Phase-field simulation of secondary dendrite growth in directional solidification of binary alloys

Phase field method was used to simulate the effect of grains orientation angle θ_(11) and azimuth θ_A of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites. In the simulation process, two single-factor influence experiments were designed for columnar crystal structures. The simulation results showed that, when θ_(11) < 45o and θ_A < 45o, as θ_(11) was enlarged, the growth direction of the secondary dendrites on the preferentially growing dendrites at the converging grain boundary(GB) presented an increasing inclination to that of preferentially growing dendrites; with increasing θ_A, the growth direction of the secondary dendrites on the preferentially growing dendrites at the converging GB exhibited greater deflection,and the secondary dendrites grew with branches; the secondary dendrites on the preferentially growing dendrites at diverging GBs grew along a direction vertical to the growth direction of the preferentially growing dendrites.When θ_A = 45o and θ_(11) = 45o, the secondary dendrites grew in a direction vertical to the growth direction of preferentially growing dendrites. The morphologies of the dendrites obtained through simulation can also be found in metallographs of practical solidification experiments. This implies that the effect of a grain's orientation angle and azimuth of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites does exist and frequently appears in the practical solidification process.

Phase field simulation of liquid-solid-eutectoid multiple phase transformations of a Fe-C binary alloy

A new continuous multi-phase transformation field model was established for liquid-solid-eutectoid transformation. Taking Fe-C alloy as an example, the model was used to simulate the evolution of the micro-morphology of the liquid-solid phase transition, and the effects of temperature, solute and free energy on the nucleation of pearlite after the liquid-solid phase transition were analyzed. The micro-morphology of pearlite was simulated. The simulation results show that the austenite structure has hereditary effect on the pearlite, the morphology of pearlite structure was similar to that of the parent austenite. The eutectoid structure at the front of pearlite grows toward the interior of austenite grains in a bifurcation manner and in the spherical coronal shape. In addition, the growth rate of pearlite was related to the shape of concave-convex interface at the nucleation site, and the growth rate at the convex interface was faster than that at the concave interface.

Multi-phase field simulation of multi-grain peritectic transition in multiple phase transformation

Taking Fe-C binary alloy as an example,based on the multi-phase field model,the nucleation and growth ofδphase,peritectic reaction,peritectic transformation,and the growth of subsequent austenite are simulated.Effects of the nucleation site of austenite on the peritectic reaction rate and the starting time of the peritectic transformation were studied.The simulation results show that theγphase,as a shell,surrounds theδphase and grows rapidly when the peritectic reaction occurs between the dendriticδgrains,and a layer ofγphase shell is formed aroundδphase after the peritectic reaction.After theδphase is surrounded byγphase completely,the membrane shell separates the L phase from theδphase,so that the phase transfers from peritectic reaction to peritectic transformation.During the peritectic transformation,since the solute diffusion coefficient of the liquid phase is much greater than that of the solid phase,the average growth rate of austenite in the liquid phase is visibly higher than that of theδphase.The peritectic reaction rate is related to the curvature of the nucleation site of theγphase on theδphase grains.The peritectic reaction rate at the large curvatures is faster than that at small curvatures.