HIGH TEMPERATURE DEFORMATION MECHANISM AND CONSTITUTIVE EQUATION OF Ti-40 BUREN RESISTANT TITANIUM ALLOY

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.

EQUATION IN COMPLEX VARIABLE OF AXISYMMETRICAL DEFORMATION PROBLEMS FOR A GENERAL SHELL OF REVOLUTION

In this paper, the equation of axisymmetrical deformation problems for a general shell of revolution is derived in one complex variable under the usual Love-Kirchhoff assumption. In the case of circular ring shells, this equation may be simplified into the equation given by F.Tdlke(1938)[3]. R.A. Clark(1950 )[4] and V. V.Novozhilov(1951)[5]. When the horizontal radius of the shell of revolution is much larger than the average radius of curvature of meridian curve, this equation in complex variable may be simplified into the equation for slander ring shells. If the ring shell is circular in shape, then this equation can be reduced into the equation in complex variable for slander circular ring shells given by this author (1979)[6]. If the form of elliptic cross-section is near a circle, then the equation of slander ring shell with near-circle ellipitic cross-section may be reduced to the complex variable equation similar in form for circular slander ring shells.

Formulation of thermo-hydro-mechanical coupling behavior of unsaturated soils based on hybrid mixture theory

Thermo-Hydro-Mechanical （THM） coupling pro- cesses in unsaturated soils are very important in both theoretical researches and engineering applications. A coupled formulation based on hybrid mixture theory is derived to model the THM coupling behavior of unsaturated soils. The free-energy and dissipative functions for different phases are derived from Taylor＇s series expansions. Constitutive relations for THM coupled behaviors of unsaturated soils, which include deformation, entropy change, fluid flow, heat conduction, and dynamic compatibility conditions on the interfaces, are then established. The number of field equations is shown to be equal to the number of unknown variables; thus, a closure of this coupling problem is established. In addition to modifications of the physical conservation equations with coupling effect terms, the constitutive equations, which consider the coupling between elastoplastic deformation of the soil skeleton, fluid flow, and heat transfer, are also derived.

Model of critical strain for dynamic recrystallization in 10%TiC/Cu-Al_2O_3 composite

Using the Gleeble-1500 D simulator, the hot deformation behavior and dynamic recrystallization critical conditions of the 10%Ti C/Cu-Al2O3(volume fraction) composite were investigated by compression tests at the temperatures from 450 °C to 850 °C with the strain rates from 0.001 s-1 to 1 s-1. The results show that the softening mechanism of the dynamic recrystallization is a feature of high-temperature flow true stress-strain curves of the composite, and the peak stress increases with the decreasing deformation temperature or the increasing strain rate. The thermal deformation activation energy was calculated as 170.732 k J/mol and the constitutive equation was established. The inflection point in the lnθ-ε curve appears and the minimum value of-(lnθ)/ε-ε curve is presented when the critical state is attained for this composite. The critical strain increases with the increasing strain rate or the decreasing deformation temperature. There is linear relationship between critical strain and peak strain, i.e., εc=0.572εp. The predicting model of critical strain is described by the function of εc=1.062×10-2Z0.0826.

Thermo-hydro-mechanical-air coupling finite element method and its application to multi-phase problems

In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air （THMA） behavior of geomaterial and using finite element-finite difference （FE-FD） scheme for so/l-water-air three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste （HLRW）, are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. （2007）, is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz （2006） is simulated in the same framework under the conditions of variable temperature hut constant air pressure.

Hot Deformation Behavior of SA508GR.4N Steel for Nuclear Reactor Pressure Vessels

A hot compression experiment （1073 1473 K, strain rates of 0. 001-10 s -1 ） of SAS08GR. 4N low alloy steel was performed using a Gleeble-3800 thermal-mechanical simulator, and the hot deformation behavior of the steel was investigated by analyzing both the true stress true strain curves and its microstructures. The thermal de formation equation and hot deformation activation energy （Q） of SA508GR. 4N steel were obtained by regression with a classic hyperbolic sine function. The hot processing map of SAS08GR. 4N steel was also established. An empirical equation for the stress peak was described for practical applications. The SA508GR. 4N steel showed a critical Zener-Hollomon parameter （lnZc） for dynamic recrystallization （DRX） of 37.44, below which full DRX may occur. The sensitivity of the SA508GR. 4N steel increased linearly with test temperature, such that higher temperatures led to enhanced workability.

Hot Deformation Behavior of As-cast AISI M2 High-speed Steel Containing Mischmetal

The hot deformation behavior of as-cast AISI M2 high-speed steel containing mischmetal （RE） has been investigated on a Gleeble-3500 simulator in the temperature range of 1000--1 150 ℃ and strain rate range of 0.01- 10 s 1 at true strain of 1.0. The mechanical behavior has been characterized using stress-strain curve analysis, kinetic analysis, processing maps, etc. Metallographic investigation was performed to evaluate the mechanism of flow insta- bility. The results show that the deformation activation energy decreases with increasing deformation temperature; the efficiency of power dissipation increases with decreasing strain rate and increasing temperature; flow instability is observed at low-to-medium temperature and higher strain rate region when the strain is smaller, but extends to lower strain rate and high temperature regions with the increment of strain, in which it is manifested as flow localization near the grain boundary. Hot deformation equations and processing maps are obtained. The optimal processing window is suggested and the deformation mechanism is dynamic recrystallization （DRX）.

Constitutive Modeling and Hot Deformation Behavior of Duplex Structured Mg–Li–Al–Sr Alloy

Hot deformation behavior of an as-extruded duplex structured Mg-9Li-3Al-2.5Sr alloy is investigated via hot compression tests conducted at 200-350℃ with strain rate of 0.001-1 s^-1.The flow behavior of Mg-9Li-3Al-2.5Sr alloy can be described accurately by hyperbolic sine constitutive equation and the average activation energy for deformation is calculated as 143.5 k J/mol.Based on a dynamic materials model,the processing maps of Mg-9Li-3Al-2.5Sr alloy which describe the variation of power dissipation efficiency are constructed as a function of temperature and strain rate.The processing maps exhibit an area of discontinuous dynamic recrystallization occurring at 280-300℃ with strain rate of 0.001-0.01 s^-1,which corresponds to the optimum hot working conditions.

High-temperature deformation behavior of a beta Ti-3.0Al-3.5Cr-2.0Fe-0.1B alloy

The high-temperature deformation behavior of a beta Ti-3.0 Al-3.5 Cr-2.0 Fe-0.1 B alloy was investigated by a Gleeble-1500 D thermal simulator. The height reduction was 50%, corresponding to a true strain of 0.693. The strain rate ranging from 0.01 to 10.00 s^-1 and the deformation temperature ranging from 800 to 950 ℃ were considered.The flow stress and the apparent activation energy for deformation, along with the constitutive equation, were used to analyze the behavior of the Ti-3.0 Al-3.5 Cr-2.0 Fe-0.1 B alloy. The processing map was established. The effect of strain rate on the microstructure at 850 ℃ was evaluated.The flow stress-strain curves indicated that the peak flow stresses increased along with an increase in the strain rate and decreased as the deformation temperature increased.Based on the true stress-true strain curves, the constitutive equation was established and followed as the ε= 6.58×10-（10）[sinh（0.0113σ）]-（3.44）exp（-245481.3/RT）. The processing map exhibited the ＂unsafe＂ region at the strain rate of10 s^-1 and the temperature of 850 ℃,and the rest region was ＂safe＂. The deformation microstructure demonstrated that both dynamic recovery（DRV） and dynamic recrystallization（DRX） existed during deformation. At the lower strain rate of 0.01 s^-1, the main deformation mechanism was the DRV, and the DRX was the dominant deformation mechanism at the higher strain rate of 1.00 s^-1.

Hot Deformation Behavior and Flow Stress Prediction of Ultra Purified 17% Cr Ferritic Stainless Steel Stabilized with Nb and Ti

The hot deformation behavior of ultra purified 17% Cr ferritic stainless steel stabilized with Nb and Ti was investigated using axisymmetric hot compression tests on a thermomechanical simulator.The deformation was carried out at the temperatures ranging from 700 to 1 100℃ and strain rates from 1to 10s-1.The microstructure was investigated using electron backscattering diffraction.The effects of temperature and strain rate on deformation behavior were represented by Zener-Hollomon parameter in an exponent type equation.The effect of strain was incorporated in the constitutive equation by establishing polynomial relationship between the material constants and strain.A sixth order polynomial was suitable to represent the effect of strain.The modified constitutive equation considering the effect of strain was developed and could predict the flow stress throughout the deformation conditions except at800℃in 1s-1 and at 700℃in 5and 10s-1.Losing the reliability of the modified constitutive equation was possibly ascribed to the increase in average Taylor factor at 800℃in 1s-1 and the increase in temperature at 700℃in 5and10s-1 during hot deformation.The optimum window for improving product quality of the ferritic stainless steels was identified as hot rolling at a low finisher entry temperature of 700℃,which can be achieved in practical production.

Hot Deformation Behavior of a Novel Ni-Cr-Mo-B Ultra-heavy Plate Steel by Hot Compression Test

Hot deformation behavior of a novel Ni-Cr-Mo-B heavy plate steel was studied by hot compression tests,which were conducted on a Gleeble-3800thermo-mechanical simulator corresponding to the temperature range of850-1 150℃ with the strain rates of 0.01-10s-1 and the true strain of 0.8.The results suggest that the majority of flow curves exhibit a typical dynamic recrystallization（DRX）behavior with an apparent single peak stress followed by agradual fall towards a steady-state stress.Important characteristic parameters of flow behavior as critical stress/strain for initiation of DRX and peak and steady-state stress/strain were derived from curves of strain hardening rate versus stress and stress versus strain,respectively.Material constants of the investigated steel were determined based on Arrhenius-type constitutive equation,and then the peak stress was predicted by the equation with the hot deformation activation energy of 379 139J/mol,and the predicted values agree well with the experimental values.Furthermore,the effect of Zener-Hollomon parameter on the characteristic points of flow curves was studied using the power law relation,and the ratio of critical stress and strain to peak stress and strain were found to be 0.91and0.46,respectively.

Static recrystallization behavior of 25CrMo4 mirror plate steel during two-pass hot deformation

The static recrystallization behavior of 25CrMo4 mirror plate steel has been determined by hot compression testing on a Gleeble 1500 thermal mechanical simulation tester. Compression tests were performed using double hit schedules at temperatures of 950-- 1 150 ~C, strain rates of 0.01--0.5 s-1 , and recrystallization time of 1--100 s. Results show that the kinetics of static recrystallization and the microstructural evolution were greatly influenced by the deformation parameters （deformation temperature, strain rate and pre strain） and the initial austenite grain size. Based on the experimental results, the kinetics model of static recrystallization has been generated and the comparison between the experimental results and the predicted results has been carried out. It is shown that the predicted results were in good agreement with the experimental results.

High temperature deformation behavior and processing map of hot isostatically pressed Ti-47.5Al-2Cr-2Nb-0.2W-0.2B alloy using gas atomization powders

The hot compressive deformation behavior of hot isostatically pressed Ti-47.5Al-2Cr-2Nb-0.2W-0.2B alloy using gas atomization powders was systematically investigated and the processing map was obtained in the temperature range of 1323-1473 Kand strain rate range of 0.001-0.5s^（-1）.The calculated activation energy in the above variational ranges of temperature and strain rate possesses a low activation energy value of approximately 365.6kJ/mol based on the constitutive relationship models developed with the Arrhenius-type constitutive model respectively considering the strain rate and deformation temperature.The hot working flow behavior during the deformation process was analyzed combined with the microstructural evolution.Meanwhile,the processing maps during the deformation process were established based on the dynamic material model and Prasad instability criterion under different deformation conditions.Finally,the optimal hot processing window of this alloy corresponding to the wide temperature range of 1353-1453 Kand the low strain rate of 0.001-0.1s^（-1） was obtained.

The deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds

In this paper,we consider the deformed Hermitian-Yang-Mills equation on closed almost Hermitian manifolds.In the case of the hypercritical phase,we derive a priori estimates under the existence of an admissible C-subsolution.As an application,we prove the existence of solutions for the deformed Hermitian-Yang-Mills equation under the condition of existence of a supersolution.

Effect of squeeze casting process on microstructures and flow stress behavior of Al-17.5Si-4Cu-0.5Mg alloy

The effects of squeeze casting process on microstructure and flow stress behavior of Al-17.5Si-4Cu-0.5Mg alloy were investigated and the hot-compression tests of gravity casting and squeeze casting alloy were carried out at 350-500°C and 0.001-5s-1.The results show that microstructures of Al-17.5Si-4Cu-0.5Mg alloys were obviously improved by squeeze casting.Due to the decrease of coarse primary Si particles,softα-Al dendrite as well as the fine microstructures appeared,and the mechanical properties of squeeze casting alloys were improved.However,when the strain rate rises or the deformation temperature decreases,the flow stress increases and it was proved that the alloy is a positive strain rate sensitive material.It was deduced that compared with the gravity casting alloy,squeeze casting alloy（solidified at 632 MPa）is more difficult to deform since the flow stress of squeeze casting alloy is higher than that of gravity casting alloy when the deformation temperature exceeds 400°C.Flow stress behavior of Al-17.5Si-4Cu-0.5Mg alloy can be described by a hyperbolic sine form with Zener-Hollomon parameter,and the average hot deformation activation energy Q of gravity casting alloy and squeeze casting alloy is 278.97 and 308.77kJ/mol,respectively.

Aerodynamic design optimization of nacelle/pylon position on an aircraft

The arbitrary space-shape free form deformation （FFD） method developed in this paper is based on non-uniform rational B-splines （NURBS） basis function and used for the integral parameterization of nacelle-pylon geometry. The multi-block structured grid deformation technique is established by Delaunay graph mapping method. The optimization objects of aerodynamic characteristics are evaluated by solving NavierStokes equations on the basis of multi-block structured grid. The advanced particle swarm optimization （PSO） is utilized as search algorithm, which com-bines the Kriging model as surrogate model during optimization. The optimization system is used for optimizing the nacelle location of DLR-F6 wing-body-pylon-nacelle. The results indicate that the aerodynamic interference between the parts is significantly reduced. The optimization design system established in this paper has extensive applications and engineering value.