In order to develop the appropriate constitutive equation which can precisely model high temperature flow stress of 6063 Al alloy, a series of isothermal hot compression tests were performed at temperatures from 573 t...In order to develop the appropriate constitutive equation which can precisely model high temperature flow stress of 6063 Al alloy, a series of isothermal hot compression tests were performed at temperatures from 573 to 773 K and strain rates from 0.5 to 50 s?1 on a Gleeble?1500 thermo-simulation machine. Zener–Hollomon parameter in an exponent-type equation was used to describe the combined effects of temperature and strain rate on hot deformation behaviour of 6063 Al alloy, whereas the influence of strain was incorporated in the developed constitutive equation by considering material constants (α,n,Q andA) to be 4th order polynomial functions of strain. The results show that the developed constitutive equation can accurately predict high temperature flow stress of 6063 Al alloy, which demonstrates that it can be suitable for simulating hot deformation processes such as extrusion and forging, and for properly designing the deformation parameters in engineering practice.展开更多
High temperature compressive deformation behaviors of as-cast Ti-43Al-4Nb-1.4W-0.6B alloy was investigated at temperatures ranging from 1323 K to 1473 K, and strain rates from 0.001 s-1 to 1 s-1. The results indicated...High temperature compressive deformation behaviors of as-cast Ti-43Al-4Nb-1.4W-0.6B alloy was investigated at temperatures ranging from 1323 K to 1473 K, and strain rates from 0.001 s-1 to 1 s-1. The results indicated that the true stress-true strain curves show a dynamic flow softening behavior. The flow curves after the friction and the temperature compensations were employed to develop constitutive equations. The effects of temperature and the strain rate on the deformation behavior were represented by Zener-Holloman exponential equation. The influence of strain was incorporated in the constitutive analysis by considering the effect of the strain on material constants by a five-order polynomial. A revised model was proposed to describe the relationships among the flow stress, strain rate and temperature and the predicted flow stress curves were in good agreement with experimental results. Appropriate deformation processing parameters were suggested based on the processing map which was constructed from friction and temperature corrected flow curves, determined as 1343 K, 0.02 s-1 and were successfully applied in the canned forging of billets to simulate industrial work condition.展开更多
Metal-core piezoelectric fibers (MPFs) are one of the new type piezoelectric devices. To investigate the piezoelectricity and the mechanical properties of the piezoelectric fibers, the constitutive equations are est...Metal-core piezoelectric fibers (MPFs) are one of the new type piezoelectric devices. To investigate the piezoelectricity and the mechanical properties of the piezoelectric fibers, the constitutive equations are established. It can describe the response of piezoelectric fibers subject to an axial force and an external voltage. A cantilever bar subject to a tip axial force and an external voltage on the electrodes is considered. The internal energy density in thermodynamic equilibrium is obtained. The total internal energy is calculated by integrating over the entire volume of the bar. The generalized displacement of the tip axial force is the tip elongation δ, and the generalized displacement of the voltage is the electrical charge Q on the electrodes. In the established constitutive equations, the excitation (input) parameters are the axial force and the external voltage, the response (output) parameters are the tip elongation and the electric charge. And the response parameters are related to the excitation parameters by a 2× 2 piezoelectric matrix. Finally, two experiments using MPF as a sensor or an actuator are performed to verify the constitutive equations. And experimental results are compared with analytical ones.展开更多
To understand the hot compression deformation characteristics of the self-developed Al-9.3Zn-2.4Mg^(-1).1Cu alloy,the hot compression tests of Al-9.3Zn-2.4Mg^(-1).1Cu alloy were investigated by Gleeble 1500 thermo-mec...To understand the hot compression deformation characteristics of the self-developed Al-9.3Zn-2.4Mg^(-1).1Cu alloy,the hot compression tests of Al-9.3Zn-2.4Mg^(-1).1Cu alloy were investigated by Gleeble 1500 thermo-mechanical simulator to determine the best hot processing conditions.The hot deformation temperatures were 300,350,400,and 450℃,and the strain rates were 1,0.1,0.01,and 0.003 s^(-1),respectively.Based on the experimental results,the constitutive equation and hot processing maps are established,and the corresponding strain rate and temperature-sensitive index are analyzed.The results show that Al-9.3Zn-2.4Mg^(-1).1Cu alloy has a dynamic softening trend and high strain rate sensitivity during the isothermal compression process.The hot deformation behavior can be described by an Arrhenius-type equation after strain compensation.The temperature has a negligible effect on the hot processing properties,while a low strain rate is favorable for the hot working of alloy.The processing maps and microstructure show that the optimal processing conditions were in the temperature range of 400-450℃and strain rate range of 0.003-0.005 s^(-1).展开更多
The hot compression tests of 7Mo super austenitic stainless(SASS)were conducted to obtain flow curves at the temperature of 1000-1200℃and strain rate of 0.001 s^(-1)to 1 s^(-1).To predict the non-linear hot deformati...The hot compression tests of 7Mo super austenitic stainless(SASS)were conducted to obtain flow curves at the temperature of 1000-1200℃and strain rate of 0.001 s^(-1)to 1 s^(-1).To predict the non-linear hot deformation behaviors of the steel,back propagation-artificial neural network(BP-ANN)with 16×8×8 hidden layer neurons was proposed.The predictability of the ANN model is evaluated according to the distribution of mean absolute error(MAE)and relative error.The relative error of 85%data for the BP-ANN model is among±5%while only 42.5%data predicted by the Arrhenius constitutive equation is in this range.Especially,at high strain rate and low temperature,the MAE of the ANN model is 2.49%,which has decreases for 18.78%,compared with conventional Arrhenius constitutive equation.展开更多
In order to study the work-ability and establish the optimum hot formation processing parameters for industrial 1060 pure aluminum, the compressive deformation behavior of pure aluminum was investigated at temperature...In order to study the work-ability and establish the optimum hot formation processing parameters for industrial 1060 pure aluminum, the compressive deformation behavior of pure aluminum was investigated at temperatures of 523?823 K and strain rates of 0.005?10 s?1 on a Gleeble?1500 thermo-simulation machine. The influence rule of processing parameters (strain, strain rate and temperature) on flow stress of pure aluminum was investigated. Nine analysis factors consisting of material parameters and according weights were optimized. Then, the constitutive equations of multilevel series rules, multilevel parallel rules and multilevel series ¶llel rules were established. The correlation coefficients (R) are 0.992, 0.988 and 0.990, respectively, and the average absolute relative errors (AAREs) are 6.77%, 8.70% and 7.63%, respectively, which proves that the constitutive equations of multilevel series rules can predict the flow stress of pure aluminum with good correlation and precision.展开更多
The hot working behaviors of 2024 and 7075 aluminum alloys were studied through constitutive analysis based on a physically-based approach which accounts for the dependence of the elastic modulus and the self-diffusio...The hot working behaviors of 2024 and 7075 aluminum alloys were studied through constitutive analysis based on a physically-based approach which accounts for the dependence of the elastic modulus and the self-diffusion coefficient of aluminum on temperature. It was demonstrated that the lattice self-diffusion activation energy of aluminum(142 k J/mol) can be used in the Zener-Hollomon parameter's formula as the deformation activation energy and the theoretical exponent of 5 can be set in the modified hyperbolic sine law to describe the peak flow stresses. By consideration of physically-based material's parameters, it was possible to conduct a comparative study on the hot flow stress of 2024 and 7075 aluminum alloys. It was concluded that the used approach in the current work can be considered as a versatile tool in future comparative hot working studies, especially in studies dedicated to alloy development.展开更多
The hot deformation behavior of AA5083 aluminum alloy was studied using isothermal compression tests with a Gleeble 3500 thermal simulator at strain rate of 0.0110 s 1 and at temperature of 300500°C.The experimen...The hot deformation behavior of AA5083 aluminum alloy was studied using isothermal compression tests with a Gleeble 3500 thermal simulator at strain rate of 0.0110 s 1 and at temperature of 300500°C.The experimental results indicate that dynamic recrystallization(DRX)tends to occur at high strain rates and temperatures,and therefore the flow stress is decreased.To predict the flow behavior under different deformation conditions,a strain-compensated constitutive equation based on Arrhenius-type equation and Zener Hollomon parameters was proposed.The flow stresses obtained from the constitutive equation are consistent with the experimental results.The average absolute relative error is only 4.52%over the entire experimental range,indicating that the proposed constitutive equation exhibits high prediction precision for the hot deformation behavior of AA5083 aluminum alloy.展开更多
A constitutive equation theory of Oldroyd fluid B type,i.e.the co-rotational derivative type,is developed for the anisotropic-viscoelastic fluid of liquid crystalline(LC)polymer.Analyzing the influence of the orientat...A constitutive equation theory of Oldroyd fluid B type,i.e.the co-rotational derivative type,is developed for the anisotropic-viscoelastic fluid of liquid crystalline(LC)polymer.Analyzing the influence of the orientational motion on the material behavior and neglecting the influence,the constitutive equation is applied to a simple case for the hydrodynamic motion when the orientational contribution is neglected in it and the anisotropic relaxation,retardation times and anisotropic viscosi- ties are introduced to describe the macroscopic behavior of the anisotropic LC polymer fluid.Using the equation for the shear flow of LC polymer fluid,the analytical expressions of the apparent viscosity and the normal stress differences are given which are in a good agreement with the experimental results of Baek et al.For the fiber spinning flow of the fluid,the analytical expression of the extensional viscosity is given.展开更多
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 AA10...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.展开更多
In this paper,the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading.Firstly,a coupled damage variable was derived,which contains two parts,i.e.,the compa...In this paper,the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading.Firstly,a coupled damage variable was derived,which contains two parts,i.e.,the compaction-induced damage and the cracking-induced damage.The compaction-induced damage variable was derived from a nonlinear stress–strain relation of the initial compaction stage,and the cracking-induced damage variable was established based on the statistical damage theory.Secondly,based on the total damage variable,a damage constitutive equation was proposed to describe the constitutive relation of rock under the monotonic uniaxial compression conditions,whereafter,the application of this model is extended to cyclic loading and unloading conditions.To validate the proposed monotonic and cyclic constitutive equations,a series of mechanical tests for marble specimens were carried out,which contained the monotonic uniaxial compression(MUC)experiment,cyclic uniaxial compression experiments under the variable amplitude(CUC-VA)and constant amplitude(CUC-CA)conditions.The results show that the proposed total damage variable comprehensively reflects the damage evolution characteristic,i.e.,the damage variable firstly decreases,then increases no matter under the conditions of MUC,CUC-VA or CUC-CA.Then a reasonable consistency is observed between the experimental and theoretical curves.The proposed cyclic constitutive equations can simulate the whole cyclic loading and unloading behaviors,such as the initial compaction,the strain hardening and the strain softening.Furthermore,the shapes of the theoretical curves are controlled by the modified coefficient,compaction sensitivity coefficient and two Weibull distributed parameters.展开更多
In order to describe the deformation behavior and the hot workability of equiatomic NiTi shape memory alloy (SMA) during hot deformation, Arrhenius-type constitutive equation and hot processing map of the alloy were d...In order to describe the deformation behavior and the hot workability of equiatomic NiTi shape memory alloy (SMA) during hot deformation, Arrhenius-type constitutive equation and hot processing map of the alloy were developed by hot compression tests at temperatures ranging from 500 to 1100 °C and strain rates ranging from 0.0005 to 0.5 s?1. The results show that the instability region of the hot processing map increases with the increase of deformation extent. The instability occurs in the low and high temperature regions. The instability region presents the adiabatic shear bands at low temperatures, but it exhibits the abnormal growth of the grains at high temperatures. Consequently, it is necessary to avoid processing the equiatomic NiTi SMA in these regions. It is preferable to process the NiTi SMA at the temperatures ranging from 750 to 900 °C.展开更多
The microstructure of 40Cr steel sample and its surface is ultra-fined through salt-bath cyclic quenching and high frequency hardening, then the superplasticity is studied under isothermal superplastic compressive def...The microstructure of 40Cr steel sample and its surface is ultra-fined through salt-bath cyclic quenching and high frequency hardening, then the superplasticity is studied under isothermal superplastic compressive deformation condition. The experimental results indicate that the stress-strain curves are shown to take place obvious superplastic flow characteristic at the temperature of 750-770℃ and at the initial strain rate of (1.7-5.0)×10-4 s-1. Its strain rate sensitivity is 0.30-0.38, the steady superplastic flow stress is 60-70MPa, the superplastic flow activation energy is 198-217kJ/mol, and it is close to α-Fe grain boundary self-diffusion activation energy. The super-plastic compressive constitute equations of this steel are correspondingly set up. Due to the finer microstructure of high frequency hardening, it appears bigger strain rate sensitivity value, smaller the steady superplastic flow stress and the superplastic flow activation energy, so it has better superplastic deformation capability.展开更多
A physical model of microstructure evolution including dislocation density rate and grain growth rate was established based on the deformation mechanism for the hot forming of a class of two-phase titanium alloys. Fur...A physical model of microstructure evolution including dislocation density rate and grain growth rate was established based on the deformation mechanism for the hot forming of a class of two-phase titanium alloys. Further, a set of mechanism-based constitutive equations were proposed, in which the microstructure variables such as grain size and dislocation density were taken as internal state variables for characterizing the current material state. In the set of constitutive equations, the contributions of different mechanisms and individual phase to the deformation behavior were analyzed. The present equations have been applied to describe a correlation of the flow stress with the microstructure evolution of the TC6 alloy in hot forming.展开更多
The hot deformation behavior of Ti-6.5Al-3.5Mo-1.5Zr-0.3Si alloy with equiaxed microstructure was characterized in the temperature range of 900~1060 ℃ and strain rate range of 10-3~10 s-1.The experimental results i...The hot deformation behavior of Ti-6.5Al-3.5Mo-1.5Zr-0.3Si alloy with equiaxed microstructure was characterized in the temperature range of 900~1060 ℃ and strain rate range of 10-3~10 s-1.The experimental results indicate that the plastic deformation behavior of the titanium alloys is rather sensitive to temperature and strain rate.In the α+β phase temperature region,all of the stress-strain curves exhibit different degrees of the flow softening after a peak stress.In the β phase temperature region,the titanium alloy shows a stress softening at high strain rates and a steady flow stress at low strain rates.On the basis of the peak stress data,the constitutive equations were constructed in the α+β phase temperature region and β phase temperature region,respectively.Activation energy parameters were calculated to be 344.923 kJ·mol-1 in the β phase temperature region and 628.3 kJ·mol-1 in the α+β phase temperature region.Microstructure of the compressed specimens in water-quenched conditions was found to be quite dependent on the conditions of deformation.展开更多
A recently proposed model coupling with the solid-fluid of the saturated sand was utilized to study the deformation band. Based on the critical state plasticity model by Borja and Andrade, the hydraulic conductivity t...A recently proposed model coupling with the solid-fluid of the saturated sand was utilized to study the deformation band. Based on the critical state plasticity model by Borja and Andrade, the hydraulic conductivity tensor was naturally treated as a function of the spatial discretization matrix about the displacement and the stress field, allowing a more realistic representation of the physical phenomenon. The fully Lagrangian form of the Darcy law was resolved by Piola algorithm, and then the flow law was gained, leading to the implementation of a modified model of the saturated sand. Then the criterion for the onset of localization was derived and utilized to detect instability. The constitutive model was implemented in a finite element program coded by FORTRAN, which was used to predict the formation and development of shear bands in plane strain compression of saturated sand. At last, the formation mechanism of the shear band was discussed. It is shown that the model works well, and the simulation sample bifurcates at 1.18% axial strain, which is in a good qualitative agreement with the experiment. The pore pressure greatly affects the onset and development of the deformation band, and it obviously increases around the localization-prone regions with the direction toward the outer side of the normal of the shear band, while the pore stress flows nearly horizontally and is distributed equally far away the shear band region.展开更多
Dominant phase during hot deformation in the two-phase region of Zr-2.5Nb-0.5Cu (ZNC) alloy was studied using activation energy calculation of individual phases. Thermo-mechanical compression tests were performed on...Dominant phase during hot deformation in the two-phase region of Zr-2.5Nb-0.5Cu (ZNC) alloy was studied using activation energy calculation of individual phases. Thermo-mechanical compression tests were performed on a two-phase ZNC alloy in the temperature range of 700-925 ℃ and strain rate range of 10-2-10 s-l, Flow stress data of the single phase were extrapolated in the two-phase range to calculate flow stress data of individual phases. Activation energies of individual phases were then calculated using calculated flow stress data in the two-phase range, Comparison of activation energies revealed that a phase is the dominant phase (deformation controlling phase) in the two-phase range. Constitutive equations were also developed on the basis of the deformation temperature range (or according to phases present) using a sine-hyperbolic type constitutive equation. The statistical analysis revealed that the constitutive equation developed for a particular phase showed good agreement with the experimental results in terms of correlation coefficient (R) and average absolute relative error (AARE).展开更多
The flow behavior of Rene 95 PM alloy was studied from 1050 to 1150 deg Cwith strain rate of 1 X 10^(-3), 1 X 10^(-2), 1 X 10^(-1) and 1 s^(-1). At a given temperature andstrain rate, flow curves exhibit a peak follow...The flow behavior of Rene 95 PM alloy was studied from 1050 to 1150 deg Cwith strain rate of 1 X 10^(-3), 1 X 10^(-2), 1 X 10^(-1) and 1 s^(-1). At a given temperature andstrain rate, flow curves exhibit a peak followed by flow softening up to a steady state. Moreover,at constant strain, flow stress increases with increasing strain rate and decreasing temperature. Anequation relating hyperbolic sine of flow stress to hot working parameters, such as strain, strainrate and temperature, was established by using multiple nonlinear regression method. A very goodagreement was found between predicted and experimental flow stress in all the strain rangeinvestigated. Application of the constitutive equation in predicting forming loads and flow behaviorand temperature distribution in both upper and lower dies in an isothermal forging process ofturbine disk of large dimension (about 630 mm) by means of a finite element code was systematicallyanalyzed.展开更多
The general expressions of constitutive equations for isotropic elastic damaged materials were derived directly from the basic law of irreversible thermodynamics. The limitations of the classical damage constitutive e...The general expressions of constitutive equations for isotropic elastic damaged materials were derived directly from the basic law of irreversible thermodynamics. The limitations of the classical damage constitutive equation based on the well-known strain equivalence hypothesis were overcome. The relationships between the two elastic isotropic damage models (i.e. single and double scalar damage models) were revealed. When a single scalar damage variable defined according to the microscopic geometry of a damaged material is used to describle the isotropic damage state, the constitutive equations contain two 'damage effect functions', which describe the different influences of damage on the two independent elastic, constants. The classical damage constitutive equation based on the strain equivalence hypothesis is only the first-order approximation of the general expression. It may be unduly simplified and may fail to describe satisfactorily the damage phenomena of practical materials.展开更多
The deformaton behavior of Ti - 6Al - 4V alloy under hot - working condition has been studied by compression testing in the temperature range 750 - 950℃ and strain rate range 0.05 - 15s -1. The flow stress decrease...The deformaton behavior of Ti - 6Al - 4V alloy under hot - working condition has been studied by compression testing in the temperature range 750 - 950℃ and strain rate range 0.05 - 15s -1. The flow stress decreases with the increase of temperature and with the decrease of strain rate. After a steep initial strain hardening, a flow softening occurs. This softening is mainly ascribed to the temperature rise and dynamic recmptallisation.By a simple extension, a classical sinushyperbolic constitutive equation can be used to describe the flow behavior of Ti - 6Al - 4V alloy. flow stress is described as a function of strain, strain rate and temperature. The parameters Q, n andaare the same at differ- ent deformation conditions, and A is a funciton of strain.展开更多
基金Project(2012B090600051)supported by Al and Mg Light Alloys Platform on the Unity of Industry,Education and Research Innovation of Guangdong Province,ChinaProject(2012B001)supported by the Ph D Start-up Fund of Guangzhou Research Institute of Non-ferrous Metals,China
文摘In order to develop the appropriate constitutive equation which can precisely model high temperature flow stress of 6063 Al alloy, a series of isothermal hot compression tests were performed at temperatures from 573 to 773 K and strain rates from 0.5 to 50 s?1 on a Gleeble?1500 thermo-simulation machine. Zener–Hollomon parameter in an exponent-type equation was used to describe the combined effects of temperature and strain rate on hot deformation behaviour of 6063 Al alloy, whereas the influence of strain was incorporated in the developed constitutive equation by considering material constants (α,n,Q andA) to be 4th order polynomial functions of strain. The results show that the developed constitutive equation can accurately predict high temperature flow stress of 6063 Al alloy, which demonstrates that it can be suitable for simulating hot deformation processes such as extrusion and forging, and for properly designing the deformation parameters in engineering practice.
基金Project(2011CB605505)supported by the National Key Fundamental Research Development Project of ChinaProjects(51301204,51174233)supported by the National Natural Science Foundation of ChinaProject(2011JQ002)supported by the Fundamental Research Funds for the Central Universities of China
文摘High temperature compressive deformation behaviors of as-cast Ti-43Al-4Nb-1.4W-0.6B alloy was investigated at temperatures ranging from 1323 K to 1473 K, and strain rates from 0.001 s-1 to 1 s-1. The results indicated that the true stress-true strain curves show a dynamic flow softening behavior. The flow curves after the friction and the temperature compensations were employed to develop constitutive equations. The effects of temperature and the strain rate on the deformation behavior were represented by Zener-Holloman exponential equation. The influence of strain was incorporated in the constitutive analysis by considering the effect of the strain on material constants by a five-order polynomial. A revised model was proposed to describe the relationships among the flow stress, strain rate and temperature and the predicted flow stress curves were in good agreement with experimental results. Appropriate deformation processing parameters were suggested based on the processing map which was constructed from friction and temperature corrected flow curves, determined as 1343 K, 0.02 s-1 and were successfully applied in the canned forging of billets to simulate industrial work condition.
基金the National High Technology Research and Development Program of China(863Pro-gram)(2007AA03Z104)~~
文摘Metal-core piezoelectric fibers (MPFs) are one of the new type piezoelectric devices. To investigate the piezoelectricity and the mechanical properties of the piezoelectric fibers, the constitutive equations are established. It can describe the response of piezoelectric fibers subject to an axial force and an external voltage. A cantilever bar subject to a tip axial force and an external voltage on the electrodes is considered. The internal energy density in thermodynamic equilibrium is obtained. The total internal energy is calculated by integrating over the entire volume of the bar. The generalized displacement of the tip axial force is the tip elongation δ, and the generalized displacement of the voltage is the electrical charge Q on the electrodes. In the established constitutive equations, the excitation (input) parameters are the axial force and the external voltage, the response (output) parameters are the tip elongation and the electric charge. And the response parameters are related to the excitation parameters by a 2× 2 piezoelectric matrix. Finally, two experiments using MPF as a sensor or an actuator are performed to verify the constitutive equations. And experimental results are compared with analytical ones.
基金Funded by the National Natural Science Foundation of China(No.52171138)Henan Provincial Science and Technology Research Project(No.222102230088)。
文摘To understand the hot compression deformation characteristics of the self-developed Al-9.3Zn-2.4Mg^(-1).1Cu alloy,the hot compression tests of Al-9.3Zn-2.4Mg^(-1).1Cu alloy were investigated by Gleeble 1500 thermo-mechanical simulator to determine the best hot processing conditions.The hot deformation temperatures were 300,350,400,and 450℃,and the strain rates were 1,0.1,0.01,and 0.003 s^(-1),respectively.Based on the experimental results,the constitutive equation and hot processing maps are established,and the corresponding strain rate and temperature-sensitive index are analyzed.The results show that Al-9.3Zn-2.4Mg^(-1).1Cu alloy has a dynamic softening trend and high strain rate sensitivity during the isothermal compression process.The hot deformation behavior can be described by an Arrhenius-type equation after strain compensation.The temperature has a negligible effect on the hot processing properties,while a low strain rate is favorable for the hot working of alloy.The processing maps and microstructure show that the optimal processing conditions were in the temperature range of 400-450℃and strain rate range of 0.003-0.005 s^(-1).
文摘The hot compression tests of 7Mo super austenitic stainless(SASS)were conducted to obtain flow curves at the temperature of 1000-1200℃and strain rate of 0.001 s^(-1)to 1 s^(-1).To predict the non-linear hot deformation behaviors of the steel,back propagation-artificial neural network(BP-ANN)with 16×8×8 hidden layer neurons was proposed.The predictability of the ANN model is evaluated according to the distribution of mean absolute error(MAE)and relative error.The relative error of 85%data for the BP-ANN model is among±5%while only 42.5%data predicted by the Arrhenius constitutive equation is in this range.Especially,at high strain rate and low temperature,the MAE of the ANN model is 2.49%,which has decreases for 18.78%,compared with conventional Arrhenius constitutive equation.
基金Project(51275414)supported by the National Natural Science Foundation of ChinaProject(2015JM5204)supported by the Natural Science Foundation of Shaanxi Province,China+1 种基金Project(Z2015064)supported by the Graduate Starting Seed Fund of the Northwestern Polytechnical University,ChinaProject(130-QP-2015)supported by the Research Fund of the State Key Laboratory of Solidification Processing(NWPU),China
文摘In order to study the work-ability and establish the optimum hot formation processing parameters for industrial 1060 pure aluminum, the compressive deformation behavior of pure aluminum was investigated at temperatures of 523?823 K and strain rates of 0.005?10 s?1 on a Gleeble?1500 thermo-simulation machine. The influence rule of processing parameters (strain, strain rate and temperature) on flow stress of pure aluminum was investigated. Nine analysis factors consisting of material parameters and according weights were optimized. Then, the constitutive equations of multilevel series rules, multilevel parallel rules and multilevel series ¶llel rules were established. The correlation coefficients (R) are 0.992, 0.988 and 0.990, respectively, and the average absolute relative errors (AAREs) are 6.77%, 8.70% and 7.63%, respectively, which proves that the constitutive equations of multilevel series rules can predict the flow stress of pure aluminum with good correlation and precision.
文摘The hot working behaviors of 2024 and 7075 aluminum alloys were studied through constitutive analysis based on a physically-based approach which accounts for the dependence of the elastic modulus and the self-diffusion coefficient of aluminum on temperature. It was demonstrated that the lattice self-diffusion activation energy of aluminum(142 k J/mol) can be used in the Zener-Hollomon parameter's formula as the deformation activation energy and the theoretical exponent of 5 can be set in the modified hyperbolic sine law to describe the peak flow stresses. By consideration of physically-based material's parameters, it was possible to conduct a comparative study on the hot flow stress of 2024 and 7075 aluminum alloys. It was concluded that the used approach in the current work can be considered as a versatile tool in future comparative hot working studies, especially in studies dedicated to alloy development.
基金Project(51474240) supported by the National Natural Science Foundation of ChinaProject(AA16380036) supported by the Science and Technology Major Project of Guangxi Autonomous Region,ChinaProject(2017BF20201) supported by the Scientific Research and Technology Development Program of Liuzhou City,China
文摘The hot deformation behavior of AA5083 aluminum alloy was studied using isothermal compression tests with a Gleeble 3500 thermal simulator at strain rate of 0.0110 s 1 and at temperature of 300500°C.The experimental results indicate that dynamic recrystallization(DRX)tends to occur at high strain rates and temperatures,and therefore the flow stress is decreased.To predict the flow behavior under different deformation conditions,a strain-compensated constitutive equation based on Arrhenius-type equation and Zener Hollomon parameters was proposed.The flow stresses obtained from the constitutive equation are consistent with the experimental results.The average absolute relative error is only 4.52%over the entire experimental range,indicating that the proposed constitutive equation exhibits high prediction precision for the hot deformation behavior of AA5083 aluminum alloy.
基金The project supported by the National Natural Science Foundation of China(19832050 and 10372100)
文摘A constitutive equation theory of Oldroyd fluid B type,i.e.the co-rotational derivative type,is developed for the anisotropic-viscoelastic fluid of liquid crystalline(LC)polymer.Analyzing the influence of the orientational motion on the material behavior and neglecting the influence,the constitutive equation is applied to a simple case for the hydrodynamic motion when the orientational contribution is neglected in it and the anisotropic relaxation,retardation times and anisotropic viscosi- ties are introduced to describe the macroscopic behavior of the anisotropic LC polymer fluid.Using the equation for the shear flow of LC polymer fluid,the analytical expressions of the apparent viscosity and the normal stress differences are given which are in a good agreement with the experimental results of Baek et al.For the fiber spinning flow of the fluid,the analytical expression of the extensional viscosity is given.
文摘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.
基金This study was financially supported by the National Natural Science Foundation of China(Nos.51978292,42077254 and 51874144).
文摘In this paper,the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading.Firstly,a coupled damage variable was derived,which contains two parts,i.e.,the compaction-induced damage and the cracking-induced damage.The compaction-induced damage variable was derived from a nonlinear stress–strain relation of the initial compaction stage,and the cracking-induced damage variable was established based on the statistical damage theory.Secondly,based on the total damage variable,a damage constitutive equation was proposed to describe the constitutive relation of rock under the monotonic uniaxial compression conditions,whereafter,the application of this model is extended to cyclic loading and unloading conditions.To validate the proposed monotonic and cyclic constitutive equations,a series of mechanical tests for marble specimens were carried out,which contained the monotonic uniaxial compression(MUC)experiment,cyclic uniaxial compression experiments under the variable amplitude(CUC-VA)and constant amplitude(CUC-CA)conditions.The results show that the proposed total damage variable comprehensively reflects the damage evolution characteristic,i.e.,the damage variable firstly decreases,then increases no matter under the conditions of MUC,CUC-VA or CUC-CA.Then a reasonable consistency is observed between the experimental and theoretical curves.The proposed cyclic constitutive equations can simulate the whole cyclic loading and unloading behaviors,such as the initial compaction,the strain hardening and the strain softening.Furthermore,the shapes of the theoretical curves are controlled by the modified coefficient,compaction sensitivity coefficient and two Weibull distributed parameters.
基金Projects(51305091,51305092,51475101)supported by the National Natural Science Foundation of ChinaProject(20132304120025)supported by the Specialized Research Fund for the Doctoral Program of Higher Education,China
文摘In order to describe the deformation behavior and the hot workability of equiatomic NiTi shape memory alloy (SMA) during hot deformation, Arrhenius-type constitutive equation and hot processing map of the alloy were developed by hot compression tests at temperatures ranging from 500 to 1100 °C and strain rates ranging from 0.0005 to 0.5 s?1. The results show that the instability region of the hot processing map increases with the increase of deformation extent. The instability occurs in the low and high temperature regions. The instability region presents the adiabatic shear bands at low temperatures, but it exhibits the abnormal growth of the grains at high temperatures. Consequently, it is necessary to avoid processing the equiatomic NiTi SMA in these regions. It is preferable to process the NiTi SMA at the temperatures ranging from 750 to 900 °C.
基金supported by State Key Laboratory of New Nonferrous Metal Materials Natural Science Foundation of He'nan Province,China(No.984040900)Natural Science Foundation of the Education Department of He'nan Province,China(No.2003430211).
文摘The microstructure of 40Cr steel sample and its surface is ultra-fined through salt-bath cyclic quenching and high frequency hardening, then the superplasticity is studied under isothermal superplastic compressive deformation condition. The experimental results indicate that the stress-strain curves are shown to take place obvious superplastic flow characteristic at the temperature of 750-770℃ and at the initial strain rate of (1.7-5.0)×10-4 s-1. Its strain rate sensitivity is 0.30-0.38, the steady superplastic flow stress is 60-70MPa, the superplastic flow activation energy is 198-217kJ/mol, and it is close to α-Fe grain boundary self-diffusion activation energy. The super-plastic compressive constitute equations of this steel are correspondingly set up. Due to the finer microstructure of high frequency hardening, it appears bigger strain rate sensitivity value, smaller the steady superplastic flow stress and the superplastic flow activation energy, so it has better superplastic deformation capability.
基金This work was financially supported by the National Natural Science Foundation of China (No.50475144), the State Key Foundation-al Research Plan (No.G2000067206), and the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Educa-tion Institutions of the Ministry of Education of China.
文摘A physical model of microstructure evolution including dislocation density rate and grain growth rate was established based on the deformation mechanism for the hot forming of a class of two-phase titanium alloys. Further, a set of mechanism-based constitutive equations were proposed, in which the microstructure variables such as grain size and dislocation density were taken as internal state variables for characterizing the current material state. In the set of constitutive equations, the contributions of different mechanisms and individual phase to the deformation behavior were analyzed. The present equations have been applied to describe a correlation of the flow stress with the microstructure evolution of the TC6 alloy in hot forming.
基金This work is financially supported by the National Key Natural Science Foundation of China ( No 5131903ZT1)
文摘The hot deformation behavior of Ti-6.5Al-3.5Mo-1.5Zr-0.3Si alloy with equiaxed microstructure was characterized in the temperature range of 900~1060 ℃ and strain rate range of 10-3~10 s-1.The experimental results indicate that the plastic deformation behavior of the titanium alloys is rather sensitive to temperature and strain rate.In the α+β phase temperature region,all of the stress-strain curves exhibit different degrees of the flow softening after a peak stress.In the β phase temperature region,the titanium alloy shows a stress softening at high strain rates and a steady flow stress at low strain rates.On the basis of the peak stress data,the constitutive equations were constructed in the α+β phase temperature region and β phase temperature region,respectively.Activation energy parameters were calculated to be 344.923 kJ·mol-1 in the β phase temperature region and 628.3 kJ·mol-1 in the α+β phase temperature region.Microstructure of the compressed specimens in water-quenched conditions was found to be quite dependent on the conditions of deformation.
基金Project(2006G007-C) supported by the Foundation of the Science and Technology Section of Ministry of Railway of ChinaProject(77206) supported by the Excellent PhD Thesis Innovation Foundation of Central South University,China
文摘A recently proposed model coupling with the solid-fluid of the saturated sand was utilized to study the deformation band. Based on the critical state plasticity model by Borja and Andrade, the hydraulic conductivity tensor was naturally treated as a function of the spatial discretization matrix about the displacement and the stress field, allowing a more realistic representation of the physical phenomenon. The fully Lagrangian form of the Darcy law was resolved by Piola algorithm, and then the flow law was gained, leading to the implementation of a modified model of the saturated sand. Then the criterion for the onset of localization was derived and utilized to detect instability. The constitutive model was implemented in a finite element program coded by FORTRAN, which was used to predict the formation and development of shear bands in plane strain compression of saturated sand. At last, the formation mechanism of the shear band was discussed. It is shown that the model works well, and the simulation sample bifurcates at 1.18% axial strain, which is in a good qualitative agreement with the experiment. The pore pressure greatly affects the onset and development of the deformation band, and it obviously increases around the localization-prone regions with the direction toward the outer side of the normal of the shear band, while the pore stress flows nearly horizontally and is distributed equally far away the shear band region.
基金financial support(Grant No.2011/36/15)from Board of Research in Nuclear Science(BRNS),India
文摘Dominant phase during hot deformation in the two-phase region of Zr-2.5Nb-0.5Cu (ZNC) alloy was studied using activation energy calculation of individual phases. Thermo-mechanical compression tests were performed on a two-phase ZNC alloy in the temperature range of 700-925 ℃ and strain rate range of 10-2-10 s-l, Flow stress data of the single phase were extrapolated in the two-phase range to calculate flow stress data of individual phases. Activation energies of individual phases were then calculated using calculated flow stress data in the two-phase range, Comparison of activation energies revealed that a phase is the dominant phase (deformation controlling phase) in the two-phase range. Constitutive equations were also developed on the basis of the deformation temperature range (or according to phases present) using a sine-hyperbolic type constitutive equation. The statistical analysis revealed that the constitutive equation developed for a particular phase showed good agreement with the experimental results in terms of correlation coefficient (R) and average absolute relative error (AARE).
文摘The flow behavior of Rene 95 PM alloy was studied from 1050 to 1150 deg Cwith strain rate of 1 X 10^(-3), 1 X 10^(-2), 1 X 10^(-1) and 1 s^(-1). At a given temperature andstrain rate, flow curves exhibit a peak followed by flow softening up to a steady state. Moreover,at constant strain, flow stress increases with increasing strain rate and decreasing temperature. Anequation relating hyperbolic sine of flow stress to hot working parameters, such as strain, strainrate and temperature, was established by using multiple nonlinear regression method. A very goodagreement was found between predicted and experimental flow stress in all the strain rangeinvestigated. Application of the constitutive equation in predicting forming loads and flow behaviorand temperature distribution in both upper and lower dies in an isothermal forging process ofturbine disk of large dimension (about 630 mm) by means of a finite element code was systematicallyanalyzed.
文摘The general expressions of constitutive equations for isotropic elastic damaged materials were derived directly from the basic law of irreversible thermodynamics. The limitations of the classical damage constitutive equation based on the well-known strain equivalence hypothesis were overcome. The relationships between the two elastic isotropic damage models (i.e. single and double scalar damage models) were revealed. When a single scalar damage variable defined according to the microscopic geometry of a damaged material is used to describle the isotropic damage state, the constitutive equations contain two 'damage effect functions', which describe the different influences of damage on the two independent elastic, constants. The classical damage constitutive equation based on the strain equivalence hypothesis is only the first-order approximation of the general expression. It may be unduly simplified and may fail to describe satisfactorily the damage phenomena of practical materials.
文摘The deformaton behavior of Ti - 6Al - 4V alloy under hot - working condition has been studied by compression testing in the temperature range 750 - 950℃ and strain rate range 0.05 - 15s -1. The flow stress decreases with the increase of temperature and with the decrease of strain rate. After a steep initial strain hardening, a flow softening occurs. This softening is mainly ascribed to the temperature rise and dynamic recmptallisation.By a simple extension, a classical sinushyperbolic constitutive equation can be used to describe the flow behavior of Ti - 6Al - 4V alloy. flow stress is described as a function of strain, strain rate and temperature. The parameters Q, n andaare the same at differ- ent deformation conditions, and A is a funciton of strain.