46761819
Modelling of the superplastic deformation of the near-a titanium alloy (Ti-2.5AL-1.8MN) using arrhenius-type constitutive model and artificial neural network
The paper focuses on developing constitutive models for superplastic deformation behaviour of near-α titanium alloy (Ti-2.5Al-1.8Mn) at elevated temperatures in a range from 840 to 890 °C and in a strain rate range from 2 × 10−4 to 8 × 10−4 s−1. Stress–strain experimental tensile tests data were used to develop the mathematical models. Both, hyperbolic sine Arrhenius-type constitutive model and artificial neural-network model were constructed. A comparative study on the competence of the developed models to predict the superplastic deformation behaviour of this alloy was made. The fitting results suggest that the artificial neural-network model has higher accuracy and is more efficient in fitting the superplastic deformation flow behaviour of near-α Titanium alloy (Ti-2.5Al-1.8Mn) at superplastic forming than the Arrhenius-type constitutive model. However, the tested results revealed that the error for the artificial neural-network is higher than the case of Arrhenius-type constitutive model for predicting the unmodelled conditions.
137112561
Heterogeneous crystal and poly-crystal plasticity modeling from a transformation field analysis within a regularized Schmid law
The regularized Schmid law (RSL) has recently been proposed as a plastic flow criterion for poly-crystals under the crude assumptions of either uniform stress or uniform strain. We first reconsider this law for application to heterogeneous intra-crystalline plasticity, with reference to a Homogeneous Equivalent Super-Crystal. We then extend the modeling to poly-crystals with the goal to account for both stress and strain heterogeneities within as well as between grains. The transformation field analysis (TFA) is used as the homogenization procedure. This TFA is known to be accurate for materials that can be described as assemblies of plastically homogeneous domains. Otherwise, the estimates of the material effective behavior that result from its application are too stiff. Because stress and strain fields are almost everywhere uniform in laminates, we consider crystal slip organizations into multi-laminate structures. It is demonstrated that laminate layers either parallel to slip planes or normal to slip directions do not contribute to the over-stiffness due to the TFA. Thus, hierarchical multi-laminate (HML) structures are introduced where the successive laminate orientations are taken parallel to the crystal slip planes. It is shown that a conveniently weighted superposition of all the possible plane hierarchies cancels out most of the undesirable TFA contributions to the overall stiffness estimates. A relevant extension to poly-crystal plasticity of this (RSL-TFA-HML) modeling is presented.
137199470
Modelling of creep-fatigue in containers during aluminium and copper extrusion
During hot extrusion of aluminium alloys, extrusion dies experience cyclic temperature changes as well as multiaxial loadings. To improve the service life of the dies, cleaner and high hot strength materials are designed as well as an optimised process control is performed. For the improvement of the process guiding and a comparison of lifetime behaviour of different hot work tool steels, modelling and simulation are appropriate means. The extrusion process has been simulated using the FE-program Deform to find the stress and temperature history at the inner diameter of the liner, i.e. the boundary conditions for the subsequent cyclic simulation of the container during service. Inelastic constitutive equations have been implemented into Abaqus Standard to describe strain hardening and time recovery effects. They include the Norton viscoplastic flow rule, thermo-mechanical isotropic hardening and two non-linear kinematic hardening laws. A damage-rate model predicts failure and thus the lifetime of the container. The procedure for the identification of material parameters for both the constitutive and the damage model is described in detail for the hot work tool steel Bohler W400 VMR (EN 1.2343).
135774025
A model for strain-induced martensitic transformation of TRIP steel with strain rate
Pre-strain is one of the key factors which can influence metal sheet mechanical properties during material multi-step deformation process. In this study, a constitutive model, which can describe the transformation-induced plasticity (TRIP) accompanying the strain-induced martensitic transformation in TRIP steel under pre-strain, is developed. The increase of nucleation site in the austenite due to the plastic deformation is formulated as the increase of the shear-band intersection. The nucleation site probability and shear-band intersection are derived not only by stress state, plasticity strain and temperature, but also by pre-strain to simulate the transformation-induced plasticity characteristic for TRIP steel. Anisotropic yield function is used to describe the sheet anisotropic property. A mixture hardening law, which is based on the pre-strain, with four phases is developed. The constitutive model is implemented into ABAQUS/UMAT to analyze the material deforming processes. Mixture hardening law of four phases with pre-strain is verified by experiment. The martensitic volume fraction is tested by X-ray to describe the comparison between experiment data and simulation. All the results are agreeable.
137107425
The flow behavior modeling of cast A356 aluminum alloy at elevated temperatures considering the effect of strain
Abstract The flow stress behavior of cast A356 aluminum alloy has been studied by a set of isothermal hot compression tests. The compression tests were carried out in the temperature range of 400–540 °C and strain rates of 0.001, 0.01 and 0.1 s −1 up to a true strain of 0.6. The effects of temperature and strain rate on deformation behavior were represented by Zener–Hollomon parameter in an exponent type equation. Employing an Arrhenius-type constitutive equation, the influence of strain has been incorporated by considering the related materials’ constants as functions of strain. The accuracy of the developed constitutive equations has been evaluated using standard statistical parameters such as correlation coefficient and average absolute relative error. The results indicate that the strain-dependent constitutive equation can lead to a good agreement between the calculated and measured flow stresses in the relevant temperature range.
137136589
The prediction of hot deformation behavior in Fe–21Mn–2.5Si–1.5Al transformation-twinning induced plasticity steel
Abstract Prediction of the material flow behavior is an essential step to optimize designing any forming processes. This may be well addressed through applying a proper constitutive equation, which relates the stress and strain to the effective deformation conditions (i.e., temperature and strain rate). Accordingly in present study, the experimental true stress–true strain data from isothermal hot compression tests, in the temperature range of 800–1100 °C and strain rates of 0.001, 0.01 and 0.1 s −1 , have been employed to develop the appropriate constitutive equations for a new grade of TRIP/TWIP steel. The effects of temperature and strain rate on the deformation behavior have been represented by Zener–Hollomon parameter in an exponent type equation. Employing an Arrhenius type constitutive equation, the influence of strain has been incorporated by considering the related material constants as functions of strain. The Q -values have been in the range of 390–424 kJ/mol for different amounts of strain. Finally, the accuracy of the developed constitutive equations has been evaluated using standard statistical parameters such as correlation coefficient and average absolute relative error. The results indicate that the proposed strain-dependent constitutive equation gives an accurate and precise estimate of the flow stress in the relevant temperature range.
137554252
A modified Zerilli–Armstrong model for alloy IC10 over a wide range of temperatures and strain rates
Abstract IC10 is a newly developed Ni3Al-based superalloy. To investigate its flow behaviors, tensile experiments were conducted over a wide range of temperatures (293–1073 K) and strain rates (10−5–10−2 s−1) on Material Test System. Experiments show that: (1) flow behaviors are not sensitive to strain rates at room temperature; (2) flow behaviors varies slightly with the temperature at the same strain rate. Z–A model, one of the most widely used models, is employed in describing the flow behaviors of IC10. Normally, the parameters in Z–A model are regarded as constants at various conditions and whole deforming process, which do not agree with the actual process and will decrease its predicted accuracies. In order to improve the predicted accuracies, Z–A model is modified by adding the functions to consider the effects of temperature, strain rate and deforming process on certain parameter. The modified model is used to predict flow behaviors of IC10 at different experiment conditions. Compared with the predicted data of original Z–A model and the experimental data, it is found that the predicted accuracy of the modified Z–A model is improved obviously. The max average relative error decreased from 6.37% to 3.86%.
135754675
A physically based constitutive model for fcc metals with applications to dynamic hardness
A constitutive model is developed in this work to describe the mechanical behavior of face centered cubic (fcc) metals under a wide range of temperatures and strain rates. The model is based on the dependence of the activation energy on temperature, strain rate, and stress. An expression for the flow stress is proposed in terms of micromechanical terms such as mobile dislocation density and Burgers vector as well as macromechanical based state variables such as stress and material constants that include threshold and transition temperature. The proposed model is used to simulate the experimental results of oxygen free high conductivity (OFHC) copper at different temperatures and strain rates in order to obtain the different model parameters. The model shows good capability in capturing the coupling between strain rate and temperature, plastic strain and strain rate, and plastic strain and temperature. The model is used to characterize the hardness at low and high strain rates for a representative strain of 8%.
135612305
Ti–6Al–4V: Deformation map and modelisation of tensile behaviour
Abstract Tensile tests have been performed on a superplastic titanium alloy. Different strain rates from 5 × 10 −4  s −1 to 5 × 10 −2  s −1 and various temperatures up to 1050 °C were explored. The results of these tests, supplemented with microstructural investigations allow, as a function of temperature and strain rate, the determination of mechanical properties such as flow stress, strain hardening and fracture strain as well as the identification of mechanisms such as grain boundary sliding, dynamic recrystallization and dynamic grain growth. A modified Norton–Hoff law is proposed to characterize the tensile behaviour of this alloy. All temperature–strain rate combinations have been grouped into a number of domains, each corresponding to a particular deformation mechanism. For each domain the Norton–Hoff parameters have been determined. Close agreement between the predicted and experimental stress–strain relationships has been achieved.
136553926
Constitutive equations for elevated temperature flow stress of Ti–6Al–4V alloy considering the effect of strain
Abstract In order to study the workability of Ti–6Al–4V alloy, the experimental stress–strain data from isothermal hot compression tests, in a wide range of temperatures (800–1050 °C) and strain rates (0.0005–1 s −1 ), were used to develop the constitutive equation of different phase regimes ( α  +  β and β phase). The effects of temperature and strain rate on deformation behaviors a represented by Zener–Holloman parameter in an exponent-type equation. The influence of strain was incorporated in constitutive analysis by considering the effect of strain on material constants. Correlation coefficient ( R ) and average absolute relative error ( AARE ) were introduced to verify the validity of the constitutive equation. The values of R and AARE were 0.997% and 9.057% respectively, which indicated that the developed constitutive equation (considering the compensation of strain) could predict flow stress of Ti–6Al–4V alloy with good correlation and generalization.
136677036
Prediction of hot compression flow curves of Ti–6Al–4V alloy in α + β phase region
Abstract Prediction of material flow behavior is essential for designing the forming process of any material. In this research, experimental flow curves of Ti–6Al–4 V alloy were obtained using the isothermal hot compression test done at 750–950 °C with 50 °C intervals and constant strain rates of 0.001, 0.005 and 0.01 s−1. For prediction of hot deformation flow curves two methods of modeling were applied. In the first method, an entire flow curve was modeled using Sellars equation. In the second one, modeling of a flow curve up to the peak point was carried out with Cingara model, and modeling beyond that was performed with a model developed based on the Johnson–Mehl–Avrami–Kolmogorov (JMAK) theory. The accuracy of each model was examined through a statistical method. Results showed that flow curve modeling using Cingara model and JMAK theory leads to results that are more consistent with the experimental data.
139604974
Superplastic deformation behaviour and microstructure evolution of near-α Ti-Al-Mn alloy
Abstract Superplastic deformation behaviour of conventional sheets of a near-α titanium alloy (Ti-2.5Al-1.8Mn) was studied by a step-by-step decrease of the strain rate and constant strain rate tests in a temperature range of 790–915 °C. The research found that superplastic deformation is possible in a temperature range of 815–890 °С and a constant strain rate range of 2 × 10 −4 to 1 × 10 −3  s −1 with elongation above 300% and m -index above 0.4. Also, the research identified the optimum superplastic temperature range of 815–850 °C and constant strain rate of 4 × 10 −4  s −1 which provide a maximum elongation of 600–650%. Strain hardening is accelerated by dynamic grain growth at high temperatures of 865 and 890 °С. High dislocation activity is observed at superplastic flow in α-phase. Constitutive modelling of superplastic deformation behaviour is performed, and possible deformation mechanisms are discussed. It is suggested that grain boundary sliding between the α-grains is accommodated by a dislocation slip/creep mechanism.
136773602
An overview on constitutive modelling to predict elevated temperature flow behaviour of fast reactor structural materials
This overview emphasized the aspects of formulation and application of various constitutive models developed by us in recent past viz. Johnson- Cook (JC), modified Zerilli-Armstrong (MZA), strain compensated Arrhenius type model and artificial neural network (ANN) model to predict elevated temperature flow behaviour of fast reactor structural materials. It has been shown that the JC model is not able to represent the high temperature flow behaviour of both alloy D9 and the modified 9Cr-1Mo as it does not incorporate the coupled effect of strain and temperature, and of strain rate and temperature. The new materials model based on Zerilli-Armstrong (ZA) equation considers the coupled effects of temperature and strain and of strain rate and temperature on the flow stress and hence has the capability to predict flow stress over a wider domain temperature and strain rate in comparison with JC model. The formulation and application of strain compensated Arrhenius type constitutive model to predict high temperature flow behaviour of alloy D9 and modified 9Cr-1Mo has been discussed. Development and application of a generic ANN based constitutive model to predict high temperature deformation behaviour of austenitic stainless steels has been highlighted. Finally, a comparative analysis of the merits and shortcomings of these models has been made.
121325603
Effect of Strain Rate Upon Plastic Flow of Steel
An experiment has been designed to check a previously proposed equivalence of the effects of changes in strain rate and in temperature upon the stress‐strain relation in metals. It is found that this equivalence is valid for the typical steels investigated. The behavior of these steels at very high rates of deformation may, therefore, be obtained by tests at moderate rates of deformation performed at low temperatures. The results of such tests are described. Aside from changing the isothermal stress‐strain relation, an increase of strain rate tends to change the conditions from isothermal to adiabatic. It is found that at low temperatures, the adiabatic stress‐strain relation in the plastic range is radically different from the isothermal, having an initial negative rather than a positive slope. This initial negative slope renders unstable homogeneous plastic deformation.
137657567
Constitutive equations to predict high temperature flow stress in a Ti-modified austenitic stainless steel
Abstract The experimental stress–strain data from isothermal hot compression tests, in a wide range of temperatures (1123–1523 K) and strain rates (10−3–102 s−1), were employed to develop constitutive equations in a Ti-modified austenitic stainless steel. The effects of temperature and strain rate on deformation behaviors were represented by Zener-Holloman parameter in an exponent type equation. The influence of strain was incorporated in the constitutive analysis by considering the effect of strain on material constants. The constitutive equation (considering the compensation of strain) could precisely predict the flow stress only at 0.1 and 1 s−1 strain rates. A modified constitutive equation (incorporating both the strain and strain rate compensation), on the other hand, could predict the flow stress throughout the entire temperatures and strain rates range except at 1123 K in 10 and 100 s−1. The breakdown of the constitutive equation at these processing conditions is possibly due to adiabatic temperature rise during high strain rate deformation.
135841406
Constitutive modeling for elevated temperature flow behavior of 42CrMo steel
Abstract In order to study the workability and establish the optimum hot formation processing parameters for 42CrMo steel, the compressive deformation behavior of 42CrMo steel was investigated at the temperatures from 850 to 1150 °C and strain rates from 0.01 to 50 s−1 on Gleeble-1500 thermo-simulation machine. The results show that the true stress–true strain curves exhibit a peak stress at a small strain, after which the flow stresses decrease monotonically until high strains, showing a dynamic flow softening. The flow stress obtained from experiments consists of four different stage, i.e., Stage I (Work hardening stage), Stage II (Stable stage), Stage III (Softening stage) and Stage IV (Steady stage). The stress level decreases with increasing deformation temperature and decreasing strain rate, which can be represented by a Zener–Hollomon parameter in an exponent-type equation. A revised model describing the relationships of the flow stress, strain rate and temperature of 42CrMo steel at elevated temperatures is proposed by compensation of strain and strain rate. The stress–strain values of 42CrMo steel predicted by the proposed model well agree with experimental results, which confirmed that the revised deformation constitutive equation gives an accurate and precise estimate for the flow stress of 42CrMo steel.
135828913
Investigation of stress exponent in the room-temperature creep of Sn–40Pb–2.5Sb solder alloy
Abstract Creep behavior of Sn–40%Pb–2.5%Sb peritectic solder alloy having two different grain sizes was studied by indentation, impression, stress relaxation and conventional creep tests at room temperature (T > 0.65 Tm) in order to evaluate the correspondence of the creep results. Stress exponent values have been determined through these methods and in all cases the calculated exponents are in good agreement. The stress exponent values in the range 2.55–3.20, depending on the testing method and grain size of the materials, indicate that grain boundary sliding is the possible mechanism during room-temperature creep deformation of this alloy.
137392951
Identifiying creep mechanisms at low stresses
There are three possible mechanisms occurring in high temperature creep at low stresses: diffusion creep, Harper–Dorn creep and grain boundary sliding. This paper examines the characteristics of these three processes and proposes two sets of measurements that may be used to give an unambiguous identification of the dominant creep mechanism. The approach is applied to published creep data and new measurements are reported for a Mg–0.55%Zr alloy which permit a clear distinction between diffusion creep and grain boundary sliding.
138847231
Flow Behavior and Constitutive Equation of Ti-6.5Al-2Sn-4Zr-4Mo-1W-0.2Si Titanium Alloy
In order to get a reliable constitutive equation for the finite element simulation, flow behavior of Ti-6.5Al-2Sn-4Zr-4Mo-1W-0.2Si alloy under high temperature was investigated by carrying a series of isothermal compression tests at temperatures of 1153-1293 K and strain rates of 0.01-10.0 s−1 on the Gleeble-1500 simulator. Results showed that the true stress-strain curves exhibited peaks at small strains, after which the flow stress decreased monotonically. Ultimately, the flow curves reached steady state at the strain of 0.6, showing a dynamic flow softening phenomenon. The effects of strain rate, temperature, and strain on the flow behavior were researched by establishing a constitutive equation. The relations among stress exponent, deformation activation energy, and strain were preliminarily discussed by using strain rate sensitivity exponent and dynamic recrystallization kinetics curve. Stress values predicted by the modified constitutive equation showed a good agreement with the experimental ones. The correlation coefficient (R) and average absolute relative error (AARE) were 98.2% and 4.88%, respectively, which confirmed that the modified constitutive equation could give an accurate estimation of the flow stress for BT25y titanium alloy.
137248598
Development of constitutive relationships for the hot deformation of boron microalloying TiAlCrV alloys
Abstract Isothermal compressive tests are performed on TiAlCrV and TiAlCrV+B alloys to study hot deformation behavior. A hyperbolic-sine Arrhenius-type equation is used to derive the constitutive equation to correlate the flow stress to the deformation temperature, and the strain rate to strain level. The results show that all experimental data of TiAlCrV and TiAlCrV+B alloys can be fully described using this hyperbolic-sine Arrhenius-type relationship. The activation energy, Q , the material constants, n and ln nA, of both alloys decrease as the deformation strain increases. The strain dependent term is successfully incorporated in the constitutive equation through the parameters, Q , n , and ln A . The preliminary results also suggest that the constitutive relationship between the flow stress and strain and between the strain rate and temperature can be used to predict the hot-workability map for the hot deformation of intermetallic alloys.
138904386
Thermomechanical processing of alpha titanium alloys : an overview
Abstract Thermomechanical processing (TMP) is associated with two major requirements: (1) the production of usable shapes through primary working (ingot breakdown) and secondary mill operations (hot rolling or forging); and (2) the optimization of mechanical properties through microstructure control during the different stages of the thermomechanical process. This paper reviews the thermomechanical processing of alpha titanium alloys in general and high temperature deformation mechanisms and microstructure control during TMP in particular.
137092513
Superplasticity in metals and ceramics
Preface 1. Introduction 2. Key historical contributions 3. Types of superplasticity 4. Mechanisms of high-temperature deformation and phenomenological relations for fine-structure superplasticity 5. Fine-structure superplastic metals 6. Fine-structure superplastic ceramics 7. Fine-structure superplastic intermetallics 8. Fine-structure superplastic composites and laminates 9. High-strain-rate superplasticity 10. Ductility and fracture in superplastic materials 11. Internal-stress superplasticity (ISS) 12. Other possible superplasticity mechanisms 13. Enhanced powder consolidation through superplastic flow 14. Superplastic forming and diffusion bonding 15. Commercial examples of superplastic products Index.
136589191
Modelling of the hot deformation behaviour of a titanium alloy using constitutive equations and artificial neural network
Abstract Hot deformation characteristics of a Ti600 titanium alloy were investigated by a Gleeble 1500D thermo-mechanical test simulator over the temperature range from 760 to 920 °C and strain rate range from 0.01 to 10 s −1 . The flow behaviour and microstructural evolution were studied. Dynamic recrystallisation (DRX) grains exhibit different shapes at different deformation temperatures, and more severe distortion around the DRX grains exists in the matrix deformed at low temperature compared with that at relatively high temperature. Phenomenological and empirical constitutive equations were established based on the hyperbolic sine Arrhenius-type model and the multiple-linear regression, respectively. An artificial neural network (ANN) model was developed to predict the flow stress. A comparative study was made on the capability of the developed models to represent the hot deformation behaviour of this alloy. The results indicate that the flow stress of Ti600 alloy is sensitively dependent on the strain rate and deformation temperature. The multiple-linear model shows a higher accuracy in tracking the flow behaviour of Ti600 alloy than the Arrhenius-type model. The ANN model is much more efficient and has higher accuracy in predicting the hot deformation flow behaviour of Ti600 alloy than both the Arrhenius-type and multiple-linear models.
135694351
Modeling of tribological properties of alumina fiber reinforced zinc–aluminum composites using artificial neural network
Abstract It is known that the strength of a metal, as well as wear resistance can be successfully improved by fiber reinforcement. In this study, multiple-layer feed-forward artificial neural network (ANN) modeling for tribological behavior of short alumina fiber reinforced zinc–aluminum composites has been established. The specific wear rate and coefficient of friction obtained from a series of the wear tests were used in the formation of training sets of ANN. Samples of composite material with 10, 15, 20 and 30 vol.% fiber contents were prepared by the pressure die-casting method. Wear tests with pin-on-disc arrangement had performed at a constant sliding speed of 1 m/s under four different loads (5, 10, 20 and 40 N). The results of experimental tests showed that wear behavior and friction coefficient of the composites were significantly affected by the fiber volume fraction. The specific wear rate decreased with increasing fiber volume fraction and increased with increasing load. The coefficients of friction of the composites were higher than that of the unreinforced matrix alloy. The modeling results confirm the feasibility of the ANN and its good correlation with the experimental results. The degrees of accuracy of the prediction were 94.2 and 99.4% for specific wear rate and friction coefficient, respectively. It is concluded that ANN is an excellent analytical tool if it is well trained. This means considerable cost and time saving. Finally, using ANN modeling data and experimental data, 3D plots and empirical expressions for specific wear rate and friction coefficient related to load and fiber volume fraction were established.
2757547
Multilayer feedforward networks are universal approximators
Abstract This paper rigorously establishes that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy, provided sufficiently many hidden units are available. In this sense, multilayer feedforward networks are a class of universal approximators.
136132383
The improvement on constitutive modeling of Nb-Ti micro alloyed steel by using intelligent algorithms
Abstract The deformation behavior of Nb-Ti micro alloyed steel was experimentally obtained in the deformation temperature range of 900–1050 °C and strain rate range of 0.1–10 s− 1. Base on the stress-strain curves, four constitutive models were established by using the modified forms of Arrhenius-type model considering compensation of strain or modified by intelligent algorithms such as artificial neural network and genetic algorithm. A comparative study has been made on the accuracy and effectiveness of the four models to predict the flow stress of Nb-Ti micro alloyed steels. The result shows that models modified by intelligent algorithms acquire higher accuracy than Arrhenius-type model considering compensation of strain. The model whose material parameters (α, n, Q and lnA) are modeled by artificial neural network performs better than the model whose material parameters (α, n, Q and lnA) are optimized by genetic algorithm. Among all the models, Arrhenius-type model considering compensation of strain with errors revised by artificial neural network obtains the highest accuracy.
135523555
Constitutive Relationship Model of Al-W Alloy Using Artificial Neural Network
Isothermal compression experiment of Al-W alloy was carried out using Gleeble1500 thermodynamic simulator within a temperature range of 420°C-570°C and a strain rate range of 0.001s-1-1s-1。And the constitutive relationship model for this alloy was successfully developed using BP neural network. In the proposed model, the input variables are strain, strain rate and deformation temperature while the flow stress is the output variable. The results show that absolute maximum error between predicted and experimental values of flow stress is less than 10.0Mpa, the correlation coefficient is 0.993. It was found that the established constitutive relationship model could provide a good representation of the test data and describe the whole deforming process better compared with the traditional method.
135946666
A comparative study on Arrhenius-type constitutive model and artificial neural network model to predict high-temperature deformation behaviour in Aermet100 steel
Abstract For predicting high-temperature deformation behaviour in Aermet100 steel, the experimental stress–strain data from isothermal hot compression tests on a Gleeble-3800 thermo-mechanical simulator, in a wide range of temperatures (1073–1473 K) and strain rates (0.01–50 s−1), were employed to develop the Arrhenius-type constitutive model and artificial neural network (ANN) model, and their predictability for high-temperature deformation behaviour of Aermet100 steel was further evaluated. The predictability of two models was quantified in terms of correlation coefficient (R) and average absolute relative error (AARE). The R and AARE for the Arrhenius-type constitutive model were found to be 0.9861 and 7.62% respectively, while the R and AARE for the feed-forward back-propagation ANN model are 0.9995 and 2.58% respectively. The breakdown of the Arrhenius-type constitutive model at the instability regimes (i.e. at 1073 K and 1173 K in 0.1, 1, 10 and 50 s−1, and at 1373 K in 50 s−1) is possibly due to that physical mechanisms in the instability regimes, where microstructure exhibits cracking, shear bands and twin kink bands, are far different from that of the stability regimes where dynamic recovery and recrystallization occur. But the feed-forward back-propagation ANN model can accurately track the experimental data across the whole hot working domain, which indicates it has good capacity to model the complex high-temperature deformation behaviour of materials associated with various interconnecting metallurgical phenomena like work hardening, dynamic recovery, dynamic recrystallization, flow instability, etc.
137380500
Development of constitutive relationship model of Ti600 alloy using artificial neural network
Abstract Constitutive equation which reflects the highly non-linear relationship of flow stress as function of strain, strain rate and temperature is a necessary mathematical model that describes basic information of materials deformation and finite element simulation. In this paper, based on the compression experiment data obtained from Gleeble-1500 thermal simulator, the prediction model for the constitutive relationship existed between flow stress and true strain, strain rate and deformation temperature for Ti600 alloy has been developed using back-propagation (BP) neural network method. A comparative evaluation of the traditional regression method and the trained network model was carried out. It was found that the established network model can not only predict flow stress better than the traditional hyperbolic sine constitutive relationship equation but also describe the whole deforming process for Ti600 alloy. Moreover, the ANN model provides a convenient and effective way to establish the constitutive relationship for Ti600 alloy.
136550917
Comparative study on constitutive relationship of as-cast Ti60 titanium alloy during hot deformation based on Arrhenius-type and artificial neural network models
Abstract Hot compression of as-cast Ti60 titanium alloy at the deformation temperatures ranging from 970 to 1120 °C with an interval of 30 °C, the strain rates ranging from 0.01 to 10.0 s−1 and the height reduction of 75% is conducted on a Gleeble-3500 thermo-mechanical simulator. The experimental stress–strain data from hot compression are employed to develop the Arrhenius-type constitutive model incorporating the strain effect and artificial neural network (ANN) model with a back-propagation learning algorithm. The strain compensated constitutive model can track the experimental data across the whole hot working domain other than that at high strain rates (⩾1 s−1). It is possibly associated with the deformation mechanisms at high strain rates, where microstructure exhibits bands of flow localization and longitudinal cracking, are far different from that at low strain rates (⩽0.1 s−1) where dynamic recrystallization occurs. Comparison of the predicted results of flow stress based on the ANN model and those acquired from the strain compensated constitutive model has been performed. It is found that the relative error of the ANN model varies from −3.42% to 4.33% while that of the strain compensated constitutive model ranges from −14.65% to 13.63%, and the average absolute relative error is 2.41% and 8.45% corresponding to the ANN model and strain compensated constitutive model, respectively. These results sufficiently indicate that the ANN model is more accurate and efficient in terms of predicting the flow stress of as-cast Ti60 titanium alloy.
135922765
Application of artificial neural network and constitutive equations to describe the hot compressive behavior of 28CrMnMoV steel
Abstract Isothermal hot compression of 28CrMnMoV steel was conducted on a Gleeble-3500 thermo-mechanical simulator in the temperature range of 1173–1473 K with the strain rate of 0.01–10 s−1 and the height reduction of 60%. Based on the experimental results, constitutive equations and an artificial neural network (ANN) model with a back-propagation learning algorithm were developed for the description and prediction of the hot compressive behavior of 28CrMnMoV steel. Then a comparative evaluation of the constitutive equations and the trained ANN model was carried out. It was obtained that the relative errors based on the ANN model varied from −3.66% to 3.46% and those were in the range from −13.60% to 10.89% by the constitutive equations, and the average absolute relative errors were 0.99% and 4.09% corresponding to the ANN model and the constitutive equations, respectively. Furthermore, the average root mean square errors of the ANN model and the constitutive equations were obtained as 1.43 MPa and 5.60 MPa respectively. These results indicated that the trained ANN model was more efficient and accurate in predicting the hot compressive behavior of 28CrMnMoV steel than the constitutive equations.
137669125
Artificial neural network modeling to predict the hot deformation behavior of an A356 aluminum alloy
Abstract Prediction of the material flow behavior is an essential step to optimize the design of any forming process. In this context, artificial neural network (ANN) may be used as a reliable modeling method for simulating and predicting the flow behavior of materials under different thermomechanical conditions. In the present study, an ANN model has been established to estimate the high temperature flow behavior of a cast A356 aluminum alloy. A series of isothermal compression tests was conducted in the temperature range of 400–540 °C and strain rates of 0.001–0.1 s −1 . A feed-forward back propagation ANN with single hidden layer composing of 20 neurons was employed to simulate the flow behavior. The neural network has been trained using an in-house database obtained from hot compression tests. Finally, in comparison with a strain-dependent Arrhenius type constitutive equation, the reliability of the proposed ANN model has been evaluated using standard statistical indices. The results indicate that the trained ANN model is a robust tool to predict the high temperature flow behavior of cast A356 aluminum alloy.
135556487
Constitutive relationship model of TC21 alloy based on artificial neural network
Abstract Constitutive equation is a necessary mathematical model to describe basic information of materials deformation and finite element simulation. There is a highly nonlinear relationship for flow stress as function of strain, strain rate and temperature. Based on the experimental data sets obtained from the isothermal compression tests conducted on a Gleeble-1500 thermal simulator, the flow behavior of TC21 alloy was studied systematically, and the constitutive relationship model for this alloy was developed using BP neural network. In the proposed model, the input variables are strain, strain rate and deformation temperature while the flow stress is the output variable. It was found that the established constitutive relationship model could provide a better representation of the test data and better describe the whole deforming process compared to the traditional method.