Microstructure refinement mechanism of undercooled Cu₅₅Ni₄₅ alloys

The solidification structure of Cu₅₅Ni₄₅ alloy undergoes first grain refinement at the undercooling degree of 54–96 K, and complete refinement occurs at ΔT = 70 K. The dendrite remelting fracture caused by chemical superheating proposed by Li [16] can clearly explain the grain refinement mechanism under low undercooling. The mechanism of dendrite remelting and fracture points out that when the undercooled melt temperature is lower than a certain temperature of the equilibrium liquidus, a large amount of solidification latent heat will be released. The release of latent heat causes the temperature of the system to rise rapidly beyond the solidus temperature, which causes the primary dendrite skeleton to superheat and remelt, and finally break into fine equiaxed crystals. According to the calculation of the remelting ratio of Li [16] to the dendrite of Ni₇₅Cu₂₅ alloy, the highest remelting ratio of about 90% can be obtained at undercooling ΔT = 40 K, and the corresponding microstructure morphology is mostly fine equiaxed grains. As the undercooling ΔT increases within a certain range, the proportion of remelting in the alloy continues to decrease, its microstructure presents equiaxed crystals and dendrites, and the proportion of dendrites waxes higher and higher. This study well confirms the mechanism of dendrites’ fragmentation due to superheating and remelting at low undercooling.

Figure 3 shows several typical solidification recalescence curves of Cu₅₅Ni₄₅ alloy. With the increase of undercooling, the rapid solidification time becomes shorter and shorter, and the maximum recalescence temperature T_R [25] decreases gradually. The maximum recalescence temperature T_R of undercooling ΔT at 54 K, 70 K, and 96 K is higher than that of equilibrium solidus, which also confirms the mechanism mentioned by Li [16], who proposed that the dendrites are broken due to superheating and remelting at low undercooling and that the grains are refined.

Fig. 3

The grain refinement structure of Cu₅₅Ni₄₅ alloy with low undercooling ΔT = 70K was characterized by EBSD. The EBSD analysis diagram is shown in Fig. 4.

Fig. 4

Here, we consider the grain boundary orientation difference less than 15°as small angle grain boundary. The solidification microstructure of Cu₅₅Ni₄₅ alloy with equiaxed grains, curved grain boundaries, and no annealing twins (Figure 2C). The red lines in Figure 4A represent small angle grain boundaries, and a large number of small angle grain boundaries can be clearly seen. In Figure 4B, different colors indicate different grain orientations, and the same or similar colors indicate the same orientation. A large number of grains with the same or similar orientations can be observed, and high-strength textures can be observed in Figure 4C.

Figure 4D is obtained by statistical calculation of grain boundary orientation difference, in which the small angle grain boundary orientation difference is as high as 69%. The mechanism of dendrite overheat remelting fracture proposed by Li [16] well explains the phenomenon of grain refinement at low undercooling. When the undercooled melt releases a large amount of latent heat of crystallization due to rapid solidification, the temperature of the system rises rapidly and exceeds the solidus temperature, resulting in the primary dendrite superheating remelting fracture, which refines into smaller equiaxed grains in the subsequent slow solidification stage.

The primary solid remelting fraction of alloy liquid during rapid solidification has a great relationship with undercooling [26]. In agreement with results presented in previous studies, Li [16] proposed a formula for remelting fraction of primary solid phase: (2) fL=k0(TR−TS)/ΔT01−(1−k0)(TR−TS)/ΔT0 {f_L} = {{{k_0}\left( {{T_R} - {T_S}} \right)/\Delta {T_0}} \over {1 - \left( {1 - {k_0}} \right)\left( {{T_R} - {T_S}} \right)/\Delta {T_0}}} where T_R is the highest recalescence temperature corresponding to the degree of undercooling ΔT , Ts is the equilibrium solidus temperature corresponding to the initial solid of the Cs component, ΔT₀ is the equilibrium crystallization temperature range corresponding to the initial solid of the Cs component, and k₀ is the equilibrium solute partition coefficient. According to the formula, the calculated results are shown in Figure 5 as dimensionless remelting fraction of Ni₅₅Cu₄₅ alloy under different undercooling degrees.

Fig. 5

The calculated results are in good agreement with the experimental results. The maximum remelting fraction is about 90% at the undercooling of about 75 K. The results show that the trend of dimensionless remelting fraction curve increases first and then decreases: the remelting fraction of Cu₅₅Ni₄₅ dendrite is very small at very low undercooling, and the corresponding microstructure is coarse dendrite. When the undercooling is 54–96 K, the dendrite remelting fraction is at a relatively high value, and a large number of equiaxed grains and proportions and relatively small dendrites can be observed in the corresponding microstructure. At moderate undercooling, the remelting fraction decreases, and the microstructure of the alloy in the undercooling range of 128–227 K presents dendrite. With the increase of undercooling, the dendrite shows strong orientation and gradually decreasing dendrite spacing. At high undercooling of 227 K, the remelting fraction has been significantly reduced, and the microstructure morphology is equiaxed grains with flat polygon. The proportion of remelted dendrites is very small, which is not enough to cause grain refinement. This shows that the grain refinement mechanism employed at high undercooling is a different one.

Grain refinement occurs when undercooling of Cu₅₅Ni₄₅ alloy is greater than 227 K. In contrast with the microstructure of the first grain refinement, the second grain refinement has smaller grain size, flat polygonal grain boundary, and annealing twins – which are not found in the first grain refinement [17]. According to the remelting fraction calculated by the dendrite remelting formula, as shown in Figure 5, the proportion of dendrite remelting is very small under high undercooling, which is not enough to refine the grains. Stress induced recrystallization mechanism [20] is one of the potential mechanisms to refine the grains of the alloy. Stress induced recrystallization indicates that with the increase of the initial undercooling, the volume fraction of dendrite in the primary solid phase formed during rapid solidification will increase, and a continuous dendrite network will gradually form in the alloy liquid. Accordingly, the dendrite skeleton also begins to have strength, and then presents deformation resistance. When the undercooling degree of the undercooled melt is high, the accumulated stress will reach the strength limit of the alloy, and the dendrite framework will undergo plastic deformation, resulting in stress fracture. The broken dendrite fragments store the strain energy, which provides the driving force for the subsequent recrystallization behavior.

EBSD technology was used to characterize the grain refinement structure of Cu₅₅Ni₄₅ alloy with high undercooling ΔT = 272 K. The EBSD analysis diagram is shown in Figure 6. The black lines in Figure 6A represent large angle grain boundaries (>15°). It is evident that a large number of large angle grain boundaries can be seen.

Fig. 6

The microstructure of ΔT = 272 K undercooling Cu₅₅Ni₄₅ alloy is polygonal equiaxed grains with flat grain boundaries and a large number of annealing twins (shown in black circle in Figure 6B), which is a strong evidence of recrystallization of the alloy. In Figure 6B, different colors indicate different grain orientations, and the same or similar colors indicate the same orientation. The disordered colors indicate that the grain orientations are randomly distributed without obvious preferred orientation. No obvious high-strength texture was observed in the Figure 6C polar diagram. According to the statistical calculation of grain boundary orientation difference, it is shown in Figure 6D that the large angle grain boundary orientation difference is as high as 90%, and the Σ3 twin grain boundary (<111>60°) is as high as 22.5%. The mechanism of dendrite superheat remelting mentioned above can not explain the EBSD characterization diagram of ΔT = 272 K undercooling, but the mechanism of stress-induced recrystallization can explain it perfectly. With the increase of undercooling, the continuous dendrite network is formed gradually. In the rapid solidification stage, the dendritic framework produces deformation resistance due to thermal strain and the alloy liquid phase in the dendrite network region flows to the crystallization front. Once the accumulated stress exceeds the strength limit of the alloy, the dendrite frame-work will break, and the strain energy stored in the broken dendrite fragments will provide the driving force for the subsequent recrystallization. In the process of recrystallization, the recrystallized small angle grain boundaries will merge and migrate rapidly under the action of driving force, resulting in the grain boundary orientation difference becoming larger and larger, which will be gradually engulfed by large angle grain boundaries. The grain boundaries will gradually become flat from bending, and finally form large angle grains with flat grain boundaries. In addition, due to the accumulated stress in the primary dendrites, the dendrites are randomly distributed after breaking, and a small part of the remelted dendrites are also randomly distributed. Therefore, no new texture is introduced during recrystallization and grain growth, and the grain orientation is random [27].

Based on the solidification shrinkage and thermal shrinkage of undercooled melt during rapid solidification, Liu [20] proposed a stress accumulation model, which can semi-quantitatively estimate the stress accumulation in the solidification structure during rapid solidification. The specific formula is as follows: (3) σS=160μ⋅a(fRS)2tfλ22×(1−fS(x))fS(x){ a⋅βS[ fS(x)−fcoh(x)+1(1−fS(x))−1(1−fcoh(x))+2ln[ 1−fS(x)1−fcoh(x) ] ]+2(1+βS)αtherΔT0ΔT3GSQ[ fS(x) ]} \matrix{ {{\sigma _S}} \hfill & = \hfill & {{{160\mu \cdot a} \over {{{\left( {f_R^S} \right)}^2}{t_f}\lambda _2^2}}} \hfill \cr {} \hfill & \times \hfill & {{{\left( {1 - {f_S}\left( x \right)} \right)} \over {{f_S}\left( x \right)}}\left\{ \matrix{ a \cdot {\beta _S}\left[ {\matrix{ {{f_S}\left( x \right) - {f_{coh}}\left( x \right)} \cr { + {1 \over {\left( {1 - {f_S}\left( x \right)} \right)}}} \cr { - {1 \over {\left( {1 - {f_{coh}}\left( x \right)} \right)}}} \cr { + 2\ln \left[ {{{1 - {f_S}\left( x \right)} \over {1 - {f_{coh}}\left( x \right)}}} \right]} \cr } } \right] \hfill \cr + {{2\left( {1 + {\beta _S}} \right){\alpha _{ther}}\Delta {T_0}\Delta T} \over {3{G_S}}}Q\left[ {{f_S}\left( x \right)} \right] \hfill \cr} \right\}} \hfill \cr } where μ represents the dynamic viscosity, α is the length of the solid-liquid coexistence zone during the recalescence process, f_s (x) is the solid volume fraction of primary dendrite, fRS f_R^S is the solid fraction, t_f is the recalescence time, λ₂ is the secondary dendrite arm spacing, β_s is the solidification shrinkage, f_coh (x) is the solid fraction of the continuous dendrite network, α_ther is the scale factor, ΔT is undercooling, ΔT₀ is the solidification range of the alloy, G_S is the temperature gradient at the solid-liquid interface in undercooled melt, and Q[ f_s (x)] is the volume flow of interdendritic liquid flow.

Based on the above equation, the stress accumulation of undercooled Cu₅₅Ni₄₅ alloy melt during rapid solidification can be obtained, which is shown in Figure 7. The diagram can explain the transformation of microstructure from oriented fine dendrites to polygonal equiaxed grains (Figure 7B, 7C).The stress accumulated in the solidified structure of Cu₅₅Ni₄₅ alloy is very small at low undercooling, but quite large at high undercooling. With the continuous increase of undercooling, the accumulated stress will exceed the strength limit of the alloy, the fine dendrites will break up, and the fine polygonal equiaxed grains will be formed again in the subsequent recrystallization stage.

Fig. 7