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.

Variation effect of strain rate on microstructure in isothermal compression of Ti-6Al-4V alloy

Isothermal compression of the Ti-6Al-4V alloy at the deformation temperatures of 950 and 980℃,height reductions of 30% and 60%,and strain rates of 0.001,0.010,0.100 and 1.000 s-1 was conducted,wherein the variations of microstructure with strain rate were investigated.The experimental results showed that the variation of the microstructure with the strain rate under one condition was significantly different from that under another condition,which meaned that the interaction between the processing parameters was great.The optimization of the strain rate under one condition was not suitable for another condition.Therefore,selecting the forging equipment and optimizing the strain rate should be based on simultaneously considering the deformation temperature and height reduction.

Isothermal compression behavior and constitutive modeling of Ti-5Al-5Mo-5V-1Cr-1Fe alloy

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.

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.

Prediction of flow stress of Mg-Nd-Zn-Zr alloy during hot compression

Isothermal hot compression tests were carried out on Mg-3.0Nd-0.2Zn-0.4Zr （mass fraction, %, NZ30K） alloy using a Gleeble-3500 thermo-simulation machine at temperatures ranging from 350 to 500 ℃and strain rates from 0.001 to 1 s^-1. A correction of flow stress for deformation heating at a high strain rate was carried out. Based on the corrected data for deformation heating, a hyperbolic sine constitutive equation was established. The constants in the constitutive equation of the hyperbolic sine form were determined as a function of strain. The flow stresses predicted by the developed equation agree well with the experimental results, which confirms that the developed constitutive equations can be used to predict the flow stress of NZ30K alloy during hot deformation.

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.

Flow behavior and microstructure evolution of 6A82 aluminium alloy with high copper content during hot compression deformation at elevated temperatures

The flow behavior and microstructure evolution of 6A82 aluminum alloy (Al?Mg?Si?Cu) with high copper content were studied on a Gleeble?1500 system by isothermal hot compression test in the temperature range from 320 to 530 °C and the strain rate range from 0.001 to 10 s?1. The results reveal that the flow stress of the alloy exhibits a continuous flow softening behavior at low temperatures of 320?390 °C, whereas it reaches steady state at high temperatures (≥460°C), which are influenced greatly by the Zener?Hollomon parameter (Z) in the hyperbolic sine with the hot deformation activation energy of 325.12 kJ/mol. Microstructure characterizations show that prominent dynamic recrystallization and coarsening of dynamic precipitation may be responsible for the continuous flow softening behavior. Due to deformation heating at high strain rates (≥1 s?1), dynamic recrystallization is more prominent in the specimen deformed at 530 °C and 10 s?1 than in the specimen deformed at 460 °C and 0.1 s?1 even though they have very close lnZ values.

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%.

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.

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.

Deformation behavior of Ti-5Al-2Sn-2Zr-4Mo-4Cr alloy with two initial microstructures during hot working

The effects of initial microstructure on the flow stress, strain rate sensitivity （m）, strain hardening exponent （n）, apparent activation energy （Q） for deformation of Ti-5Al-2Sn-2Zr-4Mo-4Cr alloy were investigated using isothermal compression tests. Results show that the alloy with Widmanst-tten alpha plates shows a higher peak stress and flow softening. Additionally, the alloy with equiaxed primary alpha exhibits an early yield drop at or above 810 ℃ and at strain rates of 0.1-5.0 s^-1. In the strain range of 0.5-0.7,m of the alloy with equiaxed primary alpha is found to be larger at 0.01 s^-1 and lower deformation temperatures. This phenomenon could be reasonably explained based on the microstructure evolution. The strain has a significant effect onn of the alloy with Widmanst-tten alpha plates, which is attributed to platelet bending/kinking and dynamic globularization ofα phase. In the strain range of 0.15-0.55,Q of the alloy with Widmanst-tten alpha plates is larger.

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.

Evaluation on prediction abilities of constitutive models considering FEA application

Constitutive model plays an important role in the numerical simulations of metal forming. However, th~ influence of the models on the calculation is vague. Based on the stress-strain data of A1 7050 and Ti-6A1-4V alloy generated by isothermal compressive tests, the Johnson-Cook （JC） and Arrhenius-type （A-type） hyperbolic sine model were fitted to obtain the constants. Flow stresses directly calculated by the equations were compared with th~ experiment results, and rigid-plastic finite element analyses （FEA） utilizing these models were employed to simulate th~ same compression processes. The results show that A-type model has higher accuracy in the direct prediction of roy stress, even outside of the fit domain. The simulation results using A-type model also have higher agreement with th~ experiment; however, the suitability is affected by the referential parameters employed in the regression process, h terms of the overall deformation and strain distributions, there are slight differences among the simulation results usint these two models.

Flow stress prediction for hot deformation processing of 2024Al-T3 alloy

Isothermal compression tests were conducted to predict the hot deformational flow stress behaviour of 2024AI-T3 alloy with respect to a wide range of strain rates （0.001-100 s l）, strains （0.1-0.5） and temperatures （573-773 K）. The prediction capabilities of various constitutive models for 2024A1 alloys and a recently developed constitutive model were evaluated using statistical parameters such as the average absolute relative error （AARE） and the correlation coefficient （R）. Models recorded the lowest AARE （4.6%） and the highest correlation coefficient （R=0.99） were developed compared with the other models. Hence, this model can track the deformational behaviour of 2027Al-T3 alloy more accurately compared with other models throughout the entire processing domain investigated.

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.

Economy of Energy during Refrigerating Machine Operation

Idealized cycles of refrigerating machines with adiabatic and isothermal compression of refrigerant vapor were investigated. Energetic characteristics of cycles： specific mass and volume cooling capacity q0 and qv, work of compression 1, refrigerating coefficient of performance e and power N for drive of compressor were compared. These characteristics were calculated for eight refrigerants at temperature of their condensation 30 ℃ and temperatures of boiling -15℃ and -30 ℃. The calculations show that the use of isothermal compression of refrigerant vapor ensures economy of energy during refrigerating machine operation.

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.