A crystal plasticity finite element(CPFE)model was established and 2D simulations were carried out to study the relationship between microvoids and the microplasticity deformation behavior of the dual-phase titanium a...A crystal plasticity finite element(CPFE)model was established and 2D simulations were carried out to study the relationship between microvoids and the microplasticity deformation behavior of the dual-phase titanium alloy under high cyclic loading.Results show that geometrically necessary dislocations(GND)tend to accumulate around the microvoids,leading to an increment of average GND density.The influence of curvature in the tip plastic zone(TPZ)on GND density is greater than that of the size of the microvoid.As the curvature in TPZ and the size of the microvoid increase,the cumulative shear strain(CSS)in the primaryα,secondaryα,andβphases increases.Shear deformation in the prismatic slip system is dominant in the primaryαphase.As the distance between the microvoids increases,the interactive influence of the microvoids on the cumulative shear strain decreases.展开更多
In order to accelerate the research on the property optimization of titanium alloy based on high-throughput methods,it is necessary to reveal the relationship between hardness and other mechanical properties which is ...In order to accelerate the research on the property optimization of titanium alloy based on high-throughput methods,it is necessary to reveal the relationship between hardness and other mechanical properties which is still unclear.In this work,taking Ti20C alloy as research object,almost all the microstructure of dual-phase titanium alloys were covered by traversing over 100 heat treatment schemes.Then,massive experiments including microstructure characterization and performance test were conducted,obtaining 51,590 pieces of microstructure data and 3591 pieces of mechanical property data.Subsequently,based on large-scale data-driven technology,the quantitative mapping relationship between hardness and other mechanical properties was deeply discussed.The results of random forest models showed that the correlation between hardness(H)and Charpy impact energy(A_(k))(or elongation,A)was hardly dependent on the microstructure types,while the relationship between H and tensile strength(R_(m))(or yield strength,R_(p0.2))was highly dependent on microstructure types.Specifically,combined with statistical analysis,it was found that the relationship between H and Ak(or A)were negatively linear.Interestingly,the relationship between H and strength was positively linear for equiaxed microstructure,and strength was linked to d^(−1/2)(d,equivalent circle diameter)ofα-grains in the form of classical Hall–Petch formula;but for other microstructures,the relationships were quadratic.Furthermore,the above rules were nearly the same in the rolling direction and transverse direction.Finally,a"four-quadrant partition map"between H and R_(p0.2)/R_(m) was established as a versatile material-screening tool,which can provide guidance for on-demand selection of titanium alloys.展开更多
The Ti-5Al-2Sn-4Zr-4Mo-2Cr-1Fe(β-CEZ)alloy is considered as a potential structural material in the aviation industry due to its outstanding strength and corrosion resistance.Electrochemical machining(ECM)is an effici...The Ti-5Al-2Sn-4Zr-4Mo-2Cr-1Fe(β-CEZ)alloy is considered as a potential structural material in the aviation industry due to its outstanding strength and corrosion resistance.Electrochemical machining(ECM)is an efficient and low-cost technology for manufacturing theβ-CEZ alloy.In ECM,the machining parameter selection and tool design are based on the electrochemical dissolution behavior of the materials.In this study,the electrochemical dissolution behaviors of theβ-CEZ and Ti-6Al-4V(TC4)alloys in NaNO3solution are discussed.The open circuit potential(OCP),Tafel polarization,potentiodynamic polarization,electrochemical impedance spectroscopy(EIS),and current efficiency curves of theβ-CEZ and TC4 alloys are analyzed.The results show that,compared to the TC4 alloy,the passivation film structure is denser and the charge transfer resistance in the dissolution process is greater for theβ-CEZ alloy.Moreover,the dissolved surface morphology of the two titanium-based alloys under different current densities are analyzed.Under low current densities,theβ-CEZ alloy surface comprises dissolution pits and dissolved products,while the TC4 alloy surface comprises a porous honeycomb structure.Under high current densities,the surface waviness of both the alloys improves and the TC4 alloy surface is flatter and smoother than theβ-CEZ alloy surface.Finally,the electrochemical dissolution models ofβ-CEZ and TC4 alloys are proposed.展开更多
Dual-phase Mg-Li alloys sheets were rolled at four different temperatures ranging from liquid nitrogen to 300℃to explore effect of rolling temperature on texture and mechanical properties of the material.Crystal plas...Dual-phase Mg-Li alloys sheets were rolled at four different temperatures ranging from liquid nitrogen to 300℃to explore effect of rolling temperature on texture and mechanical properties of the material.Crystal plasticity simulation was utilized to illustrate the influence of slip activity on rolling texture development.The results show that the rolling texture is largely depended on deformation temperature.Unlike commercial Mg alloys,the critical resolved shear stress of basal slip inα-Mg phase of Mg-Li alloy decreased more significantly by increasing temperature compared to that of pyramidal<c+a>slip.Enhancement of basal slip by increasing temperature triggered a decrease of split angle of basal poles for the double-peak texture.Prismaticslip largely enhanced by increasing temperature upon 200℃,which induced a wider orientation spread along the transverse direction.For theβ-Li phase,the promotion of{110}<111>slip system at elevated temperature triggered the enhancement of{211}<110>and{111}<211>texture components.The cryo-rolled sample exhibited the highest strength compared to the others due to a strong hardening behavior at this temperature.A two-stage hardening behavior was observed in these as-rolled dual-phase alloys.Strain transition at phase boundaries could be the reason for appearance of this two-stage hardening.展开更多
Magnetron sputtering deposition with regulated Cu target power was used for depositing Cu-containing high-entropy alloy nitride(Cu-(HEA)N)films on TC4 titanium alloy substrates.The microscopic morphologies,surface com...Magnetron sputtering deposition with regulated Cu target power was used for depositing Cu-containing high-entropy alloy nitride(Cu-(HEA)N)films on TC4 titanium alloy substrates.The microscopic morphologies,surface compositions,and thicknesses of the films were characterized using SEM+EDS;the anti-corrosion,wear resistance and antibacterial properties of the films in simulated seawater were investigated.The experimental results show that all four Cu-(HEA)N films are uniformly dense and contained nanoparticles.The film with Cu doping come into contact with oxygen in the air to form cuprous oxide.The corrosion resistance of the(HEA)N film without Cu doping on titanium alloy is better than the films with Cu doping.The Cu-(HEA)N film with Cu target power of 16 W shows the best wear resistance and antibacterial performance,which is attributed to the fact that Cu can reduce the coefficient of friction and exacerbate corrosion,and the formation of cuprous oxide has antibacterial properties.The findings of this study provide insights for engineering applications of TC4 in the marine field.展开更多
To clarify the correlation of single-crystalline structure with corrosion performance in high-strength TiAl alloys, electrochemical and surface characterization was performed by comparing Ti–45Al–8Nb dual-phase sing...To clarify the correlation of single-crystalline structure with corrosion performance in high-strength TiAl alloys, electrochemical and surface characterization was performed by comparing Ti–45Al–8Nb dual-phase single crystals with their polycrystalline counterparts in NaCl solution. Polarization curves show a lower corrosion rate and a higher pitting potential of ~280 mV for the dual-phase single crystals. Electrochemical impedance spectroscopy and potentiostatic polarization plots revealed a higher impedance of the charge transfer through the compact passive film. Surface composition analysis indicated a compact film with more content of Nb, as twice as that in the film on the polycrystals.Our results reflect that the dual-phase Ti–45Al–8Nb single crystals possess a higher corrosion resistance in NaCl solution, compared with their polycrystalline counterpart, arising from a more homogeneous microstructure and composition distribution.展开更多
Titanium(Ti)alloys are widely used in high-tech fields like aerospace and biomedical engineering.Laser additive manufacturing(LAM),as an innovative technology,is the key driver for the development of Ti alloys.Despite...Titanium(Ti)alloys are widely used in high-tech fields like aerospace and biomedical engineering.Laser additive manufacturing(LAM),as an innovative technology,is the key driver for the development of Ti alloys.Despite the significant advancements in LAM of Ti alloys,there remain challenges that need further research and development efforts.To recap the potential of LAM high-performance Ti alloy,this article systematically reviews LAM Ti alloys with up-to-date information on process,materials,and properties.Several feasible solutions to advance LAM Ti alloys are reviewed,including intelligent process parameters optimization,LAM process innovation with auxiliary fields and novel Ti alloys customization for LAM.The auxiliary energy fields(e.g.thermal,acoustic,mechanical deformation and magnetic fields)can affect the melt pool dynamics and solidification behaviour during LAM of Ti alloys,altering microstructures and mechanical performances.Different kinds of novel Ti alloys customized for LAM,like peritecticα-Ti,eutectoid(α+β)-Ti,hybrid(α+β)-Ti,isomorphousβ-Ti and eutecticβ-Ti alloys are reviewed in detail.Furthermore,machine learning in accelerating the LAM process optimization and new materials development is also outlooked.This review summarizes the material properties and performance envelops and benchmarks the research achievements in LAM of Ti alloys.In addition,the perspectives and further trends in LAM of Ti alloys are also highlighted.展开更多
Titanium alloys are excellent structural materials in engineering fields,but their poor tribological properties limit their further applications.Electroless plating is an effective method to enhance the tribological p...Titanium alloys are excellent structural materials in engineering fields,but their poor tribological properties limit their further applications.Electroless plating is an effective method to enhance the tribological performance of alloys,but it is difficult to efficiently apply to titanium alloys,due to titanium alloy’s strong chemical activity.In this work,the electroless Nickel-Boron(Ni-B)coating was successfully deposited on the surface of titanium alloy(Ti-6AL-4V)via a new pre-treatment process.Then,linearly reciprocating sliding wear tests were performed to evaluate the tribological behaviors of titanium alloy and its electroless Ni-B coatings.It was found that the Ni-B coatings can decrease the wear rate of the titanium alloy from 19.89×10^(−3)mm^(3)to 0.41×10^(−3)mm^(3),which attributes to the much higher hardness of Ni-B coatings.After heat treatment,the hardness of Ni-B coating further increases corresponding to coating crystallization and hard phase formation.However,heat treatment does not improve the tribological performance of Ni-B coating,due to the fact that higher brittleness and more severe oxidative wear exacerbate the damage of heat-treated coatings.Furthermore,the Ni-B coatings heat-treated both in air and nitrogen almost present the same tribological performance.The finding of this work on electroless coating would further extend the practical applications of titanium alloys in the engineering fields.展开更多
Characterization of hot deformation behavior of Ti-6Al-4V-0.5Ni-0.5Nb titanium alloy was investigated through isothermal compression at various temperatures from 750 to 1050℃and strain rate from 0.01 to 10 s^(-1).The...Characterization of hot deformation behavior of Ti-6Al-4V-0.5Ni-0.5Nb titanium alloy was investigated through isothermal compression at various temperatures from 750 to 1050℃and strain rate from 0.01 to 10 s^(-1).The isothermal compression experiment results showed that the peak stress of Ti-6Al-4V-0.5Ni-0.5Nb titanium alloy decreased with the temperature increasing and the strain rate decreasing.The softening mechanism was dynamic recovery below T_(β)and changed to dynamic recrystallization above T_(β).The arrheniustype relationship was used to calculate the constitutive equation of Ti-6Al-4V-0.5Ni-0.5Nb alloy in two-phase regions.It was found that the apparent activation energies were 427.095 kJ·mol^(-1)in theα+βphase region and 205.451 kJ·mol^(-1)in theβphase region,respectively.On the basis of dynamic materials model,the processing map is generated,which shows that the highest peak efficiency of power dissipation of 56%occurs at about 1050℃/0.01 s^(-1).It can be found in the processing maps that the strain had significant effect on the peak region of power dissipation efficiency of Ti-6Al-4V-0.5Ni-0.5Nb alloy.Furthermore,optimized hot working regions were investigated and validated through microstructure observation.The optimum thermo mechanical process condition for hot working of Ti-6Al-4V-0.5Ni-0.5Nb titanium alloy was suggested to be in the temperature range of 950-1000℃with a strain rate of 0.01-0.1 s^(-1).展开更多
A new rhombohedral phase(termed R′)in a solution-aging-treated titanium alloy(Ti-4.5Al-6.5Mo-2Cr-2Nb-1V-1Sn-1Zr,wt.%)was identified.Its accurate Bravais lattice parameters were determined by a novel unit cell reconst...A new rhombohedral phase(termed R′)in a solution-aging-treated titanium alloy(Ti-4.5Al-6.5Mo-2Cr-2Nb-1V-1Sn-1Zr,wt.%)was identified.Its accurate Bravais lattice parameters were determined by a novel unit cell reconstruction method based on conventional selected-area electron diffraction(SAED)technique.The orientation relationship between R'phase and BCC phase was revealed.The results show that the R′phase is found to have 48crystallographically equivalent variants,resulting in rather complicated SAED patterns with high-order reflections.A series of in-situ SAED patterns were taken along both low-and high-index zone axes,and all weak and strong reflections arising from the 48 variants were properly explained and directly assigned with self-consistent Miller indices,confirming the presence of the rhombohedral phase.Additionally,some criteria were also proposed for evaluating the indexed results,which together with the Bravais lattice reconstruction method shed light on the microstructure characterization of even unknown phases in other alloys.展开更多
Hot deformation of sintered billets by powder metallurgy(PM)is an effective preparation technique for titanium alloys,which is more significant for high-alloying alloys.In this study,Ti–6.5Al–2Zr–Mo–V(TA15)titaniu...Hot deformation of sintered billets by powder metallurgy(PM)is an effective preparation technique for titanium alloys,which is more significant for high-alloying alloys.In this study,Ti–6.5Al–2Zr–Mo–V(TA15)titanium alloy plates were prepared by cold press-ing sintering combined with high-temperature hot rolling.The microstructure and mechanical properties under different process paramet-ers were investigated.Optical microscope,electron backscatter diffraction,and others were applied to characterize the microstructure evolution and mechanical properties strengthening mechanism.The results showed that the chemical compositions were uniformly dif-fused without segregation during sintering,and the closing of the matrix craters was accelerated by increasing the sintering temperature.The block was hot rolled at 1200℃ with an 80%reduction under only two passes without annealing.The strength and elongation of the plate at 20–25℃ after solution and aging were 1247 MPa and 14.0%,respectively,which were increased by 24.5%and 40.0%,respect-ively,compared with the as-sintered alloy at 1300℃.The microstructure was significantly refined by continuous dynamic recrystalliza-tion,which was completed by the rotation and dislocation absorption of the substructure surrounded by low-angle grain boundaries.After hot rolling combined with heat treatment,the strength and plasticity of PM-TA15 were significantly improved,which resulted from the dense,uniform,and fine recrystallization structure and the synergistic effect of multiple slip systems.展开更多
In this study,a novel strategy for developingα+βdual-phase titanium alloys with low Young's modulus and high yield strength was proposed,and a Ti-15Nb-5Zr-4Sn-1 Fe alloy was developed through theoretical composi...In this study,a novel strategy for developingα+βdual-phase titanium alloys with low Young's modulus and high yield strength was proposed,and a Ti-15Nb-5Zr-4Sn-1 Fe alloy was developed through theoretical composition design and microstructure manipulation.After hot-rolling and subsequent annealing,a high volume fraction of ultrafine grainedαphase embedded in metastableβ-matrix was formed in the microstructure as intended.Consequently,this alloy exhibits both low Young's modulus(61 GPa)and high yield strength(912 MPa).The experimental results prove that the proposed strategy is appropriate for developing titanium alloys with superior yield strength-to-modulus ratio than those of conventional metallic biomedical materials.Present study might shed light on the research and development of advanced biomedical titanium alloys with low Young's modulus and high yield strength.展开更多
Titanium alloy has been applied in the field of aerospace manufacturing for its high specific strength and hardness.Nonetheless,these properties also cause general problems in the machining,such as processing ineffici...Titanium alloy has been applied in the field of aerospace manufacturing for its high specific strength and hardness.Nonetheless,these properties also cause general problems in the machining,such as processing inefficiency,serious wear,poor workpiece face quality,etc.Aiming at the above problems,this paper carried out a comparative experimental study on titanium alloy milling based on the CAMCand BEMC.The variation law of cutting force and wear morphology of the two tools were obtained,and the wear mechanism and the effect of wear on machining quality were analyzed.The conclusion is that in contrast with BEMC,under the action of cutting thickness thinning mechanism,the force of CAMC was less,and its fluctuation was more stable.The flank wear was uniform and near the cutting edge,and the wear rate was slower.In the early period,the wear mechanism of CAMC was mainly adhesion.Gradually,oxidative wear also occurred with milling.Furthermore,the surface residual height of CAMC was lower.There is no obvious peak and trough accompanied by fewer surface defects.展开更多
Hot isostatic pressing parameters are critical to Ti60 high temperature titanium alloy castings which have wide application perspective in aerospace.In order to obtain optimal processing parameters,the effects of hot ...Hot isostatic pressing parameters are critical to Ti60 high temperature titanium alloy castings which have wide application perspective in aerospace.In order to obtain optimal processing parameters,the effects of hot isostatic pressing parameters on defects,composition uniformity,microstructure and mechanical properties of Ti60 cast high temperature titanium alloy were investigated in detail.Results show that increasing temperature and pressure of hot isostatic pressing can reduce defects,especially,the internal defects are substantially eliminated when the temperature exceeds 920℃or the pressure exceeds 125 MPa.The higher temperature and pressure can improve the microstructure uniformity.Besides,the higher pressure can promote the composition uniformity.With the temperature increases from 880℃to 960℃,α-laths are coarsened.But with increasing pressure,the grain size of prior-βphase,the widths ofα-laths andα-colony are reduced.The tensile strength of Ti60 alloy is 949 MPa,yield strength is 827 MPa,and the elongation is 11%when the hot isostatic pressing parameters are 960℃/125 MPa/2 h,which exhibits the best match between the strength and plasticity.展开更多
Acetabular cups,which are among themost important implants in total hip arthroplasty,are usually made from titanium alloys with high porosity and adequate mechanical properties.The current three-dimensional(3D)printin...Acetabular cups,which are among themost important implants in total hip arthroplasty,are usually made from titanium alloys with high porosity and adequate mechanical properties.The current three-dimensional(3D)printing approaches to fabricate customized acetabular cups have some inherent disadvantages such as high cost and energy consumption,residual thermal stress,and relatively low efficiency.Thus,in this work,a direct ink writing method was developed to print a cup structure at room temperature,followed by multi-step heat treatment to form microscale porous structure within the acetabular cup.Our method is facilitated by the development of a self-supporting titanium-6 aluminum-4 vanadium(Ti64)ink that is composed of Ti64 particles,bentonite yield-stress additive,ultraviolet curable polymer,and photo-initiator.The effects of Ti64 and bentonite concentrations on the rheological properties and printability of inks were systematically investigated.Moreover,the printing conditions,geometrical limitations,and maximum curing depth were explored.Finally,some complex 3D structures,including lattices with different gap distances,honeycomb with a well-defined shape,and an acetabular cup with uniformly distributed micropores,were successfully printed/fabricated to validate the effectiveness of the proposed method.展开更多
The evolution of the microstructure and tensile properties of dual-phase Al0.6CoCrFeNi high-entropy alloys(HEAs)subjected to cold rolling was investigated.The homogenized Al0.6CoCrFeNi alloys consisted of face-centere...The evolution of the microstructure and tensile properties of dual-phase Al0.6CoCrFeNi high-entropy alloys(HEAs)subjected to cold rolling was investigated.The homogenized Al0.6CoCrFeNi alloys consisted of face-centered-cubic and body-centered-cubic phases,presenting similar mechanical behavior as the as-cast state.The yield and tensile strengths of the alloys could be dramatically enhanced to^1205 MPa and^1318 MPa after 50%rolling reduction,respectively.A power-law relationship was discovered between the strain-hardening exponent and rolling reduction.The tensile strengths of this dual-phase HEA with different cold rolling treatments were predicted,mainly based on the Hollomon relationship,by the strain-hardening exponent,and showed good agreement with the experimental results.展开更多
An accurate flow stress model was established by considering the parameters of strain rate,strain and temperature as well asβ→a+βphase transformation in order to develop the plastic forming theory of TC18 titanium ...An accurate flow stress model was established by considering the parameters of strain rate,strain and temperature as well asβ→a+βphase transformation in order to develop the plastic forming theory of TC18 titanium alloy.Firstly,the phase transition kinetics of TC18 titanium alloy during isothermal and continuous cooling at 1073 and 1273 K was studied by thermodynamic calculation,meanwhile,the relationship of volume fraction of phase transition with temperature and time was obtained.Constitutive models were calculated by investigating flow behaviors under hot compression tests with the strain rates of 0.001-1s^(-1) and temperatures of 973-1223 K in the singleβand a+βregions in TC18 titanium alloy,respectively.By combining the phase transformation dynamic kinetics with constitutive models,an accurate flow stress model was established,providing theoretical basis and data support for the hot forging of TC18 titanium alloy.展开更多
The microstructure and mechanical properties of the TB8 titanium alloy were controlled by a secondary processing technology of solution-equal channel angular pressing(ECAP)-aging treatment,which combined strong plasti...The microstructure and mechanical properties of the TB8 titanium alloy were controlled by a secondary processing technology of solution-equal channel angular pressing(ECAP)-aging treatment,which combined strong plastic deformation with heat treatment. The effects of ECAP and heat treatment on the microstructure and properties of the titanium alloy were systematically investigated by optical microscopy(OM), scanning electron microscopy(SEM), hardness tests, and tensile property analysis. The results indicate that the metallographic structure without ECAP treatment is mainly equiaxed β-phase, while that after ECAP treatment is equiaxed β-phase with grain fragmentation, slip bands, and new small grains. After 850 ℃ solutionECAP-520 ℃ aging treatment, the titanium alloy has the smallest grain size, while the directionality of tissue growth along the ECAP direction is the most apparent. Under the same solution-aging conditions, the hardness of the titanium alloy increases from 431.5 to 531.2 HV compared to that without ECAP treatment, i e, increases by 23.11%, and the tensile strength increases from 1 045.30 to 1 176.25 MPa, i e, increases by 12.5%.展开更多
As an important green manufacturing process,dry grinding has problems such as high grinding temperature and insufficient cooling capacity.Aiming at the problems of sticking and burns in dry grinding of titanium alloys...As an important green manufacturing process,dry grinding has problems such as high grinding temperature and insufficient cooling capacity.Aiming at the problems of sticking and burns in dry grinding of titanium alloys,grinding performance evaluation of molybdenum disulfide(MoS_(2))solid lubricant coated brazed cubic boron carbide(CBN)grinding wheel(MoS_(2)-coated CBN wheel)in dry grinding titanium alloys was carried out.The lubrication mechanism of MoS_(2)in the grinding process is analyzed,and the MoS_(2)-coated CBN wheel is prepared.The results show that the MoS_(2)solid lubricant can form a lubricating film on the ground surface and reduce the friction coefficient and grinding force.Within the experimental parameters,normal grinding force decreased by 42.5%,and tangential grinding force decreased by 28.1%.MoS_(2)lubricant can effectively improve the heat dissipation effect of titanium alloy grinding arc area.Compared with common CBN grinding wheel,MoS_(2)-coated CBN wheel has lower grinding temperature.When the grinding depth reaches 20μm,the grinding temperature decreased by 30.5%.The wear of CBN grains of grinding wheel were analyzed by mathematical statistical method.MoS_(2)lubricating coating can essentially decrease the wear of grains,reduce the adhesion of titanium alloy chip,prolong the service life of grinding wheel,and help to enhance the surface quality of workpiece.This research provides high-quality and efficient technical support for titanium alloy grinding.展开更多
Hardness tests and transmission electron microscopy were used to investigate the strategy of tailoring the phase fraction of precipitates in an Al-Zn-Mg-Cu alloy strengthened by T’ and η’ phases. Different phase fr...Hardness tests and transmission electron microscopy were used to investigate the strategy of tailoring the phase fraction of precipitates in an Al-Zn-Mg-Cu alloy strengthened by T’ and η’ phases. Different phase fractions of T’ and η’ phases are presented in samples subjected to either single or two stages of ageing treatments at 120 and 150 ℃.For both types of ageing, the precipitation of η’ phase is found to be promoted by ageing at lower temperature and its phase fraction increases with prolonging ageing time at 120 ℃;whereas the phase fractions of T’ and η’ phases almost remain constant during ageing at 150 ℃. Besides, the strain fields produced by T’ and η’ phases were analyzed by using the geometric phase analysis technique, and on a macroscale the contributions of T’ and η’ phases to precipitation strengthening have been quantitatively predicted by combining the size, phase fraction and number density of precipitates.展开更多
基金the National Key Research and Development Program of China(No.2021YFB3702603).
文摘A crystal plasticity finite element(CPFE)model was established and 2D simulations were carried out to study the relationship between microvoids and the microplasticity deformation behavior of the dual-phase titanium alloy under high cyclic loading.Results show that geometrically necessary dislocations(GND)tend to accumulate around the microvoids,leading to an increment of average GND density.The influence of curvature in the tip plastic zone(TPZ)on GND density is greater than that of the size of the microvoid.As the curvature in TPZ and the size of the microvoid increase,the cumulative shear strain(CSS)in the primaryα,secondaryα,andβphases increases.Shear deformation in the prismatic slip system is dominant in the primaryαphase.As the distance between the microvoids increases,the interactive influence of the microvoids on the cumulative shear strain decreases.
基金This work was financially supported by the National Natural Science Foundation of China(Nos.51901102 and 52101005).
文摘In order to accelerate the research on the property optimization of titanium alloy based on high-throughput methods,it is necessary to reveal the relationship between hardness and other mechanical properties which is still unclear.In this work,taking Ti20C alloy as research object,almost all the microstructure of dual-phase titanium alloys were covered by traversing over 100 heat treatment schemes.Then,massive experiments including microstructure characterization and performance test were conducted,obtaining 51,590 pieces of microstructure data and 3591 pieces of mechanical property data.Subsequently,based on large-scale data-driven technology,the quantitative mapping relationship between hardness and other mechanical properties was deeply discussed.The results of random forest models showed that the correlation between hardness(H)and Charpy impact energy(A_(k))(or elongation,A)was hardly dependent on the microstructure types,while the relationship between H and tensile strength(R_(m))(or yield strength,R_(p0.2))was highly dependent on microstructure types.Specifically,combined with statistical analysis,it was found that the relationship between H and Ak(or A)were negatively linear.Interestingly,the relationship between H and strength was positively linear for equiaxed microstructure,and strength was linked to d^(−1/2)(d,equivalent circle diameter)ofα-grains in the form of classical Hall–Petch formula;but for other microstructures,the relationships were quadratic.Furthermore,the above rules were nearly the same in the rolling direction and transverse direction.Finally,a"four-quadrant partition map"between H and R_(p0.2)/R_(m) was established as a versatile material-screening tool,which can provide guidance for on-demand selection of titanium alloys.
基金supported by the National Natural Science Foundation of China(No.92160301)the Industrial Technology Development Program,China(No.JCKY2021605 B026)。
文摘The Ti-5Al-2Sn-4Zr-4Mo-2Cr-1Fe(β-CEZ)alloy is considered as a potential structural material in the aviation industry due to its outstanding strength and corrosion resistance.Electrochemical machining(ECM)is an efficient and low-cost technology for manufacturing theβ-CEZ alloy.In ECM,the machining parameter selection and tool design are based on the electrochemical dissolution behavior of the materials.In this study,the electrochemical dissolution behaviors of theβ-CEZ and Ti-6Al-4V(TC4)alloys in NaNO3solution are discussed.The open circuit potential(OCP),Tafel polarization,potentiodynamic polarization,electrochemical impedance spectroscopy(EIS),and current efficiency curves of theβ-CEZ and TC4 alloys are analyzed.The results show that,compared to the TC4 alloy,the passivation film structure is denser and the charge transfer resistance in the dissolution process is greater for theβ-CEZ alloy.Moreover,the dissolved surface morphology of the two titanium-based alloys under different current densities are analyzed.Under low current densities,theβ-CEZ alloy surface comprises dissolution pits and dissolved products,while the TC4 alloy surface comprises a porous honeycomb structure.Under high current densities,the surface waviness of both the alloys improves and the TC4 alloy surface is flatter and smoother than theβ-CEZ alloy surface.Finally,the electrochemical dissolution models ofβ-CEZ and TC4 alloys are proposed.
基金F.Guo thanks for the support of Chongqing Research Program of Basic Research and Frontier Technology Scientific Research(cstc2019jcyj-msxmX0111)University Innovation Research Group of Chongqing(CXQT20023)+1 种基金Scientific Research Foundation of Chongqing University of Technology(2017ZD35)L.Y.Jiang is sponsored by Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN201901127).
文摘Dual-phase Mg-Li alloys sheets were rolled at four different temperatures ranging from liquid nitrogen to 300℃to explore effect of rolling temperature on texture and mechanical properties of the material.Crystal plasticity simulation was utilized to illustrate the influence of slip activity on rolling texture development.The results show that the rolling texture is largely depended on deformation temperature.Unlike commercial Mg alloys,the critical resolved shear stress of basal slip inα-Mg phase of Mg-Li alloy decreased more significantly by increasing temperature compared to that of pyramidal<c+a>slip.Enhancement of basal slip by increasing temperature triggered a decrease of split angle of basal poles for the double-peak texture.Prismaticslip largely enhanced by increasing temperature upon 200℃,which induced a wider orientation spread along the transverse direction.For theβ-Li phase,the promotion of{110}<111>slip system at elevated temperature triggered the enhancement of{211}<110>and{111}<211>texture components.The cryo-rolled sample exhibited the highest strength compared to the others due to a strong hardening behavior at this temperature.A two-stage hardening behavior was observed in these as-rolled dual-phase alloys.Strain transition at phase boundaries could be the reason for appearance of this two-stage hardening.
基金Funded by the National Natural Science Foundation of China(No.52071252)the Key Research and Development Plan of Shaanxi Province Industrial Project(Nos.2021GY-208,2022GY-407,and 2021ZDLSF03-11)the China Postdoctoral Science Foundation(No.2020M683670XB)。
文摘Magnetron sputtering deposition with regulated Cu target power was used for depositing Cu-containing high-entropy alloy nitride(Cu-(HEA)N)films on TC4 titanium alloy substrates.The microscopic morphologies,surface compositions,and thicknesses of the films were characterized using SEM+EDS;the anti-corrosion,wear resistance and antibacterial properties of the films in simulated seawater were investigated.The experimental results show that all four Cu-(HEA)N films are uniformly dense and contained nanoparticles.The film with Cu doping come into contact with oxygen in the air to form cuprous oxide.The corrosion resistance of the(HEA)N film without Cu doping on titanium alloy is better than the films with Cu doping.The Cu-(HEA)N film with Cu target power of 16 W shows the best wear resistance and antibacterial performance,which is attributed to the fact that Cu can reduce the coefficient of friction and exacerbate corrosion,and the formation of cuprous oxide has antibacterial properties.The findings of this study provide insights for engineering applications of TC4 in the marine field.
基金financially supported by the CityU internal supports under “The Structural Material Development Funding” program (No. CityU 7004894)National Natural Science Foundation of China (Nos. 51901086 and 51731006)Natural Science Foundation of Jiangsu Province, China (Nos. BK20190977 and BK 20180984)。
文摘To clarify the correlation of single-crystalline structure with corrosion performance in high-strength TiAl alloys, electrochemical and surface characterization was performed by comparing Ti–45Al–8Nb dual-phase single crystals with their polycrystalline counterparts in NaCl solution. Polarization curves show a lower corrosion rate and a higher pitting potential of ~280 mV for the dual-phase single crystals. Electrochemical impedance spectroscopy and potentiostatic polarization plots revealed a higher impedance of the charge transfer through the compact passive film. Surface composition analysis indicated a compact film with more content of Nb, as twice as that in the film on the polycrystals.Our results reflect that the dual-phase Ti–45Al–8Nb single crystals possess a higher corrosion resistance in NaCl solution, compared with their polycrystalline counterpart, arising from a more homogeneous microstructure and composition distribution.
基金financially supported by the Young Individual Research Grants(Grant No:M22K3c0097)Singapore RIE 2025 plan and Singapore Aerospace Programme Cycle 16(Grant No:M2215a0073)led by C Tan+2 种基金supported by the Singapore A*STAR Career Development Funds(Grant No:C210812047)the National Natural Science Foundation of China(52174361 and 52374385)the support by US NSF DMR-2104933。
文摘Titanium(Ti)alloys are widely used in high-tech fields like aerospace and biomedical engineering.Laser additive manufacturing(LAM),as an innovative technology,is the key driver for the development of Ti alloys.Despite the significant advancements in LAM of Ti alloys,there remain challenges that need further research and development efforts.To recap the potential of LAM high-performance Ti alloy,this article systematically reviews LAM Ti alloys with up-to-date information on process,materials,and properties.Several feasible solutions to advance LAM Ti alloys are reviewed,including intelligent process parameters optimization,LAM process innovation with auxiliary fields and novel Ti alloys customization for LAM.The auxiliary energy fields(e.g.thermal,acoustic,mechanical deformation and magnetic fields)can affect the melt pool dynamics and solidification behaviour during LAM of Ti alloys,altering microstructures and mechanical performances.Different kinds of novel Ti alloys customized for LAM,like peritecticα-Ti,eutectoid(α+β)-Ti,hybrid(α+β)-Ti,isomorphousβ-Ti and eutecticβ-Ti alloys are reviewed in detail.Furthermore,machine learning in accelerating the LAM process optimization and new materials development is also outlooked.This review summarizes the material properties and performance envelops and benchmarks the research achievements in LAM of Ti alloys.In addition,the perspectives and further trends in LAM of Ti alloys are also highlighted.
基金Supported by Sichuan Provincial Science and Technology Program of China(Grant No.2018JY0245)National Natural Science Foundation of China(Grant No.51975492)Natural Science Foundation of Southwest University of Science and Technology of China(Grant No.19xz7163).
文摘Titanium alloys are excellent structural materials in engineering fields,but their poor tribological properties limit their further applications.Electroless plating is an effective method to enhance the tribological performance of alloys,but it is difficult to efficiently apply to titanium alloys,due to titanium alloy’s strong chemical activity.In this work,the electroless Nickel-Boron(Ni-B)coating was successfully deposited on the surface of titanium alloy(Ti-6AL-4V)via a new pre-treatment process.Then,linearly reciprocating sliding wear tests were performed to evaluate the tribological behaviors of titanium alloy and its electroless Ni-B coatings.It was found that the Ni-B coatings can decrease the wear rate of the titanium alloy from 19.89×10^(−3)mm^(3)to 0.41×10^(−3)mm^(3),which attributes to the much higher hardness of Ni-B coatings.After heat treatment,the hardness of Ni-B coating further increases corresponding to coating crystallization and hard phase formation.However,heat treatment does not improve the tribological performance of Ni-B coating,due to the fact that higher brittleness and more severe oxidative wear exacerbate the damage of heat-treated coatings.Furthermore,the Ni-B coatings heat-treated both in air and nitrogen almost present the same tribological performance.The finding of this work on electroless coating would further extend the practical applications of titanium alloys in the engineering fields.
基金Funded by the National Key R&D Program of China(Nos.2021YFB3700804,2021YFB3700803)Shaanxi Provincial Innovation Capability Support Plan(No.2023KJXX-091)。
文摘Characterization of hot deformation behavior of Ti-6Al-4V-0.5Ni-0.5Nb titanium alloy was investigated through isothermal compression at various temperatures from 750 to 1050℃and strain rate from 0.01 to 10 s^(-1).The isothermal compression experiment results showed that the peak stress of Ti-6Al-4V-0.5Ni-0.5Nb titanium alloy decreased with the temperature increasing and the strain rate decreasing.The softening mechanism was dynamic recovery below T_(β)and changed to dynamic recrystallization above T_(β).The arrheniustype relationship was used to calculate the constitutive equation of Ti-6Al-4V-0.5Ni-0.5Nb alloy in two-phase regions.It was found that the apparent activation energies were 427.095 kJ·mol^(-1)in theα+βphase region and 205.451 kJ·mol^(-1)in theβphase region,respectively.On the basis of dynamic materials model,the processing map is generated,which shows that the highest peak efficiency of power dissipation of 56%occurs at about 1050℃/0.01 s^(-1).It can be found in the processing maps that the strain had significant effect on the peak region of power dissipation efficiency of Ti-6Al-4V-0.5Ni-0.5Nb alloy.Furthermore,optimized hot working regions were investigated and validated through microstructure observation.The optimum thermo mechanical process condition for hot working of Ti-6Al-4V-0.5Ni-0.5Nb titanium alloy was suggested to be in the temperature range of 950-1000℃with a strain rate of 0.01-0.1 s^(-1).
基金financial supports from the National Natural Science Foundation of China(No.51071125)the Major Project of Department of Education of Jiangxi Province,China(No.GJJ210605)。
文摘A new rhombohedral phase(termed R′)in a solution-aging-treated titanium alloy(Ti-4.5Al-6.5Mo-2Cr-2Nb-1V-1Sn-1Zr,wt.%)was identified.Its accurate Bravais lattice parameters were determined by a novel unit cell reconstruction method based on conventional selected-area electron diffraction(SAED)technique.The orientation relationship between R'phase and BCC phase was revealed.The results show that the R′phase is found to have 48crystallographically equivalent variants,resulting in rather complicated SAED patterns with high-order reflections.A series of in-situ SAED patterns were taken along both low-and high-index zone axes,and all weak and strong reflections arising from the 48 variants were properly explained and directly assigned with self-consistent Miller indices,confirming the presence of the rhombohedral phase.Additionally,some criteria were also proposed for evaluating the indexed results,which together with the Bravais lattice reconstruction method shed light on the microstructure characterization of even unknown phases in other alloys.
基金supported by the National Natural Science Foundation of China(No.52274359)Guangdong Basic and Applied Basic Research Foundation,China(No.2022A1515110406)+3 种基金Beijing Natural Science Foundation,China(No.2212035)the Fundamental Research Funds for the Central Universities,China(Nos.FRF-TP-19005C1Z and 00007718)the Aeroengine Group University Research Cooperation Project,China(No.HFZL2021CXY021)the State Key Lab of Advanced Metals and Materials,University of Science and Technology Beijing,China(Nos.2021Z-03 and 2022Z-14).
文摘Hot deformation of sintered billets by powder metallurgy(PM)is an effective preparation technique for titanium alloys,which is more significant for high-alloying alloys.In this study,Ti–6.5Al–2Zr–Mo–V(TA15)titanium alloy plates were prepared by cold press-ing sintering combined with high-temperature hot rolling.The microstructure and mechanical properties under different process paramet-ers were investigated.Optical microscope,electron backscatter diffraction,and others were applied to characterize the microstructure evolution and mechanical properties strengthening mechanism.The results showed that the chemical compositions were uniformly dif-fused without segregation during sintering,and the closing of the matrix craters was accelerated by increasing the sintering temperature.The block was hot rolled at 1200℃ with an 80%reduction under only two passes without annealing.The strength and elongation of the plate at 20–25℃ after solution and aging were 1247 MPa and 14.0%,respectively,which were increased by 24.5%and 40.0%,respect-ively,compared with the as-sintered alloy at 1300℃.The microstructure was significantly refined by continuous dynamic recrystalliza-tion,which was completed by the rotation and dislocation absorption of the substructure surrounded by low-angle grain boundaries.After hot rolling combined with heat treatment,the strength and plasticity of PM-TA15 were significantly improved,which resulted from the dense,uniform,and fine recrystallization structure and the synergistic effect of multiple slip systems.
基金the National Natural Science Foundation of China(Nos.51671012,51831006 and 51971009)the International Science and Technology Cooperation Program of China(No.2015DFA51430)the Fundamental Research Funds for the Central Universities。
文摘In this study,a novel strategy for developingα+βdual-phase titanium alloys with low Young's modulus and high yield strength was proposed,and a Ti-15Nb-5Zr-4Sn-1 Fe alloy was developed through theoretical composition design and microstructure manipulation.After hot-rolling and subsequent annealing,a high volume fraction of ultrafine grainedαphase embedded in metastableβ-matrix was formed in the microstructure as intended.Consequently,this alloy exhibits both low Young's modulus(61 GPa)and high yield strength(912 MPa).The experimental results prove that the proposed strategy is appropriate for developing titanium alloys with superior yield strength-to-modulus ratio than those of conventional metallic biomedical materials.Present study might shed light on the research and development of advanced biomedical titanium alloys with low Young's modulus and high yield strength.
基金Supported by National Natural Science Foundation of China(Grant No.51975168).
文摘Titanium alloy has been applied in the field of aerospace manufacturing for its high specific strength and hardness.Nonetheless,these properties also cause general problems in the machining,such as processing inefficiency,serious wear,poor workpiece face quality,etc.Aiming at the above problems,this paper carried out a comparative experimental study on titanium alloy milling based on the CAMCand BEMC.The variation law of cutting force and wear morphology of the two tools were obtained,and the wear mechanism and the effect of wear on machining quality were analyzed.The conclusion is that in contrast with BEMC,under the action of cutting thickness thinning mechanism,the force of CAMC was less,and its fluctuation was more stable.The flank wear was uniform and near the cutting edge,and the wear rate was slower.In the early period,the wear mechanism of CAMC was mainly adhesion.Gradually,oxidative wear also occurred with milling.Furthermore,the surface residual height of CAMC was lower.There is no obvious peak and trough accompanied by fewer surface defects.
基金financially supported by the National Key Research and Development Program of China(Grant No.2020YFB2008300)。
文摘Hot isostatic pressing parameters are critical to Ti60 high temperature titanium alloy castings which have wide application perspective in aerospace.In order to obtain optimal processing parameters,the effects of hot isostatic pressing parameters on defects,composition uniformity,microstructure and mechanical properties of Ti60 cast high temperature titanium alloy were investigated in detail.Results show that increasing temperature and pressure of hot isostatic pressing can reduce defects,especially,the internal defects are substantially eliminated when the temperature exceeds 920℃or the pressure exceeds 125 MPa.The higher temperature and pressure can improve the microstructure uniformity.Besides,the higher pressure can promote the composition uniformity.With the temperature increases from 880℃to 960℃,α-laths are coarsened.But with increasing pressure,the grain size of prior-βphase,the widths ofα-laths andα-colony are reduced.The tensile strength of Ti60 alloy is 949 MPa,yield strength is 827 MPa,and the elongation is 11%when the hot isostatic pressing parameters are 960℃/125 MPa/2 h,which exhibits the best match between the strength and plasticity.
基金supported by the Micro Grant (PG20473) at the University of Nevada, Reno, USA
文摘Acetabular cups,which are among themost important implants in total hip arthroplasty,are usually made from titanium alloys with high porosity and adequate mechanical properties.The current three-dimensional(3D)printing approaches to fabricate customized acetabular cups have some inherent disadvantages such as high cost and energy consumption,residual thermal stress,and relatively low efficiency.Thus,in this work,a direct ink writing method was developed to print a cup structure at room temperature,followed by multi-step heat treatment to form microscale porous structure within the acetabular cup.Our method is facilitated by the development of a self-supporting titanium-6 aluminum-4 vanadium(Ti64)ink that is composed of Ti64 particles,bentonite yield-stress additive,ultraviolet curable polymer,and photo-initiator.The effects of Ti64 and bentonite concentrations on the rheological properties and printability of inks were systematically investigated.Moreover,the printing conditions,geometrical limitations,and maximum curing depth were explored.Finally,some complex 3D structures,including lattices with different gap distances,honeycomb with a well-defined shape,and an acetabular cup with uniformly distributed micropores,were successfully printed/fabricated to validate the effectiveness of the proposed method.
基金the Natural Science Foundation of Shanxi Province,China(Nos.201901D111105 and 201901D111114)Transformation of Scientific and Technological Achievements Programs of Higher Education Institutions in Shanxi Province,China(2019)+2 种基金the Opening Project of the State Key Laboratory of Explosion Science and Technology(Beijing Institute of Technology)(No.KFJJ20-13M)the Graduate Science and Technology Innovation Fund Project of Shanxi Province,China(No.2019BY044)the State Key Lab of Advanced Metals and Materials of China(No.2020-Z09).
文摘The evolution of the microstructure and tensile properties of dual-phase Al0.6CoCrFeNi high-entropy alloys(HEAs)subjected to cold rolling was investigated.The homogenized Al0.6CoCrFeNi alloys consisted of face-centered-cubic and body-centered-cubic phases,presenting similar mechanical behavior as the as-cast state.The yield and tensile strengths of the alloys could be dramatically enhanced to^1205 MPa and^1318 MPa after 50%rolling reduction,respectively.A power-law relationship was discovered between the strain-hardening exponent and rolling reduction.The tensile strengths of this dual-phase HEA with different cold rolling treatments were predicted,mainly based on the Hollomon relationship,by the strain-hardening exponent,and showed good agreement with the experimental results.
基金Funded by the National Natural Science Foundation of China(No.52075058)the Natural Science Foundation of Chongqing(No.cstc2021jcyj-msxmX1112)the Research and Demonstration of Key Technologies for Forging High-performance Aluminum Alloys for Aerospace Applications(No.Z20210348)。
文摘An accurate flow stress model was established by considering the parameters of strain rate,strain and temperature as well asβ→a+βphase transformation in order to develop the plastic forming theory of TC18 titanium alloy.Firstly,the phase transition kinetics of TC18 titanium alloy during isothermal and continuous cooling at 1073 and 1273 K was studied by thermodynamic calculation,meanwhile,the relationship of volume fraction of phase transition with temperature and time was obtained.Constitutive models were calculated by investigating flow behaviors under hot compression tests with the strain rates of 0.001-1s^(-1) and temperatures of 973-1223 K in the singleβand a+βregions in TC18 titanium alloy,respectively.By combining the phase transformation dynamic kinetics with constitutive models,an accurate flow stress model was established,providing theoretical basis and data support for the hot forging of TC18 titanium alloy.
基金the Key R&D Plan of Zhenjiang in 2018 (No.GY2018021)。
文摘The microstructure and mechanical properties of the TB8 titanium alloy were controlled by a secondary processing technology of solution-equal channel angular pressing(ECAP)-aging treatment,which combined strong plastic deformation with heat treatment. The effects of ECAP and heat treatment on the microstructure and properties of the titanium alloy were systematically investigated by optical microscopy(OM), scanning electron microscopy(SEM), hardness tests, and tensile property analysis. The results indicate that the metallographic structure without ECAP treatment is mainly equiaxed β-phase, while that after ECAP treatment is equiaxed β-phase with grain fragmentation, slip bands, and new small grains. After 850 ℃ solutionECAP-520 ℃ aging treatment, the titanium alloy has the smallest grain size, while the directionality of tissue growth along the ECAP direction is the most apparent. Under the same solution-aging conditions, the hardness of the titanium alloy increases from 431.5 to 531.2 HV compared to that without ECAP treatment, i e, increases by 23.11%, and the tensile strength increases from 1 045.30 to 1 176.25 MPa, i e, increases by 12.5%.
基金Supported by National Natural Science Foundation of China(Grant Nos.92160301,92060203,52175415,52205475)Science Center for Gas Turbine Project of China(Grant Nos.P2022-AB-IV-002-001,P2023-B-IV-003-001)+1 种基金Jiangsu Provincial Natural Science Foundation of China(Grant No.BK20210295)Graduate Research and Innovation Projects in Jiangsu Province of China(Grant No.KYCX22_0339).
文摘As an important green manufacturing process,dry grinding has problems such as high grinding temperature and insufficient cooling capacity.Aiming at the problems of sticking and burns in dry grinding of titanium alloys,grinding performance evaluation of molybdenum disulfide(MoS_(2))solid lubricant coated brazed cubic boron carbide(CBN)grinding wheel(MoS_(2)-coated CBN wheel)in dry grinding titanium alloys was carried out.The lubrication mechanism of MoS_(2)in the grinding process is analyzed,and the MoS_(2)-coated CBN wheel is prepared.The results show that the MoS_(2)solid lubricant can form a lubricating film on the ground surface and reduce the friction coefficient and grinding force.Within the experimental parameters,normal grinding force decreased by 42.5%,and tangential grinding force decreased by 28.1%.MoS_(2)lubricant can effectively improve the heat dissipation effect of titanium alloy grinding arc area.Compared with common CBN grinding wheel,MoS_(2)-coated CBN wheel has lower grinding temperature.When the grinding depth reaches 20μm,the grinding temperature decreased by 30.5%.The wear of CBN grains of grinding wheel were analyzed by mathematical statistical method.MoS_(2)lubricating coating can essentially decrease the wear of grains,reduce the adhesion of titanium alloy chip,prolong the service life of grinding wheel,and help to enhance the surface quality of workpiece.This research provides high-quality and efficient technical support for titanium alloy grinding.
基金supports from the National Natural Science Foundation of China(No.51871033).
文摘Hardness tests and transmission electron microscopy were used to investigate the strategy of tailoring the phase fraction of precipitates in an Al-Zn-Mg-Cu alloy strengthened by T’ and η’ phases. Different phase fractions of T’ and η’ phases are presented in samples subjected to either single or two stages of ageing treatments at 120 and 150 ℃.For both types of ageing, the precipitation of η’ phase is found to be promoted by ageing at lower temperature and its phase fraction increases with prolonging ageing time at 120 ℃;whereas the phase fractions of T’ and η’ phases almost remain constant during ageing at 150 ℃. Besides, the strain fields produced by T’ and η’ phases were analyzed by using the geometric phase analysis technique, and on a macroscale the contributions of T’ and η’ phases to precipitation strengthening have been quantitatively predicted by combining the size, phase fraction and number density of precipitates.