Modeling of grain size in isothermal compression of Ti-6Al-4V alloy using fuzzy neural network

Isothermal compression of Ti-6Al-4V alloy was conducted in the deformation temperature range of 1093-1303 K, the strain rates of 0.001, 0.01, 0.1, 1.0, and 10.0 s-1, and the height reductions of 20%-60% with an interval of 10%. After compression, the effect of the processing parameters including deformation temperature, strain rate, and height reduction on the flow stress and the microstructure was investigated. The grain size of primary a phase was measured using an OLYMPUS PMG3 microscope with the quantitative metallography SISC IAS V8.0 image analysis software. A model of grain size in isothermal compression of Ti-6A1-4V alloy was developed using fuzzy neural net- work （FNN） with back-propagation （BP） learning algorithm. The maximum difference and the average difference between the predicted and the experimental grain sizes of primary a phase are 13.31% and 7.62% for the sampled data, and 16.48% and 6.97% for the non-sampled data, respectively. It can be concluded that the present model with high prediction precision can be used to predict the grain size in isothermal compression of Ti-6Al-4V alloy.

Prediction model for flow stress during isothermal compression in α+β phase field of TC4 alloy

Isothermal compression of TC4 alloy was performed on a Thermecmaster-Z simulator at the deformation temperatures ranging from 1093 to 1243 K, the strain rates ranging from 0.001 to 10.000 s^-l and a maximum strain of 0.8. The experimental results show that the flow stress increases with the decrease in the deformation temperature and the increase in the strain rate. The apparent activation energy for deformation is much lower at lower strain rates than that at higher strain rates. The flow stress model considering strain compensation was established. The average relative error between the calculated flow stress and experimental results is about 7.69%, indicating that the present model could be used to accurately predict the flow stress during high temperature in α＋β phase field of TC4 alloy.

Deformation characteristic of semi-solid ZCuSn10 copper alloy during isothermal compression

The compression tests were carried out by Gleeble-1500 thermo-mechanical simulator with samples of semi-solid ZCuSnl0 alloy prepared by strain-induced melt activation （SIMA） process. The original microstruc- ture and the deformation temperature of semi-solid ZCuSnl0 alloy are different. The strain is 0.2, and the strain rate is 1 s-1 for the compression test. The results show that when the semi-solid ZCuSnl0 alloy was pre- pared by SIMA process, the liquid fraction of semi-solid microstructure increases, and the solid grain is smaller, more uniform and more inclined to be round as the roiling pre-deformation increasing. The results also indicate that the deformation resistance of ZCuSnl0 alloy in semi-solid state decreases with the deformation temperature increas- ing or the solid fraction of original microstructure de- creasing. The stress-strain curves of the isothermal compression can be divided into quasi-elastic deformation stage and plastic deformation stage, and there are three deformation zones in the samples after isothermal com- pression, namely the difficult deformation zone, the large deformation zone and the free deformation zone. In the three deformation zones, the main deformation mechanism is flow of liquid incorporating solid particles （FLS） mechanism, plastic deformation of solid particles （PDS） mechanism and liquid flow （LF） combining with FLS mechanism, respectively.

Microstructure evolution in the high temperature compression of Ti-5.6Al-4.8Sn-2.0Zr alloy

Isothermal compression of a Ti-5.6Al-4.8Sn-2.0Zr alloy was conducted on a Thermecmaster-Z simulator at the deformation temperatures ranging from 960 to 1060℃, the strain rates ranging from 0.001 to 10.0 s^-1, and the maximum height reduction of 70.0%. In the two-phase region of the Ti-5.6Al-4.8Sn-2.0Zr alloy, the volume fraction of α phase decreases with an increase in deformation temperature, but the grain size has a slight variation with deformation temperature. The strain rate affects both morphologies and grain size of the α phase in the isothermal compression of the Ti-5.6Al-4.8Sn-2.0Zr alloy. The optimal height reduction also contributes to the small and well-distributed α phase in the isothermal compression of Ti-5.6Al-4.8Sn-2.0Zr alloy.

Molar volume, thermal expansivity and isothermal compressibility of trans-decahydronaphthalene up to 200MPa and 446K

The molar volume isotherms of trans-decahydronaphthalene （C10H18） between 293 and 446 K and at pressures from 10 to 200 MPa have been determined. A modified Tait equation of state is used to fit each experimental molar volume isotherm with a maximum average deviation of 0.029%. The thermal expansivity （cubic expansion coefficient） α and isothermal compressibility κ were determined by fitting the slopes of the isobaric curves and isotherms, respectively. The coefficients in the equation Vm=C1＋C2T＋C3T^2-C4p-C5pT have been fitted with an average deviation of 1.03%.

THE GLOBAL EXISTENCE OF STRONG SOLUTIONS TO THE 3D COMPRESSIBLE ISOTHERMAL NAVIER-STOKES EQUATIONS

This paper concerns the global existence of strong solutions to the 3 D compressible isothermal Navier-Stokes equations with a vacuum at infinity.Based on the special structure of the Zlotnik inequality,the time uniform upper bounds for density are established through some time-dependant a priori estimates under the assumption that the total mass is suitably small.

Relation between Tolman length and isothermal compressibility for simple liquids

The Tolman length δ 0 of a liquid with a plane surface has attracted increasing theoretical attention in recent years,but the expression of Tolman length in terms of observable quantities is still not very clear.In 2001,Bartell gave a simple expression of Tolman length δ 0 in terms of isothermal compressibility.However,this expression predicts that Tolman length is always negative,which is contrary to the results of molecular dynamics simulations（MDS） for simple liquids.In this paper,this contradiction is analyzed and the reason for the discrepancy in the sign is found.In addition,we introduce a new expression of Tolman length in terms of isothermal compressibility for simple fluids not near the critical points under some weak restrictions.The Tolman length of simple liquids calculated by using this formula is consistent with that obtained using MDS regarding the sign.

Optimization of TC11 alloy forging parameters using processing maps

Isothermal compression of TC11 alloy at the deformation temperatures ranging from 1023 to 1323 K with an interval of 20 K, the strain rates of 0.001, 0.1, 1.0, and 10.0 s-1, and the height reductions of 50% and 70% was conducted on a Gleeble-1500D thermomechanical simulator. According to the experimental results, the isothermal compression and the processing maps of TC11 alloy at different strains were drawn by using the dynamic material model （DMM）. Based on the processing maps, the proper forging parameters, including a combination of defor-mation temperature and strain rate, vary with the strain in different phases of TC11 alloy.

Comparative Study on Constitutive Models to Predict Flow Stress of Fe-Cr-Ni Preform Reinforced Al-Si-Cu-Ni-Mg Composite

The isothermal compression tests were carried out on Gleeble-3500 thermal-mechanical simulation machine in a temperature range of 298-473 K and strain rate range of 0.001-10 s^-1. The experimental results show that the flow stress data are negatively correlated with temperature for temperature softening, and the strain rates sensitivity of this composite increases with elevating temperature. Based on the experimental data, Johnson-Cook, modified Johnson-Cook and Arrhenius constitutive models were established. The accuracy of these three constitutive models was analyzed and compared. The results show that the values predicted by Johnson-Cook model could not agree well with the experimental values. The prediction accuracy of Arrhenius model is higher than that of Johnson-Cook model but lower than that of the Modified Johnson-Cook model.

Analysis of equation of state and thermodynamic functions for trans-decahydronaphthalene up to 200 MPa and 446 K

This paper develops a modified Tait equation of state （EOS） for trans-decahydronaphthalene with four parameters A, B, V0 and P0 being treated as linear functions of temperature. The coefficients contained in these functions are determined through fitting the experimental compression data in the literature between 293 K and 446 K and at pressures from 10 to 200 MPa. Expressions for the thermal expansivity, isothermal compressibility and thermodynamic quantities are deduced and the numerical results are analytically derived. The numerical results show that the precision of the modified Tait EOS developed in this paper is superior to the EOS in the literature.

High Temperature Behavior of Isothermally Compressed M50 Steel

The isothermal compression of M50 steel is carried out on a Gleeble-3500 thermo-mechanical simulator in temperature range of 1 223-1 423 K and strain rates range of 10-70 s^-1. The results show that the carbides play a significant role in the flow behavior and microstructure evolution during isothermal compression of M50 steel. The average apparent activation energy for deformation in isothermal compression of M50 steel is （281.1±42.6） kJ·mol^-1 at the strains of 0.4-0.8. The dynamic recrystallization of austenite grains occurs in isothermal compression of M50 steel at 1 363 K and 1 393 K, enhancing with the increase of strain rate and/or strain. The volume fraction of the carbides decreases with the increase of deformation temperature during isothermal compression of M50 steel and the fine carbides inhibit the dynamic recrystallization of austenite grain. With the occurrence of dynamic recrystallization, the austenite grains are refined, leading to a minor increase in the flow stress and apparent activation energy for deformation in isothermal compression of M50 steel. The austenite grains begin to coarsen at 1 423 K and dynamic recrystallization is limited. Hot working of M50 steel should not be performed above 1 393 K in order to achieve good workability.

Spatial Correlation in Typical Binary Polycondensation Systems: An Essential Extension of the Kirkwood-Buff Theory

We present the isothermal susceptibility(XT)for the typical binary polycondensation system of Af-Bg type,and relate XT to the weight-average degree of polymerization in terms of the Kirkwood-Buff(KB)theory.The investigation is based on a new expression of XT for mixtures,which is still expressed by the KB integrals(KBIs)but endowed with an explicit physical interpretation.For polymerization systems,it is proposed that the KBIs can be further decomposed according to whether there exists a bond between particles when conversions(extents of reaction)of functional groups are incorporated into the KBIs.In this way,XT is directly decomposed into its relevant components as well.This is especially useful to reveal the relationship between local structures and average properties of various polymerization systems.As a consequence,the effect of polymerization on XT is greatly simplified in comparison with the free energy route.Therefore,we have provided a very simple method to carry out some thermodynamic properties of polymerization systems.

Hot workability characteristics of Rene88DT superalloy with directionally solidified microstructure

The hot deformation characteristics of Rene88DT superalloy with directionally solidified micro- structure produced by electroslag remelting continuous directionally solidification （ESR-CDS） were studied in the temperature range of 1,040-1,140 ℃ and strain rate range of 0.001-1.000 s-1 by hot compression tests. Flow curves for Rene88DT alloy with initial directionally solidified （DS） microstructure exhibit pronounced peak stresses at the early stage of deformation followed by the occurrence of dynamic softening phenomenon. Rene88DT alloy with DS micro- structure shows higher flow peak stresses compared with HIPed P/M superalloy FGH4096, but the disparities in peak stresses between ESR-CDSed Rene88DT and HIPed P/M superalloy FGH4096 reduce as temperature increases. The improvement of hot workability of DS alloy with columnar grains avoiding the maximum shear stress comes true. A hot deformation constitutive equation as a function of strain that describes the dependence of flow stress on strain rate and temperature is established. Hot deformation apparent acti- vation energy （Q） varies not only with the strain rate and temperature but also with strain. The strain rate sensitivity exponent （m） map is established at the strain of 0.8, which reveals that global dynamic recrystallization （DRX） shows a relatively high m value in a large strain compression. Optimum parameters are predicted in two regions： T = 1,100-1,130 ℃, ε = 0.100-1.000 s-1 and T = 1,080- 1,100 ℃, ε = 0.010-100 s-1, which is based on pro- cessing maps and deformation microstructure observations.

Microstructure evolutions and interfacial bonding behavior of Ni-based superalloys during solid state plastic deformation bonding

As an advanced solid state bonding process,plastic deformation bonding(PDB)is a highly reliable metallurgical joining method that produces significant plastic deformation at the bonding interface of welded joints through thermo-mechanical coupling.In this study,PDB behavior of IN718 superalloy was systematically investigated by performing a series of isothermal compression tests at various processing conditions.It was revealed that new grains evolved in the bonding area through discontinuous dynamic recrystallization(DDRX)at 1000–1150℃.Electron backscattered diffraction(EBSD)and transmission electron microscopy(TEM)results revealed that the bonding of joints is related with interfacial grain boundary(IGB)bulging process,which is considered as a nucleation process of DRXed grain under different deformation environments.During recrystallization process,the bonded interface moved due to strain-induced boundary migration(SIBM)process.Stored energy difference(caused by accumulation of dislocations at the bonding interface)was the dominant factor for SIBM during DRX.The mechanical properties of the bonded joints were dependent upon the recrystallized microstructure and SIBM ensued during PDB.

Evolution of grain size and grain shape during thermomechanical processing in a powder metallurgical nickel-based superalloy

With a strain rate range of 0.01–10 s^(−1) and a deformation temperature range of 1110–1200℃,the isothermal compression test was performed on one powder metallurgy superalloy which is macroscopic segregation free.Using electron backscatter diffraction,the effect of strain rate and deformation temperature on grain shape and grain size of superalloys during thermal deformation was studied.The results established that exquisite and equiaxed dynamic recrystallization(DRX)grains are procured at supernal deformation temperature and high strain rate because of the high dislocation density.At the same time,the interaction between high DRX nucleation rate and low grain growth rate at high strain rate is favorable in making finer DRX grains.The equivalent medial grain size expanded with lowering strain rate and elevating proof temperature.Moreover,the grain shape was researched by the effective method of aspect ratio.Most aspect ratio of original grains is 0.61,and the aspect ratio has important implications for DRX and grain growth process.The average aspect ratio increases slightly when deformation temperature rises from 1110 to 1140℃,while the average aspect ratio increases memorably as the deformation temperature is higher than 1140℃.

Static recrystallization behavior of SA508Gr.4N reactor pressure vessel steel during hot compressive deformation

The two-pass isothermal hot compression method was used to study the effect of different thermal deformation conditions on static recrystallization behavior in Ni-Cr-Mo series SA508Gr.4N low alloy steel with interval holding time ranging from 1 to 300 s,temperature ranging from 950 to 1150℃,strain rate ranging from 0.01 to 1 s^(-1),true strains ranging from 0.1 to 0.2,and initial austenite grain size ranging from 175 to 552μm.It can be concluded that the static recrystallization volume fraction gradually increases with the increase in the deformation temperature,strain rate,strain and pass interval,and the decrease in the initial grain size,which is mainly due to the increase in the deformation energy storage and dislocations.Moreover,strain-induced grain boundary migration is the nucleation mechanism for static recrystallization of SA508Gr.4N low alloy steel.Based on the stress-strain curve,the predicted value obtained from the established static recrystallization kinetics model is in good consistence with the experimental value,and the static recrystallization thermal activation energy of SA508Gr.4N steel was calculated as 264,225.99 J/mol.