Hot Compressive Deformation Characteristics of Al-9.3Zn-2.4Mg-1.1Cu Alloy

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).

Cyclic constitutive equations of rock with coupled damage induced by compaction and cracking

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.

CONSTITUTE EQUATIONS OF 40Cr STEEL UNDER SUPERPLASTIC COMPRESSIVE DEFORMATION

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.

A set of microstructure-based constitutive equations in hot forming of a titanium alloy

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.

GENERAL EXPRESSIONS OF CONSTITUTIVE EQUATIONS FOR ISOTROPIC ELASTIC DAMAGED MATERIALS

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.

DEVELOPMENT OF CONSTITUTE EQUATIONS FOR Ti-6Al-4V ALLOY UNDER HOT-WORKING CONDITION

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.

THE CONSTITUTIVE EQUATIONS FOR MIXED HARDENING ORTHOTROPIC MATERIAL

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.

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY (Ⅱ)—LINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

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.

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY(Ⅰ)—NONLINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

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.

NEW POINTS OF VIEW ON THE NONLOCAL FIELD THEORY AND THEIR APPLICATIONS TO THE FRACTURE MECHANICS(Ⅱ)——RE-DISCUSS NONLINEAR CONSTITUTIVE EQUATIONS OF NONLOCAL THERMOELASTIC BODIES

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.

Processing map and dynamic recrystallization behaviours of 316LN-Mn austenitic stainless steel

The hot deformation behaviours of 316LN-Mn austenitic stainless steel were investigated by uniaxial isothermal compression tests at different temperatures and strain rates.The microstructural evolutions were also studied using electron backscatter diffraction.The flow stress decreases with the increasing temperature and decreasing strain rate.A constitutive equation was established to characterize the relationship among the deformation parameters,and the deformation activation energy was calculated to be 497.92 k J/mol.Processing maps were constructed to describe the appropriate processing window,and the optimum processing parameters were determined at a temperature of 1107-1160℃ and a strain rate of 0.005-0.026 s^(-1).Experimental results showed that the main nucleation mechanism is discontinuous dynamic recrystallization(DDRX),followed by continuous dynamic recrystallization(CDRX).In addition,the formation of twin boundaries facilitated the nucleation of dynamic recrystallization.

FEM Analysis of Spring-backs in Age Forming of Aluminum Alloy Plates

The age forming technology, characterized by huge spring-backs, has been developed to manufacture large integral wing-skin panel parts, which necessitates devising a method of predicting spring-backs. A 7B04-T7451 aluminum alloy creep test in tension is accomplished at 155 ℃, and the creep curves are obtained. The material constants of the mechanism-based creep constitutive equations are determined through experiments. The age forming process and the spring-backs of 7B04 aluminum alloy plates are analyzed using the commercial finite element software ABAQUS. The effects of plate thickness and forming time on spring-backs are researched. The spring-backs decrease with the increase of plate thickness and forming time. The test results verify the reliability of the finite element method （FEM） analysis.

Constitutive relationship of IN690 superalloy by using uniaxial compression tests

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.

CONSTITUTIVE EQUATION OF CO-ROTATIONAL DERIVATIVE TYPE FOR ANISOTROPIC-VISCOELASTIC FLUID

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.

Deformation behavior and microstructure of an Al-Zn-Mg-Cu-Zr alloy during hot deformation

The hot deformation behavior and microstructures of Al-7055 commercial alloy were investigated by axisymmetric hot compres- sion at temperatures ranging from 300℃ to 450℃ and strain rates from 10^-2 to 10 s^-1, respectively. Microstructures of deformed 7055 alloy were investigated by transmission electron microscopy （TEM）. The dependence of peak stress on deformation temperature and strain rate can be expressed by the hyperbolic-sine type equation. The hot deformation activation energy of the alloy is 146 kJ/mol. Moreover, the flow stress curves predicted by the modified constitutive equations are reasonably consistent with the experimental results, which confirms that the proposed deformation constitutive equations can provide evidence for the selection of hot forming parameters. TEM results indicate that dy- namic recovery is the main softening mechanism during hot deformation.

Hot compression deformation behavior of AISI 321 austenitic stainless steel

The hot compression behavior of AISI 321 ll00~C and the strain rates of 0.01-1 s-1 using a Baehr austenitic stainless steel was studied at the temperatures of 950- DIL-805 deformation dilatometer. The hot deformation equations and the relationship between hot deformation parameters were obtained. It is found that strain rate and deformation temperature significantly influence the flow stress behavior of the steel. The work hardening rate and the peak value of flow stress increase with the decrease of deformation temperature and the increase of strain rate. In addition, the activation energy of deformation （Q） is calculated as 433.343 kJ/mol. The microstructural evolution during deformation indicates that, at the temperature of 950~C and the strain rate of 0.01 s-1, small circle-like precipitates form along grain boundaries; but at the temperatures above 950~C, the dissolution of such precipitates occurs. Energy-dispersive X-ray analyses indicate that the precipitates are complex carbides of Cr, Fe, Mn, Ni, and Ti.

A comparative study on the hot flow stress of Mg-Al-Zn magnesium alloys using a simple physically-based approach

A comparative study was carried out on the hot flow stress of AZ31,AZ61,and AZ91 magnesium alloys.Their hot working behaviors were studied through constitutive analysis based on a simple physically-based approach which accounts for the dependence of the Young's modulus and the self-diffusion coefficient of magnesium on temperature.Since the main difference between these alloys is the difference in their amount of aluminum,the differences in constitutive behavior were quantitatively characterized by relating the hot flow stress to amount of Al,which was not possible without the consideration of physically-based parameters.It was concluded that the used approach in the current work can be considered as a versatile tool in future hot working and alloy development studies.

Statistical Tensile Strength for High Strain Rate of Aramid and UHMWPE Fibers

Dynamic tensile impact properties of aramid (Technora) and UHMWPE (DC851) fiber bundles were studied at two high strain rates by means of reflecting type Split Hopkinson Bar, and stress-strain curves of fiber yarns at different strain rates were obtained. Experimental results show that the initial elastic modulus, failure strength and unstable strain of aramid fiber yarns are strain rate insensitive, whereas the initial elastic modulus and unstable strain of UHMWPE fiber yarns are strain rate sensitive. A fiber-bundle statistical constitutive equation was used to describe the tensile behavior of aramid and UHMWPE fiber bundles at high strain rates. The good consistency between the simulated results and experimental data indicates that the modified double Weibull function can represent the tensile strength distribution of aramid and UHMWPE fibers and the method of extracting Weibull parameters from fiber bundles stress-strain data is valid.

Dependence of flow strength and deformation mechanisms in common wrought and die cast magnesium alloys on orientation,strain rate and temperature

The controlling plastic deformation mechanisms(i.e.slip or twinning)and the structural crash performance of Mg alloys are strongly influenced by loading mode,texture and microstructure.This paper summarizes the main results from an experimental program to assess these effects for commercial Mg alloy extrusions(AM30 and AZ31),sheet(AZ31),and high pressure die castings(HPDC,AM50 and AM60).Uniaxial tensile and compressive tests were performed over a wide range of strain rate and temperature(i.e.0.00075–2800 s^(−1) and 100℃ to−150℃)using conventional servo-hydraulic and high-strain-rate universal test machines and a split-Hopkinson-bar(SHB)apparatus.In primarily-slip-dominant deformation,the true stress–strain curves showed approximate power-law behavior,and the effects of strain rate and temperature on yield strength could be approximately described by constitutive equations linearly dependent on the rate parameter,Tln(5.3×10^(7)/ɛ˙)where T is test temperature in Kelvin andɛ˙is strain rate in s^(−1).In primarily-twin-dominant deformation,the effects of strain rate and temperature on yield and initial flow stress were negligible or small from quasi-static to 2800 s^(−1) owing to the athermal characteristics of mechanical twinning;the effects may become more pronounced with exhaustion of twinning and increasing proportion of slip.

Hot deformation behavior and microstructure evolution of as-cast AZ91D magnesium alloy without pre-homogenization treatment

The deformation behavior and the microstruc-ture evolution of as-cast AZ91D magnesium alloy without pre-homogenization treatment were systematically inves-tigated. The flow stress behavior was studied by com-pression tests in strain rate range of 0.001-1.000 s^-1 and deformation temperature range of 220-380 ℃ with a maximum deformation strain of 60 %. The dependence of flow stress on deformation temperature and strain rate was described by hyperbolic sine constitutive equation. Through regression analysis, the average apparent activa- tion energy and coefficient of strain rate sensitivity were estimated to be 181.98 kJ.mol^-1 and 0.14, respectively. The results also reveal that the variation of peak stress depends on strain rate and deformation temperature. Microstructure observation shows that, at temperatures higher than 300 ℃ and strain rates lower than 0.01 s^-1, DRX developed extensively at the grain boundaries and in the core of coarse grains, resulting in a more homogeneous microstructure. Furthermore, the effects of strain, defor-mation temperature, strain rate, and eutectic β phase on the microstructure evolution of as-cast AZ91D magnesium alloy were discussed.