Modeling constitutive relationship of 6013 aluminum alloy during hot plane strain compression based on Kriging method

Hot plane strain compression tests of 6013 aluminum alloy were conducted within the temperature range of 613?773 K and the strain rate range of 0.001?10 s?1. Based on the corrected experimental data with temperature compensation, Kriging method is selected to model the constitutive relationship among flow stress, temperature, strain rate and strain. The predictability and reliability of the constructed Kriging model are evaluated by statistical measures, comparative analysis and leave-one-out cross-validation (LOO-CV). The accuracy of Kriging model is validated by the R-value of 0.999 and the AARE of 0.478%. Meanwhile, its superiority has been demonstrated while comparing with the improved Arrhenius-type model. Furthermore, the generalization capability of Kriging model is identified by LOO-CV with 25 times of testing. It is indicated that Kriging method is competent to develop accurate model for describing the hot deformation behavior and predicting the flow stress even beyond the experimental conditions in hot compression tests.

Constitutive modeling of hot deformation behavior of X20Cr13 martensitic stainless steel with strain effect

Hot deformation behavior ofX20Cr13 martensitic stainless steel was investigated by conducting hot compression tests on Gleeble-1500D thermo-mechanical simulator at the temperature ranging from 1173 to 1423 K and the strain rate ranging from 0.001 to 10 s^-1. The material constants of a and n, activation energy Q and A were calculated as a function of strain by a fifth-order polynomial fit. Constitutive models incorporating deformation temperature, strain rate and strain were developed to model the hot deformation behavior of X20Cr13 martensitic stainless steel based on the Arrhenius equation. The predictable efficiency of the developed constitutive models of X20Cr13 martensitic stainless steel was analyzed by correlation coefficient and average absolute relative error which are 0.996 and 3.22%, respectively.

Heat transfer model for microwave hot in-place recycling of asphalt pavements

In order to solve for temperature fields in microwave heating for recycling asphalt mixtures, a two-dimensional heat transfer model for the asphalt mixtures within the heating range is built based on the theory of unsteady heat conduction. Four onedimensional heat transfer models are established for the asphalt mixtures outside the heating range, which are simplified into four half-infinite solids. The intensity of the radiation electric field is calculated through experiment by using heating water loads. It is suggested that the mathematical model of boundary conditions can be established in two ways, which are theoretical deduction and experimental reverse. The actual temperature field is achieved by fitting temperatures of different positions collected in the heating experiment. The simulant temperature field, which is solved with the Matlab PDE toolbox, is in good agreement with the actual temperature field. The results indicate that the proposed models have high precision and can be directly used to calculate the temperature distribution of asphalt pavements.

Unified Degradation Model in Low Gate Voltage Range During Hot-Carrier Stressing of p-MOS Transistors

Hot carrier effects of p MOSFETs with different oxide thicknesses are studied in low gate voltage range.All electrical parameters follow a power law relationship with stress time,but degradation slope is dependent on gate voltage.For the devices with thicker oxides,saturated drain current degradation has a close relationship with the product of gate current and electron fluence.For small dimensional devices,saturated drain current degradation has a close relationship with the electron fluence.This degradation model is valid for p MOSFETs with 0 25μm channel length and different gate oxide thicknesses.

Opti mization and Model of Laminar Cooling Control Systemfor Hot Strip Mills

The structure of laminar cooling control system for hot rolling was introduced and the control mode, cooling strategy, segment tracking and model recalculation were analyzed. The parameters of air/water cooling models were optimized by regressing the data gathering in situ, and satisfactory effect was obtained. The coiling temperature can be controlled within ±15℃.

Self-Learning and Its Application to Laminar Cooling Model of Hot Rolled Strip

The mathematical model for online controlling hot rolled steel cooling on run-out table （ROT for abbreviation） was analyzed, and water cooling is found to be the main cooling mode for hot rolled steel. The calculation of the drop in strip temperature by both water cooling and air cooling is summed up to obtain the change of heat transfer coefficient. It is found that the learning coefficient of heat transfer coefficient is the kernel coefficient of coiler temperature control （CTC） model tuning. To decrease the deviation between the calculated steel temperature and the measured one at coiler entrance, a laminar cooling control self-learning strategy is used. Using the data acquired in the field, the results of the self-learning model used in the field were analyzed. The analyzed results show that the self-learning function is effective.

Modeling of hot deformation behavior and prediction of flow stress in a magnesium alloy using constitutive equation and artificial neural network(ANN)model

The aim of the present study was to investigate the modeling and prediction of the high temperature flow characteristics of a cast magnesium(Mg-Al-Ca)alloy by both constitutive equation and ANN model.Toward this end,hot compression experiments were performed in 250-450℃and in strain rates of 0.001-1 s^(−1).The true stress of alloy was first and foremost described by the hyperbolic sine function in an Arrhenius-type of constitutive equation taking the effects of strain,strain rate and temperature into account.Predictions indicated that unlike low strain rates and high temperature with dominant DRX activation,in relatively high strain rate and low temperature values,the precision of the models become decreased due to activation of twinning phenomenon.At that moment and for a better evaluation of twinning effect during deformation,a feed-forward back propagation ANN was developed to study the flow behavior of the investigated alloy.Then,the performance of the two suggested models has been assessed using a statistical criterion.The comparative assessment of the gained results specifies that the well-trained ANN is much more precise and accurate than the constitutive equations in predicting the hot flow behavior.

Three-Di mensional Model for Strip Hot Rolling

A three-dimensional model for strip hot rolling was developed, in which the plastic deformation of strip, the thermal crown of rolls, roll deflection and flattening were calculated by rigid-plastic finite element method, finite difference method, influential function method and elastic finite element method respectively. The roll wear was taken into consideration. The model can provide detailed information such as rolling pressure distribution, contact pressure distribution between backup rolls and work rolls, deflection and flattening of work rolls, lateral distribution of strip thickness, and lateral distribution of front and back tensions. The finish rolling on a 1 450 mm hot strip mill was simulated.

HOT DUCTILITY OF 304HC STAINLESS STEEL AND THE MODEL OF RESISTANCE TO DEFORMATION

The ductility map of 304HC stainless was determined by using the Gleeble-1500 dynamic thermal-mechanical simulator. The effect of Cu on the hot ductility of 304HC stainless steel was analyzed and the mathematical model of resistance to deformation was established. The microstructure, inclusion and fracture surface were studied by using the method of micro structure analysis, scanning, energy spectrum and electron microscope. The results show that Cu has effect on the hot ductility, and the hot ductility of 304HC stainless steel decrease with the increase of content of Cu. The deformation temperature also has much effect on the hot ductility, the suitable deformation temperature are 1100-1200℃. The reason of it is that the Cu rich chemical compounds were precipitated from austenite phase during cooling. The Cu rich chemical compounds are brittle substance such as Cu2S, Cu2O and ε-Cu etc.

MODELING OF FERRITE GRAIN GROWTH OF LOW CARBON STEELS DURING HOT ROLLING

For most commercial steels the prediction of the final properties depends on accurately calculating the room temperature ferrite grain size. A grain growth model is proposed for low carbon steels Q235B during hot rolling. By using this model, the initial ferrite grain size after continuous cooling and ferrite grain growing in coiling procedure can be predicted. In-plant trials were performed in the hot strip mill of Ansteel. The calculated final ferrite grain sizes are in good agreement with the experimental ones. It is helpful both for simulation of microstructure evolution and prediction of mechanical properties.

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 compressiontest on a Gleeble?3500machine in the deformation temperature range between623and773K and the strain rate range between0.01and20s?1.The results show that the flow stress decreases with decreasing strain rate and increasing deformation temperature.Basedon the experimental results,Arrhenius constitutive equations and artificial neural network(ANN)model were established toinvestigate the flow behavior of the alloy.The calculated results show that the influence of strain on material constants can berepresented by a6th-order polynomial function.The ANN model with16neurons in hidden layer possesses perfect performanceprediction of the flow stress.The predictabilities of the two established models are different.The errors of results calculated by ANNmodel were more centralized and the mean absolute error corresponding to Arrhenius constitutive equations and ANN model are3.49%and1.03%,respectively.In predicting the flow stress of experimental aluminum alloy,the ANN model has a betterpredictability and greater efficiency than Arrhenius constitutive equations.

Recrystallization model for hot-rolling of 5182 aluminum alloy

A recrystallization model for hot rolling of 5182 aluminum alloy was presented by means of the fractional softening during double interval deformation. It is found that the recrystallization rate depends on strain rate more sensitively than deformation temperature, and the time for full recrystallization is very short as strain rate is greater than 1?s -1 . Using the recrystallization—time—temperature curves, the desirable hot rolled microstructure can be obtained by controlling the rolling speed, temperature and cooling rate before cooling during the last pass in reversing mill.[

Hot deformation behavior and constitutive modeling of Q345E alloy steel under hot compression

Q345E as one of typical low alloy steels is widely used in manufacturing basic components in many fields because of its eminent formability under elevated temperature. In this work, the deformation behavior of Q345E steel was investigated by hot compression experiments on Gleeble-3500 thermo-mechanical simulator with the temperature ranging from 850 ℃ to 1150 ℃ and strain rate ranging from 0.01 s-1 to 10 s-1. The experimental results indicate that dynamic softening of Q345E benefits from increasing deformation temperature and decreasing strain rate. The mathematical relationship between dynamic softening degree and deformation conditions is established to predict the dynamic softening degree quantitatively, which is further proved by some optical microstructures of Q345E. In addition, the experimental results also reveal that the stress level decreases with increasing deformation temperature and decreasing strain rate. The constitutive equation for flow stress of Q345E is formulated by Arrihenius equation and the modified Zener-Hollomon parameter considering the compensation of both strain and strain rate. The flow stress values predicted by the constitutive equation agree well with the experimental values, realizing the accurate prediction of the flow stress of Q345E steel under hot deformation.

Prediction on hot deformation behavior of spray-formed 7055 aluminum alloy via phenomenological models

Hot compression tests in the temperature range of 340-450 ℃ and strain rate range of 0.001-1 s^-1 of spray-formed 7055 aluminum alloy were carried out to study its hot deformation behavior. Three phenomenological models including Johnson-Cook, modified Fields-Backofen and Arrhenius-type were introduced to predict the flow stresses during the compression process. And then, a comparative predictability of the phenomenological models was estimated in terms of the relative errors, correlation coefficient（R）, and average absolute relative error（AARE）. The results indicate that Johnson-Cook model and modified Fields-Backofen model cannot well predict the hot deformation behavior due to the large deviation in the process of line regression fitting. Arrhenius-type model obtains the best fit through combining the effect of strain rate and temperature.

Flow behavior modeling of IMI834 titanium alloy during hot tensile deformation

A proper constitutive model was developed to predict the hot tensile flow behavior of IMI834 titanium alloy in α+β region. Hot tensile tests were performed at 800–1025 °C and 0.001–0.1 s−1. The constitutive model was developed through an Arrhenius-type equation at strains of 0.08–0.22 to characterize the hot tension behavior. It was found that the activation energies for hot tensile deformation of IMI834 titanium alloy are in the range of 519–557 kJ/mol at different strain values. The accuracy of predicted flow stress curves was evaluated using standard statistical parameters. These curves are appropriately found to be in good agreement with the experimental ones.

New constitutive equation utilizing grain size for modeling of hot deformation behavior of AA1070 aluminum

A new phenomenological and empirically-based constitutive model was proposed to modify the term in the original Johnson−Cook constitutive model.The new model can be used to describe and predict the flow stress of AA1070 aluminum with different initial grain sizes in the hot working process.This developed model considers thermal softening,strain-rate hardening,strain hardening,initial grain size,and interactions with each other and can correctly model the behavior of AA1070 at elevated temperature with different strains,strain rates,and initial grain sizes.The hot flow behavior of AA1070 was investigated through compression tests over wide ranges of temperature from 623 to 773 K,strain rate from 0.005 to 0.5 s−1 and initial grain size from 50 to 450μm.Results show that the initial grain size has a significant effect on the flow behavior of AA1070.Then,correlation coefficient(R),average absolute relative error(AARE),and relative error were examined for comparative predictability of the model.Results show that flow stresses for different initial grain sizes calculated by the new proposed model perfectly correlate with experimental ones,with a mean relative error of 1.19%,which confirms that the new modified Johnson−Cook relation can give a precise estimation of the hot flow stress of AA1070 aluminum by considering the initial grain size.

Work roll thermal contour prediction model of nonoriented electrical steel sheets in hot strip mills

The demands for profile and flatness of nonoriented electrical steels are becoming more and more severe. The temperature field and thermal contour of work rolls are the key factors that affect the profile and flatness control in the finishing trains of the hot rolling. A theoretic mathematical model was built by a two-dimensional finite difference to calculate the temperature field and thermal contour at any time within the entire rolling campaign in the hot rolling process. To improve the calculating speed and precision, some special solutions were introduced, including the development of this model, the simplification of boundary conditions, the computation of heat transfer coefficient, and the narrower mesh along the edge of the strip. The effects of rolling pace and work roll shifting on the temperature field and thermal contour of work rolls in the hot rolling process were demonstrated. The calculated results of the prediction model are in good agreement with the measured ones and can be applied to guiding profile and flatness control of nonoriented electrical steel sheets in hot strip mills.

Modeling of metadynamic recrystallization kinetics after hot deformation of low-alloy steel Q345B

Based on the steady-state strain measured by single-pass hot compression tests,the method by a double-pass hot compression testing was developed to measure the metadynamic-recrystallization kinetics.The metadynamic recrystallization behavior of low-alloy steel Q345B during hot compression deformation was investigated in the temperature range of 1 000-1 100℃,the strain rate range of 0.01-0.10 s -1 and the interpass time range of 0.5-50 s on a Gleeble-3500 thermo-simulation machine.The results show that metadynamic recrystallization during the interpass time can be observed.As the deformation temperature and strain rate increase,softening caused by metadynamic recrystallization is obvious.According to the data of thermo-simulation,the metadynamic recrystallization activation energy is obtained to be Qmd=100.674 kJ/mol and metadynamic recrystallization kinetics model is set up.Finally,the error analysis of metadynamic recrystallization kinetics model proves that the model has high accuracy(correlation coefficient R=0.988 6).

Constitutive model for a new kind of metastable β titanium alloy during hot deformation

The constitutive model was developed to describe the relationship among flow stress,strain,strain rate,and deformation temperature completely,based on the characteristics of flow stress curves for a new kind of metastable β Ti2448 titanium alloy from isothermal hot compression tests,in a wide range of temperatures（1023-1123 K） and strain rates（63-0.001 s-1）.During this process,the adopted hyperbolic sine function based on the unified viscoplasticity theory was used to model the flow behavior of alloy undergoing flow softening caused by dynamic recovery（DRV） at high strain rates（≥1 s-1）.The standard Avrami equation was adopted to represent the softening mechanism attributed to dynamic recrystallization（DRX） at low strain rates（1 s-1）.Additionally,the material constants were determined by optimization strategy,which is a new method to solve the nonlinear constitutive equation.The stress—strain curves predicted by the developed constitutive model agree well with the experimental results,which con-rms that the developed constitutive model can give an accurate estimate of the-ow stress of Ti2448 titanium alloy and provide an effective method to model the flow behavior of metastable β titanium alloys during hot deformation.

Integrated Modelling of Microstructure Evolution and Mechanical Properties Prediction for Q&P Hot Stamping Process of Ultra‑High Strength Steel

High strength steel products with good ductility can be produced via Q&P hot stamping process,while the phase transformation of the process is more complicated than common hot stamping since two-step quenching and one-step carbon partitioning processes are involved.In this study,an integrated model of microstructure evolution relating to Q&P hot stamping was presented with a persuasively predicted results of mechanical properties.The transformation of diffusional phase and non-diffusional phase,including original austenite grain size individually,were considered,as well as the carbon partitioning process which affects the secondary martensite transformation temperature and the subsequent phase transformations.Afterwards,the mechanical properties including hardness,strength,and elongation were calculated through a series of theoretical and empirical models in accordance with phase contents.Especially,a modified elongation prediction model was generated ultimately with higher accuracy than the existed Mileiko’s model.In the end,the unified model was applied to simulate the Q&P hot stamping process of a U-cup part based on the finite element software LS-DYNA,where the calculated outputs were coincident with the measured consequences.