Established Constitutive Equations Research Articles

Effect of initial grain size on hot deformation behavior and recrystallization mechanism of Al-Zn-Mg-Cu alloy

Grain size is industrially important for improving mechanical properties and formability. In order to investigate the effect of grain size on the hot workability and deformation mechanisms, Al-Zn-Mg-Cu alloys with different initial grain sizes, 241.2, 100.4 and 48.4 μm, were subjected to hot compression tests. Using the established constitutive equation, the rheological behavior is described and the influence of the initial grain on the thermal deformation behavior is analyzed. Electron back-scatter diffraction (EBSD) analysis was used to study the dynamic recrystallization (DRX) mechanisms of Al-Zn-Mg-Cu alloys with different initial grain sizes. The microstructures obtained under various deformation conditions were analyzed. The results show that decreasing the initial grain size enhances both the peak stress and the activation energy for thermal deformation. Meanwhile, the dynamic recrystallization mechanism varies depending on the initial grain size. Continuous dynamic recrystallization (CDRX) is the primary DRX nucleation mode for coarse-grained alloys. Nonetheless, discontinuous dynamic recrystallization (DDRX) is predominant for alloys with fine grains.

Study on Hot Deformation Behavior and Processing Maps of Cobalt‐Based Superalloy GH5188

True stress–strain data are obtained through the thermal compression test of the cobalt‐based superalloy GH5188 at the temperature range of 1080–1180 °C and the strain rate of 0.1–10 s−1, and the Arrhenius constitutive equation considering the effects of temperature, strain rate, and strain is established. The microscopic deformation mechanism and the appropriate process range are proposed based on the analysis of the dynamic material model and electron backscattered diffraction (EBSD). The results show that the established constitutive equation exhibits predictive ability, and the calculated thermal activation energy Q value is 446.1054 KJ mol−1; when the strain is 0.7, the GH5188 superalloy undergoes dynamic recrystallization (DRX) at 1130 °C in the form of discontinuous DRX; when the temperature is 1180 °C, the degree of DRX is significantly improved, and evenly distributed equiaxed grains are obtained; when the strain is 0.2, 0.4, and 0.6, DRX is mainly affected by the degree of deformation, and its occurrence is accompanied by the generation of Σ3. Combined with the analysis of the processing maps and EBSD diagrams, the optimal thermal deformation parameters of GH5188 alloy are determined as follows: the strain is 0.7, the deformation temperature is about 1180 °C, and the strain rate is about 1 s−1.

Effect of Ultrasonic Vibration on Tensile Mechanical Properties of Mg-Zn-Y Alloy

Ultrasonic vibration assisted (UVA) plastic forming technology has proven to be a highly effective processing method, particularly for materials that are challenging to deform. In this research, UVA tensile tests were carried out on Mg98.5Zn0.5Y1 alloy at different vibration frequencies and amplitudes. The experimental results indicate that, compared with conventional tensile tests, the yield strength and tensile strength of Mg98.5Zn0.5Y1 alloy exhibit a decrease. Furthermore, the application of ultrasonic vibration demonstrates an ability to enhance the material’s elongation and plasticity. In order to further predict the stress-strain relationship in the metal tensile process, a hybrid constitutive model coupling the frequency and amplitude of ultrasonic vibration was developed based on the modified Johnson Cook model. The calculated results of the constitutive equation are in good agreement with the experimental results, indicating that the established constitutive equation can accurately predict the trend of alloy stress change at different amplitudes and frequencies. It establishes a theoretical foundation for scrutinizing the deformation mechanisms of the alloy under ultrasonic vibration. Furthermore, Abaqus finite element analysis software was employed to simulate and analyze the UVA tensile process, elucidating the impact of ultrasonic vibration on stress distribution, strain patterns, and material flow in the tensile behavior of Mg98.5Zn0.5Y1 alloys.

Temperature rises and constitutive equation of homogenized 6063 aluminum alloy for extrusion

The effect of temperature rises on the flow stress and constitutive equation of homogenized 6063 aluminum alloy was studied by theoretical analysis, numerical simulation, and experiments. The results showed that the temperature rises increased with the decreases of deformation temperatures and the increases of strain rates, which caused the flow softening. The modification of the flow stresses of 6063 aluminum alloy was carried out. A strain compensation constitutive equation based on the Arrhenius equation and Zener-Hollomon parameter was introduced to predict the flow behavior of 6063 aluminum alloy. The calculated flow stresses were consistent with the experimental results, and its average absolute relative error was only 3.25%. Finally, the established constitutive equation was substituted into the Deform-3D software. The corresponding extrusion experiments were carried out. The maximum extrusion pressures and maximum exit temperatures in the numerical simulation were in good agreement with those in the experiments, which confirmed the accuracy and reliability of the established constitutive equation.

Hot deformation and dynamic recrystallization behavior of a Cu-9Ni-6Sn-0.04Cr alloy

Hot deformation behavior of Cu-9Ni-6Sn-0.04Cr alloy has been investigated by isothermal compression tests in the temperature range of 750 ∼ 900 ℃ and the strain rate range of 0.01 ∼ 10 s−1. By using Arrhenius equation, the activation energy Q of Cu-9Ni-6Sn-0.04Cr alloy is 218 kJ/mol. The predicted flow stresses obtained from the established constitutive equation are consistent with the experimental results for the alloy. The results indicate that proposed constitutive equation offers a high precision for predicting the hot deformation behavior of the Cu-9Ni-6Sn-0.04Cr alloy. In addition, according to the evolution of microstructures, dynamic recrystallization process is the main softening mechanism during hot deformation in Cu-9Ni-6Sn-0.04Cr alloy. Combining the characteristics of dynamic recrystallization process with Zener–Hollomon parameter value, it is shown that continuous dynamic recrystallization is the main dynamic recrystallization mechanism in the high Z value condition. Moreover, and continuous dynamic recrystallization and discontinuous dynamic recrystallization are the main dynamic recrystallization mechanisms in the middle and low Z value condition, the discontinuous dynamic recrystallization is dominated by bulging and nucleation. This study can provide reliable hot working parameters for Cu-Ni-Sn alloy fabrication.

The hot deformation behaviors and constitutive modeling of Hastelloy C276

Hastelloy C276 is widely used in the new generation of nuclear power plants, and hot deformation is the optimum way to form the C276 part. In this investigation, the hot deformation and constitutive modeling of Hastelloy C276 alloy are researched, and the processing maps are drawn. The results show that strain rate and hot deformation temperature have remarkable impacts on the deformation behaviors of the Hastelloy C276 alloy. The yield behavior and the flow stress are predicted based on the Arrhenius constitutive equation, and the correlation coefficients are 0.9613 and 0.9837, indicating the high prediction ability of the established constitutive equation. Rising the deformation temperature can decrease the unstable deformation area, and the studied alloy can be deformed at low strain rates. With the increased strain rate, flow localization occurs, which is not suitable for the hot deformation.

Hot deformation behavior, processing map, microstructure evolution and dynamic recrystallization mechanism of Mg-5Al-0.6Sc alloy

In this study, the hot compression test of as-cast Mg-5Al-0.6Sc alloy was performed on Gleeble-3500 simulator, and the effect of deformation temperature (T: 250–400 °C) and strain rate (ε̇: 0.001 –1 s−1) on hot deformation mechanism of the alloy were systematically investigated. The thermal deformation behavior, microstructure evolution, texture and dynamic recrystallization (DRX) mechanism of the alloy were analyzed in detail by combining the constitutive equation, processing map and electron backscatter diffraction (EBSD) technology. The results demonstrated that the flow stress decreased with the increase of T and decrease of ε̇. The established constitutive equation could accurately predict the hot deformation behavior of the alloy, and the calculated average activation energy (Q) is 144.58 kJ/mol. Based on processing map, the optimal processing area is within 300–350 °C, 0.001 s − 1 and 350–400 °C, 0.001 s−1 - 0.01 s−1. The microstructure at 350 °C and 0.001 s−1 is more uniform and exhibits low residual stress level. The increase of T and decrease of ε̇ are both conducive to the occurrence of DRX. DRX mechanism includes discontinuous DRX (DDRX), continuous DRX (CDRX), deformation twin induced DDRX and CDRX. In addition, both DRXed grains and unDRXed grains showed typical<0001>// CD texture. Combined with the in-grain misorientation axis (IGMA) analysis, when T is 250 °C and 300 °C, the deformation is dominated by basal<a>dislocations and prismatic<a>dislocations, and the proportion of twinning and DRX is extremely low. When T is 350 °C and 400 °C, the pyramidal Ⅱ<c+a>dislocations is activated greatly, and the DRX fraction increases significantly, which become the predominant deformation mechanism.

Coating optimization of yield pseudoplastic paste-based stereolithography 3D printing of alumina ceramic core

Yield pseudoplastic paste is prepared for self-supported stereolithography (SLA) 3D printing with critical shear stress of 290.7 Pa and viscosity of 28810 mPa·s under strain rate of 30 s−1. Simulation analysis of paste coating is carried out based on established constitutive equation. Furthermore, corresponding stress field is analyzed under different layer thicknesses (25–100 μm) and blade speeds (1.5–4.5 mm/s). Then, flexural strength, porosity, surface roughness and microstructure of components, printed with different layer thicknesses and sintered at different temperatures, are systematically investigated. Finally, complex-shaped cores are fabricated with flexural strength of 38.56±1.45 MPa, porosity of 21.57±0.8% and surface roughness of Ra < 3 μm. The optimized parameters include layer thickness of 25–50 μm, blade speed of 3.5 mm/s, and sintering temperature of 1300 oC. Moreover, step-like undulating fracture morphology of the core is observed along printing layer, which shows that the coating process has an important influence on the mechanical properties of ceramic parts.

Hot compression deformation behavior and processing maps of Al–0.5Mg–0.4Si–0.1Cu alloy

To improve the hot working stability of Al–0.5Mg–0.4Si–0.1Cu alloy, isothermal compression tests were performed at the temperature range of 350–500 °C and strain rate of 0.001–10 s−1. Strain-compensated Arrhenius constitutive equation containing Zener–Hollomon parameters was established to describe the hot deformation behavior. Its accuracy was evaluated within the whole strain range and the established constitutive equation can well predict the flow behavior. In addition, intrinsic machinability was further analyzed by constructing processing maps under different true strains based on dynamic material models. Microstructures are in fine agreement with processing maps and flow instability occurred mainly in high strain rate regions due to the presence of adiabatic shear bands and flow localization. Dynamic softening mechanism of the alloy mainly stems from dynamic recovery and partial dynamic recrystallization. Based on processing maps and microstructure observations, optimal process parameters of alloy were obtained, which are beneficial to optimize its hot working parameters.

Dynamic behavior description and three-dimensional cutting simulation of SiCp/Al composites with high volume fraction

According to the dynamic behavior characteristics of SiCp/Al composites, the constitutive equation of high volume fraction composites is established by SHPB dynamic compression test, shear lag model and effective medium approximation method, and the calculation results are in good agreement with the experiments. The established constitutive equation is then imported into Abaqus to establish a three-dimensional cutting simulation model, which is combined with cutting experiments to analyze the dynamic removal mechanism of material during the cutting process and the cutting surface formation process. The results show that the formation and propagation of holes and cracks play an important role in the formation of chips. The failure removal mode of SiC particles is an important factor affecting the cutting surface morphology. The research results provide an important theoretical basis and research means for the study of cutting mechanism of SiCp/Al composites with high volume fraction.

Experimental mechanics and numerical prediction on stress relaxation and unrecoverable damage characteristics of rubber materials

Stress relaxation and unrecoverable damage deformation are common phenomenon in rubber materials, which greatly induces instability of geometrical dimension and deteriorates the mechanical performances. The present work proposes experimental mechanics and numerical prediction for studying stress relaxation and unrecoverable damage characteristics. A time-dependent strain energy principle is established to describe the relaxation decay over time, and a quasi-plastic function is combined by considering the plastic flow criteria in order to depict the unrecoverable deformation after stress relaxation. Experimental study is conducted on multi-modes hyper-elastic mechanics and stress relaxation performances, and key parameters of the proposed constitutive model are identified by multi-island genetic algorithm (MIGA). The established constitutive equation is integrated in finite element simulation, and the numerical prediction is conducted. Combined experimental results clearly present nonlinear elastic properties, time-decay relaxation, and unrecoverable damage deformation of rubber materials. The numerical results are in good agreement with experiment ones, and the mechanism of relaxation and damage characteristics are explored. Additionally, based on the time-temperature superposition principle (TTSP) method, long-term stress relaxation behavior at low temperature is estimated by the short-term high-temperature test. This work provides efficient methods of experimental mechanics and numerical prediction for predicting the stress relaxation and damage characteristics of rubber materials, which could be also beneficial for characterizing rubber-base devices in engineering applications.

Construction of hot deformation processing maps for 9Cr-1Mo steel through conventional and ANN approach

The behavior of hot deformed flow curves in a 9Cr-1Mo steel have been analysed using constitutive and artificial neural network (ANN) approaches. At each temperature (850 ° C-1100 ° C) various strain rates (0.001 s−1–10 s−1) of deformation behavior has been analysed. The corrections of flow stress due to the adiabatic temperature rise during hot deformation have been made through artificial neural network (ANN) method and compared it with the linear interpolation (conventional) method. The temperature corrected (conventional) flow stress has been compared and analyzed with the predicted flow stress data obtained by established constitutive equation. Additionally, the experimental flow stresses obtained by thermomechanical simulator have also been compared and analyzed with predicted flow stresses obtained by ANN method. Further, the predicted and corrected flow stress curves obtained by ANN method have been compared and analyzed. The processing maps at 0.6 true strain based on flow stress data corrected through both ANN and conventional methods have been compared. Upon analyzing the safe and unsafe domains of the maps with the corresponding microstructures, the ANN approach depicted the best precise results over that of the conventional method. Variation in strain hardening rate and correlated it with EBSD analysis have also been carried out to analyze the variation in hardness for some of the deformed specimens.

Constitutive Equation and Hot Processing Map of a Nitrogen-Bearing Martensitic Stainless Steel

The hot deformation behavior of a nitrogen-bearing martensitic stainless steel was researched by the isothermal compression test in the temperature range of 950–1150 °C and strain rate range of 0.01–10 s−1 with a Gleeble-3800 thermal-mechanical simulating tester. A strain compensated sine-hyperbolic Arrhenius-type constitutive equation was developed to describe the relationship between true stress and deformation parameters such as temperature, strain rate and true strain. The hot deformation activation energy is calculated to be from 407 to 487 KJ mol−1. It is validated by the standard statistical parameters that the established constitutive equation can accurately predict the true stress. The processing maps at different true strains were constructed based on the dynamic material model (DMM) and the true stress data obtained from the hot compression tests. Two unstable regions which should be avoided during hot working were observed from the processing map. In addition, the optimum hot working parameters are located in the domain of 1000–1150 °C/0.1–1 s−1 with the peak power dissipation efficiency of 39.9%, in which complete dynamic recrystallization (DRX) occurs.

Hot deformation behavior of Mg95.21Zn1.44Y2.86Mn0.49 alloy containing LPSO phase

The Mg-Zn-Y-Mn alloy containing LPSO phase is a new type of high-strength Mg alloy system, and research on its hot deformation behavior has not been carried out. The hot compression experiments (compression deformation amount is 70%) of the as-homogenized Mg95.21Zn1.44Y2.86Mn0.49 alloy were performed at a temperature range of 250–500 °C and a strain rate range of 0.001–5 s−1 on a Gleeble-1500D thermo-mechanical simulator, and the flow behavior and microstructure evolution of the alloy during the deformation process were studied. According to the established constitutive equation, the stress index of the test alloy during hot compression deformation was 16.17, and the activation energy Q of hot deformation was 393.32 kJ/mol. The microstructure after deformation showed that incomplete dynamic recrystallization (DRX) began to occur at 350 °C, and complete DRX occurred at 450 °C, forming equiaxed fine recrystallized grains. Due to the presence of the LPSO phase, the activation energy Q of the experimental alloy was higher than the conventional Mg alloys.

Dynamic triaxial constitutive model for rock subjected to initial stress

AbstractBuilding on the existing model, an improved constitutive model for rock is proposed and extended in three dimensions. The model can avoid the defect of non-zero dynamic stress at the beginning of impact loading, and the number of parameters is in a suitable range. The three-dimensional expansion method of the component combination model is similar to that of the Hooke spring, which is easy to operate and understand. For the determination of model parameters, the shared parameter estimation method based on the Levenberg–Marquardt and the Universal Global Optimization algorithm is used, which can be well applied to models with parameters that do not change with confinement and strain rates. According to the established dynamic constitutive equation, the stress–strain curve of rock under the coupling action of the initial hydrostatic pressure load and constant strain-rate impact load can be estimated theoretically. By comparing the theoretical curve with the test data, it is shown that the dynamic constitutive model is suitable for the rock under the initial pressure and impact load.

Characterization of hot deformation behavior of 30Si2MnCrMoVE low-alloying ultra-high-strength steel by constitutive equations and processing maps

Isothermal compression tests of as-forged 30Si2MnCrMoVE low-alloying ultra-high-strength steel were carried out on a Gleeble 3500 thermal simulator at the deformation temperatures of 950–1150 °C and strain rates of 0.01–10 s−1. Based on the classical stress–dislocation density relationship and the kinematics of the dynamic recrystallization, the constitutive equations of the work hardening dynamical recovery period and dynamical recrystallization period were developed by using the work hardening curve and Avrami equation, which shows good agreement with the experimental value. Processing maps at the strain of 0.90 were constructed based on dynamic material model and were analyzed combined with microstructure observation under different conditions. The optimum parameter based on the processing maps was obtained and verified by a supplementary experiment. The power dissipation maps and instability maps at strains of 0.05–0.90 were also constructed, and the evolution law was analyzed in detail. The established constitutive equation and hot processing maps can provide some guidance for hot working process.

Constitutive Model and Processing Maps for a Ti‐55511 Alloy in β Region

The flow behavior of a high‐strength Ti alloy (Ti‐55511) in the β region is studied by hot compressive experiments. A dislocation density–based constitutive equation, together with processing maps, is established to describe the flow behavior and hot workability of the studied Ti alloy. It is found that the strain rate () and temperature (T) distinctly influence the hot compressive deformation behavior. The flow stress increases distinctly with a rising or reducing T. The main softening mechanism in the β region is dynamic recovery (DRV). The established constitutive equation based on the work hardening (WH) and DRV mechanisms has the desired prediction accuracy, and the correlation coefficient between the predicted and experimental results is 0.9912. The processing maps indicate that a high strain rate (0.4–10 s−1) easily causes unstable deformation, whereas low and medium strain rates (0.001–0.2 s−1) are suitable for hot compressive deformation of the studied alloy.

Numerical Analysis and Experimental Studies on the Residual Stress of W/2024Al Composites.

W/2024Al composites can be used for radiation shielding with desirable mechanical properties such as high strength, excellent corrosion resistance, and low density. The quench-induced residual stresses in W/2024Al composites were studied by experimental measurements and numerical analysis using ABAQUS software. Due to the accurate calculation of heat transfer coefficients and the established constitutive equation for description of the variation of yield stress at elevated temperature with different strain rates, the prediction of residual stresses in as-quenched composite blocks achieved by finite element method (FEM) is reliable. Moreover, X-ray diffraction and crack-compliance method were carried out to measure the stresses that developed at the surface and interior of the composites to validate the simulation results. Quenching residual stresses of composite blocks were investigated by taking the influence of quenching medium temperature into consideration. In addition, a comparative study on residual stress magnitudes of as-quenched 2024Al and W/2024Al composites was conducted, and the results show that stress magnitudes of W/2024Al composites are lower than that of 2024Al due to lower thermal gradients during the quenching process.

Development of Constitutive Relationship for Thermomechanical Processing of Al-SiC Composite Eliminating Deformation Heating

Constitutive equations are useful for computational or numerical tools in describing the thermomechanical behavior of Al/SiC composites to develop the lightweight component using bulk metal forming. In this study, the uniaxial compression test of powder metallurgy-based Al/7 vol.% SiCp composite samples in the temperature range of 250-500 °C and at the strain rates of 0.001, 0.007, 0.05, 0.3, 2.2 and 15 s−1 was performed on a Gleeble-3800 thermomechanical simulator. An equation correlating actual (measured) temperature with the true stress in real time has been established for each of the strain rates. Further, the true stress was corrected by eliminating the effect of deformation heating using this equation based on the experimental observations. The temperature-corrected true stress data were then used for development of constitutive equations using the Arrhenius model, strain-compensated Arrhenius model and modified Johnson–Cook (m-JC) model. The material parameters in the m-JC model were calculated at different combinations of temperatures and strain rates. The established constitutive equations are validated with temperature-corrected true stress from the experiment. Further, these equations are verified with the experimental true stress that was obtained using different inputs of temperatures and strain rates in a compression test. The correlation coefficient (R) and absolute average relative error reflect the accuracy of constitutive models. The result indicates that the calculated true stress by the established strain-compensated Arrhenius model is in good agreement with that of experimentally measured true stress with a correlation coefficient of 0.996 and relative error of 3.83%.

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.