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
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
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
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
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 traction of a new aviation lubricating oil was measured on a self-made test rig. The calculating formulae of the rheological parameters of the oil such as Erying stress, limiting shear stress and shear elastic mod...The traction of a new aviation lubricating oil was measured on a self-made test rig. The calculating formulae of the rheological parameters of the oil such as Erying stress, limiting shear stress and shear elastic modulus were obtained under the condition of the high shear strain rate in elastohydrodynamic lubrication(EHL). The constitutive equation of this oil was determined and verified by test. The results of experiments show that the behavior of the new aviation lubricating oil behaves as visco-elastic fluid and the theoretical value agrees fairly well with the measured data, which implies that the constitutive equation of this oil is correct and feasible.展开更多
Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of. constitutive equivalence it is demonstrated that the mu...Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of. constitutive equivalence it is demonstrated that the multiphase solid, composed of several kinds of homogeneous elastic-plastic media that conform to the generalized normality rule, has the same type of constitutive equations as its constituents have that also conform to the generalized normality rule.展开更多
Based on the experimental results of local temperature field formed in the evolution period of defects, the defect field is defined by this internal temperature field. The evolutionary processes of statistically corre...Based on the experimental results of local temperature field formed in the evolution period of defects, the defect field is defined by this internal temperature field. The evolutionary processes of statistically correlative meso-scopic defects are analysed with the growth rate and nucleation rate of the meso-defect, and it is deemed that the dynamic failure process of the viscoelastic material with defects can be quantitatively described by the normal method of the procedure of heat wave transmission. The defect field is regarded as a complex system of the union of the real sets and null sets, its main characteristics depending on the stratum hypothesis about the activities of the subsystems of the highest stratum described by ordered parameters. The fluctuation of ordered parameters is demonstrated by means of the projection operator method. The constitutive equation with ordered parameters for the meso-defect evolutionary state of viscoelastic material with defects is deduced from the nonlinear rheological dynamic approach, and its solution is obtained.展开更多
To simulate the DIWA353 steel used in boiler nearby recrystallization temperature accurately by using finite element,the high temperature constitutive model of this material must be researched firstly.Thermal simulati...To simulate the DIWA353 steel used in boiler nearby recrystallization temperature accurately by using finite element,the high temperature constitutive model of this material must be researched firstly.Thermal simulation experimental machine is used to do the high temperature hot compression experiments for the DIWA353 steel used in boiler under different strain rates and temperatures nearby recrystallization temperature.Multi-bank data of true stress-true strain is gotten,and the hot deformation activation energy of DIWA353 is obtained,and the constitutive equation of steady-state flow stress under the circumstance of high temperature is constructed.The results show that DIWA353 steel is positive strain rate sensitized material when it is at temperature of 850-1050 ℃,and the steady-state flow stress decreases with the increase of deformation temperature,but increases with the increase of strain rate.展开更多
Ti - 40 alloy is a single β phase burn resistant titanium alloy.Its high temperature deformation mech- anism is studied and its stress - strain curves are examined he use of Gleeble - 1500 thermal -simulator. The r...Ti - 40 alloy is a single β phase burn resistant titanium alloy.Its high temperature deformation mech- anism is studied and its stress - strain curves are examined he use of Gleeble - 1500 thermal -simulator. The results reveal that there are abrupt flow stress drops followed b steady state.The magnitude of the flow stress drop increases with strain rote and decreases with temperature.Deformation activation energy, Q, is 247. 5 KJ/mol. The deformation mechanism of Ti - 40 alloy is controlled by the lattice diffusion Its constitutive equation is set up, i. e.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
A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid-liquid crystalline (LC) polymers. A concept of anisotropic viscoelastic simple fluid is introduced....A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid-liquid crystalline (LC) polymers. A concept of anisotropic viscoelastic simple fluid is introduced. The stress tensor instead of the velocity gradient tensor D in the classic Leslie-Ericksen theory is described by the first Rivlin-Ericksen tensor A and a spin tensor W measured with respect to a co-rotational coordinate system. A model LCP-H on this theory is proposed and the characteristic unsymmetric behaviour of the shear stress is predicted for LC polymer liquids. Two shear stresses thereby in shear flow of LC polymer liquids lead to internal vortex flow and rotational flow. The conclusion could be of theoretical meaning for the modern liquid crystalline display technology. By using the equation, extrusion-extensional flows of the fluid are studied for fiber spinning of LC polymer melts, the elongational viscosity vs. extension rate with variation of shear rate is given in figures. A considerable increase of elongational viscosity and bifurcation behaviour are observed when the orientational motion of the director vector is considered. The contraction of extru- date of LC polymer melts is caused by the high elongational viscosity. For anisotropic viscoelastic fluids, an important advance has been made in the investigation on the constitutive equation on the basis of which a seriesof new anisotropic non-Newtonian fluid problems can be addressed.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 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
A constitutive equation reflecting the flow behavior of Superalloy In718 during the counter-blow hammer forging process was developed in terms of the relationship of flow stress and hot-deformation parameters,such as ...A constitutive equation reflecting the flow behavior of Superalloy In718 during the counter-blow hammer forging process was developed in terms of the relationship of flow stress and hot-deformation parameters,such as strain,strain rate,and deformation temperature.A new simplified approach for the complex multi-pass stress-strain curves has been attempted.The simulation curves calculated by constitutive equation are consistent with the experimental data.展开更多
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.
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.
基金This project is supported by National Key Projects of China(MKPT-2001-004).
文摘The traction of a new aviation lubricating oil was measured on a self-made test rig. The calculating formulae of the rheological parameters of the oil such as Erying stress, limiting shear stress and shear elastic modulus were obtained under the condition of the high shear strain rate in elastohydrodynamic lubrication(EHL). The constitutive equation of this oil was determined and verified by test. The results of experiments show that the behavior of the new aviation lubricating oil behaves as visco-elastic fluid and the theoretical value agrees fairly well with the measured data, which implies that the constitutive equation of this oil is correct and feasible.
文摘Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of. constitutive equivalence it is demonstrated that the multiphase solid, composed of several kinds of homogeneous elastic-plastic media that conform to the generalized normality rule, has the same type of constitutive equations as its constituents have that also conform to the generalized normality rule.
基金The project supported by National Natural Science Foundation of China(NNSF 19632002).
文摘Based on the experimental results of local temperature field formed in the evolution period of defects, the defect field is defined by this internal temperature field. The evolutionary processes of statistically correlative meso-scopic defects are analysed with the growth rate and nucleation rate of the meso-defect, and it is deemed that the dynamic failure process of the viscoelastic material with defects can be quantitatively described by the normal method of the procedure of heat wave transmission. The defect field is regarded as a complex system of the union of the real sets and null sets, its main characteristics depending on the stratum hypothesis about the activities of the subsystems of the highest stratum described by ordered parameters. The fluctuation of ordered parameters is demonstrated by means of the projection operator method. The constitutive equation with ordered parameters for the meso-defect evolutionary state of viscoelastic material with defects is deduced from the nonlinear rheological dynamic approach, and its solution is obtained.
基金Sponsored by the Heilongjiang Province Science and Technology Department(Grant No.GC06A515)
文摘To simulate the DIWA353 steel used in boiler nearby recrystallization temperature accurately by using finite element,the high temperature constitutive model of this material must be researched firstly.Thermal simulation experimental machine is used to do the high temperature hot compression experiments for the DIWA353 steel used in boiler under different strain rates and temperatures nearby recrystallization temperature.Multi-bank data of true stress-true strain is gotten,and the hot deformation activation energy of DIWA353 is obtained,and the constitutive equation of steady-state flow stress under the circumstance of high temperature is constructed.The results show that DIWA353 steel is positive strain rate sensitized material when it is at temperature of 850-1050 ℃,and the steady-state flow stress decreases with the increase of deformation temperature,but increases with the increase of strain rate.
文摘Ti - 40 alloy is a single β phase burn resistant titanium alloy.Its high temperature deformation mech- anism is studied and its stress - strain curves are examined he use of Gleeble - 1500 thermal -simulator. The results reveal that there are abrupt flow stress drops followed b steady state.The magnitude of the flow stress drop increases with strain rote and decreases with temperature.Deformation activation energy, Q, is 247. 5 KJ/mol. The deformation mechanism of Ti - 40 alloy is controlled by the lattice diffusion Its constitutive equation is set up, i. e.
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.
基金the National Natural Science Foundation of China(10372100,19832050)(Key project).
文摘A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid-liquid crystalline (LC) polymers. A concept of anisotropic viscoelastic simple fluid is introduced. The stress tensor instead of the velocity gradient tensor D in the classic Leslie-Ericksen theory is described by the first Rivlin-Ericksen tensor A and a spin tensor W measured with respect to a co-rotational coordinate system. A model LCP-H on this theory is proposed and the characteristic unsymmetric behaviour of the shear stress is predicted for LC polymer liquids. Two shear stresses thereby in shear flow of LC polymer liquids lead to internal vortex flow and rotational flow. The conclusion could be of theoretical meaning for the modern liquid crystalline display technology. By using the equation, extrusion-extensional flows of the fluid are studied for fiber spinning of LC polymer melts, the elongational viscosity vs. extension rate with variation of shear rate is given in figures. A considerable increase of elongational viscosity and bifurcation behaviour are observed when the orientational motion of the director vector is considered. The contraction of extru- date of LC polymer melts is caused by the high elongational viscosity. For anisotropic viscoelastic fluids, an important advance has been made in the investigation on the constitutive equation on the basis of which a seriesof new anisotropic non-Newtonian fluid problems can be addressed.
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 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.
文摘A constitutive equation reflecting the flow behavior of Superalloy In718 during the counter-blow hammer forging process was developed in terms of the relationship of flow stress and hot-deformation parameters,such as strain,strain rate,and deformation temperature.A new simplified approach for the complex multi-pass stress-strain curves has been attempted.The simulation curves calculated by constitutive equation are consistent with the experimental data.