow stress values are in a good agreement with the experimental results and it is confirmed that the formulated constitutive equation is accurate and reliable to predict the flow stress of Al–4%Cu preforms during hot compression at elevated temperature.     

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).     

Hot tensile deformation behaviors and constitutive model of an Al–Zn–Mg–Cu alloy

The hot tensile deformation behaviors of an Al–Zn–Mg–Cu alloy are studied by uniaxial tensile tests under the deformation temperature of 340–460 °C and strain rate of 0.01–0.001 s⁻¹. The effects of deformation temperature and strain rate on the hot tensile deformation behaviors and fracture characteristics are discussed in detail. The Arrhenius-type constitutive model is developed to predict the peak stress under the tested deformation condition. The results show that: (1) The true stress–true strain curves under all the tested deformation conditions are composed of four distinct stages, i.e., elastic stage, uniform deformation stage, diffusion necking stage and localized necking stage. The flow stress decreases with the increase of deformation temperature or the decrease of strain rate. (2) The elongation to fracture increases with the increase of deformation temperature. Under the tested conditions, the strain rate sensitivity coefficient varies between 0.1248 and 0.2059, which indicates that the main deformation mechanism is the lattice diffusion-controlled dislocation climb. (3) The localized necking causes the final fracture of specimens under all the deformation conditions. Microvoids coalescence is the main fracture mechanism under relatively low deformation temperatures. With the increase of deformation temperature, the intergranular fracture occurs. (4) The peak stresses predicted by the developed model well agree with the experimental results, which indicate the validity of the developed model.     

Flow behavior and processing map for hot deformation of ATI425 titanium alloy

Flow behavior and processing map play important roles in the hot deformation process of titanium alloys. In this research, compression Gleeble tests have been carried out to investigate the stress–strain relationship at temperatures ranging from 700 to 1000℃ and strain rates ranging from 0.001 to 1 s~(-1) for ATI 425 titanium alloy. Arrhenius type constitutive equation was obtained to describe the compressive flow behavior with modification of additional deformation dead zone, friction model, temperature model and strain rate. The introduction of novel calculation method for value in Arrhenius equation gives more accurate fitting than traditional one. Processing maps were drawn based on the distribution of dissipator co-content, and optimized deformation temperature and strain rate range obtained. It is proven to be accurate and effective through the experimental results. The microstructure analysis shows that more dynamic recrystallization can be achieved in the area with larger value on the processing map.