Arrhenius-type Constitutive Model Research Articles

Processing Maps and Optimized Plastic Behavior Model of TC4 Titanium Alloy Diffusion Bonded Joint at α+β Region Temperatures

The hot processing maps and optimized Arrhenius constitutive model of the TC4 diffusion bonded joint were investigated based on high temperature tensile tests in the temperature range of 1024–1174 K and strain rate range of 0.0001–0.1 s–1. The optimal hot processing parameter in the tensile deformation mode was 0.0001–0.001 s–1/1124 K and 0.0001–0.1 s–1/1174 K, respectively, when the true strain was 0.2. A modified strain compensated Arrhenius-type constitutive model of the joint by combining the evolutionary algorithm and generalized reduced gradient was established. The values of correlation coefficient and average absolute relative error were 0.989 and 7.29%, respectively, indicating the good prediction capabilities.

Thermal Deformation Behavior and Microstructural Evolution of Multicomponent Mg-Li-Zn-Al-Y Alloys under Hot Compression.

High-temperature compression tests on Mg-11.5Li-2.5Zn-0.35Al-0.3Y (in wt.%) were carried out on a Gleeble-3500 thermal simulator. Flow stress and microstructural evolution were analyzed at different temperatures (T = 473 K, 523 K, 573 K, and 623 K) and strain rates (ε˙ = 1 s-1, 0.1 s-1, 0.01 s-1, and 0.001 s-1). On this basis, the constitutive model of the alloy was established using the Arrhenius-type constitutive model, and the thermal processing map of the alloy was drawn based on the DMM (dynamic material modeling) theory. The experimental results show that the flow stress of the Mg-11.5Li-2.5Zn-0.35Al-0.3Y alloy decreases with an increase in temperature and a decrease in strain rate. The grain size increases uniformly with the increase in temperature, while a sudden increase occurs with the decrease in strain rate. The predicted value of the model is compared with the experimental value to verify the correctness of the model, and the correlation coefficient, R = 0.9690, was calculated, which further proves the applicability of the model to the Mg-11.5Li-2.5Zn-0.35Al-0.3Y alloy. This alloy can be safely plastic-deformed 473 K~623 K and 0.001 s-1~1 s-1.

Constitutive model for hot deformation behaviors of Al/Cu bimetal composites based on their components

The hot deformation behavior of Al/Cu bimetal composites was investigated using isothermal compression tests at temperatures of 400–500 °C and strain rates of 0.001–0.1 s−1 by considering the effects of volume fractions of composite components (30%–51% Al). In this regard, new proper constitutive equations were developed using Arrhenius-type and the rule of mixture (ROM) models. Experimental flow stress (FS) showed that processing parameters and volume fraction affect the flow behavior of composite as the volume fraction of copper has a more substantial impact on the flow behavior of the composite rods at elevated temperatures. The values of correlation coefficient (r) and average relative error of the developed Arrhenius-type constitutive equation and ROM model were 0.9826, 0.9742 and 0.9718, and also 0.18%, 1.69% and –0.84% for volume fractions of 51%, 42% and 30% Al, respectively. The results indicate that the newly developed constitutive model can successfully predict the hot working behavior of the considered bimetal composite. Finally, the microstructure of composites was investigated under different processing conditions. The dominant mechanisms for three considered volume fractions were identified at different temperatures, strains, and strain rates specified for the hot deformation of the Al/Cu composite.

Influence of temperature on deformation and damage mechanisms of wire + arc additively manufactured 2219 aluminum alloy

This work investigates the deformation and damage mechanisms of wire + arc additive manufacturing (WAAM) 2219 aluminum alloy over a broad temperature range of 77 K to 523 K. It is found that the strength and work hardening rate increase significantly with decreasing the temperature from 523 K to 77 K, and the fracture mode transitions from transgranular fracture mode to a mixture of intergranular and transgranular fracture ones. The large elongations to fracture are very similar for the specimens tested at 77 K and 523 K. This is mainly attributed to higher uniform elongation before necking at 77 K and higher post-necking elongation at 523 K. The cracking of α-Al + θ (Al2Cu) eutectics is the primary mechanism of micro-void nucleation, independent of the test temperature. The nucleated micro-voids, along with larger gas pore defects introduced by WAAM, extend along the tensile direction. In addition, as the temperature increases from 77 K to 523 K, the fracture mechanism transitions from high strain localization to extensive necking, leading to higher dislocation density, more grain fragmentation and micro-void nucleation, and more significant grain elongation and void growth. True stress and strain responses over the studied temperature range (77 ∼ 523 K) and strain rate range (0.0001 ∼ 0.01 s−1) are well predicted using an improved Arrhenius-type constitutive model, by considering the activation energy of deformation as a function of temperature.

A High-Temperature Strain-Compensated Arrhenius-Type Constitutive Model and an Improved Avrami-Type Dynamic Recrystallization Model of 40CrNiMo

A High-Temperature Strain-Compensated Arrhenius-Type Constitutive Model and an Improved Avrami-Type Dynamic Recrystallization Model of 40CrNiMo

Constitutive modeling for elevated temperature flow behavior of a novel Cr-Si alloyed hot stamping steel

The flow behavior of a novel Cr-Si alloyed hot stamping steel (Cr-Si steel) at elevated temperature was investigated via isothermal compression tests on a Gleeble-3500 thermomechanical simulator with a temperature range of 600 ∼ 900 °C and a strain rate range of 0.1 ∼ 10 s−1. Subsequently, the Arrhenius-type constitutive model, comprising strain compensation, was established in accordance with the friction and adiabatic heating corrected stress-strain curves. Furthermore, the predictability and prediction accuracy of the constitutive model were verified. The results reveal that at a constant strain rate, the flow stress of the Cr-Si steel initially increases as the strain increases before tending to stabilize, owning to the combined effects of work hardening and dynamic recovery. The peak flow stresses decrease as the temperatures increase and the strain rates decrease. The constitutive model can accurately predict the elevated temperature constitutive relationship of the Cr-Si steel during the hot stamping process.

Hot Deformation Behavior and Processing Maps of an As-Cast Al-5Mg-3Zn-1Cu (wt%) Alloy.

One of the key issues limiting the application of Al-Mg-Zn-Cu alloys in the automotive industry is forming at a low cost. Isothermal uniaxial compression was accomplished in the range of 300-450 °C, 0.001-10 s-1 to study the hot deformation behavior of an as-cast Al-5.07Mg-3.01Zn-1.11Cu-0.01Ti alloy. Its rheological behavior presented characteristics of work-hardening followed by dynamic softening and its flow stress was accurately described by the proposed strain-compensated Arrhenius-type constitutive model. Three-dimensional processing maps were established. The instability was mainly concentrated in regions with high strain rates or low temperatures, with cracking being the main instability. A workable domain was determined as 385-450 °C, 0.001-0.26 s-1, in which dynamic recovery (DRV) and dynamic recrystallization (DRX) occurred. As the temperature rose, the dominant dynamic softening mechanism shifted from DRV to DRX. The DRX mechanisms transformed from continuous dynamic recrystallization (CDRX), discontinuous dynamic recrystallization (DDRX), and particle-stimulated nucleation (PSN) at 350 °C, 0.1 s-1 to CDRX and DDRX at 450 °C, 0.01 s-1, and eventually to DDRX at 450 °C, 0.001 s-1. The eutectic T-Mg32(AlZnCu)49 phase facilitated DRX nucleation and did not trigger instability in the workable domain. This work demonstrates that the workability of as-cast Al-Mg-Zn-Cu alloys with low Zn/Mg ratios is sufficient for hot forming.

Investigation on the fracture mechanism and constitutive relations of a typical Ni-based superalloy

The hot tensile behavior of a typical Ni-based superalloy is elucidated using a microcomputer-controlled electronic universal testing machine at various deformation temperatures (920–1010 °C) and strain rates (0.001–0.01 s−1). Further, the influence of deformation parameters on the fracture characteristics is clarified. The results reveal that the tensile stress speedily rises to a peak level, beyond which it continuously declines until the final rupture. Moreover, numerous dimples exist on the fracture surface, and tenacity nests appear between adjacent dimples, suggesting that micro-void coalescence is the primary failure mechanism. Meanwhile, almost completed dynamic recrystallization (DRX) at elevated deformation temperature and slow strain rate promotes the intergranular fracture of the tested superalloy. Besides, an Arrhenius-type (AT) constitutive model and an artificial neural network (ANN) combined with particle swarm optimization (PSO) algorithms are established and validated. The maximum value of the mean absolute relative error (MARE) for the AT model is 9.74%, while it decreases to 4.20% for the PSO-ANN model. The correlation coefficient (R) increases from 0.9050 for the AT model to 0.9737 for the PSO-ANN model. Overall, it is demonstrated that the established PSO-ANN model has a high prediction performance and is an effective model for reproducing the hot tensile behavior of the tested superalloy.

The Comparation of Arrhenius-Type and Modified Johnson–Cook Constitutive Models at Elevated Temperature for Annealed TA31 Titanium Alloy

Constitutive models play a significant role in understanding the deformation behavior of materials and in optimizing the manufacturing process. In order to improve the reliability of calculation results, the high temperature flow behavior of TA31 titanium alloy obtained from an annealed hot-rolled plate has been investigated by a Gleeble-3500 thermo-mechanical simulator. The isothermal hot compression tests are conducted in the temperature range of 850 to 1050 °C and the strain rate range from 0.001 to 10 s-1 with a height reduction of 60%. The annealed TA31 shows a dynamic recovery characteristic during thermo-mechanical processing. The experimental data have been used to develop an Arrhenius-type constitutive model and a modified Johnson-Cook model under the consideration of coupling effect on strain, temperature, and strain rate, as well as the strain-softening phenomenon. The material parameters are determined by a global optimization method based on the initial values by means of a regression method. A comparation of the predicted results has been performed based on the modified Johnson-Cook model and those acquired from the Arrhenius-type model. The correlation coefficient and average absolute relative error of the modified Johnson-Cook model are 4.57% and 0.9945, respectively. However, when the optimization method has been applied, they are 15.77% and 0.9620 for the Arrhenius-type model, respectively. These results indicate that the modified Johnson-Cook model is more accurate and efficient in predicting the flow stress of annealed TA31 titanium alloy under a set of model material parameters. Furthermore, the simple mathematical expression of this model is helpful to incorporate it into the finite element software to obtain detailed and valuable information during the thermo-mechanical processing simulation for TA31 in further work.

A comparative study on modified and optimized Zerilli-Armstrong and arrhenius-type constitutive models to predict the hot deformation behavior in 30Si2MnCrMoVE steel

To better understand the elevated temperature flow behaviors of 30Si2MnCrMoVE low-alloy ultra-high strength steel, hot compressive deformation tests were performed at a wide range of forming temperatures (1123–1423 K) and strain rates (0.01–1s−1). The constitutive equations of the material were established through the physical-based modified Zerilli-Armstrong (ZA) and phenomenological Arrhenius-type models, along with the optimized ZA model of strain compensation constructed based on the modified ZA model. Suitability of these models were evaluated by comparing the correlation coefficient and absolute average error between the prediction and experimental data, its ability to predict the deformation behavior, and the amount of calculation required for the material constants. Results show that the modified ZA model cannot accurately describe the flow behavior of the 30Si2MnCrMoVE steel in the abovementioned hot working zone. The optimized ZA model and Arrhenius-Type model based on strain compensation require similar computational effort, and both can effectively predict the high temperature flow behavior of 30Si2MnCrMoVE steel. Relatively, the Arrhenius type model has the highest prediction accuracy.

Hot deformation behavior and strain compensation constitutive model of equiaxed fine grain diffusion-welded micro-duplex TC4 titanium alloy

In this work, two-stage diffusion bonding of micro-duplex TC4 titanium alloy was carried out to study the flow behavior and constitutive models of the bonding joint and the base metal after the same thermal cycling during the hot forming process. Microstructure and mechanical properties test were used to verify the good quality of the equiaxed fine grain diffusion-welded TC4 alloy. Quasi-static tensile experiment was carried out at temperatures ranging from 750–900 °C and strain rates of 0.0001–0.1 s−1. The joint showed the weak dynamic recovery at strain rates of 0.01–0.1 s−1 and temperatures of 750–850 °C. At strain rates of 0.0001–0.001 s−1 and temperatures of 850–900 °C, the flow stress of joint presented steady-state characteristics. Different deformation conditions lead to the remarkable difference of dynamic softening performance between the joint and heat-treated base metal, but the flow stress in elastic and strain hardening stages exhibited similar behavior. The strain compensated Arrhenius-type constitutive models of TC4 joint and heat-treated base metal were developed respectively. The fifth-order polynomial functions between the material property correlation coefficients and strain were obtained. The models have shown good correlation, with correlation coefficient values of 0.984 and 0.99. The percentage average absolute relative error for the models were found to be 10% and 9.46%, respectively.

Deformation Behavior and Constitutive Model of 34CrNi3Mo during Thermo-Mechanical Deformation Process.

With higher creep strength and heat resistance, 34CrNi3Mo has been widely used in the production of engine rotors, steam turbine impellers, and turbine blades. To investigate the hot deformation behaviors of 34CrNi3Mo steel, hot compressive tests were conducted on a Gleeble-3500 thermomechanical simulator, under the temperature range of 1073 K–1373 K and strain rate ranges of 0.1 s−1–20 s−1. The results show that the flow stress of 34CrNi3Mo steel under high temperatures is greatly influenced by the deformation temperature and strain rate, and it is the result of the interaction between strain hardening, dynamic recovery, and recrystallization. Under the same deformation rate, as the deformation temperature increases, the softening effect of dynamic recrystallization and dynamic recovery gradually increases, and the flow stress gradually decreases. Under the same deformation temperature, with the increase of strain rate, the influence of strain hardening on 34CrNi3Mo steel is gradually in power, and the flow stress gradually increases. To predict the flow stress of 34CrNi3Mo steel accurately, a modified Arrhenius-type constitutive model considering the effects of strain, temperature, and strain rate at the same time was made based on the experiment data. On this basis, the evolution law of deformation activation and instability characteristics of 34CrNi3Mo steel were investigated, and the processing map of 34CrNi3Mo steel was established. The formability of 34CrNi3Mo steel under high temperature deformation was revealed, which provided a theoretical foundation of the equation of reasonable hot working process.

Stress Response Behavior, Microstructure Evolution and Constitutive Modeling of 22MnB5 Boron Steel under Isothermal Tensile Load

22MnB5 boron steel has become one of the main choices for lightweight vehicles due to its extremely high mechanical properties. To explore the intrinsic relationship between the thermoforming process and thermo-mechanical behavior for constitutive modeling and thermoforming of vehicle structure, thermal tensile tests in wide ranges of deformation temperature (500 °C to 950 °C) and strain rate (0.01 s−1 to 10 s−1) were performed using a Gleeble-1500D thermal simulator with hot-rolled 22MnB5 boron steel. With increasing applied strain and strain rate, the flow stress increases gradually and then tends to saturation after reaching peak stress, except for that at 0.01 s−1 and 500 °C. With increasing deformation temperature, the microstructure transforms from a mixture of bainite, ferrite and pearlite to lath-shaped martensite accompanied with some residual austenite. At 950 °C, the average size of martensite decreases with increasing applied strain rate. After thermoforming with austenitizing temperature of 950 °C, lath-shaped martensite accompanied with some residual austenite is obtained in a thermoformed U-shaped structural part, resulting in a dramatical increase in tensile strength. In contrast, the tensile strength of sidewall is slightly higher than that of bottom. Based on the Arrhenius-type constitutive model, a modified constitutive model is constructed with a relative error of less than 5%, which can well describe the flow stress behavior of the studied 22MnB5 boron steel.

Hot deformation behavior of multilayered Ti/Ni composites during isothermal compression

The hot deformation behavior of multilayered Ti/Ni composites was studied by isothermal compression tests in the temperature range of 500–700 °C and strain rate range of 0.001–10.0 s−1. The Arrhenius-type constitutive model was constructed and the constants were determined for the composites. In addition, the processing maps were constructed using the principle of the dynamic materials model (DMM). The results show that the Arrhenius-type model can provide an accurate prediction of the flow behavior of the multilayered Ti/Ni composites under different conditions. The higher energy dissipation efficiency is observed at medium & high temperature/low strain rate. The unstable region of the multilayered Ti/Ni composites is large due to the presence of interfaces. At strain of 1.0, the optimum processing parameters of the multilayered Ti/Ni composites are at 630–700 °C/0.001–0.003 s−1 with a peak power dissipation of 0.40. Additionally, the deformation mechanism of Ni layers is mainly work hardening at 500–700 °C/0.001–10.0 s−1, whereas the deformation mechanism of Ti layers is mainly dynamic recovery at 700 °C/0.001 s−1 and work hardening at 500–600 °C/0.001 s−1 and 700 °C/0.1–10.0 s−1.

Hot Deformation Behavior of a Beta Metastable TMZF Alloy: Microstructural and Constitutive Phenomenological Analysis

A metastable beta TMZF alloy was tested by isothermal compression under different conditions of deformation temperature (923 to 1173 K), strain rate (0.172, 1.72, and 17.2 s−1), and a constant strain of 0.8. Stress–strain curves, constitutive constants calculations, and microstructural analysis were performed to understand the alloy’s hot working behavior in regards to the softening and hardening mechanisms operating during deformation. The primary softening mechanism was dynamic recovery, promoting dynamic recrystallization delay during deformation at higher temperatures and low strain rates. Mechanical twinning was an essential deformation mechanism of this alloy, being observed on a nanometric scale. Spinodal decomposition evidence was found to occur during hot deformation. Different models of phenomenological constitutive equations were tested to verify the effectiveness of flow stress prediction. The stress exponent n, derived from the strain-compensated Arrhenius-type constitutive model, presented values that point to the occurrence of internal stress at the beginning of the deformation, related to complex interactions of dislocations and dispersed phases.

WARM DEFORMATION BEHAVIOR OF A 65MN SPRING STEEL

The warm deformation behavior of 65Mn spring steel has been carried out by a thermomechanical simulator. The deformation temperatures are in the range of 550 ~ 700℃ and strain rates are in the range of 0.001 ~ 1 s-1. The deformation activation energy is calculated to be 486.829 KJ•mol-1. The strain compensated Arrhenius-type constitutive model was established. The relationship materials constants and strain were fitted with an 8th order polynomial. It was found that the strain has a significant influence on the instability map. At the strain is 0.3, the optimum flow zone may take place with the deformation temperatures higher than 626 ℃ and strain rate in the range of 0.001 ~ 1 s-1.

Hot compressive deformation behaviour and constitutive equations of Mg–Pb–Al–1B–0.4Sc alloy

ABSTRACT The hot compression features and microstructural evolution of Mg–Pb–Al–1B–0.4Sc alloy deformed at the strain rate range of 0.001–1 s−1 and the temperature range of 493–613 K were investigated by isothermal compression tests. The results show that the flow stress is significantly influenced by deformation conditions. The true stress decreases with the raised temperature or the reduced strain rate. The Zuzin-type model and Arrhenius-type constitutive model were employed to predict the flow behaviour of Mg–Pb–Al–1B–0.4Sc alloy. The values of and in the Arrhenius-type model are 6.353% and 9.595, respectively, which are smaller than the 13.653% and 24.662 of the Zuzin-type model, indicating that the Arrhenius-type model is more suitable for predicting the flow stress of this alloy. The processing maps and microstructure show that the optimum strain rates and temperatures are 0.001–0.015 s−1 and 550–613 K, respectively.

An investigation of hot deformation behavior of Zn–22Al alloy and development of its processing maps during isothermal compression

In this paper, the hot deformation behavior of Zn–22Al alloy was investigated by performing hot compression tests under different deformation conditions. The Arrhenius-type constitutive model was developed and the constants were determined for this alloy. In addition, the processing map was constructed using the principle of the dynamic materials model (DMM). The results show that the Arrhenius-type model, with an activation energy of 63.722 kJ/mol, can provide an accurate prediction of the flow behavior of the alloy at various conditions. The higher energy dissipation efficiency was observed in the high-temperature ranges and low strain rates. The results showed that the unstable processing zone of Zn–22Al alloy has mainly occurred at high strain rates and low-temperature region. Besides, it is found that the strain has less significant effects on instability parameter and power dissipation efficiency.

The high temperature deformation behavior of a triplex (ferrite+ austenite+ martensite) low density steel

Abstract The present work deals with the high temperature deformation behavior of Fe-11.15Mn-5.6Al-0.07C (wt.%) triplex ferrite-based lightweight steel in the temperature range of 800–1100 °C under the strain rate of 0.001 to 0.1s−1. The compressive high temperature flow curves under the various thermomechanical conditions were accompanied by a considerable fractional softening. According to the detailed microstructural analysis, the observed flow softening was discussed relying on the occurrence of dynamic strain induced transformation and dynamic recrystallization. In this respect, a sine hyperbolic Arrhenius-type constitutive model was developed considering the three dimensional variation of the materials’ constant with strain, strain rate and temperature. This provided a proper condition for accurate assessment of the strain compensation mechanisms. The capability of the modified and un-modified constitutive models in prediction of the high temperature flow behavior of experimented low density steel were compared. According to the verified model, activation energy (Q) maps were developed and discussed in correlation with the characterized microstructure evolutions. The Q-plots were divided into three domains and a transition range was recognized at ~1100–1250 K, the extent of which decreased with increasing imposed strain. The low energy domains were attributed to the (i) activation of load transition as an effective strain compensation mechanism and the occurrence of dynamic austenite to ferrite transformation, and (ii) the high dislocation annihilation rate at high temperatures.

Role of Grain Size and Oxide Dispersion Nanoparticles on the Hot Deformation Behavior of AA6063: Experimental and Artificial Neural Network Modeling Investigations

The hot deformation behavior of coarse-grained (CG), ultrafine-grained (UFG), and oxide dispersion-strengthened (ODS) AA6063 is experimentally recognized though carrying out compression tests at different temperatures (300–450 °C) and strain rates (0.01–1 s−1). Microstructural studies conducted by TEM and EBSD indicate that dynamic softening mechanisms including dynamic recovery and dynamic recrystallization become operative in all the investigated materials depending on the regime of deformation. Moreover, the high temperature flow behavior is considerably influenced by the initial grain structure and the presence of reinforcement particles. The constitutive and artificial neural network (ANN) models were used to study the high-temperature flow behavior of the investigated alloys. To establish an accurate ANN model, material characteristics along with the processing parameters are deliberated. An Arrhenius type constitutive model with a strain-compensation term is employed to predict the flow stress of AA6063 alloys. The relative error associated with the constitutive and ANN models in the prediction of the flow stress is obtained 9.56% and 2.02%, respectively. The analysis indicates that the developed ANN model is more accurate in the prediction of flow stress with at least 78% less error in comparison to the constitutive model.