Determination Of Atomic Diffusion Coefficient Of Powder Densification And Its Numerical Simulation

Powder sintering is a kind of preparation technology which uses heat energy to condense powder particles into bulk materials.Densification plays an important role in powder sintering,which directly affects the porosity,pore distribution,grain size,defect content,especially dislocation density,and thus the micro structure and causative performance of the final bulk materials.For powder sintering with specific alloy composition,the microstructure and density of the sintered bulk alloys largely depend on the densification mechanism dominated by the powder physical properties and process parameters.The influencing factors related to densification kinetics,such as densification rate,viscous flow activation energy Qvis,stress sensitivity index n,and deformation activation energy Qdem,can reflect densification behavior and kinetics to a certain extent.In essence,the powder metallurgical bond formed by powder sintering is the result of atomic diffusion.The atomic diffusion coefficient related to powder densification can describe the powder densification kinetics directly and accurately Therefore,scientific researchers should pay attention to the densification kinetics of the powder sintering process,and reveal the inherent influence of sintering variables,including powders physical properties and process parameters,on the densification kinetics,and quantify the degree of their influences.By doing so,scientific researchers can achieve the purpose of obtaining high-density and high-performance alloys by regulating sintering variablesIn this dissertation,the powder densification kinetics of crystalline and amorphous Ti40.6Zr9.4Cu37.5Ni9.4Sn3.1 alloy powders was studied by comparing experiment and simulation results.Experimentally,the theoretical frameworks for calculating the atomic diffusion coefficient of crystalline and amorphous alloy powders were established respectively,which considered the influence of pressure and current on the atomic diffusion coefficient Furthermore,the powders physical properties(particle size,distribution,shape and defect content)and the sintering process parameters(pressure,current and heating rate)on the atomic diffusion coefficient,a kinetic factor of densification,of the powder particles were determined,and the relationship between atomic diffusion coefficient and densification behavior was described quantitatively.From simulation viewpoint,the secondary-developed Fortran subroutine was used to establish the constitutive equations of electro-thermal-mechanical sintering of crystalline and amorphous powders respectively.The influence of sintering variables on densification mechanism was analyzed by establishing the density distribution field,stress field and temperature field during the sintering processFirst,based on the Arrhenius equation,diffusion creep theory,and Frenkel model,a theoretical framework for calculating the atomic diffusion coefficient of crystalline powders was established.It was found that the atomic diffusion coefficient of ball-milled crystalline alloy powders under the electro-thermal-mechanical sintering is higher than that of atomized crystalline alloy powder.The atomic diffusion coefficient increases with the particles size of the powders,and the quantified atoms diffusion coefficient D value is significantly higher than the measured value by the radioactive tracer method.By comparing the densification behaviors of current mode and no-current mode,the difference in the atomic diffusion coefficient between these two modes was determined,confirming that the electromigration effect of the current can accelerate the atomic diffusion of the crystalline powders.In addition,regarding the sintering pressure as the external driving force for powder densification,the pressure-dependent atomic diffusion coefficient increases with the sintering pressure.It was confirmed that the atomic diffusion coefficient of crystalline powders can be used as an important kinetic parameter of densification to characterize the mass transfer ability and control the densification mechanism for crystalline powder.Secondly,based on the Arrhenius equation,Stokes-Einstein equation,and Frenkel model,a theoretical framework for calculating the atomic diffusion coefficients of the amorphous powders was established.The results showed that the higher defect content of the ball-milled amorphous powders and the increase in the heating rate can reduce the viscosity of the supercooled liquid region;the drastic change in the particle shape makes the original point and line contacts between the powders particles change into line and surface contacts,which increases the contact area greatly;the electromigration effect of current on the atoms leads to a decrease in the diffusion activation energy,a larger atomic diffusion coefficient D,and also greater densification rate.Although the pressure does not change the diffusion activation energy,it affects the diffusion constant and thus increases the value of D.It was confirmed once again that the atomic diffusion coefficient of powder densification can be used as an important densification kinetic parameter for characterizing the mass transfer ability and controlling the powders densification mechanism.Moreover,through the experimental comparison of the densification behavior of amorphous and crystalline powders,it was found that the amorphous powders exhibit superplasticity and good formability during its wide supercooled liquid region.Therefore,the sintering of amorphous powders provided an effective way for powder metallurgy to prepare high-density and high-performance titanium alloys.Thirdly,the constitutive equation of Ti40.6Zr9.4Cu37.5Ni9.4Sn3.1 crystalline alloy powders was established by combining the powders ellipsoidal yield criterion,flow rule and the viscoplastic stress-strain relationship of the bulk materials.Then,the constitutive equation,?ij?p=G/T[sinh(??eq)]nexp(-Qdef/RT)?/?eq[2+?2/2Sij+1-?2/3?kk?ij],was compiled by the secondary-developed Usermat subroutine,and the simulation of electro-thermal-mechanical densification process of the crystalline powders was realized by the FEM software of Ansys.Taking the current data of the electro-thermal-mechanical sintering of the atomized powders under different pressures in Chapter 3 as the boundary conditions,the voltage at both ends and the time-dependent temperature curves measured by thermocouple and temperature-displacement curves at 15,30,45,60 MPa were obtained,which maintained a relatively high agreement degree with the experimentally measured values.The simulation results showed that the greater the pressure,the smaller the internal temperature gradient of the powders and the more uniform the temperature distribution.As a result,the overall density of the sintered bulk alloys is increased,and the density distribution gradient is reduced,which corresponds to the internal temperature distribution of powders.In addition,compared with radial stress,angular stress and shear stress,the axial stress derived from the external load always plays a dominant role,which verifies the feasibility to amend the theoretical model for calculating the atomic diffusion coefficient of powders by the axial pressure.Finally,corresponding to the three specific regions of the amorphous powders,supercooled liquid region,amorphous crystallization region,and crystalline stable region in the continuous heating process,the stepwise constitutive equations at different temperatures were established.For the supercooled liquid region,the corresponding constitutive equation,?ijvpg=G1?cexp(-G*/RT)sinh[?/3?cexp(-G/RT)?0exp(H*/RT)]?/?eq[2+?2/2sij+1-?2/3?kk?ij],was established by combining the powders ellipsoidal yield criterion,the flow rule and the free volume model of the amorphous alloy in the supercooled liquid region.For the amorphous crystallization region,a crystallization kinetic model under different heating rates was constructed according to the DSC curve,and the constitutive equations in the supercooled liquid region and the crystalline stable region were weighted averaged according to the mixing rule,Tg?T?Tx,?ijvp=?ij-g?p;T?T?Tf,?ij??=(1-Vc)?ij-g??+Vc?ij-c?p;Tf?T;?ij?p=?ij-c?p.With the help of secondary-developed Fortran subroutine,the densification of electro-thermal-mechanical amorphous powders was realized.Taking the current data of the electro-thermal-mechanical sintering of the atomized powders under different pressures in Chapter 4 as the boundary conditions,the variation of voltage at both ends and temperature with time measured by thermocouple and the temperature-displacement curves at 15,30,45,60 MPa were obtained,which maintain a relatively high agreement degree with the experimentally measured values.It was confirmed that the constitutive equations of the amorphous powders proposed can describe the electro-thermal-mechanical densification behavior.In addition,the temperature field,stress field and density field of the powders obtained from the simulation deeply revealed the influence mechanism of pressure and temperature on the densification of the amorphous powders.By comparing the simulated densification behavior of amorphous and crystalline powders,the advantages of amorphous powders sintering were further clarified for preparing high-density bulks.In summary,this dissertation revealed the influence of powders physical properties and process parameters on the densification during amorphous/crystalline powders sintering based on experimental research,theoretical calculation and numerical simulation,and finally clarified the advantages of the amorphous powder sintering to fabricate high-performance and high-density titanium alloys.