Arrhenius Constitutive Model Research Articles

Hot Deformation Behavior and Processing Map of High-Strength Nickel Brass

The flow behavior of a new kind of high-strength nickel brass used as automobile synchronizer rings was investigated by hot compression tests with a Gleeble-3500 isothermal simulator at strain rates ranging from 0.01 to 10 s−1 and a wide deformation temperature range of 873–1073K at intervals of 50 K. The experimental results show that flow stress increases with increasing strain rate and decreasing deformation temperature, and discontinuous yielding appeared in the flow stress curves at higher strain rates. A modified Arrhenius constitutive model considering the compensation of strain was established to describe the flow behavior of this alloy. A processing map was also constructed with strain of 0.3, 0.6, and 0.9 based on the obtained experimental flow stress–strain data. In addition, the optical microstructure evolution and its connection with the processing map of compressed specimens are discussed. The predominant deformation mechanism of Cu-Ni-Al brass is dynamic recovery when the deformation temperature is lower than 973 K and dynamic recrystallization when the deformation temperature is higher than 973 K according to optical observation. The processing map provides the optimal hot working temperature and strain rate, which is beneficial in choosing technical parameters for this high-strength alloy.

Parameter Optimization in the Thermo-mechanical V-Bending Process to Minimize Springback of Inconel 625 Alloy

The present research deals with experimental and finite element analysis for minimization of springback in the V-bending process for Inconel 625 alloy. Different material properties were determined at three distinct temperatures (303 K, 473 K and 673 K) and deformation speeds (1 mm/min, 5 mm/min and 10 mm/min). Temperature was found to have significant effect on the flow stress of the material. Taguchi analysis was applied to find springback of Inconel 625 by considering four process parameters (temperature, punch speed, holding time and orientation of the sheet) and at the three predetermined levels of settings. Based upon signal-to-noise ratio analysis, temperature (46.93%) was found to be the most influential parameter affecting the springback followed by holding time (26.29%), sheet orientation (24.07%) and punch speed (2.69%). The optimized setting for the minimum springback of Inconel 625 alloy obtained after the conformation test was 673 K temperature, 1 mm/min punch speed, 90 s holding time and 90° to the rolling direction of a sheet. The springback was significantly reduced by 69.63% with the optimized setting of process parameters. The springback factor was also evaluated, and it was found to be directly proportional to the temperature and holding time and inversely proportional to the punch speed, but no particular trend was followed for the sheet orientation as a process parameter. The Arrhenius constitutive model with both Barlat and Hill yield criteria was implemented by adopting user-defined material (UMAT) subroutine for finite element analysis. Numerically computed springback from Barlat criterion was found to be in good relation with the experimental results.

Hot deformation behavior of the AA6016 matrix composite reinforced with in situ ZrB2 and Al2O3 nanoparticles

The hot deformation tests of in situ ZrB2 and Al2O3 nanoparticles reinforced AA6016 matrix composite were studied at deformation temperature of 300 °C–450 °C and strain rate of 0.001–1 s−1. In this paper, the ZrB2 and Al2O3 nanoparticles were successfully prepared by direct melt reaction method firstly. Based on experimental results, the flow stress increased rapidly with the increasing true strain and decreased with the increasing temperature. Constitutive equation of the composite can be established based on the Arrhenius constitutive model. The processing map based on dynamic material model showed two stable processable domains: Domain A(300–360 °C/0.08–0.01 s−1), which was controlled by dynamic recovery and domain B(410–430 °C/0.37–1 s−1), which was typical dynamic recrystallization structure. The microstructural changes of the samples after deformed were observed through optical microscope (OM), scanning electron microscope (SEM) and transmission electron microscope (TEM). It was concluded that these two kinds of reinforced particles can greatly promote recrystallization nucleation at high temperatures. Thus, domain B is optimum hot processing window.

Hot Deformation Behavior and Processing Map of As-Cast 40CrNiMo Alloy Steel

The as-cast 40CrNiMo alloy steel with uniform microstructure is obtained through vacuum casting by using metal mold. The hot deformation behavior of as-cast 40CrNiMo alloy steel is investigated by isothermal compression tests. The Arrhenius constitutive model and processing maps of as-cast 40CrNiMo alloy steel are constructed. The results indicate that the true stress–strain curves present typical dynamic recovery type under low deformation temperature and high strain rate. With the increases in deformation temperature or the decreases in strain rate, the true stress–strain curves gradually transform to dynamic recrystallization type. Through the analysis of processing maps and microstructures, it can be found that the area of plastic instability increases with the increase in the strain and gradually expands to the region of high deformation temperature and low strain rate. The deformation temperature range of 850-1050 °C and strain rate range of 0.001-0.01 s−1 are recommended as the reasonable hot-working process conditions. Results of this research can provide references for the selection of process parameters in casting–forging combination forming of 40CrNiMo alloy steel.

A Comparative Study on Arrhenius Equations and BP Neural Network Models to Predict Hot Deformation Behaviors of a Hypereutectoid Steel

In order to predict the high-temperature deformation behavior of hypereutectoid steel, the hot compression tests were conducted in the strain rate range of (0.001~1) s -1 and the deformation temperature range of (950~1100)°C. The experimental data were employed to develop the Arrhenius constitutive model and BP neural network model, and their predictability for high temperature flow stress of hypereutectoid steel was further evaluated. Comparatively, a higher correlation coefficient (R) can be obtained for the BP neural network model compared with the Arrhenius constitutive equations. And the relative error within ±1% was more than 68.75% for the BP neural network model, while only 18.75% for the constitutive equations. The BP neural network model is considered more efficient and accurate to predict the hot deformation behavior than the Arrhenius constitutive equations. Moreover, the well-trained BP neural network model is employed to predict the flow stress varying with the deformation temperature and strain rate. The flow stress decreases with the increasing deformation temperature and decreasing strain rate, which is in accordance with the experimental evaluation. The results indicate that BP neural network model is an efficient tool for modelling and predicting the flow behavior of hypereutectoid steels in high temperature applications.

Study on constitutive model for new generation aero-space structural Cr4Mo4Ni4V steel

In recent years, Cr4Mo4Ni4V with high-strength has been developed in China and been considered as a next generation bearing steel. In the present work, the hot deformation behavior of Cr4Mo4Ni4V bearing steel was investigated via isothermal hot compression tests using Gleeble-3500. To accurately describe the hot deformation behavior of the Cr4Mo4Ni4V bearing steel, the Arrhenius constitutive model considering strain compensation and the physically-based constitutive model considering dynamic recovery and dynamic recrystallization were employed and the stress-strain data were utilized. The results showed that the Arrhenius constitutive model considering strain compensation has a crucial problem because change in the microstructure at a given strain for different deformation conditions was disregarded. However, the physically-based constitutive model considering dynamic recovery and dynamic recrystallization could resolve the problem in Arrhenius constitutive model considering strain compensation. Finally, the predictive power of two models was evaluated via correlation coefficient and average absolute relative error. The results confirm that the predictive power of physically-based constitutive model is better than Arrhenius constitutive model considering strain compensation for Cr4Mo4Ni4V steel.

A comparative study at the flow behavior description of 2A14 alloy using BP-ANN and strain compensated Arrhenius model

In this work, a back-propagation artificial neural network (BP-ANN) and Arrhenius constitutive model were used to predict the stress-strain curves of 2A14 aluminum alloy based on the results of isothermal compression tests conducted at the temperature of 648 K–723 K and the strain rate of 0.01 −10 A series of statistical analyses were introduced to compare the accuracy of predictions of the two models. The average absolute relative error (AARE) , correlation coefficient (R) , relative error and standard deviation were 0.4338%, 0.9997, 0.2384, 0.0242 by BP-ANN model and 3.06%, 0.9941, 1.7993, 2.6610 by Arrhenius constitutive model, respectively, which indicates that the trained BP-ANN model is more precise than the Arrhenius constitutive model. Then the finite element simulations were conducted under the same deformation conditions on the basis of the pure experimental results and pure BP-ANN predicted results. As a result, the stroke load curve and the distributions of the effective strain are similar, which further proves that the BP-ANN model have a good capability to predict the flow behavior of 2A14 alloy.

Drying Characteristics of Blackberry Fruits in a Convective Hot-air Dryer

In this study, blackberry fruits were dried in a pilot-scale hot-air dryer to identify the drying characteristics of the fruits. The air velocity was set as 1 m·s−1, and the temperature range was set as 54 to 75 °C. Fick’s law of diffusion was used to describe heat transfer during the decreasing rate period. Effective diffusivity values were calculated, and the Arrhenius constitutive model was used to describe the temperature dependence of these values. The Page, logarithmic, approximation of diffusion, two-term, and Midilli et al. models were used to fit the experimental data. A nonlinear regression analysis was used to calculate rate constants and model coefficients. The present findings revealed that among the tested models, the Midilli et al. model best described the experimental data; therefore, it was concluded that the model could be used to describe the drying characteristics of blackberry fruits.

Constitutive Modelling of a New High-Strength Low-Alloy Steel Using Modified Zerilli–Armstrong and Arrhenius Model

Isothermal hot compressive deformation tests were performed on a new high-strength low-alloy (HSLA) steel designated as “Steel A” over a range of temperatures (950–1100 °C) and constant strain rates (0.0003—1 s−1). Using the hot deformation flow behaviour data, material constants to establish constitutive relations using revised Zerilli–Armstrong and phenomenological strain-included Arrhenius model were identified. The potential of the established constitutive equations to describe the high-temperature flow behaviour of the material was then compared with standard statistical parameters such as correlation coefficient (R) and average absolute relative error (AARE). The Arrhenius constitutive model proposed by Sellars and Tegart was found to describe the high-temperature flow behaviour of “Steel A” quite accurately, and hence, this model can be used in simulations of complicated metal-forming processes. The results obtained are presented and discussed here.

Hot compression deformation behavior of biomedical Ni–Ti alloy

Biomedical Ti-55.78 (wt%) Ni alloy samples were prepared by vacuum induction melting, and their hot compression deformation behavior was studied in the deformation temperature range of 750–950 °C, the strain rate range of 0.001–1.000 s−1 and the true strain range of 0.1–0.7. The constitutive equation of the as-cast biomedical Ni–Ti alloy was established based on the Arrhenius constitutive model, and error analysis of the constitutive equation was carried out. The processing zone and unstable thermal deformation zone of the as-cast biomedical Ni–Ti alloy were obtained by establishing hot processing maps based on a dynamic material model. The results showed that deformation temperature and strain rate were the main factors affecting the flow stress. The results of error verification of the constitutive equation show that the predicted flow stress curves agree well with the measured ones. Therefore, the constitutive equation based on Arrhenius can accurately predict the high temperature flow stress of as-cast biomedical Ni–Ti alloy. The optimum parameters for forging process of biomedical Ni–Ti alloy are the strain rate less than 0.003 s−1 and the hot deformation temperature range of 930–950 °C.

A modified constitutive model and hot compression instability behavior of Cu-Ag alloy

Abstract The hot compressive deformation behaviors of Cu−6wt.%Ag alloy were studied experimentally in the temperature range of 973−1123 K and the strain rate range of 0.01−10 s−1. The stress increases and reaches the maximum value when the true strain is very small, and then the stress changes slowly and tends to be stable under the action of work hardening, dynamic recovery and recrystallization. The material parameters of the conventional Arrhenius constitutive model are only related to strain under different deformation conditions, and the prediction error is large, which cannot accurately characterize the hot deformation behavior of the alloy. To describe the hot deformation behavior of the alloy accurately, a modified constitutive model was established by considering the simultaneous influence of forming temperature, strain rate and strain. The results indicate that correlation coefficient (R) and the average absolute relative error (AARE) are 0.993 and 4.2%, respectively. The modified constitutive model can accurately describe the hot deformation behavior of Cu−6wt.%Ag alloy.

Hot Deformation Characteristics and Processing Map of FV520B Martensitic Precipitation-Hardened Stainless Steel

Hot deformation characteristics of FV520B martensitic precipitation-hardened stainless steel were investigated in the temperature range of 850-1150 °C and strain rate range of 0.005-0.5 s−1 with true strain 0.8 by using Gleeble-3500 thermo-mechanical simulator. Critical stress and corresponding critical strain for dynamic recrystallization initiation were calculated. The constitutive equation was developed by employing Arrhenius constitutive model to represent the nonlinear relationship of true stress and deformation parameters including temperature, strain rate and strain. The correlation coefficient and average absolute relative error are 0.9979 and 2.225%, which indicates the good predictive accuracy of the established constitutive equations. Processing maps were constructed at different plastic strains levels based on dynamic material model (DMM) and established constitutive equation. Combining the processing map with microstructure, the optimum region for good workability is designated as the temperature range of 1050-1125 °C and strain rate range of 0.027-0.23 s−1 with peak efficiency of 0.32. Homogeneous fine and equiaxed dynamic recrystallization (DRX) grains can be found in this optimum according to the microstructure metallographic pictures.

Strain Compensation Constitutive Model and Parameter Optimization for Nb-Contained 316LN

Hot deformation behavior of Nb-contained 316LN was investigated using a series of compression tests performed on a Gleeble-1500D simulator at temperature of 950–1200 °C and strain rate of 0.01~1 s−1. Based on the strain compensation method, a modified Arrhenius constitutive model considering the comprehensive effects of temperature, strain rate, and strain on flow stress was established, and the accuracy of the proposed model was evaluated by introducing correlation coefficient (R) and average relative error (AARE). The values of R and AARE were calculated as 0.995 and 4.48%, respectively, proving that the modified model has a high accuracy in predicting the flow stress of Nb-contained 316LN. The microstructure evolution and the dynamic recrystallization (DRX) mechanism of the experimental material were explicated by optical microscopy (OM), electron back scattered diffraction (EBSD), and transmission electron microscopy (TEM). It was found that continuous dynamic recrystallization (CDRX) characterized by subgrain evolution and discontinuous dynamic recrystallization (DDRX) featured by grain boundary nuclei are two main dynamic recrystallization (DRX) mechanisms of Nb-contained 316LN. Furthermore, based on the results of microstructure analyses, optimum parameters were obtained as temperature ranges of 1100~1200 °C and strain rate ranges of 0.01~1 s−1.

Modelling for the flow behavior of a new metastable beta titanium alloy by GA-based Arrhenius equation

The hot compression tests of a new metastable beta titanium alloy (Ti-5Al-5Mo-5V-3Cr-1Zr alloy) were conducted at the temperature range of 1033–1123 K with an interval of 30 K and the strain rates of 0.001–1 s−1 on a Gleeble-3500 isothermal simulator for the acquisition of true stress strain curves. The true stress strain curves at the experimental conditions show different curve-types which reveal different microstructure evolution mechanisms including dynamic recrystallization (DRX), dynamic globularization (DG) and dynamic recovery (DRV). The Arrhenius constitutive model of this alloy was developed based on the experimental results and used to predict the true stress. Based on the developed Arrhenius model, a genetic-algorithm-based (GA-based) Arrhenius model was constructed and applied in true stress prediction. To validate the superiority of the GA-based Arrhenius model in true stress prediction, statistical indicators including mean value (μ), standard deviation (ω), correlation coefficient (R) and average absolute relative error (AARE) were introduced to assess and compare the experimental values and the prediction values. As a result, the μ-value, ω-value, R-value and AARE-value of Arrhenius equation method are −3.8998%, 5.505 62%, 0.9960 and 5.1817% respectively and of the GA-based Arrhenius equation method are 0.0505%, 0.8083%, 0.9999 and 0.6099% respectively, which means the GA-based Arrhenius equation method is promoted in true stress prediction and high accuracy finite element simulation can be achieved by this method.

Hot Deformation Behavior and Dynamic Recrystallization Characteristics in a Low-Alloy High-Strength Ni–Cr–Mo–V Steel

This study presented a quantitative investigation of deformation behavior and dynamic recrystallization of low-alloy high-strength Ni–Cr–Mo–V steels during hot deformation. A series of isothermal compression experiments were performed at temperatures ranging from 800 to 1200 °C and strain rates from 0.01 to 10 s−1 with a height reduction of 60%. A complete Arrhenius constitutive model and processing maps were developed. The results showed that the constitutive model had the ability to predict the flow stress with an average absolute relative error of < 5.7%. The processing maps constructed at strains of 0.2, 0.4, and 0.8 showed that flow instability was prone to occur at higher strain. Dynamic recrystallization tended to take place at higher temperatures (900–1200 °C) and lower strain rates (0.01–1 s−1). The critical strain for the onset of dynamic recrystallization was determined, and a kinetics model was developed. The predicted results for recrystallization volume fraction and flow stress were compared with the experimental data, which indicated that the model was accurate and reliable.

Constitutive Behavior and Processing Map of T2 Pure Copper Deformed from 293 to 1073 K

The deformation behavior of T2 pure copper compressed from 293 to 1073 K with strain rates from 0.01 to 10 s−1 was investigated. The constitutive equations were established by the Arrhenius constitutive model, which can be expressed as a piecewise function of temperature with two sections, in the ranges 293-723 K and 723-1073 K. The processing maps were established according to the dynamic material model for strains of 0.2, 0.4, 0.6, and 0.8, and the optimal processing parameters of T2 copper were determined accordingly. In order to obtain a better understanding of the deformation behavior, the microstructures of the compressed samples were studied by electron back-scattered diffraction. The grains tend to be more refined with decreases in temperature and increases in strain rate.

Influence of Deformation Conditions on the Critical Damage Factor of AZ31 Magnesium Alloy

The influence of deformation conditions on the critical damage factor of AZ31 magnesium alloy was analyzed in this paper. Physical experiments and numerical simulation were used to study the critical damage factor. Compression test was carried out using a Gleeble 1500 device at temperatures between 250°C and 400°C, as well as strain rates from 0.01 s−1 to 1 s−1. True stress‐strain curves of samples were obtained. Based on experimental data, an Arrhenius constitutive model was constructed. Material performance parameters and constitutive model were inputted into the finite element program DEFORM. Simulation results show that the maximum damage appears on the outer edge of the upsetting drum, and damage softening behavior is more sensitive to strain rate. According to the concept of damage sensitive rate, its values were computed. The intersection of line fitted and horizontal axis was obtained in the fracture step, and its relative maximum damage value was as the critical damage factor. The distribution of the critical damage value shows that it is not a constant but fluctuates within the range of 0.1445–0.3759, and it is more sensitive to strain rate compared with temperature.

Flow behavior of Al–6.2Zn–0.70Mg–0.30Mn–0.17Zr alloy during hot compressive deformation based on Arrhenius and ANN models

The hot deformation behavior of Al–6.2Zn–0.70Mg–0.30Mn–0.17Zr alloy was investigated by isothermal compression test on a Gleeble–3500 machine in the deformation temperature range between 623 and 773 K and the strain rate range between 0.01 and 20 s−1. The results show that the flow stress decreases with decreasing strain rate and increasing deformation temperature. Based on the experimental results, Arrhenius constitutive equations and artificial neural network (ANN) model were established to investigate the flow behavior of the alloy. The calculated results show that the influence of strain on material constants can be represented by a 6th-order polynomial function. The ANN model with 16 neurons in hidden layer possesses perfect performance prediction of the flow stress. The predictabilities of the two established models are different. The errors of results calculated by ANN model were more centralized and the mean absolute error corresponding to Arrhenius constitutive equations and ANN model are 3.49% and 1.03%, respectively. In predicting the flow stress of experimental aluminum alloy, the ANN model has a better predictability and greater efficiency than Arrhenius constitutive equations.

Strain-rate sensitivity of powder metallurgy superalloys associated with steady-state DRX during hot compression process

Strain-rate sensitivity (SRS) is an important parameter to describe the thermodynamic behavior in plastic deformation process. In this research, the variation of SRS associated with steady-state DRX in P/M superalloys was quantitatively investigated. Based on the theoretical analysis and microstructural observation of the alloy after deformation, the SRS coefficient was employed to identify the deformation mechanism of the alloy. Meanwhile, the corresponding relationship between SRS coefficient m, stress exponent n and deformation mechanism was revealed. The stress exponent n in the Arrhenius constitutive model of P/M superalloys was calculated. In addition, it is found there is a relatively stable stress exponent range (n = 4-6), indicating that dislocation evolution played as the major hot deformation mechanism for P/M FGH4096 superalloy. Furthermore, the Bergstrom model and Senkov model were used and combined together to estimate the SRS coefficient in the steady-state DRX and the m value maintains at 0.2-0.22, which are consistent with the microstructural evolution during hot deformation process. The SRS coefficient distribution map and power dissipation efficiency distribution map were finally constructed associated with the microstructural evolution during hot deformation, which can be used to optimize the processing parameters of the superalloys.

High-Temperature Mechanical Properties and Constitutive Modelling of Ti6Al4V Sheets

In this paper, tensile tests were performed at elevated temperature and strain rate in order to investigate the plastic flow behavior, anisotropic characteristics and microstructural evolution of Ti6Al4V sheets under testing conditions similar to the ones experienced during hot stamping operations. It is shown that the Ti6Al4V anisotropic characteristics under the investigated forming conditions, different from the ones of the superplastic regime, are influenced by the variation of the material texture as a function of the testing temperature. The Ti6Al4V flow stress behavior was analyzed as a function of the deformation temperature and strain rate. Afterwards, the Arrhenius constitutive model was proposed to predict the flow behavior of Ti6Al4V sheets at elevated temperature and strain rate. The statistical analysis of its predictive capabilities suggests that the Arrhenius model guarantees a good accuracy in reproducing the flow behavior of Ti6Al4V sheets.