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Continuous extrusion is a very promising technique for forming Cu–Cr–Zr alloys which takes the upward continuous casted rods as raw materials. While the hot deformation behavior and constitutive equation of as-cast rods have never been reported. In the present study, the hot deformation behavior of as-cast Cu–Cr–Zr rods with columnar grains was investigated. The results showed that the flow stress at 500 °C is higher than that at 400 °C. The reason for that can be attributed to the dynamic precipitation process, which was confirmed by TEM observations. At this temperature, partial CDRX dominates the softening mechanism while at high temperatures DRV and DDRX play a critical role. The constitutive equation was then established and the deformation activation energy was determined to be 541.93 kJ/mol. The high activation energy was attributed to the large solidified columnar grains. At high strains, stable metal flows can be obtained at high strain rates and high temperatures according to the processing maps, which indicates that a high-speed deformation at a high temperature is favorable to the plastic forming of this material. This investigation thus provides valuable information on how to process the Cu–Cr–Zr rods by plastic deformation methods, for example, continuous extrusion. [ABSTRACT FROM AUTHOR]

Prediction of roll separating force (RSF) is necessary to design new rolling mills, optimise the number of passes and for online control of dimensional accuracy. The intricacy of deformation and complex mixed boundary conditions of velocity and friction makes exact analytical prediction of RSF in a bar or shape rolling quite difficult. Hence, the formula for the prediction of RSF while bar rolling is developed in this research using sticking and slipping friction, assuming the process is equivalent to compression of the simple rectangular bar between two flat plates. The concept of the weak plane strain is also incorporated in the proposed formula. Sinel'nikove's formula derives the contact area between the roll and material. Considering the direct significance of the contact area on the value of RSF, the factors in the said formula are corrected based on a graphical method. Shida's formula is used to calculate the flow stress. The proposed formula is compared with more than fifty distinct experimental findings found in the literature. It is found that the formula is in good agreement with majority of the experimental data. The derived simplified analytical formula can be successfully applied to most types of passes in such industries. [ABSTRACT FROM AUTHOR]

The mechanical properties of welded joints are heterogeneous, which result in complicated stress distribution in welded structures subjected to external loads. An accurate description of heterogeneous weld properties may facilitate the prediction of stress evolution and damage development in welded structures. The heterogeneous mechanical properties of thick welded joints are difficult to be measured directly because the stress–strain data obtained by tensile tests only represent the average properties of the specimen. In this paper, a two-dimensional flow stress model that varies in the transverse and thickness directions is proposed to calculate the heterogeneous mechanical properties of thick welded joints. The boundaries of the welding zones in the friction stir welded joints are clarified by using metallographic analysis. The microhardness tests are performed to reveal the variation of flow stress in the transverse and thickness directions. A force equilibrium equation is established to determine the flow stress functions in different welding zones. The two-dimensional flow stress model is implemented into finite element analysis to predict the mechanical behaviors of thick welded joints. The results show that the stress–strain relations and strain fields predicted by the two-dimensional flow stress model are in good agreement with experimental ones. The strain hardening behaviors of the welded joints are different in the thickness direction, and the maximum strain is concentrated on the thermo-mechanically affected zone and the heat affected zone. The proposed model may be used to predict the complex mechanical behaviors of thick welded joints. [ABSTRACT FROM AUTHOR]

The microstructural evolution of austenite during hot deformation determines the mechanical properties of steel products. Consequently, industrial applications necessitate a thorough comprehension and modeling of this process. Under varied hot deformation conditions, the flow stress, microstructure evolution, and constitutive modeling of a Cu-bearing steel were examined. At various temperatures and strain rates, compression experiments are conducted, and the resulting microstructures were studied by electron backscatter diffraction (EBSD). Our results indicate that fine prior austenite grains with an average diameter of 22.1 m and a high-angle grain boundary density of 0.25 m1 were produced at a deformation temperature of 950 °C and a strain rate of 1 s−1. The dominating rotating cube components ({001}) in the sample deformed at 1150 °C were gradually replaced by the γ-fiber texture component as the deformation temperature decreased. To accurately predict the flow behavior of this steel, we proposed an improved Arrhenius constitutive model that accounts for strain rate and adiabatic temperature rise. With a correlation coefficient (Rc) of 0.9936, a root mean square error (RMSE) of 4.92%, and a relative error (δ) of 6.05 MPa, our results demonstrate that this model predicts the flow stress of the experimental steel with good precision. This research contributes to the development of high-performance steel products by shedding light on the microstructural evolution and flow behavior of Cu-containing steels under hot deformation conditions.

A trustworthy prediction of flow stress behaviour is essential to optimise the hot working process parameters. It also helps accurately capture the finite element simulations of many complex processes. In this work, modification in the Johnson–Cook (JC) model has been proposed for better prediction of the flow stress behaviour of the 92W–5Co–3Ni alloy. Initially, uniaxial compression tests were conducted at different strain rates (1 s−1, 25 s−1, 50 s−1, 75 s−1, and 100 s−1) and temperatures (323 K, 473 K, 673 K, 873 K) using Gleeble-3800 thermo-mechanical simulator. It was confirmed that flow stress variation is sensitive to both strain rate and temperature change. Subsequently, various microstructural parameters were evaluated, such as grain size, tungsten–tungsten contiguity (W/W contiguity), tungsten–tungsten connectivity (W/W connectivity), dihedral angle, neck length, solid volume fraction, and matrix volume fraction. Afterwards, the phenomenological-based constitutive models, namely, Johnson–Cook (JC) and modified Johnson–Cook (m-JC), were initially established. The analysis of flow stress prediction based on various statistical parameters revealed that both models demonstrate poor flow stress prediction capabilities with correlation coefficient (R) of 0.7715 and 0.7925, respectively. An improved Johnson–Cook model (i-JC) was proposed, replacing the strain term with the Ludwigson hardening equation and varying the coefficient of strain rate hardening term with plastic strain and strain rate. The i-JC model significantly improved the accuracy of flow stress prediction with a correlation coefficient (R) of 0.9891, average absolute relative error (AARE) of 1.35%, and standard deviation of 1.33%. [ABSTRACT FROM AUTHOR]

Compression tests of the Cu-1.5Ti and Cu-1.5Ti-0.5Fe alloys were carried out using the Gleeble-1500D hot deformation simulator. The deformation temperature was 750–900 °C and the strain rate was 0.1–0.003 s−1. The Cu-1.5Ti-0.5Fe alloy clearly shows higher rheological stress and displays dynamic recovery and dynamic recrystallization characteristics under the same deformation conditions. The constitutive equations of the alloys were established. The activation energy of the Cu-1.5Ti alloy was 341.76 kJ/mol, which increased to 378.03 kJ/mol with the addition of 0.5 wt% Fe. After 750 °C and 0.003 s−1 deformation the Cu4Ti phase precipitated in Cu-1.5Ti alloy. Adding 0.5 wt% Fe caused dynamic recrystallization during hot deformation. The hot-deformed Cu-1.5Ti-0.5Fe alloy had more dislocations and finer grains with Cu4Ti and Fe2Ti precipitated phases.

This study investigates the compression deformation behavior of an Mg-Gd-Y-Nd-Zr alloy at temperatures ranging from 293 K to 573 K and strain rates ranging from 293K to 573K and strain rates ranging from 1000 s−1 to 2100 s−1 using a split Hopkinson pressure bar. A modified Johnson-Cook (JC) constitutive model and a backpropagation neural network (BPNN) model based on the improved whale optimization algorithm (IWOA) are established. Four statistical metrics, including correlation coefficient (R), mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE), are employed to evaluate the predictive accuracy of the two models. The findings indicate that the flow stress of the alloy is sensitive to strain, strain rate, and temperature. Increasing strain and strain rate or decreasing deformation temperature results in higher flow stress. Error calculations revealed that the modified Johnson-Cook constitutive model has an R of 0.98731, a MAPE of 7.3653%, a MAE of 19.6305 MPa, and a RMSE of 26.5704 MPa. In contrast, the model established using the IWOA-BPNN has an R of 0.99996, a MAPE of 0.58894%, a MAE of 1.2671 MPa, and a RMSE of 1.7709 MPa. The IWOA-BPNN model demonstrates higher accuracy and accurately predicts the flow stress of the alloy.

A machine learning technique leveraging artificial intelligence (AI) has emerged as a promising tool for expediting the exploration and design of novel high entropy alloys (HEAs) while predicting their mechanical properties at both room and elevated temperatures. In this paper, we predict the flow stress of hot-compressed CoCrFeNiV HEAs using conventional (qualitative and quantitative models) and advanced machine learning approaches across various temperature and strain rate conditions. Conventional modeling methods, including the modified Johnson-Cook (JC), modified Zerilli–Armstrong (ZA), and Arrhenius-type constitutive equations, are employed. Simultaneously, machine learning models are utilized to forecast flow stress under different hot working conditions. The performance of both conventional and machine learning models is evaluated using metrics such as coefficient of determination (R2), mean abosolute error (MAE), and root mean squared error (RMSE). The analysis reveals that the gradient boosting machine learning model shows superior prediction accuracy (with value R2 = 0.994, MAE = 7.77%, and RMSE = 9.7%) compared to conventional models and other machine learning approaches.

Aiming at the aging deformation of turbine blades in turbine engines under complex stress, Waspaloy nickel-based alloy was taken as the research object to carry out aging treatment and complete quasi-static high temperature mechanical tensile tests of Waspaloy nickel-based alloy at 600, 700 and 750 ℃. The flow stress of Waspaloy nickel-based alloy at high temperature plastic section was predicted by Ludwik and Hollomon empirical formulas, and the mean error (Er) and root mean square error (RMSE) were introduced to evaluate the accuracy of the flow stress prediction. The results show that the hardness of Waspaloy nickel-based alloy is improved effectively after aging treatment, but its plastic properties are reduced. The tensile strength and elongation of Waspaloy nickel-based alloy are negatively correlated with the loading temperature in the range of 600 ~ 750 ℃. Ludwik model owns higher accuracy than Hollomon model in flow stress prediction, but there is a still large error in flow stress prediction in high temperature and high strain region. Based on the Ludwik model, the exponential term is introduced, and the modified Ludwik model have a better prediction result in the flow stress of Waspaloy nickel-based alloy at high temperature plastic section. [ABSTRACT FROM AUTHOR]

This study explores isothermal hot compression of the as‐extruded 7005 aluminum alloy within a temperature range of 573–823 K, with strain rates from 0.001 to 1 s−1 and a strain of 1.2. Three constitutive equations, employing hyperbolic sine, power law, and exponential functions, were formulated and compared to predict rheological peak stress accuracy and applicability. The results indicate that the hyperbolic sine function is suitable across all stress levels, the power law function for low stress (<56 MPa), and the exponential function for high stress (>56 MPa). Introducing a strain compensation function enhances hyperbolic sine function accuracy. The stress exponent (n) and activation energy (Q) decrease with increased deformation, indicating a transition in the deformation mechanism from early‐stage dislocation climb to later‐stage dislocation glide. At 773 K with strain >0.6, the presence of precipitates maintains the n value at approximately 4. Solute atoms (Zn, Mg, and Zr) and precipitates (MgZn2 and Al3Zr) impede diffusion and dislocation motion, resulting in deformation activation energies surpassing pure aluminum. Additionally, kernel average misorientation maps demonstrate that higher deformation temperatures and lower strain rates reduce internal residual stresses. [ABSTRACT FROM AUTHOR]

This study documents an investigation of the flow stress properties and microstructural features of Ti6Al4V (ELI) alloy produced using laser powder bed fusion (LPBF). Selected heat treatment strategies were applied to the material to obtain different microstructures. The influence of quasi-static strain rates and temperature on the obtained microstructures of this material and their strain hardening properties are documented in this study. All microstructures of the alloy formed in this study were found to be sensitive to quasi-static strain rates and temperatures, where their flow stresses increased with increasing strain rate and decreased for tests conducted at elevated temperatures. The strain hardening rates of the fine microstructures were found to be high compared to those of coarse microstructures. The strain hardening rates for the various forms of LPBF Ti6Al4V (ELI) examined here were found to diminish with increasing test temperature. Though the deformed surfaces of the built samples were largely dominated by adiabatic shear bands (ASBs), the absence of ASBs was noted for all samples tested at a temperature of 500 °C and an imposed strain of 30%. [ABSTRACT FROM AUTHOR]

A systematic analytical study of the mathematical properties of the previously constructed nonlinear model for shear flow of thixotropic viscoelastic-plastic media is continued. For arbitrary six material parameters and an (increasing) material function that control the model, the basic properties of the families of stress-strain curves at constant strain rates and relaxation curves generated by the model, and the features of the evolution of the structuredness under these types of loading are analytically studied. The dependences of these curves on time, shear rate, initial strain and initial structuredness of the material, as well as on the material parameters and function of the model, are studied. Several indicators of the applicability of the model are found which are convenient to check with experimental data. It was examined what effects typical for viscoelastic-plastic media can be described by the model and what unusual effects (unusual properties) are generated by a change in structuredness in comparison with typical stress-strain curves and relaxation curves of structurally stable materials. In particular, it has been proved that stress-strain curves can be both increasing functions and can have decreasing sections resembling a "yield tooth" or damped oscillations, that all stress-strain curves (SSCs) possess horizontal asymptotes (steady flow stress), monotonically dependent on shear rate, and flow stress increases with shear rate growth, that the instantaneous shear modulus, on the contrary, depends on the initial structuredness, but does not depend on shear rate. Under certain restrictions on the material parameters, the model is also capable of providing a bilinear form of stress-strain curves, which is typical for an ideal elastoplastic model, but with strain rate sensitivity. It has been established that the family of stress-strain curves does not have to be increasing either in initial structuredness or in shear rate: in a certain range of shear rates, in which the equilibrium position is a "mature" focus and pronounced oscillations of stress-strain curves are observed, it is possible to intertwine stress-strain curves with different shear rates. It is proved that for any material parameters and functions, all stress relaxation curves decrease and have a common zero asymptote as time tends to infinity. The analysis proved the ability of the model to describe behavior of not only liquid-like viscoelastoplastic media, but also solid-like (thickening, hardening, hardened) media: creep, relaxation, recovery, a number of typical properties of experimental relaxation curves, creep and stress-strain curves, strain rate and strain hardening, flow under constant stress and so on. [ABSTRACT FROM AUTHOR]

The deteriorated plasticity arising from the insoluble precipitates may lead to cracks during the rolling of FeCrAl alloys. The microstructure evolution and hot deformation behavior of an FeCrAl alloy were investigated in the temperature range of 750–1200 °C and strain rate range of 0.01–10 s−1. The flow stress of the FeCrAl alloy decreased with an increasing deformation temperature and decreased strain rate during hot working. The thermal deformation activation energy was determined to be 329.49 kJ/mol based on the compression test. Then, the optimal hot working range was given based on the established hot processing maps. The hot processing map revealed four small instability zones. The optimal working range for the material was identified as follows: at a true strain of 0.69, the deformation temperature should be 1050–1200 °C, and the strain rate should be 0.01–0.4 s−1. The observation of key samples of thermally simulated compression showed that discontinuous dynamic recrystallization started to occur with the temperate above 1000 °C, leading to bended grain boundaries. When the temperature was increased to 1150 °C, the dynamic recrystallization resulted in a microstructure composed of fine and equiaxed grains. [ABSTRACT FROM AUTHOR]

The hot deformation behavior of Al-Zn/martensitic stainless steel particles-based composite (Al-Zn/6 %SSp), was examined in this study. The composite was tested using isothermal compression at 200–350 °C/0.01–10 s−1 and a global strain of 0.5. From the results, it was noticed that the composite’s flow stress increased with strain rate increase and drop in temperature. The constitutive equation from the hot-worked composites resulted in an estimated activation energy of 226.27 kJ/mol, which was 58 % more than that for the self-diffusion of aluminum alloy (142 kJ/mol). These findings suggest dynamic recrystallization (DRX) as the dominant deformation mechanism, as confirmed from the microstructures of the hot worked samples mostly at high temperatures and strain rates. Work hardening was predicted to dominate the deformation process by the stress exponent (n) value of 10.36 (which exceeded 5), but this was inconsistent with the microstructural observations. Comparing the linear fitting of calculated flow stress data with the estimated flow stress yielded a correlation coefficient (R2) of approximately 0.97. This observation demonstrates an effective relationship involving the calculated stress with the computed stress value for the composite material that was fabricated. Based on the processing map analysis, the instability regime occurs at 200270 °C/0.01–10 s−1. The stable domain established was at 280–340◦C/0.01–10 s−1 which is most suitable for achieving the best microstructural conditions for enhanced service performance.

Residual stress is caused by non–uniform deformation caused by non–uniform force, heat and composition, which is of great significance in engineering applications. It is assumed that the residual stress is always the upper limit of the elastic limit, so the reduction of the flow stress will reduce the residual elastic stress. It is particularly important to control the flow stress in metal materials. Compared with traditional methods, the use of electropulsing treatment (EPT) technology stands out due to its energy–efficient, highly effective, straightforward and pollution–free characteristics. However, there are different opinions about the mechanism of reducing flow stress through EPT due to the conflation of the effects from pulsed currents. Herein, a clear correlation is identified between induced stress levels and the application of pulsed electrical current. It was found that the decrease in flow stress is positively correlated with the current density and the duration of electrical contact and current action time. We first systematically and comprehensively summarize the influence mechanisms of EPT on dislocations, phase, textures and recrystallization. An analysis of Joule heating, electron wind effect, and thermal–induced stress within metal frameworks under the influence of pulsed currents was conducted. And the distribution of electric, thermal and stress fields under EPT are discussed in detail based on a finite element simulation (FES). Finally, some new insights into the issues and challenges of flow stress drops caused by EPT are proposed, which is critically important for advancing related mechanism research and the revision of theories and models.

The hot deformation behavior and microstructure of Fe-12.5Cr–4Al–2Mo-0.03Nb-0.08Y alloy were studied under conditions of 800 °C–1200 °C/0.01 s−1∼10 s−1 using a combination of hot compression experiments, EBSD and TEM characterization. The results indicate that the deformation temperature and strain rate have a significant impact on the flow stress and microstructure of the alloy, especially the deformation temperature. The constitutive equation constructed in this paper can reflect the hot deformation process and accurately calculate flow stress value of the FeCrAl alloy in corresponding states. The FeCrAl alloy undergoes DRV and DRX during hot deformation. DDRX grains distributed along the original grain boundaries mainly formed at low deformation temperatures and high strain rates, while CDRX grains mainly formed at high deformation temperatures and low strain rates and characterized by the internal distribution of the original grains. Moreover, the orientation of DDRX grains is mostly different from that of adjacent original grains, while the orientation of CDRX grains is relatively close to that of the original grains.

The constitutive model refers to the mapping relationship between the stress and deformation conditions (such as strain, strain rate, and temperature) after being loaded. In this work, the hot deformation behavior of a Ni-Cr-Mo steel was investigated by conducting isothermal compression tests using a Gleeble-3800 thermal simulator with deformation temperatures ranging from 800 °C to 1200 °C, strain rates ranging from 0.01 s−1 to 10 s−1, and deformations of 55%. To analyze the constitutive relation of the Ni-Cr-Mo steel at high temperatures, five machine learning algorithms were employed to predict the flow stress, namely, back-propagation artificial neural network (BP-ANN), Random Committee, Bagging, k-nearest neighbor (k-NN), and a library for support vector machines (libSVM). A comparative study between the experimental and the predicted results was performed. The results show that correlation coefficient (R), root mean square error (RMSE), mean absolute value error (MAE), mean square error (MSE), and average absolute relative error (AARE) obtained from the Random Committee on the testing set are 0.98897, 8.00808 MPa, 5.54244 MPa, 64.12927 MPa2 and 5.67135%, respectively, whereas the metrics obtained via other algorithms are all inferior to the Random Committee. It suggests that the Random Committee can predict the flow stress of the steel more effectively. [ABSTRACT FROM AUTHOR]

Residual stress is caused by non–uniform deformation caused by non–uniform force, heat and composition, which is of great significance in engineering applications. It is assumed that the residual stress is always the upper limit of the elastic limit, so the reduction of the flow stress will reduce the residual elastic stress. It is particularly important to control the flow stress in metal materials. Compared with traditional methods, the use of electropulsing treatment (EPT) technology stands out due to its energy–efficient, highly effective, straightforward and pollution–free characteristics. However, there are different opinions about the mechanism of reducing flow stress through EPT due to the conflation of the effects from pulsed currents. Herein, a clear correlation is identified between induced stress levels and the application of pulsed electrical current. It was found that the decrease in flow stress is positively correlated with the current density and the duration of electrical contact and current action time. We first systematically and comprehensively summarize the influence mechanisms of EPT on dislocations, phase, textures and recrystallization. An analysis of Joule heating, electron wind effect, and thermal–induced stress within metal frameworks under the influence of pulsed currents was conducted. And the distribution of electric, thermal and stress fields under EPT are discussed in detail based on a finite element simulation (FES). Finally, some new insights into the issues and challenges of flow stress drops caused by EPT are proposed, which is critically important for advancing related mechanism research and the revision of theories and models. [ABSTRACT FROM AUTHOR]

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The hot deformation behavior of titanium matrix composites plays a crucial role in determining the performance of the formed components. Therefore, it is significant to establish an accurate constitutive relationship between material deformation parameters and flow stress. In this study, hot compression experiments were conducted on a (2.5 vol%TiB + 2.5 vol%TiC)/TC4. The experiments were performed under temperatures ranging from 1013.15 to 1133.15 K and strain rates ranging from 0.001 to 0.1 s−1. Based on the stress–strain data obtained from the experiment, the constitutive models were established by using the Arrhenius model and the BP neural network algorithm, respectively. Considering the relationship between strain rate, hot working temperature, and flow stress, a comparative analysis was conducted to evaluate the prediction accuracy of two different constitutive models. The research results indicate that the flow stress of (2.5 vol%TiB + 2.5 vol%TiC)/TC4 increases with decreasing temperature and increasing strain rate, and the stress–strain curve shows obvious work hardening and softening behaviors. Both the Arrhenius model and the BP neural network algorithm are effective in predicting the hot compression flow stress of (2.5 vol%TiB + 2.5 vol%TiC)/TC4, but the average relative error and root mean square error of the BP neural network algorithm are smaller and the correlation coefficient is higher, thus possessing higher accuracy and reliability. [ABSTRACT FROM AUTHOR]

The work is devoted to the study of random statistical processes in two-phase flows. The objective is to obtain new computational and experimental data on the influence of previously undetermined factors on the trajectories of particle motion, their segregation, and the formation of a locally continuous flow field of the dispersed phase in supersonic turbulent two-phase flows. The results of computational and experimental study of the flow features of a two-phase supersonic flow are presented. A new experimental method was applied for analysis of influence of random statistical factors on the particle distribution in a high-speed carrier flow. The physical basis of the proposed method is to indicate the flow rate of the dispersed phase by means of particle adhesion to an obstacle installed in the flow. In order to analyze the segregation of the dispersed phase in the flow, the approach of quasi-continuumization of individual particle trajectories is applied. The method obtains a locally continuous flow stress field for dispersed phase flow. Empirical coefficients resulting from the influence of random statistical factors on the motion of dispersed particles in a two-phase flow are determined. The obtained computational and experimental data clarify the prediction of the distribution and segregation of dispersed phase particles with a size of 15–40 microns in a supersonic free flow. [ABSTRACT FROM AUTHOR]

The present work deals with the hot deformation behavior of selective laser melted 316L stainless steel with an emphasize on the involved recrystallization mechanisms. Toward this end, a series of hot compression test have been conducted in the temperature range of 700–1000 °C under the various strain rates of 0.001, 0.01 and 0.1s−1. The flow pattern analysis through Jonas-Poliak method verifies the occurrence of dynamic recrystallization in whole investigated temperature range. The intensified substructure development and continuous recrystallization is identified as the main softening mechanism in the course of thermomechanical processing. This causes appearance of a broad peak and low softening fraction in corresponding flow curves. The cellular substructure in the as-printed state facilitates low-angle into high-angle boundaries conversion, which provide a proper condition for the occurrence of continuous mechanisms and increases the rate of recrystallization. However, detailed investigation of the sub-boundary maps indicates the contribution of discontinuous and geometric dynamic recrystallization mechanisms. Dynamic recrystallization causes substantial refinement; and the percentage of the grain holding size lower than 10 μm increases from 2 % in printed microstructure to 16.8 % and 24 % in the microstructure deformed at 700 and 1000 °C.

In advanced solid-state manufacturing processes such as friction stir welding, the metal's temperature ranges from room temperature to the solidus temperature. The material strength in the temperature range is generally required for investigating the mechanical behaviors. In this communication paper, an analytical model is proposed for describing the thermal softening of aluminum alloys for room temperature to solidus temperature, in which the concept of temperature-dependent transition between two thermal softening regimes is implemented. It is demonstrated that the proposed model compares favorably to the well-known Sellars–Tegart model and Johnson–Cook model. The constants of the proposed model for nine typical engineering commercial aluminum alloys are documented. [ABSTRACT FROM AUTHOR]

This article reports the flow stress behaviour of two P92 steels at a temperature range of 850–1000°C and a strain rate of 0.1–10 s−1 using the Gleeble® 3500 thermomechanical simulator. A physically-based constitutive model was used to analyse the effects of deformation conditions on the flow stress behaviour during deformation. This model incorporates the influence in the variation of Young's modulus and the self-diffusion coefficient as affected by temperature. The study developed constitutive equations that predict the flow stress behaviour of the two steels investigated. From the constitutive analysis of the results, the stress exponent n was: 9.8 (steel A) and 10.3 (steel B). The model used the self-diffusion activation energy of steel. The statistical parameters: correlation coefficient of 0.99 (for steel A and B), the absolute average relative error of 2.18% (steel A) and 2.20% (steel B) quantified the applicability of the model. The quantification results show that the constitutive equations developed have high accuracy in predicting the workability of the two P92 steels. The study has shown that this method is applicable in predicting the metal flow pattern of two P92 steels in the metalworking processes. [ABSTRACT FROM AUTHOR]

This research is focused on the modeling of the deformation behavior of thin austenitic stainless steel sheets to consider size effect in microscale. First, the material with two different thicknesses is heat treated to obtain different grain sizes, and then they are characterized by the uniaxial tensile tests. The experimental results show that flow stress decreases with the reduction of the sheet thickness and the increase of the grain size. The decline of the flow stress curve is associated with the decrease of the strength coefficient and increase of the hardening exponent as the plastic deformation is scaled down to the microscale. To better model the behavior of the material in the microscale, a new constitutive model is proposed based on the Swift equation to take into account the geometry and grain size effect. This model is also defined in the finite element model of the uniaxial tensile test. It is found that the flow stress curve predicted by the proposed constitutive model shifts down by the decrease of the number of grains across the thickness, which are consistent with the experimental results. In addition, the finite element model with the proposed constitutive model predicts accurately the deformation load in the uniaxial tensile tests. It can be concluded that the proposed constitutive model can provide a good description of the flow stress by considering the interactive effect of specimen and grain sizes and can be used in the modeling of material behavior in microforming processes. [ABSTRACT FROM AUTHOR]

Knowing the behavior of hot deformation and microstructure changes of API-5CT-L80 alloy steel is of great importance in the production of oil and gas industry pipes. For this purpose, in this research, the thermomechanical behavior of this steel was investigated by isothermal hot compression test in the temperature range of 1173 to 1373 K and strain rates of 0.001 to 1 s-1 s. The experimental results showed that the hot deformation behavior of steel is a softening behavior caused by the dynamic recrystallization phenomenon that in some conditions, the material shows complex behavior in the form of multi-peaked curves. The results of the microstructural investigation showed that with the increase in the deformation temperature, the formed grains have a larger size compared to the low temperature state, and more martensite phases are formed, which are more elongated martensite blades compared to the phases formed at low temperatures. The effect of strain rate was also significant like the effect of temperature because the rate of deformation had an inverse effect on grain growth, so recrystallized grains have enough time to grow at low strain rates. At high strain rates, the pearlite phases appeared more polygonal, and very small nucleation were observed in the austenitic boundaries of the ferrite and Wiedmannstein phase, which did not have enough time to grow, and at high strain rates, the martensite blades also tend to thin. [ABSTRACT FROM AUTHOR]

This study aims to investigate the hot ductility and fracture mechanisms of microalloyed steel commonly used in industrial production, especially when it starts as a rolling stock material. In order to simulate the typical thermomechanical processes experienced by this steel, the samples have been exposed to a solution treatment at 1200 °C followed by a well-defined precipitation treatment cycle before deformation. The experiments on hot deformation have been conducted at a consistent deformation rate of 1.96x10-3 s-1 over a range of temperatures ranging from 700 °C to 1050 °C. Through thorough analysis, a correlation between the extent of damage experienced during the hot deformation process and the specific fracture characteristics observed in specimens deformed under tension has been established. This link between damage and fracture type provides insights into the key factors that influence the overall mechanical behavior of microalloyed steel under these conditions. The findings of this investigation have substantial implications for the industrial production of microalloyed steel and can contribute to a more informed approach in selecting appropriate process parameters and optimizing the material's hot ductility and fracture resistance. [ABSTRACT FROM AUTHOR]

The mechanical properties and rate-sensitive deformation of T4 and T6 AA6063 aluminum alloys have been analyzed at 298 K, 78 K, and 4 K. The strength, ductility, and work hardening capacity of two alloys increase with decreasing deformation temperature. Plastic deformation of AA6063-T4 is accompanied by adiabatic flow stress instabilities at 4 K and the Portevin-Le Chatelier (PLC) effect at 298 K. The alloy shows a better synergy of flow stress and work hardening than the T6 condition, determined by the underlying microstructure. The limited ability of dislocation storage in T6 alloy arises from shearing β″ particles and the enhanced dislocation annihilation occurring in pure Al matrix. The failure of the alloys is promoted by void nucleation at intermetallic particles before the Considére criterion is fulfilled. AA6063-T6 exhibits positive strain rate sensitivity (SRS) at three temperatures. Dislocations-β″ particle interactions determine its SRS and are a rate-controlling process at 298 K. AA6063-T4 shows negative strain rate sensitivity (nSRS) at 298 K controlled by dislocation-solute interactions. Data for SRS and thermodynamic deformation parameters characterizing different mechanisms in T4 and T6 alloys between 4 K and 298 K are discussed. The results indicate that plastic deformation produces vacancies by jogs' dragging at 298 K, but this process does not occur at 78 K and 4 K.

An accurate constitutive model is imperative to describe the deformation behavior of aluminum alloy in numerical simulation of thermal plastic forming process. In this study, isothermal uniaxial compressions of 2A12-T4 aluminum alloy were conducted by Gleeble-3500 thermal-mechanical simulator under the temperature of 300–450 °C and strain rate of 0.01–10 s−1. Three different Arrhenius constitutive models, including strain compensation (SC), genetic algorithm (GA) and K-function modification (KM), were established basing on the double correction of the true stress–strain curve by considering the effect of temperature variation and interfacial friction. The prediction accuracy of three models were assessed by the correlation coefficient (R), average absolute relative error (AARE) and the logarithm of the mean square error (ln (MSE)). The results show that the newly KM constitutive model considering the coupling effect of temperature and strain rate showed excellent agreement with the experimental data and best prediction capability with lowest error. Hot processing map based on the Murty-Rao criterion shows that high temperature and low strain rate is suitable for stable forming. In order to verify the reliability of the proposed model in numerical simulation, the established KM Arrhenius constitutive equation is secondarily developed in DEFORM 3D software and used in the hot compression process under the stable forming conditions obtained from hot processing map. The simulated force–displacement curves and maximum load values under forming conditions were well match with the experiment trends, which proved the reliability of the KM constitutive equation in the finite element numerical simulation.

The current study investigates the high-temperature deformation behaviour, and microstructural evolution of the laser powder bed fused, Ti modified Al 2024 alloy. The high-temperature performance was evaluated using a hot compression test performed in the temperature range of 200–350 °C and strain rate range of 0.1–10 s−1. The flow behaviour at elevated temperatures at different strain rates can provide us insight into the high temperature application and can also be utilized for optimization of deformation-based post processing technique. The deformation-based post processing method utilizes work hardening to improve the mechanical properties and to reduce the inherent defect of additively manufactured parts, such as pores and lack of fusion. The optimal deformation conditions for these processes can be obtained from the processing map. The flow stress during different deformation conditions (strain, strain rate and temperature) was predicted using different phenomenological models such as Johnson-Cook (JC) model, strain compensated Arrhenius equation, and artificial neural network (ANN). The JC model was observed to be the least suited method in the current investigation, whereas the ANN method was observed to be best suited for predicting flow stress with an average absolute relative error of 0.5% and a correlation coefficient of 0.9998. Different deformation mechanisms such as dynamic recovery (DRV) and dynamic recrystallization (DRX) were investigated for different deformation conditions using empirical models, finite element analysis (FEA) and microstructural characterization using TEM, and EBSD. The primary DRX mechanism in the current study was observed to be continuous dynamic recrystallization or CDRX mechanism.

This study documents an investigation of the flow stress properties and microstructural features of Ti6Al4V (ELI) alloy produced using laser powder bed fusion (LPBF). Selected heat treatment strategies were applied to the material to obtain different microstructures. The influence of quasi-static strain rates and temperature on the obtained microstructures of this material and their strain hardening properties are documented in this study. All microstructures of the alloy formed in this study were found to be sensitive to quasi-static strain rates and temperatures, where their flow stresses increased with increasing strain rate and decreased for tests conducted at elevated temperatures. The strain hardening rates of the fine microstructures were found to be high compared to those of coarse microstructures. The strain hardening rates for the various forms of LPBF Ti6Al4V (ELI) examined here were found to diminish with increasing test temperature. Though the deformed surfaces of the built samples were largely dominated by adiabatic shear bands (ASBs), the absence of ASBs was noted for all samples tested at a temperature of 500 °C and an imposed strain of 30%.

The deteriorated plasticity arising from the insoluble precipitates may lead to cracks during the rolling of FeCrAl alloys. The microstructure evolution and hot deformation behavior of an FeCrAl alloy were investigated in the temperature range of 750–1200 °C and strain rate range of 0.01–10 s−1. The flow stress of the FeCrAl alloy decreased with an increasing deformation temperature and decreased strain rate during hot working. The thermal deformation activation energy was determined to be 329.49 kJ/mol based on the compression test. Then, the optimal hot working range was given based on the established hot processing maps. The hot processing map revealed four small instability zones. The optimal working range for the material was identified as follows: at a true strain of 0.69, the deformation temperature should be 1050–1200 °C, and the strain rate should be 0.01–0.4 s−1. The observation of key samples of thermally simulated compression showed that discontinuous dynamic recrystallization started to occur with the temperate above 1000 °C, leading to bended grain boundaries. When the temperature was increased to 1150 °C, the dynamic recrystallization resulted in a microstructure composed of fine and equiaxed grains.

With the advancement in computational approaches and experimental, simulation, and modeling tools in recent decades, a trial-and-validation method is attracting more attention in the materials community. The development of powder metallurgy Ni-based superalloys is a vivid example that relies on simulation and experiments to produce desired microstructure and properties in a tightly controlled manner. In this research, we show an integrated approach to predicting the grain size of industrial forgings starting from lab-scale cylindrical compression by employing modeling and experimental validation. (a) Cylindrical compression tests to obtain accurate flow stress data and the hot working processing window; (b) double-cone tests of laboratory scale validation; (c) sub-scale forgings for further validation under production conditions; and (d) application and validation on full-scale industrial forgings. The procedure uses modeling and simulation to predict metal flow, strain, strain rate, temperature, and the resulting grain size as a function of thermo-mechanical processing conditions. The models are calibrated with experimental data until the accuracy of the modeling predictions is at an acceptable level, which is defined as the accuracy at which the results can be used to design and evaluate industrial forgings. [ABSTRACT FROM AUTHOR]

The uniaxial warm tensile experiments were carried out in deformation temperatures (50–250 °C) and strain rates (0.005 to 0.0167 s − 1 ) to investigate the material workability and to predict flow stress of AZ31B magnesium alloy. The back–propagation artificial neural network (BP–ANN) model, a hybrid models with a genetic algorithm (GABP–ANN), and a constrained nonlinear function (CFBP–ANN) were investigated. In order to train the exploited machine learning models, the process parameters such as strain, strain rate, and temperature were accounted as inputs and flow stress was considered as output; moreover, the experimental flow stress values were also normalized to constructively run the neural networks and to achieve better generalization and stabilization in the trained network. Additionally, the proposed model's closeness and validness were quantified by coefficient of determination ( R 2 ), relative mean square error (RMSE), and average absolute relative error (AARE) metrics. The computed statistical outcomes disclose that the flow stress predicted by both GABP–ANN and CFBP–ANN models exhibited better closeness with the experimental data. Moreover, compared with the GABP–ANN model outcomes, the CFBP–ANN model has a relatively higher predictability. Thus, the outcomes confirm that the proposed CFBP–ANN model can result in the accurate description of AZ31 magnesium alloy deformation behavior, showing potential for the purpose of practicing finite element analysis. [ABSTRACT FROM AUTHOR]

A mathematical model is developed to consider the impact of microstructural parameters, including the volume fraction and the average particle size of martensite, on the flow stress and strain‐hardening behavior of dual‐phase microstructure. In this regard, the micromechanical approach is applied for partitioning the stress and strain in ferrite and martensite. Martensite carbon content and geometrically necessary dislocations, generated from austenite‐to‐martensite transformation, and strain accommodation at the ferrite–martensite interface, are involved to modify the partitioned stress of martensite and ferrite, respectively. Having partitioned stress in each phase, the global stress is estimated as the function of steel chemical composition, ferrite grain size, martensite particle size, aspect ratio, and volume fraction. To evaluate the applicability of the proposed model, four dual‐phase steels containing 12, 25, 34, and 48% volume fractions of martensite are prepared from the intermediate quenching process, and then after the strain‐hardening stages are investigated. Comparing the experimental result and model output reveals that the presented model shows good predictive capabilities to identify strain‐hardening stages and estimate the inverse of the strain‐hardening exponent. [ABSTRACT FROM AUTHOR]

Nylon 66 is an engineering plastic with the advantageous characteristics of light weight, heat resistance, high strength, and high rigidity; it has been used in automobile parts as a substitute for aluminum alloys. There have also been many studies on the mechanical properties of nylon 66. However, the flow stress in nylon 66 after necking has not been thoroughly investigated yet due to the difficulty in identifying local stress. In this study, a flow stress optimization method based on the digital image correlation (DIC) method and response surface method, is proposed. The averaged true stress–true plastic strain curve is first obtained by a quasi-static tensile test via DIC. Subsequently, the flow stress is optimized via the response surface method to obtain the actual flow stress state after necking. The accurate flow stress in the specimen can be obtained based on the relationship between the global load force and distance between the two shoulders of the specimen grip parts that is unaffected by the cross-sectional area change during necking. The results indicate that the average true stress recorded from the experiment overestimates the flow stress after necking. The optimized flow stress exhibits the maximum decrease of 9%. The accuracy of the optimized flow stress is evaluated by comparison with the true strain distribution on the specimen that is accurately measured via DIC. [ABSTRACT FROM AUTHOR]

Constitutive equations were recognized for AZ31B magnesium alloy at higher temperatures and strain rates from conventional empirical models like the original Johnson–Cook (JC), modified JC, and modified Zerilli–Armstrong (ZA) models for capturing the material warm deformation behavior. Uniaxial warm tensile tests were performed at temperatures (50 to 250 °C) and strain rates (0.005 to 0.0167 s − 1 ) to probe AZ31 magnesium alloy flow stress values. Depending on the calculated flow stress, constitutive equations were recognized, and these established models were assessed by the coefficient of determination ( R 2 ), relative mean square error (RMSE), and average absolute relative error (AARE) metrics. The results demonstrated that the flow stress calculated by the modified JC and ZA models revealed good agreement against the test data. Thus, the outcomes confirmed that the recognized modified JC and modified ZA models could effectively forecast AZ31 magnesium alloy flow behavior by capturing the material deformation behavior accurately. [ABSTRACT FROM AUTHOR]

As a kind of special energy field assisted plastic forming, electric pulse assisted plastic forming combines multiple physical fields, such as thermal, electrical, magnetic and mechanical effects, has multiple effects on metal. It has a good industrial application prospect in the fields of directional microstructure regulation of materials and preparation of new materials. The flow stress of metal materials can be effectively reduced by electro-pulse assisted forming. The action mechanism of pulse current includes thermodynamics (Joule heating effect) and kinetic (pure electro-plastic effect or athermal effect). Thermodynamically, electric pulses can be used to provide the energy for dislocation migration and atomic diffusion, and aid in microstructure changes such as recrystallization, phase transition and microcrack healing of metals. In terms of dynamics, electric pulse has an effect on the speed and path of dislocation structure evolution. On this basis, a series of theoretical models for accurately predicting the flow stress of materials in electrically assisted forming process were formulated by combining the stress–strain constitutive relationship considering the temperature rise effect and the pure electro-plastic effect. The accuracy of the predicting model is greatly enhanced by the introduction of electrical parameters. The mechanism for electrically assisted forming was further revealed.

The hot deformation behavior of titanium matrix composites plays a crucial role in determining the performance of the formed components. Therefore, it is significant to establish an accurate constitutive relationship between material deformation parameters and flow stress. In this study, hot compression experiments were conducted on a (2.5 vol%TiB + 2.5 vol%TiC)/TC4. The experiments were performed under temperatures ranging from 1013.15 to 1133.15 K and strain rates ranging from 0.001 to 0.1 s−1. Based on the stress–strain data obtained from the experiment, the constitutive models were established by using the Arrhenius model and the BP neural network algorithm, respectively. Considering the relationship between strain rate, hot working temperature, and flow stress, a comparative analysis was conducted to evaluate the prediction accuracy of two different constitutive models. The research results indicate that the flow stress of (2.5 vol%TiB + 2.5 vol%TiC)/TC4 increases with decreasing temperature and increasing strain rate, and the stress–strain curve shows obvious work hardening and softening behaviors. Both the Arrhenius model and the BP neural network algorithm are effective in predicting the hot compression flow stress of (2.5 vol%TiB + 2.5 vol%TiC)/TC4, but the average relative error and root mean square error of the BP neural network algorithm are smaller and the correlation coefficient is higher, thus possessing higher accuracy and reliability.

Goat milk gels (GMGs) are popular food due to their high water content, low-calorie density, appealing taste, texture enhancers, stability, and satiety-enhancing characteristics, making them ideal for achieving food security and zero hunger. The GMGs were optimized using the central composite design matrix of response surface methodology using goat milk powder (35–55 g), whole milk powder (10–25 g), and potato powder (10–15 g) as independent variables. In contrast, complex modulus, flow stress, and forward extrudability were chosen as dependent variables. The maximum value of complex modulus 33670.9 N, good flow stress 7863.6 N, and good extrudability 65.32 N was achieved under optimal conditions. The optimized goat milk gel was fortified with ascorbic acid-coated iron oxide nanoparticle (magnetic nature) decorated alginate-chitosan nanoparticles (AA-MNP@CANPs), making it nutritionally rich in an economically feasible way—the decorated AA-MNP@CANPs characterized for size, shape, crystallinity, surface charge, and optical characteristics. Finally, the optimized fortified smart GMGs were further characterized via Scanning electron microscopy, Rheology, Texture profile analysis, Fourier transforms infrared (FTIR), and X-Ray Diffraction (XRD). The fortified smart GMGs carry more nutritional diversity, targeted iron delivery, and the fundamental sustainability development goal of food security.