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The grain refinement of aluminum using Al–Ti and Al–Ti–B master alloys has been extensively investigated in recent years. The work majority was focused on Al–Ti–B master alloy due to its proficient refinement effect (Ding, Xia, & Zhao, 2014). The most widely used master alloy is Al-5Ti-1B, which contains 5 wt.% Ti and 1 wt.% B (Xiaoming Wang, Liu, Dai, & Han, 2015). According to the calculated Al-Ti partial phase diagram (FACTSAGE, 2001) up to 2 wt.% Ti, shown in Figure 1, the primary microstructure of the master alloy contains a mixture of TiAl3 compound and α-Al (FCC_Al) solid solution. Al–Ti was considered a more simple and understandable master alloy (Arnberg, Bäckerud, & Klang, 1982; Guzowski, Sigworth, & Sentner, 1987). The existence of Al3Ti phase in the Al–Ti grain refiner enhances the α-Al nucleation than any other heterogeneous nucleating secondary phases (Easton & StJohn, 1999). While, there is a large percentage of TiB2 phase inside the Al3Ti particles, in the Al–Ti–B master alloy, which effectively nucleate the α-Al grains by forming compounded particles (Xiaoming Wang et al., 2015). It has been found that TiB2 itself does not nucleate α-Al grains unless extra titanium than the stoichiometry of TiB2 in the Al-Ti-B master alloys exists (J. Wang, Horsfield, Schwingenschlögl, & Lee, 2010).
Figure 1.
Calculated Al-Ti partial phase diagram in the Al terminal side showing a peritectic reaction of liquid aluminum and Al3Ti to form α-Al
Relationship Between Grain Size and Mechanical Properties
The main role of the grain refiners is to develop fine equiaxed grains in the cast structure either by increasing the number of nucleation sites or by grain multiplications (Mohamad, 2011). Fine structures have greater total grain boundary area that blocks the dislocation movement from one place to another more than coarse-grained structures (Callister & Rethwisch, 2007). Thus, fine-grained materials are having superior mechanical properties than coarse-grained materials (Xiaoming Wang & Han, 2016). The relationship between yield stress and grain size can be described mathematically by the Hall-Petch equation (Hall, 1951; Petch, 1953):
(1) where,
σy is the yield stress (MPa) and
d is the average grain diameter (mm).
σo and
ky are material parameters that are affected by alloy content, grain shape and crystallographic texture (MPa).
σo is a frictional stress that is around 10 MPa for pure Al and increases with increasing the alloy content due to solid solution hardening.
ky represents the capability of grain size hardening for a given alloy system, which can be described as the slip transmission difficulty across the grain boundary (Schempp, Cross, Häcker, Pittner, & Rethmeier, 2013). The
ky for aluminum alloys ranges between 2 and 6 N/mm
3/2 (Embury, 1996).