Multiphase Field Numerical Simulation Of Lamellar Growth In Binary Eutectic Alloys

Eutectic growth, as a basic solidification mode in binary and multicomponentalloys system, exists in the liquid-solid transformation of many important structuraland functional materials. Although the eutectic growth theory has been establishedfor several decades, the reliable analysis from the point view of mathematics andnumerical calculation could be performed only in recent years. Moreover, theexperimental research using organic transparent alloys offered a series of preciseexperimental data. The integration of these two aspects brings a deeper insight intothe understanding of eutectic growth. However, as so far, the spacing selection andevolution of morphological instabilities deviating from regular basic state oflamellar eutectics are still open questions, which are also the unsolved problemsthrough analysis method and experimental research in past years. In this thesis, withmultiphase field method, the steady-state growth under constant velocity andnon-steady-state growth under varying velocity of eutectic basic state are simulated,the morphology evolution and morphological stability in eutectic growth aredescribed in details, and the adjustment mechanisms of lamellar spacing arediscussed. With Folch's multiphase field model with the term of antitrapping current,the steady-state eutectic growth and its building process are investigatedquantitatively, and the formation of 1λO oscillatory instability under the condition oflarge initial lamellar spacing is also quantitatively described. The major researchwork and conclusions are as follows.1. Selection rule of morphological instabilityThe lamellar growth in the directionally solidified CBr₄-C₂Cl₆ eutectic alloyswith three different volume fractions ofβphase, i.e. 0.2(hypoeutectic composition),0.29(eutectic composition) and 0.5(hypoeutectic composition) are simulated. It isfound that with the increase of initial lamellar spcing, the sequences of morphologyevolution after destabilization of basic state are as following: basic state→2λO, basicstate→1λO→2λO, basic state→2λO→T-2λO→T→T-1λO. In the parameter space consisting of dimensionless composition and dimensionless lamellar spacing, themorphology selection is quite consistent with the experimental results. The researchof morphology stability of eutectic lamellae shows that the lager temperaturegradient, solute diffusivity in liquid phase and interface energy favor the growth ofregular basic state. Through investigating the source of destabilization wavelength, itis found that the formation of primary instabilities is attributed to the destabilizingwavelengths to approach 1λor 2λin the two-dimensional lateral periodic diffusionfield and the one-dimensional diffusion field, respectively.By the comparison between the morphological instability selections indirectional solidification and isothermal solidification, it is shown that these twosolidification modes have little impact on the morphology selection when thevolume fractions of two phases differ largely, while there are great impact when thevolume fractions of two phases differ little, and the 2λO morphological instability isthe exclusive mode during destabilization of the regular basic state growth inisothermal solidification.2.Mechanism of the lamellar spacing adjustment during non-steady-stategrowth under varying velocity.The eutectic growth is simulated under three kinds of variable pulling speed, i.e.step change, linear change and oscillatory change. The simulated results show thatfor the growth under these three kinds of varying velocity, both the average interfacevelocity and the average interface undercooling show hysteresis effect against thestart time of varying velocity, and the adjustment mode of lamellar spacing isaffected by the kinds of varying velocity. When the step increase or decrease invelocity is imposed, the lamellar spacing adjustment is completed through abruptbranching or progressive annihilation and lamellar growth, respectively. Moreover,there is a strong asymmetry between these two processes during lamellar adjustment,which is accordant with the experimental results. In the case of linear increase invelocity, the lamellar spacing is adjusted through progressive branching, while in thecase of linear decrease in velocity, the mechanism of lamellar spacing adjustment issimilar to that under step decrease in velocity. A mimetic 1λO oscillatory mode is observed when an oscillatory pulling speed with small amplitude is applied, whilewith a large amplitude, an alternative varying process of lamellar branchingrefinement and lamellar coarsening by lamellae merging and annihilation could befound.3. Pb-Sn eutectic growthCoupled with CALPHAD, the steady-state growth of Pb-Sn eutectic alloy withsub-regular solution model in directional solidification is simulated by multiphasefield method. It indicates that there exists periodic distribution of solute Sn in liquidphases of the front of liquid/solid interface and in solid phases, respectively. On theother hand, because of the different volume fractions of two solid phases, the diffuseroute of solute Sn approaching c_E at front ofβ/L interface is further than that at frontα/L interface. The simulated eutectic microstructure is good agreement withexperimental results.4. Quantitative simulation of the directional solidification for model alloyBy Folch's multiphase field model, the process of eutectic growth of the modelalloy from initial plane interface to curving interface of steady state is simulated.The interface average velocity with initial negative value gradually converges to thereal pulling velocity. And the trijunction which oscillates initially, converges to thestable site in the end during the building process of steady-state growth, meanwhile,the contact angle approaches the theoretical value. Compared with the modelwithout the term of antitrapping current, the effect of antitrapping current cause theconvergence of average interface undercooling as interface thickness parameterdecreases. The complex nonlinear behavior of trijunctions during the formation of1λO oscillatory instability is analyzed, and it shows the periodically oscillatorycharacteristic of the average interface undercooling and average interface velocity,and the movement trajectory of two neighboring trijuctions is of mirror symmetry.