High Temperature Constitutive Model Research Articles

Enhancing the high-temperature constitutive modeling of In706 superalloy using advanced artificial neural networks and attentive staged optimization algorithm

High-temperature constitutive models derived from the Arrhenius equation play a pivotal role in the hot-forging processes of nickel-based superalloys such as In706. However, existing models have limitations owing to insufficient data points, leading to the potential loss of vital information and the need for elaborate modeling methodologies. This study proposes an innovative optimization approach that leverages the attentive staged optimization algorithm (ASOA) and advanced artificial neural networks to enhance the accuracy and efficiency of In706 superalloy modeling. ASOA is a batch-based, multi-stage optimization algorithm inspired by the attention mechanism concept in deep learning. It allocates time and computational resources to the most deserving data for optimization and is well-suited for handling large volumes of data. In this paper, ASOA was employed to perform two rounds of fitting on the thermal simulation experimental data, resulting in the determination of the critical strain ϵc and identifying suitable Arrhenius equation material parameters for each set of deformation conditions. Subsequently, a full parameter responsive constitutive model was established for In706, capable of handling a comprehensive set of deformation conditions and providing a more detailed representation of the high-temperature behavior of the In706 alloy. In developing the FPR model, we designed a fully connected neural network and employed a cosine annealing dual-error dynamic adjust function to address error amplification during training. The cosine annealing learning rate scheduling strategy with amplitude attenuation was also implemented to dynamically adjust the learning rate. As a result, the model developed using the proposed approach outperforms traditional models and shows remarkable potential for the precise and efficient optimization of In706 alloy. The high performance of the final model showcases the prospect of our approach in future development and optimization of superalloys.

Effect of Nb-Ti Microalloyed Steel Precipitation Behavior on Hot Rolling Strip Shape and FEM Simulation.

Strip shape control is a hotspot and challenge in strip rolling, where the development trend of rolling technology is towards high strength, high toughness, and a large width-to-thickness ratio. The influence of material microstructure evolution on strip shape control is being increasingly emphasized. In this paper, a Nb-Ti microalloyed steel is taken as the research object. Thermodynamic and kinetic models focusing on the precipitation of the austenite phase are established to quantify the precipitation process. A coupled model of rolls and strips is built using ABAQUS 2022 software, where the precipitation strengthening model and high-temperature constitutive model are embedded into the finite element model (FEM) through subroutines. A two-dimensional alternating differential model is employed to acquire real-time temperature differences in the width direction of the strip. The effects of precipitation inclusion and exclusion on the strip crown under different operating conditions are compared and analyzed. The results indicate that as the temperature decreases, the strengthening effect increases, reaching around 40 MPa at temperatures above 1000 °C and 96.6 MPa at 800 °C. Furthermore, the inclusion of crown in the precipitation consideration is more sensitive to overall temperature changes, but as the strip width decreases, the sensitivity of crown to temperature decreases. The research findings of this paper provide guidance for improving strip shape control and reducing abnormalities during the rolling process.

Elevated-temperature mechanical property and constitutive model of Galfan-coated and full-locked steel cables

Steel cables are an essential stress-bearing member in pre-tensioned steel structures. Their exposure to fire may lead to prestress loss, which may cause structural failure or even overall collapse. This study used a non-contact strain measurement system to investigate the mechanical properties of 1670 MPa Galfan-coated steel cable and 1570 MPa full-locked steel cable at elevated temperatures. The test results showed that the mechanical properties of the two types of cable decayed significantly with the increase in temperature. At 700 °C, the ultimate strength of Galfan-coated steel cable was only 2.36% of that at room temperature, and that of full-locked steel cable was 3.56%. By analyzing the stress-strain relationships between the yielding and hardening stages at 9 test temperature levels, it was found that the high-temperature nominal yield strength could be taken as the stress at the strain level of 1.25% for both types of steel cables. Based on the full stress-strain curves at each temperature level, the calculation formulae for high-temperature reduction factors of elastic modulus, proportional limit, nominal yield strength, and ultimate strength of Galfan-coated and full-locked steel cables were proposed. Besides, the high-temperature constitutive models of the two cable types were also proposed based on the experimental data. The findings of this study can improve the fire safety of pre-tensioned steel structures.

A modified Johnson–Cook constitutive model for titanium alloy TA31 and its implementation into FE

Abstract The accuracy of high-temperature constitutive models is essential for the establishment and optimization of thermomechanical processing, and is one of the most relevant factors determining the reliability of finite element simulation results. In this study, attention is paid to propose a new coupled Johnson–Cook constitutive model for predicting the flow behaviors of titanium alloy TA31 composed of bimodal microstructure, and to implement it in the finite element software Abaqus. The proposed model not only takes into account the strain softening phenomenon of titanium alloy but also the coupled interactions of strain, strain rate and temperature. The correlation coefficient R and average absolute relative error AARE of the modified constitutive equation were 0.9885 and 3.6%, respectively. The mathematical formulation of the new constitutive model allows for accurate predictions of the flow stress of TA31 titanium alloy, while retaining a low identification cost of the unknown coefficients. A subroutine VUHARD of this model was developed, and its reliability was verified in the case of the modeling of one element test. It is helpful to understand the deformation behavior of titanium alloy TA31 and provide valuable references for optimizing the thermomechanical processing.

Application of Four Different Models for Predicting the High-Temperature Flow Behavior of 1420 Al–Li Alloy

In this paper, the high-temperature rheological behavior of 1420 aluminum–lithium alloy under experimental conditions (temperatures of 350–475 °C and strain rates of 0.01–10 s−1) was systematically investigated using a Gleeble-3500 thermal simulation tester (temperature 350~475 °C, strain rate of 0.01~10 s−1). Based on the flow stress curves of this alloy, four different types of high-temperature constitutive models of the alloy were constructed: the Arrhenius (AR) model, the Modified Johnson–Cook (MJC) model, the Modified Zerilli–Armstrong (MZA) model, and the VOCE model. The prediction accuracy of the four constitutive models was compared, and the response of the accuracy of the four constitutive models to the deformation parameters (temperature, deformation rate, and strain) was analyzed. The results showed that the VOCE, AR, and MZA models had high overall prediction accuracy with average absolute relative error (AARE) of 1.8933%, 3.9912%, and 7.8422%, respectively. The VOCE model could achieve the prediction of large strain deformation resistance under small strain with small batch experimental conditions for the corresponding conditions. The AR model had optimal prediction accuracy for the high-rate deformation process. The MJC model had the optimal prediction accuracy for the low-temperature low-rate deformation process. The MZA model had better prediction accuracy for the low-rate high-temperature deformation process. The 1420 aluminum–lithium alloy process parameters selection area constitutive model matching diagram was constructed.

Constitutive Model Parameter Identification Based on Optimization Method and Formability Analysis for Ti6Al4V Alloy.

Titanium alloy is widely applied in aerospace, medical, shipping and other fields due to its high specific strength and low density. The purpose of this study was to analyze the formability of Ti6Al4V alloys at elevated temperatures. An accurate constitutive model is the basic condition for accurately simulating the plastic forming of materials, and it is an important basis for optimizing the parameters of the hot forging forming process. In this study, the optimization algorithm was used to accurately identify the high-temperature constitutive model parameters of Ti6Al4V titanium alloy, and the hot working diagram was established to optimize the hot forming process parameters. The optimal forming conditions of Ti6Al4V titanium alloy are given. Ti6Al4V alloy was subjected to high-temperature compression tests at 800–1000 °C and at strain rates of 0.01–5 s−1 on a Gleeble-1500D thermal/mechanical simulation machine. Each parameter of the Hansel–Spittel constitutive model was taken as an independent variable, and the accumulated error between the stress calculated by the constitutive model and the stress obtained by experimentation was used as an objective function. Based on response surface methodology, an inverse optimization method for identifying the parameters of the high-temperature constitutive model of Ti6Al4V alloy is proposed in this paper. An orthogonal test design was adopted to obtain sample point data, and a third-order response surface approximate model was established. The genetic algorithm (GA) was applied to reversely optimize the parameters of the constitutive model. To verify the accuracy of the optimized constitutive model, the average absolute relative error (AARE) and correlation coefficient (R) were used to evaluate the reliability of optimized constitutive model. The R value of the model was 0.999, and the AARE value was 0.048, respectively, indicating that the established high-temperature constitutive model for Ti6Al4V alloy has good calculation accuracy. The flow stress behavior of the material could be accurately delineated. Meanwhile, in order to study the formability of Ti6Al4V alloy, the hot processing map of the alloy, based on a dynamic material model, was established in this paper. The optimum hot working domains of the Ti6Al4V alloy were determined within 840–920 °C/0.01–0.049 s−1 and 940–980 °C/0.11–1.65 s−1; the hot processing map was verified in combination with the microstructure, and the fine and equiaxed grains and a large amount of β phase could be found at 850 °C/0.01 s−1.

NUMERICAL ANALYSIS OF FIRE BEHAVIOR OF CONCRETE SLABS IN FULL-SCALE STEEL-FRAME STRUCTURE

The influence of the position and quantity of fire span on the fire behavior of concrete floor in the structure is studied. Based on Vulcan software, using thick plate element and beam-column element, combined with EC2 material high temperature constitutive model, the temperature and deformation of fire top floor (corner and middle) and second floor (four) in a steel frame structure are simulated numerically. The influence of concrete expansion strain on the deformation of floor slab under fire is analyzed, and the membrane mechanism, crack distribution and internal force development of steel beam are investigated. The results show that: the predicted results of floor temperature and deformation are in a good agreement with the experimental results, and the concrete expansion strain has a decisive influence on the mid-span deformation of the fire zone in the structure, that is, when the expansion strain is larger, the predicted deformation is larger; the boundary conditions have a decisive influence on the membrane mechanism and crack distribution of the heated plate, and the heated plates have three kinds of membrane mechanisms: ring type, opposite-edge U type and diagonal U type. The bending moment and axial force of the steel beam near the heated grid gradually increase, and the increase of the axial force of the steel beam is relatively large.

Hot deformation characterization of Ti–Nb alloy based on GA-LSSVM and 3D processing map

Abstract The thermal compression tests of Ti–Nb alloy under T = 790–940 °C and e ˙ = 0.001–10s−1 were carried out on the thermal simulation testing machine of Gleeble-3500. The flow stress curves were obtained, and the high-temperature rheological properties of the alloy were analyzed. The 3D activation energy maps were calculated and constructed. The LSSVM model of constitutive relation was established, and the penalty coefficient γ and kernel parameter δ of the LSSVM model were optimized by the genetic algorithm (GA). The constitutive model of the alloy based on the GA-LSSVM algorithm was constructed. The predicted value of the model was also compared with the experimental data. The polar reciprocity model (PRM) and dynamic material model (DMM) were used to establish the 3D processing map of the alloy and appropriate thermal processing parameters. The results indicated that T and e ˙ have a great influence on the flow stress of Ti–Nb alloy. Ti–Nb alloy is a negative temperature-sensitive and a positive strain rate-sensitive material. The correlation coefficient (R) of the GA-LSSVM algorithm constitutive model is 0.9958. The model has high prediction accuracy and strong generalization ability, which provide a new method for establishing a high-temperature constitutive model of materials. The PRM processing map is more accurate in optimizing the processing parameters of Ti–Nb alloy than that of the DMM processing map through analyzing the 3D processing map and observing the microstructure. The instability modes in the instability region of the alloy mainly include local flow. The stability region's predominant deformation mechanism is DRX. The 870–940 °C and 0.001–0.01s−1 are the best parameters during the processing of Ti–Nb alloy.

The Parameters Identification of High-Temperature Constitutive Model Based on Inverse Optimization Method and 3D Processing Map of Cr8 Alloy Steel.

As a novel kind of cold roller steel, Cr8 alloy steel has the characteristics of high hardness, high wear resistance and good toughness, which can effectively prolong the service life of the roller that is an important part of the steel rolling mill. How to accurately define the constitutive model parameters of metal materials is the major problem, because it seriously affects the accuracy of numerical simulation results of the roller hot forming process. In the study of Cr8 alloy steel’s thermal deformation behavior of the present paper, the high temperature compression test was done on a Gleebel-1500D thermal/force simulation testing machine. A novel method of parameter identification was proposed based on inverse optimization. The Hansel–Spittel constitutive model was established by using the inverse optimization method. To carry out the verification on the accuracy of the established constitutive model, the predicted flow-stress of constitutive model was made a contrast to the experimental flow-stress, and the standard statistical parameters were also applied to further evaluation. The results showed a relatively high prediction accuracy of the Hansel–Spittel constitutive model based on the inverse optimization algorithm. Meanwhile, to obtain optimal parameters of Cr8 alloy steel in the thermal processing, 3D thermal processing maps concerning strain-rate, strain and temperature were built based on the dynamic material model. According to the 3D processing map, the most adequate thermal processing parameters of Cr8 alloy steel were obtianed as follows: strain 0.2–0.4, strain-rate 0.05–0.005 s−1, temperature 1100–1150 °C.

Development and Application of High-Temperature Constitutive Model of HNi55-7-4-2 Alloy

The constitutive model is still not available for theoretical and engineering analysis of HNi55-7-4-2 alloy, which is a new type of wear-resistant brass alloy widely applied to car synchronizer rings and ship condenser tubes etc. In the current investigation, a friction-corrected stress-strain curve was obtained through a hot-compression test to develop the high-temperature constitutive model of HNi55-7-4-2 alloy based on the Hansel–Spittel model. By comparing predicted flow stress and a simulated force-stroke curve with experimental results, the proposed constitutive model was verified. The developed constitutive model was applied to numerically simulate the hot precision forging of a synchronizer ring. The simulation results based on two process plans on material flow and forging defects were validated by process experiment. The Hansel–Spittel high-temperature constitutive model proposed in this work enables the theoretical and engineering analysis of HNi55-7-4-2 alloy.

Research on Constitutive Relation of TC11 Titanium Alloy Based on PSO-LSSVM

In order to accurately predict the flow behavior of the TC11 titanium, the uniaxial compressive tests of TC11 titanium alloy were carried out by Gleeble-1500 thermal simulator with the temperature in the range of 900∼1050°C, and the strain rate of 0.1∼10s−1. Then the particle swarm optimization (PSO) was used to optimize the parameters of the least square support vector machine (LSSVM) model, and a high-temperature constitutive model of TC11 titanium alloy based on PSO-LSSVM was established, and the average relative error between the predicted value and the experimental value of the established constitutive model based on PSO-LSSVM is 1.51%, and the correlation coefficient is 0.997. The established constitutive model can accurately predict the high temperature flow behavior of TC11 titanium alloy. This indicated that a new method for establishing the constitutive model is provided.

New method to develop High temperature constitutive model of metal based on the Arrhenius-type model

The isothermal compressions of Mg-Gd-Y-Zn-Zr alloy in a temperature range of 653–773 K and strain rate range of 0.001-1 s−1 were conducted. The Arrhenius-type equation is widely applied to describe the complex behavior of the flow stress at elevated temperatures. Linear regression is the most common method to solve material constants of the Arrhenius-type equation in previous research. In prevent study, a new method is proposed to solve material constants. The new method combines an iterative method with regression analysis, and it transforms the Arrhenius-type equation into a system of equations of two equations. Moreover, to improving convergence speed, we introduce an offset error into one equation in the system of equations and propose methods to determine the initial guess. A comparative study has been made between the new method and the regression method. The result shows compared with the regression method, the new method improves the prediction accuracy of the Arrhenius-type equation, and it decreases the number of regression operations when the same average absolute relative error (AARE) value is used as a criterion.

High temperature tensile damage behavior of ZrB2-based composite: Experimental investigation and modeling

The uniaxial tensile behaviors of ZrB2-SiC-graphite composites at the room temperature of 1400 °C, 1600 °C and 1800 °C, were investigated respectively, in which the tensile direction is parallel to the basic plane of the graphite. The tensile deformation and damage behavior were discussed through high temperature tensile experiments and the prediction model. Results showed that ZrB2-SiC-graphite composites displayed an evident nonlinear tensile behavior with the increase of temperature. Tensile deformation increased with the increase of temperature, and the maximum deformation at 1800 °C was almost seven times than the value at the room temperature. Furthermore, a damaged high temperature constitutive model was applied to describe the nonlinear condition, and to predict tensile stress-strain relationship and tensile deformation and strain. Numerical tensile deformation was in good accordance with the experimental result, which illustrated the applicability of this model for tensile behavior in the condition of high temperature. Additionally, numerical results showed that the value and range of mechanical damage increased with the increase of temperatures, and a rapid increase above the brittle-ductile transition temperature.

High-temperature constitutive model for three-dimensional needled C/C-SiC composite under tensile loading

Tensile experiments of three-dimensional needled C/C-SiC composite from room temperature to 1800℃ were performed to investigate tensile behavior. The damage characteristics and macroscopic mechanical behavior of the composite are relevant to the testing temperature and off-axis angles of the tensile loading. The tensile strength increased while the modulus decreased with the increase of temperature. A high-temperature nonlinear constitutive model was established to analyze the nonlinear stress–strain relationship of the composite. Plastic strain accumulation and stiffness degeneration were described by the plasticity and damage theories. The effect of temperature on the tensile behavior of the composite was particularly considered in this model by introducing a thermal damage variable. The proposed constitutive model can predict the stress–strain behavior of the material subjected to different off-axis tensile load, and at different temperatures. Fairly good agreement was achieved between the predicted and experimental results.

Research on the High Temperature Constitutive Model of 300M Ultrahigh Strength Steel

300M ultrahigh strength steel has good mechanical properties. It has been widely used in the force bearing components of aircraft. In this paper, By using Gleeble1-500D thermal simulator, we studied the change regularity of stress-strain curve of 300M steel using hot compression deformation when temperature is from 800°C to1100°C, strain rate is from 0.001 S-1to 1 S-1 and the strain is 0.7.The experimental results showed that when the strain rate is constant, the flow stress and the peak stress decrease with the increase of deformation temperature. When the deformation temperature is constant, the flow stress and peak stress increase with the increase of strain rate. From the test, we got the true stress-strain curve, calculated the thermal deformation constants such as the deformation activation energy of 300M ultrahigh strength steel. Eventually, we built the thermal deformation constitutive model in hyperbolic sine form of 300M steel.

The Network Prediction of Hot Temperature Flow Stress and Dynamic Recrystallization of AZ61 Alloy

In this paper, the Back-Propagation neural network (BP network) and the establishment of the AZ61 magnesium alloy high temperature constitutive model and test data obtained for training the neural network, after training the neural network to become a knowledge-based constitutive model formed AZ61 magnesium alloy flow stress and dynamic recrystallization of the neural network model tested by the neural network model with traditional regression methods predict contrast, results showed that the higher the accuracy of the neural network model for dealing with a large number of test data to establish the constitutive relations of materials with high stress and promotion of value.

Induction heating apparatus for high temperature testing of thermo-mechanical properties

A low cost high temperature test facility designed and built for the purpose of thermo-mechanical testing is described. An induction heater provides variable heating rates, simple operation and easy access for temperature and strain measurement. Specially designed high temperature specimen grips with water-cooling allow for testing over long periods of time. Contact temperature and strain measurements are utilised to provide accurate and reliable results. Detail is given on the experimental procedure including calibration of the thermocouple temperature measurement. A validation study of the thermal expansion and tensile Young’s Modulus of carbon steel 1020 at temperatures up to 850 °C proves the accuracy of the test set-up and procedure. Results are given for the stress–strain curves of aluminium alloy 7000 T4 at various temperatures to further demonstrate the capabilities of the test facility. The measured thermo-mechanical properties of these materials were used to develop high temperature constitutive models for implementation in finite element thermal–structural analysis of hypersonic structures.

Implicit Integration and Consistent Tangent Modulus of a Time-Dependent Non-Unified Constitutive Model.

This paper is concerned with the implicit integration and consistent tangent modulus of a high-temperature constitutive model, in which time-dependent inelastic strain rate consists of the transient part affected by kinematic and isotropic hardenings and the steady part depending on stress and temperature. Such a model is useful for high-temperature structure analysis and is practical because of the ease in determining material constants. The implicit integration is shown to result in two scalar-valued equations, and the consistent tangent modulus is derived in a general form by introducing a set of fourth-rank constitutive parameters into discretized kinematic hardening. The constitutive model is, then, implemented in a finite element program and applied to lead-free solder joint analysis. It is demonstrated that the implicit integration is very accurate if the kinematic hardening model of Ohno and Wang is employed, and that the consistent tangent modulus affords parabolic convergence to the Newton-Raphson iteration for solving nodal force equilibrium equations.