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
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
A dimensionless stress yield criterion is proposed to describe the mixed hardening of orthotropic material,including kinematic hardening and proportional hardening, and the associated plastic flow law is derived. The ...A dimensionless stress yield criterion is proposed to describe the mixed hardening of orthotropic material,including kinematic hardening and proportional hardening, and the associated plastic flow law is derived. The generalized effective stress_strain formulae can be obtained correspondingly based on the experimental stress_strain curves in various simple stress states. The initial plastic anisotropy is influenced by the elastic anisotropy. The yield criterion can be reduced to Huber_Mises Criterion for isotropic materials and associated constitutive equations can be degenerated into Prandtl_Reuss equations.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 linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the for...The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot's equations for saturated porous media. The Darcy's laws of unsaturated soil were proved. It is shown that Biot's equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.展开更多
The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory. The soils were treated as the mixture composed of three constituents. First, from the rese...The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory. The soils were treated as the mixture composed of three constituents. First, from the researches of soil mechanics, some basic assumptions about the unsaturated soil mixture were made, and the entropy inequality of unsaturated soil mixture was derived. Then, with the common method usually used to deal with the constitutive problems in mixture theory, the nonlinear constitutive equations were obtained. Finally, putting the constitutive equations of constituents into the balance equations of momentum, the nonlinear field equations of constituents were set up. The balance equation of energy of unsaturated soil was also given, and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed.展开更多
In this paper, nonlinear constitutive equations are deduced strictly according to the constitutive axioms of rational continuum mechanics. The existing judgments are modified and improved. The results show that the co...In this paper, nonlinear constitutive equations are deduced strictly according to the constitutive axioms of rational continuum mechanics. The existing judgments are modified and improved. The results show that the constitutive responses of nonlocal thermoelastic body are related to the curvature and higher order gradient of its material space, and there exists an antisymmetric stress whose average value in the domain occupied by thermoelastic body is equal to zero. The expressions of the antisymmetric stress and the nonlocal residuals are given. The conclusion that the directions of thermal conduction and temperature gradient are consistent is reached. In addition, the objectivity about the nonlocal residuals and the energy conservation law of nonlocal field is discussed briefly, and a formula for calculating the nonlocal residuals of energy changing with rigid motion of the spatial frame of reference is derived.展开更多
In order to predict flow instability of wear-resistant steel BTW1, the hot compressions of wear-resistant steel BTW1 were firstly performed at the temperature of 900-1150 ℃ and at the strain rate of 0.05-15 s-1. Then...In order to predict flow instability of wear-resistant steel BTW1, the hot compressions of wear-resistant steel BTW1 were firstly performed at the temperature of 900-1150 ℃ and at the strain rate of 0.05-15 s-1. Then, the constitutive relation was established based on Arrhenius-type hyperbolic sine equation. The results demonstrated that the flow stress depended on the deformation temperature and strain rate. When the deformation temperature kept constant, the flow stress increased as the strain rate increased. When the strain rate remained constant, the flow stress decreased as the temperature increased. The flow stresses calculated by constitutive equations were in a good agreement with experimental results. The apparent activation energy for deformation in the above processing region was estimated to be 369 kJ tool-1. A processing map could be obtained by the superimposition of an instability map on a power dissipation map. Based on the analysis of processing map and the microstructures, the theological instability regimes of strain rate and temperature for hot deformation of wear-resistant steel BTWl had been identified.展开更多
To investigate the hot deformation behavior of powder-forged (P/F) Fe-0. 5C:-2Cu steel, the hot compres- sion tests were conducted at temperatures ranging from 900 to 1000 ℃ and strain rates from 0.1 to 10 s-1 usi...To investigate the hot deformation behavior of powder-forged (P/F) Fe-0. 5C:-2Cu steel, the hot compres- sion tests were conducted at temperatures ranging from 900 to 1000 ℃ and strain rates from 0.1 to 10 s-1 using Gleeble-1500 thermal simulator. The true stress-true strain curves at different temperatures and strain rates of P/F steel were obtained. It is found that dynamic recovery only occurs as strain rate is 10 s 1 at 900 ℃, and the dynamic recrystallization is the main softening mechanism. The flow stress increases with decreasing temperature and increas- ing strain rate. The experimental data are employed to develop constitutive equations on the basis of the Arrhenius- type equation by introducing the strain with nonlinear fitting. The flow stresses prediel:ed by the proposed constitu- tive equations are in good agreement with the experimental values, and the correlation coefficient (R2) and the aver- age absolute relative error (AARE) are 0. 995 25 and 3.07% respectively. These results indicate the proposed consti- tutive equations can effectively describe the hot deformation behavior of the material.展开更多
Mechanical response and simulation for constitutive equation with distributed order derivatives were considered.We investigated the creep compliance,creep recovery,relaxation modulus,stress–strain behavior under harm...Mechanical response and simulation for constitutive equation with distributed order derivatives were considered.We investigated the creep compliance,creep recovery,relaxation modulus,stress–strain behavior under harmonic deformation for each case of two constitutive equations.We express these responses and results as easily computable forms and simulate them by using MATHEMATICA 8.The results involve the exponential integral function,convergent improper integrals on the infinite interval(0,+∞)and the numerical integral method for the convolution integral.For both equations,stress responses to harmonic deformation display hysteresis phenomena and energy dissipation.The two constitutive equations characterize viscoelastic models of fluid-like and solid-like,respectively.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 deformation behavior of IN690 superalloy was characterized in a temperature range of 1273-1473 K and a strain rate range of 0.01-10 s^-1 using uniaxial compression tests on process annealed material.The consti...The hot deformation behavior of IN690 superalloy was characterized in a temperature range of 1273-1473 K and a strain rate range of 0.01-10 s^-1 using uniaxial compression tests on process annealed material.The constitutive relations between flow stress and effective strain,effective strain rate as well as deformation temperature were studied.It can be concluded that the flow stress significantly reduces with the deformation temperature of IN690 superalloy increasing.Whereas,there is a significant increase of flow stress when the strain rate increases from 0.1 s^-1 to 10 s^-1.Based on the hyperbolic-sine Arrhenius-type equation,a constitutive equation considering compensation of strain was developed.The activation energy and the material constants(Q,n and ln A) decrease as the deformation strain increases.The strain dependent term is successfully incorporated in the constitutive equation through a quartic equation.A good agreement between the experimental data and the predicted results has been achieved,indicating that the proposed constitutive equation and the methods of determing the material constants are suitable to model the high temperature deformation behavior of IN690 superalloy.展开更多
In this paper, the generalized Prandtl-Reuss (P-R) constitutive equations of elastic-plastic material in the presence of finite deformations through a new approach are studied. It analyzes the generalized P-R equation...In this paper, the generalized Prandtl-Reuss (P-R) constitutive equations of elastic-plastic material in the presence of finite deformations through a new approach are studied. It analyzes the generalized P-R equation based on the material corotational rate and clarifies the puzzling problem of the simple shear stress oscillation mentioned in some literature. The paper proposes a modified relative rotational rate with which to constitute the objective rates of stress in the generalized P-R equation and concludes that the decomposition of total deformation rate into elastic and plastic parts is not necessary in developing the generalized P-R equations. Finally, the stresses of simple shear deformation are worked out.展开更多
A viscoplastic constitutive model is introduced,which takes into account nonproportional cyclic additional hardening and the effects of nonproportional cyclic loading history and inelastic strain amplitude history.In ...A viscoplastic constitutive model is introduced,which takes into account nonproportional cyclic additional hardening and the effects of nonproportional cyclic loading history and inelastic strain amplitude history.In the model,a variable q of memory on the inelastic strain amplitude during loading is introduced,a new nonproportionality is defined,a cyclic saturated isotropic deformation resistance parameter Q,is given,and the evolution equations of the isotropic deformation resistance with the memory on the previous loading history are proposed.The present model is applied to the description of the complex cyclic deformation behavior of 1Cr18Ni9Ti stainless steel,and the predictions are in good agreement with the experimental results.This shows that the model describes the deformation behavior of nonproportional cyclic loadings and their histories very well.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
The total stress response of material is decomposed into a sum of an equilibrium stress response and a non-equilibrium overstress response. Correspondingly, the rate-independent intrinsic time and the rate-dependent i...The total stress response of material is decomposed into a sum of an equilibrium stress response and a non-equilibrium overstress response. Correspondingly, the rate-independent intrinsic time and the rate-dependent intrinsic time are defined respectively. Additional hardening functions for describing the isotropic and anisotropic nonproportional effects are assumed to be related to the accumulation of plastic strain component along the normal of equilibrium stress trajectory, in which the effects of geometry of the loading path are included. An endochronic constitutive model for rate-dependent, nonproportional cyclic plasticity is formulated and applied to simulate the stress responses of stainless steel XCrNil8. 9 for some typical loading programs at different loading rates. A comparison between predicted results and experimental ones by Haupt and Lion shows that the former are in agreement with the latter.展开更多
By combining the Bodner-Partom constitutive model and equivalent stressfunction, finite element methods and program on analyzing non-elastic deformation and stress forthermal viscoplastic material are studied in this ...By combining the Bodner-Partom constitutive model and equivalent stressfunction, finite element methods and program on analyzing non-elastic deformation and stress forthermal viscoplastic material are studied in this paper, and it's the first time that this materialmodel is used in a kind of engineering software-MARC. Thermal viscoplastic behavior of hightemperature alloy GH536 specimen with gap is analyzed by this program. The research results show itis feasible to analyze thermal viscoplastic behavior of specimen or structure by applying B-P model.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
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
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.
文摘A dimensionless stress yield criterion is proposed to describe the mixed hardening of orthotropic material,including kinematic hardening and proportional hardening, and the associated plastic flow law is derived. The generalized effective stress_strain formulae can be obtained correspondingly based on the experimental stress_strain curves in various simple stress states. The initial plastic anisotropy is influenced by the elastic anisotropy. The yield criterion can be reduced to Huber_Mises Criterion for isotropic materials and associated constitutive equations can be degenerated into Prandtl_Reuss equations.
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 linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot's equations for saturated porous media. The Darcy's laws of unsaturated soil were proved. It is shown that Biot's equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.
文摘The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory. The soils were treated as the mixture composed of three constituents. First, from the researches of soil mechanics, some basic assumptions about the unsaturated soil mixture were made, and the entropy inequality of unsaturated soil mixture was derived. Then, with the common method usually used to deal with the constitutive problems in mixture theory, the nonlinear constitutive equations were obtained. Finally, putting the constitutive equations of constituents into the balance equations of momentum, the nonlinear field equations of constituents were set up. The balance equation of energy of unsaturated soil was also given, and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed.
文摘In this paper, nonlinear constitutive equations are deduced strictly according to the constitutive axioms of rational continuum mechanics. The existing judgments are modified and improved. The results show that the constitutive responses of nonlocal thermoelastic body are related to the curvature and higher order gradient of its material space, and there exists an antisymmetric stress whose average value in the domain occupied by thermoelastic body is equal to zero. The expressions of the antisymmetric stress and the nonlocal residuals are given. The conclusion that the directions of thermal conduction and temperature gradient are consistent is reached. In addition, the objectivity about the nonlocal residuals and the energy conservation law of nonlocal field is discussed briefly, and a formula for calculating the nonlocal residuals of energy changing with rigid motion of the spatial frame of reference is derived.
基金This work was supported by the National Natural Science Foundation of China (No. U1510131) and the Applied Basic Research Project of Shanxi Province (Nos. 201701D121078 and 201701D221143).
文摘In order to predict flow instability of wear-resistant steel BTW1, the hot compressions of wear-resistant steel BTW1 were firstly performed at the temperature of 900-1150 ℃ and at the strain rate of 0.05-15 s-1. Then, the constitutive relation was established based on Arrhenius-type hyperbolic sine equation. The results demonstrated that the flow stress depended on the deformation temperature and strain rate. When the deformation temperature kept constant, the flow stress increased as the strain rate increased. When the strain rate remained constant, the flow stress decreased as the temperature increased. The flow stresses calculated by constitutive equations were in a good agreement with experimental results. The apparent activation energy for deformation in the above processing region was estimated to be 369 kJ tool-1. A processing map could be obtained by the superimposition of an instability map on a power dissipation map. Based on the analysis of processing map and the microstructures, the theological instability regimes of strain rate and temperature for hot deformation of wear-resistant steel BTWl had been identified.
基金the support received from Suzhou Kunlun Advanced Manufacturing Technologies and Equipment Co.,Ltd
文摘To investigate the hot deformation behavior of powder-forged (P/F) Fe-0. 5C:-2Cu steel, the hot compres- sion tests were conducted at temperatures ranging from 900 to 1000 ℃ and strain rates from 0.1 to 10 s-1 using Gleeble-1500 thermal simulator. The true stress-true strain curves at different temperatures and strain rates of P/F steel were obtained. It is found that dynamic recovery only occurs as strain rate is 10 s 1 at 900 ℃, and the dynamic recrystallization is the main softening mechanism. The flow stress increases with decreasing temperature and increas- ing strain rate. The experimental data are employed to develop constitutive equations on the basis of the Arrhenius- type equation by introducing the strain with nonlinear fitting. The flow stresses prediel:ed by the proposed constitu- tive equations are in good agreement with the experimental values, and the correlation coefficient (R2) and the aver- age absolute relative error (AARE) are 0. 995 25 and 3.07% respectively. These results indicate the proposed consti- tutive equations can effectively describe the hot deformation behavior of the material.
基金the Natural Science Foundation of Shanghai(No.14ZR1440800)the Course Construction Project of Shanghai Municipal Education Commission(No.33210M161020).
文摘Mechanical response and simulation for constitutive equation with distributed order derivatives were considered.We investigated the creep compliance,creep recovery,relaxation modulus,stress–strain behavior under harmonic deformation for each case of two constitutive equations.We express these responses and results as easily computable forms and simulate them by using MATHEMATICA 8.The results involve the exponential integral function,convergent improper integrals on the infinite interval(0,+∞)and the numerical integral method for the convolution integral.For both equations,stress responses to harmonic deformation display hysteresis phenomena and energy dissipation.The two constitutive equations characterize viscoelastic models of fluid-like and solid-like,respectively.
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).
基金support of the National Natural Science Foundation of China under Contract Number 50831008
文摘The hot deformation behavior of IN690 superalloy was characterized in a temperature range of 1273-1473 K and a strain rate range of 0.01-10 s^-1 using uniaxial compression tests on process annealed material.The constitutive relations between flow stress and effective strain,effective strain rate as well as deformation temperature were studied.It can be concluded that the flow stress significantly reduces with the deformation temperature of IN690 superalloy increasing.Whereas,there is a significant increase of flow stress when the strain rate increases from 0.1 s^-1 to 10 s^-1.Based on the hyperbolic-sine Arrhenius-type equation,a constitutive equation considering compensation of strain was developed.The activation energy and the material constants(Q,n and ln A) decrease as the deformation strain increases.The strain dependent term is successfully incorporated in the constitutive equation through a quartic equation.A good agreement between the experimental data and the predicted results has been achieved,indicating that the proposed constitutive equation and the methods of determing the material constants are suitable to model the high temperature deformation behavior of IN690 superalloy.
文摘In this paper, the generalized Prandtl-Reuss (P-R) constitutive equations of elastic-plastic material in the presence of finite deformations through a new approach are studied. It analyzes the generalized P-R equation based on the material corotational rate and clarifies the puzzling problem of the simple shear stress oscillation mentioned in some literature. The paper proposes a modified relative rotational rate with which to constitute the objective rates of stress in the generalized P-R equation and concludes that the decomposition of total deformation rate into elastic and plastic parts is not necessary in developing the generalized P-R equations. Finally, the stresses of simple shear deformation are worked out.
基金The project supported by National Natural Science Foundation of China
文摘A viscoplastic constitutive model is introduced,which takes into account nonproportional cyclic additional hardening and the effects of nonproportional cyclic loading history and inelastic strain amplitude history.In the model,a variable q of memory on the inelastic strain amplitude during loading is introduced,a new nonproportionality is defined,a cyclic saturated isotropic deformation resistance parameter Q,is given,and the evolution equations of the isotropic deformation resistance with the memory on the previous loading history are proposed.The present model is applied to the description of the complex cyclic deformation behavior of 1Cr18Ni9Ti stainless steel,and the predictions are in good agreement with the experimental results.This shows that the model describes the deformation behavior of nonproportional cyclic loadings and their histories very well.
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.
基金the National Natural Science Foundationthe Science Foundation of the Overseas Chinese Affairs Office of China.
文摘The total stress response of material is decomposed into a sum of an equilibrium stress response and a non-equilibrium overstress response. Correspondingly, the rate-independent intrinsic time and the rate-dependent intrinsic time are defined respectively. Additional hardening functions for describing the isotropic and anisotropic nonproportional effects are assumed to be related to the accumulation of plastic strain component along the normal of equilibrium stress trajectory, in which the effects of geometry of the loading path are included. An endochronic constitutive model for rate-dependent, nonproportional cyclic plasticity is formulated and applied to simulate the stress responses of stainless steel XCrNil8. 9 for some typical loading programs at different loading rates. A comparison between predicted results and experimental ones by Haupt and Lion shows that the former are in agreement with the latter.
基金This project was supported by NPU Youth Science Technology Innovation Foundation (020102).
文摘By combining the Bodner-Partom constitutive model and equivalent stressfunction, finite element methods and program on analyzing non-elastic deformation and stress forthermal viscoplastic material are studied in this paper, and it's the first time that this materialmodel is used in a kind of engineering software-MARC. Thermal viscoplastic behavior of hightemperature alloy GH536 specimen with gap is analyzed by this program. The research results show itis feasible to analyze thermal viscoplastic behavior of specimen or structure by applying B-P model.
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 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.