Recrystallized grains, less than 200 nm in diameter were observed in heavily shear zones of a high strength low alloy steel and a Ni-based alloy, and Also grain refinement, less than 3 μm in diameter was made in high...Recrystallized grains, less than 200 nm in diameter were observed in heavily shear zones of a high strength low alloy steel and a Ni-based alloy, and Also grain refinement, less than 3 μm in diameter was made in high purity aluminum by ECAE at ambient temperature. The experimental results showed that high strain rate and large deformation could induce dynamic recrystallization.Based on dislocation dynamics and grain orientation change enhanced by plastic deformation,a model for the recrystallization process is developed. The model is used to explain the ultra fine grains which are formed at a temperature still much lower than that for the conventional recrystallization展开更多
The measurements by Huibin XU et al of the stress-dependence ot hysteresis in a NiTi shape memo ry alloy are modeled by catastrophe theory. The cusp catastrophe is used with the strain as the behaviour variable and t...The measurements by Huibin XU et al of the stress-dependence ot hysteresis in a NiTi shape memo ry alloy are modeled by catastrophe theory. The cusp catastrophe is used with the strain as the behaviour variable and the control parameters being functions of the stress and the temperature. A two constant model is found to be preferred to a four constant model.展开更多
The coherent elastic strain-induced morphological transformation of a binarycubic model alloy was simulated with different strain energy parameters. The microscopic diffusionequation was combined with the theory of mi...The coherent elastic strain-induced morphological transformation of a binarycubic model alloy was simulated with different strain energy parameters. The microscopic diffusionequation was combined with the theory of microscopic elasticity. The results show that when thestrain energy is neglected, the randomly distributed equiaxed particles are obtained with isotropiccharacteristic. It is coarsening that follows the Ostwald ripening mechanism: smaller particlesdwindle and larger particles grow; when the elastic strain is considered, plate precipitates tend toalign along the elastically soft directions <01> with anisotropic characteristic. The particlesgrow in the soft directions and coarsen further; particles dwindle in out of the soft directions.While the coarsening of the particles localized in the same row or column follows the rule: smallerparticles shrink and larger ones grow.展开更多
Structural fatigue of NiTi shape memory alloys is a key issue that should be solved in order to promote their engineering applications and utilize their unique shape memory effect and super-elasticity more sufficientl...Structural fatigue of NiTi shape memory alloys is a key issue that should be solved in order to promote their engineering applications and utilize their unique shape memory effect and super-elasticity more sufficiently. In this paper, the latest progresses made in experimental and theoretical analyses for the structural fatigue features of NiTi shape memory alloys are reviewed. First, macroscopic experimental observations to the pure mechanical and thermo-mechanical fatigue features of the alloys are summarized; then the state-of-arts in the mechanism analysis of fatigue rupture are addressed; further, advances in the construction of fatigue failure models are provided; finally, summary and future topics are outlined.展开更多
The magnetic behaviors of the Fe–Mn–Al alloy are simulated on the Bethe lattice by using a trimodal random bilinear exchange interaction(J) distribution in the Blume–Capel(BC) model. Ferromagnetic(J 〉 0) or ...The magnetic behaviors of the Fe–Mn–Al alloy are simulated on the Bethe lattice by using a trimodal random bilinear exchange interaction(J) distribution in the Blume–Capel(BC) model. Ferromagnetic(J 〉 0) or antiferromagnetic(J 〈 0)bonds or dilution of the bonds(J = 0) are assumed between the atoms with some probabilities. It is found that the secondor the first-order phase boundaries separate the ferromagnetic(F), antiferromagnetic(AF), paramagnetic(P), or spin-glass(SG) phases from the possible other one. In addition to the tricritical points, the special points at which the second- and the first-order and the spin-glass phase lines meet are also found. Very rich phase diagrams in agreement with the literature are obtained.展开更多
A three-dimensional friction stir welding (FSW) process model has been developed based on fluid mechanics. The material transport in the welding process has been regarded as a laminar, viscous, and non-Newtonian liq...A three-dimensional friction stir welding (FSW) process model has been developed based on fluid mechanics. The material transport in the welding process has been regarded as a laminar, viscous, and non-Newtonian liquid that flows past a rotating pin. A criterion to divide the weld zone has been given on the basis of cooperation of velocity field and viscosity field. That is, the η0-easy-flow zone that existed near the tool pin corresponded to the weld nugget zone; the area between the η0-easy-flow zone and η1-viscosity band is corresponded to the thermal-mechanical affected zone (TMAZ). The model gives some useful information to improve the understanding of material flow in FSW through the simulation result of velocity distribution. In order to appraise the friction stir pin design, three kinds of pin geometry, one is column pin, the second is taper pin, and the last one is screw threaded taper pin, were used in the model. The pin geometry seriously affected the simulation result of velocity distribution in the η0-easy-flow zone. The velocity distribution in the η0-easy-flow zone can be considered as the criterion of optimizing friction stir tool design. This study will benefit to direct the friction stir tool design.展开更多
Two constitutive models,the modified Johnson-Cook model and the logarithm linear relation model based on empirical approach and data analysis,were presented to illustrate compressive deformation of magnesium alloys AZ...Two constitutive models,the modified Johnson-Cook model and the logarithm linear relation model based on empirical approach and data analysis,were presented to illustrate compressive deformation of magnesium alloys AZ80 under multiple loading directions and strain rates.The results of stress-strain curve analysis and sensitivity index analysis suggested that the stress held large fluctuations in loading direction of 90°.Model testing signified that the logarithm linear relation model was more proper than the modified Johnson-Cook model in view of relative mean square error and correlation coefficients.Moreover,numerical simulation building on established models also indicated that the logarithm linear model is more precise than the modified Johnson-Cook model.展开更多
The calculated results of thermodynamic properties in ternary Au-Ga-Sb system by general solution model were presented in this paper.The calculations were carried out in nine cross sections from all three corners in t...The calculated results of thermodynamic properties in ternary Au-Ga-Sb system by general solution model were presented in this paper.The calculations were carried out in nine cross sections from all three corners in the temperature range of 973–1,573 K,and integral molar excess Gibbs energies,partial molar Gibbs energies,activity coefficients and activities for all components are obtained.The activity of gold and gallium shows negative deviation from Rault's law for all investigated sections,while antimony activity is close to the line of ideal conditions and even coincides with the line for high content of antimony in the alloy.Data obtained by calculation were compared with those found in literature.It is concluded that compared values show reasonable good agreement.展开更多
Because atoms in high-entropy alloys (HEAs) coordinate in very different and distorted local environ- ments in the lattice sites, even for the same type of constituent, their point defects could highly vary. Therefo...Because atoms in high-entropy alloys (HEAs) coordinate in very different and distorted local environ- ments in the lattice sites, even for the same type of constituent, their point defects could highly vary. Therefore, theoretical determination of the thermodynamic quantities (i.e., defect formation enthalpies) of various point defects is rather challenging because each corresponding thermodynamic quantity of all involve constituents is not unique. The knowledge of these thermodynamic quantities is prerequisite for designing novel HEAs and understanding the mechanical and physical behaviors of HEAs. However, to date there has not been a good method to theoretically derive the defect formation enthalpies of HEAs. Here, using first-principles calculations within the density functional theory (DFT) in combina- tion of special quasi-random structure models (SQSs), we have developed a general method to derive corresponding formation enthalpies of point defects in HEAs, using vacancy formation enthalpies of a four-component equiatomic fcc-type FeCoCrNi HEA as prototypical and benchmark examples. In difference from traditional ordered alloys, the vacancy formation enthalpies of FeCoCrNi HEA vary in a highly wide range from 0.72 to 2.89 eV for Fe, 0.88-2.90 eV for Co, 0.78-3.09 eV for Cr, and 0.91-2.95 eV for Ni due to high-level site-to-site lattice distortions and compositional complexities. On average, the vacancy formation enthalpies of 1.58 eV for Fe, 1.61 eV for Cr, 1.70 eV for Co and 1.89 eV for Ni are all larger than that (1.41 eV) of pure fcc nickel. This fact implies that the vacancies are much more difficult to be created than in nickel, indicating a reasonable agreement with the recent experimental observation that FeCoCrNi exhibits two orders of amplitudes enhancement of radiation tolerance with the suppression of void formation at elevated temperatures than in pure nickel.展开更多
A model was developed to describe the microstracture evolution in a directionally solidified ternary monotectic alloy.The directional solidification experiments were carried out on Al-3Pb-lSn(wt%) alloys by using a ...A model was developed to describe the microstracture evolution in a directionally solidified ternary monotectic alloy.The directional solidification experiments were carried out on Al-3Pb-lSn(wt%) alloys by using a Bridgman apparatus.The microstracture evolution in the directionally solidified sample was calculated.The numerical results agree well with the experimental ones.It is demonstrated that the nucleation of the minority phase droplets occur at two different positions.One corresponds to the liquid-liquid decomposition,which occurs in front of the solidification interface.The other is at the liquid/solid interface.The nucleation rate of the minority phase droplets at the liquid/solid interface is significantly higher than at the position in front of the solidification interface.The characteristic of the nucleation process leads to a bimodal size distribution of the minority particles in the directionally solidified sample.展开更多
For better controllability in actuations,it is desirable to create Functionally Graded Shape Memory Alloys(FG-SMAs)in the actuation direction.It can be achieved by applying different heat treatment processes to crea...For better controllability in actuations,it is desirable to create Functionally Graded Shape Memory Alloys(FG-SMAs)in the actuation direction.It can be achieved by applying different heat treatment processes to create the gradient along the radius of a SMA cylinder.Analytical solutions are derived to predict the macroscopic behaviors of such a functionally graded SMA cylinder.The Tresca yield criterion and linear hardening are used to describe the different phase transformations with different gradient parameters.The numerical results for an example of the model exhibit different pseudo-elastic behaviors from the non-gradient case,as well as a variational hysteresis loop for the transformation,providing a mechanism for easy actuation control.When the gradient disappears,the model can degenerate to the non-gradient case.展开更多
As human improve their ability to fabricate materials, alloys have evolved from simple to complex compositions, accordingly improving functions and performances,promoting the advancements of human civilization. In rec...As human improve their ability to fabricate materials, alloys have evolved from simple to complex compositions, accordingly improving functions and performances,promoting the advancements of human civilization. In recent years, high-entropy alloys(HEAs) have attracted tremendous attention in various fields. With multiple principal components, they inherently possess unique microstructures and many impressive properties, such as high strength and hardness, excellent corrosion resistance, thermal stability, fatigue,fracture, and irradiation resistance, in terms of which they overwhelm the traditional alloys. All these properties have endowed HEAs with many promising potential applications.An in-depth understanding of the essence of HEAs is important to further developing numerous HEAs with better properties and performance in the future. In this paper, we review the recent development of HEAs, and summarize their preparation methods, composition design, phase formation and microstructures, various properties, and modeling and simulation calculations. In addition, the future trends and prospects of HEAs are put forward.展开更多
Developments of new sheet metal forming technology and theory in China are reviewed in detail in this paper.Advances of crystal plasticity on the deformation mechanism of Mg alloy are firstly described, especially its...Developments of new sheet metal forming technology and theory in China are reviewed in detail in this paper.Advances of crystal plasticity on the deformation mechanism of Mg alloy are firstly described, especially its applications on the prediction of sheet forming process. Then, a new macroscopic constitutive model is introduced, which possesses an enhanced description capacity of tension/compression anisotropy and anisotropic hardening. In order to take into account the twinning process of hexagonal close-packed material, a modified hierarchical multi-scale model is also established with adequate accuracy in a shorter computational time. The advanced forming limit of sheet metal, mainly about aluminum alloy, is also investigated. Besides the above theory developments, some new sheet metal forming technologies are reviewed simultaneously. The warm forming technology of Mg alloy is discussed. New processes to form sheet parts and to bend tubes are proposed by using hard granules. On the other hand, a new kind of ultra-high-strength steel based on typical22 Mn B5 by introducing more residual austenite and Cu-rich phase to increase the elongation and strength and its novel forming method that integrates hot stamping and quenching participation are proposed. Progresses in sheet hydroforming,press forging and electromagnetic forming of sheet metal parts are also summarized.展开更多
Temperature rise is a significant factor influencing microstructure during(α+β) deformation of TA15 titanium alloy.An experiment was designed to explore microstructure evolution induced by temperature rise due to...Temperature rise is a significant factor influencing microstructure during(α+β) deformation of TA15 titanium alloy.An experiment was designed to explore microstructure evolution induced by temperature rise due to deformation heat.The experiment was carried out in(α+β) phase field at typical temperature rise rates.The microstructures of the alloy under different temperature rise rates were observed by scanning electron microscopy(SEM).It is found that the dissolution rate of primary equiaxed a phase increases with the increase in both temperature and temperature rise rate.In the same temperature range,the higher the temperature rise rate is,the larger the final content and grain size of primary equiaxed a phase are due to less dissolution time.To quantitatively depict the evolution behavior of primary equiaxed a phase under any temperature rise rates,the dissolution kinetics of primary equiaxed a phase were well described by a diffusion model.The model predictions,including content and grain size of primary equiaxed a phase,are in good agreement with experimental observations.The work provides an important basis for the prediction and control of microstructure during hot working of titanium alloy.展开更多
文摘Recrystallized grains, less than 200 nm in diameter were observed in heavily shear zones of a high strength low alloy steel and a Ni-based alloy, and Also grain refinement, less than 3 μm in diameter was made in high purity aluminum by ECAE at ambient temperature. The experimental results showed that high strain rate and large deformation could induce dynamic recrystallization.Based on dislocation dynamics and grain orientation change enhanced by plastic deformation,a model for the recrystallization process is developed. The model is used to explain the ultra fine grains which are formed at a temperature still much lower than that for the conventional recrystallization
文摘The measurements by Huibin XU et al of the stress-dependence ot hysteresis in a NiTi shape memo ry alloy are modeled by catastrophe theory. The cusp catastrophe is used with the strain as the behaviour variable and the control parameters being functions of the stress and the temperature. A two constant model is found to be preferred to a four constant model.
基金National Natural Science Foundation of China (No.50071046).
文摘The coherent elastic strain-induced morphological transformation of a binarycubic model alloy was simulated with different strain energy parameters. The microscopic diffusionequation was combined with the theory of microscopic elasticity. The results show that when thestrain energy is neglected, the randomly distributed equiaxed particles are obtained with isotropiccharacteristic. It is coarsening that follows the Ostwald ripening mechanism: smaller particlesdwindle and larger particles grow; when the elastic strain is considered, plate precipitates tend toalign along the elastically soft directions <01> with anisotropic characteristic. The particlesgrow in the soft directions and coarsen further; particles dwindle in out of the soft directions.While the coarsening of the particles localized in the same row or column follows the rule: smallerparticles shrink and larger ones grow.
基金supported by the National Natural Science Foundation of China (11532010)
文摘Structural fatigue of NiTi shape memory alloys is a key issue that should be solved in order to promote their engineering applications and utilize their unique shape memory effect and super-elasticity more sufficiently. In this paper, the latest progresses made in experimental and theoretical analyses for the structural fatigue features of NiTi shape memory alloys are reviewed. First, macroscopic experimental observations to the pure mechanical and thermo-mechanical fatigue features of the alloys are summarized; then the state-of-arts in the mechanism analysis of fatigue rupture are addressed; further, advances in the construction of fatigue failure models are provided; finally, summary and future topics are outlined.
文摘The magnetic behaviors of the Fe–Mn–Al alloy are simulated on the Bethe lattice by using a trimodal random bilinear exchange interaction(J) distribution in the Blume–Capel(BC) model. Ferromagnetic(J 〉 0) or antiferromagnetic(J 〈 0)bonds or dilution of the bonds(J = 0) are assumed between the atoms with some probabilities. It is found that the secondor the first-order phase boundaries separate the ferromagnetic(F), antiferromagnetic(AF), paramagnetic(P), or spin-glass(SG) phases from the possible other one. In addition to the tricritical points, the special points at which the second- and the first-order and the spin-glass phase lines meet are also found. Very rich phase diagrams in agreement with the literature are obtained.
文摘A three-dimensional friction stir welding (FSW) process model has been developed based on fluid mechanics. The material transport in the welding process has been regarded as a laminar, viscous, and non-Newtonian liquid that flows past a rotating pin. A criterion to divide the weld zone has been given on the basis of cooperation of velocity field and viscosity field. That is, the η0-easy-flow zone that existed near the tool pin corresponded to the weld nugget zone; the area between the η0-easy-flow zone and η1-viscosity band is corresponded to the thermal-mechanical affected zone (TMAZ). The model gives some useful information to improve the understanding of material flow in FSW through the simulation result of velocity distribution. In order to appraise the friction stir pin design, three kinds of pin geometry, one is column pin, the second is taper pin, and the last one is screw threaded taper pin, were used in the model. The pin geometry seriously affected the simulation result of velocity distribution in the η0-easy-flow zone. The velocity distribution in the η0-easy-flow zone can be considered as the criterion of optimizing friction stir tool design. This study will benefit to direct the friction stir tool design.
基金Item Sponsored by National Natural Science Foundation of China(11271339)Plan for Scientific Innovation Talent of Henan Province of China
文摘Two constitutive models,the modified Johnson-Cook model and the logarithm linear relation model based on empirical approach and data analysis,were presented to illustrate compressive deformation of magnesium alloys AZ80 under multiple loading directions and strain rates.The results of stress-strain curve analysis and sensitivity index analysis suggested that the stress held large fluctuations in loading direction of 90°.Model testing signified that the logarithm linear relation model was more proper than the modified Johnson-Cook model in view of relative mean square error and correlation coefficients.Moreover,numerical simulation building on established models also indicated that the logarithm linear model is more precise than the modified Johnson-Cook model.
基金financially supported by the Ministry of Education,Science and Technological Development of the Republic of Serbia (Nos.34005 and 172037)
文摘The calculated results of thermodynamic properties in ternary Au-Ga-Sb system by general solution model were presented in this paper.The calculations were carried out in nine cross sections from all three corners in the temperature range of 973–1,573 K,and integral molar excess Gibbs energies,partial molar Gibbs energies,activity coefficients and activities for all components are obtained.The activity of gold and gallium shows negative deviation from Rault's law for all investigated sections,while antimony activity is close to the line of ideal conditions and even coincides with the line for high content of antimony in the alloy.Data obtained by calculation were compared with those found in literature.It is concluded that compared values show reasonable good agreement.
基金supported by the National Science Fund for Distinguished Young Scholars (No. 51725103)by the National Natural Science Foundation of China (Grant Nos. 51671193 and 51474202)+7 种基金by the Science Challenging (Project No. TZ2016004)by the “Hundred Talented Project” of the Chinese Academy of Sciencesfinancially supported by the National Natural Science Foundation of China (Nos. 51671018 and 51671021)111 Project (No. B07003)International S&T Cooperation Program of China (No. 2015DFG52600)the Program for Changjiang Scholars and Innovative Research Team in University of China (No. IRT 14R05)the Projects of SKL-AMM-USTB (Nos. 2016Z-04, 2016-09 and 2016Z-16)supported by the Hong Kong URC grant under the contract with City University of Hong Kong
文摘Because atoms in high-entropy alloys (HEAs) coordinate in very different and distorted local environ- ments in the lattice sites, even for the same type of constituent, their point defects could highly vary. Therefore, theoretical determination of the thermodynamic quantities (i.e., defect formation enthalpies) of various point defects is rather challenging because each corresponding thermodynamic quantity of all involve constituents is not unique. The knowledge of these thermodynamic quantities is prerequisite for designing novel HEAs and understanding the mechanical and physical behaviors of HEAs. However, to date there has not been a good method to theoretically derive the defect formation enthalpies of HEAs. Here, using first-principles calculations within the density functional theory (DFT) in combina- tion of special quasi-random structure models (SQSs), we have developed a general method to derive corresponding formation enthalpies of point defects in HEAs, using vacancy formation enthalpies of a four-component equiatomic fcc-type FeCoCrNi HEA as prototypical and benchmark examples. In difference from traditional ordered alloys, the vacancy formation enthalpies of FeCoCrNi HEA vary in a highly wide range from 0.72 to 2.89 eV for Fe, 0.88-2.90 eV for Co, 0.78-3.09 eV for Cr, and 0.91-2.95 eV for Ni due to high-level site-to-site lattice distortions and compositional complexities. On average, the vacancy formation enthalpies of 1.58 eV for Fe, 1.61 eV for Cr, 1.70 eV for Co and 1.89 eV for Ni are all larger than that (1.41 eV) of pure fcc nickel. This fact implies that the vacancies are much more difficult to be created than in nickel, indicating a reasonable agreement with the recent experimental observation that FeCoCrNi exhibits two orders of amplitudes enhancement of radiation tolerance with the suppression of void formation at elevated temperatures than in pure nickel.
基金supported by the National Natural Science Foundation of China(Nos.51471173,51271185 and 51031003)China Manned Space Engineering
文摘A model was developed to describe the microstracture evolution in a directionally solidified ternary monotectic alloy.The directional solidification experiments were carried out on Al-3Pb-lSn(wt%) alloys by using a Bridgman apparatus.The microstracture evolution in the directionally solidified sample was calculated.The numerical results agree well with the experimental ones.It is demonstrated that the nucleation of the minority phase droplets occur at two different positions.One corresponds to the liquid-liquid decomposition,which occurs in front of the solidification interface.The other is at the liquid/solid interface.The nucleation rate of the minority phase droplets at the liquid/solid interface is significantly higher than at the position in front of the solidification interface.The characteristic of the nucleation process leads to a bimodal size distribution of the minority particles in the directionally solidified sample.
基金the financial support of National Natural Science Foundation of China (no.11502284, 51505483, 11772041)the Fundamental Research Funds for the Central Universities (3122016C006) of China
文摘For better controllability in actuations,it is desirable to create Functionally Graded Shape Memory Alloys(FG-SMAs)in the actuation direction.It can be achieved by applying different heat treatment processes to create the gradient along the radius of a SMA cylinder.Analytical solutions are derived to predict the macroscopic behaviors of such a functionally graded SMA cylinder.The Tresca yield criterion and linear hardening are used to describe the different phase transformations with different gradient parameters.The numerical results for an example of the model exhibit different pseudo-elastic behaviors from the non-gradient case,as well as a variational hysteresis loop for the transformation,providing a mechanism for easy actuation control.When the gradient disappears,the model can degenerate to the non-gradient case.
基金supported by the National Natural Science Foundation of China (51471025 and 51671020)
文摘As human improve their ability to fabricate materials, alloys have evolved from simple to complex compositions, accordingly improving functions and performances,promoting the advancements of human civilization. In recent years, high-entropy alloys(HEAs) have attracted tremendous attention in various fields. With multiple principal components, they inherently possess unique microstructures and many impressive properties, such as high strength and hardness, excellent corrosion resistance, thermal stability, fatigue,fracture, and irradiation resistance, in terms of which they overwhelm the traditional alloys. All these properties have endowed HEAs with many promising potential applications.An in-depth understanding of the essence of HEAs is important to further developing numerous HEAs with better properties and performance in the future. In this paper, we review the recent development of HEAs, and summarize their preparation methods, composition design, phase formation and microstructures, various properties, and modeling and simulation calculations. In addition, the future trends and prospects of HEAs are put forward.
文摘Developments of new sheet metal forming technology and theory in China are reviewed in detail in this paper.Advances of crystal plasticity on the deformation mechanism of Mg alloy are firstly described, especially its applications on the prediction of sheet forming process. Then, a new macroscopic constitutive model is introduced, which possesses an enhanced description capacity of tension/compression anisotropy and anisotropic hardening. In order to take into account the twinning process of hexagonal close-packed material, a modified hierarchical multi-scale model is also established with adequate accuracy in a shorter computational time. The advanced forming limit of sheet metal, mainly about aluminum alloy, is also investigated. Besides the above theory developments, some new sheet metal forming technologies are reviewed simultaneously. The warm forming technology of Mg alloy is discussed. New processes to form sheet parts and to bend tubes are proposed by using hard granules. On the other hand, a new kind of ultra-high-strength steel based on typical22 Mn B5 by introducing more residual austenite and Cu-rich phase to increase the elongation and strength and its novel forming method that integrates hot stamping and quenching participation are proposed. Progresses in sheet hydroforming,press forging and electromagnetic forming of sheet metal parts are also summarized.
基金financially supported by the National Natural Science Foundation of China (Nos.51175427 and 51205317)the Open Fund of State Key Laboratory of Materials Processing and Die & Mould Technology of China (No.P2014-005)+1 种基金the Marie Curie International Research Staff Exchange Scheme within the 7th EC Framework Programme (FP7) (No.318968)the Programme of Introducing Talents of Discipline to Universities (No.B08040)
文摘Temperature rise is a significant factor influencing microstructure during(α+β) deformation of TA15 titanium alloy.An experiment was designed to explore microstructure evolution induced by temperature rise due to deformation heat.The experiment was carried out in(α+β) phase field at typical temperature rise rates.The microstructures of the alloy under different temperature rise rates were observed by scanning electron microscopy(SEM).It is found that the dissolution rate of primary equiaxed a phase increases with the increase in both temperature and temperature rise rate.In the same temperature range,the higher the temperature rise rate is,the larger the final content and grain size of primary equiaxed a phase are due to less dissolution time.To quantitatively depict the evolution behavior of primary equiaxed a phase under any temperature rise rates,the dissolution kinetics of primary equiaxed a phase were well described by a diffusion model.The model predictions,including content and grain size of primary equiaxed a phase,are in good agreement with experimental observations.The work provides an important basis for the prediction and control of microstructure during hot working of titanium alloy.