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
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
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 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
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
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 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
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
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
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
Foam plays a crucial role in conditioning the mechanical properties of coarse-grained soil during earth pressure balance shield tunneling.Experimental findings have shown that an appropriate foam injection ratio impro...Foam plays a crucial role in conditioning the mechanical properties of coarse-grained soil during earth pressure balance shield tunneling.Experimental findings have shown that an appropriate foam injection ratio improves the workability and compressibility of conditioned soil,while reducing its shear strength under undrained conditions.Understanding how foam operates in soil pores is essential for interpreting these phenomena.This study utilized a theoretical two-dimensional(2D)model to analyze the effects of gas saturation,gas-liquid interface,and gas dissolution on the undrained mechanical properties of foamconditioned soil.Based on these analyses,a constitutive equation was developed,using the transition void ratio,compression index and contact coefficient as key parameters to describe the relationships among vertical stress σ_(v),void ratio e_(c),and shear strengthτ.The undrained mechanical properties calculated by the 2D model align well with experimental observations,indicating that while foam enhances the bonding force between soil particles,both excessive and insufficient gas saturation,along with larger contact angles,notably undermine this enhancement,resulting in unsuitable workability.A gas saturation of 0.5-0.8 is recommended for soil conditioning.Under typical chamber pressures,the effects of gas-liquid interface and gas dissolution on compressibility and shear strength are negligible.The constitutive equation demonstrates excellent agreement with experimental data,and can well predict the variations in σ_(v)-e_(c)-τ.This study contributes to understanding the role of foam in soil pores,and the developed constitutive equation serves as a valuable reference for describing the undrained mechanical behavior of foam-conditioned coarse-grained soil.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
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
Hot compression behavior of Ti-5 Al-5 Mo-5 V-1 Cr-1 Fe alloy with an equiaxed（α＋β） starting microstructure was investigated by isothermal compression test and optical microscopy. Based on the true strain-stress d...Hot compression behavior of Ti-5 Al-5 Mo-5 V-1 Cr-1 Fe alloy with an equiaxed（α＋β） starting microstructure was investigated by isothermal compression test and optical microscopy. Based on the true strain-stress data with temperature correction, constitutive models with a high accuracy were developed and processing maps were established. Strain inhomogeneity at different locations in the compressed sample is reduced by raising temperature, leading to a uniform distribution of α phases. For the temperature range of 800-840 ℃ with a strain rate of 10 s^-1, the transformed volume fraction of α phase increases and the average grain size of α phase decreases slightly with increasing the temperature, indicating co-existence of dynamic recovery and dynamic recrystallization. Flow localization and faint β grain boundaries are observed at the strain rate of 10 s^-1 in the temperature range of 860-900 ℃. The processing map analysis shows that hot working of Ti-5 Al-5 Mo-5 V-1 Cr-1 Fe alloy should be conducted with the strain rate lower than 0.01 s^-1 to extend its workability.展开更多
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.
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.
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.
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.
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 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.
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financial support from the National Natural Science Foundation of China(Grant No.51979144)the State Key Laboratory of Hydroscience and Engineering(Grant No.SKLHSE-2024-B-02).
文摘Foam plays a crucial role in conditioning the mechanical properties of coarse-grained soil during earth pressure balance shield tunneling.Experimental findings have shown that an appropriate foam injection ratio improves the workability and compressibility of conditioned soil,while reducing its shear strength under undrained conditions.Understanding how foam operates in soil pores is essential for interpreting these phenomena.This study utilized a theoretical two-dimensional(2D)model to analyze the effects of gas saturation,gas-liquid interface,and gas dissolution on the undrained mechanical properties of foamconditioned soil.Based on these analyses,a constitutive equation was developed,using the transition void ratio,compression index and contact coefficient as key parameters to describe the relationships among vertical stress σ_(v),void ratio e_(c),and shear strengthτ.The undrained mechanical properties calculated by the 2D model align well with experimental observations,indicating that while foam enhances the bonding force between soil particles,both excessive and insufficient gas saturation,along with larger contact angles,notably undermine this enhancement,resulting in unsuitable workability.A gas saturation of 0.5-0.8 is recommended for soil conditioning.Under typical chamber pressures,the effects of gas-liquid interface and gas dissolution on compressibility and shear strength are negligible.The constitutive equation demonstrates excellent agreement with experimental data,and can well predict the variations in σ_(v)-e_(c)-τ.This study contributes to understanding the role of foam in soil pores,and the developed constitutive equation serves as a valuable reference for describing the undrained mechanical behavior of foam-conditioned coarse-grained soil.
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.
基金financial supports of China Scholarship Council,Beijing Science Foundation(No.2154051)Doctoral Fund of the Ministry of Education of China(No.20130006120005)the National Natural Science Foundation of China(No.51401020)
基金Project(BS2013CL034)supported by the Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province,ChinaProject(51401115)supported by the National Natural Science Foundation of ChinaProject(GN2013001)supported by Independent Innovation Foundation of Shandong University,China
文摘Hot compression behavior of Ti-5 Al-5 Mo-5 V-1 Cr-1 Fe alloy with an equiaxed（α＋β） starting microstructure was investigated by isothermal compression test and optical microscopy. Based on the true strain-stress data with temperature correction, constitutive models with a high accuracy were developed and processing maps were established. Strain inhomogeneity at different locations in the compressed sample is reduced by raising temperature, leading to a uniform distribution of α phases. For the temperature range of 800-840 ℃ with a strain rate of 10 s^-1, the transformed volume fraction of α phase increases and the average grain size of α phase decreases slightly with increasing the temperature, indicating co-existence of dynamic recovery and dynamic recrystallization. Flow localization and faint β grain boundaries are observed at the strain rate of 10 s^-1 in the temperature range of 860-900 ℃. The processing map analysis shows that hot working of Ti-5 Al-5 Mo-5 V-1 Cr-1 Fe alloy should be conducted with the strain rate lower than 0.01 s^-1 to extend its workability.
