3.3. Isothermal Artificial Ageing Simulation
Figure 7 depicts the mesh analysis for the 220 °C-4 h simulation of the Al-0.9Mg-0.6Si ternary system. For the lower values of cells (500–800–1100), severe deviation is estimated among the successive simulations, for the precipitate fraction, in the range between 20–30%. On the contrary, the analysis with 1700–2000 cells, appears to provide much more similar results, with a slight deviation, lower than 2%. Such a deviation can be thought of as acceptable, and consequently, between the two analyses, the 1700 × 1700 is selected due its lower overall simulation time. The analysis of 1700 × 1700 cells, with cell dimension equal to 11.8 nm and interface width equal to 35.4 nm (3 × 11.8), will be implemented for the subsequent ageing simulations. Choosing the 1700 × 1700 cells,
Figure 8 presents the precipitate fraction for the 180–200 °C ageing simulations.
For the 180 °C ageing, the estimated wt.% of Mg2Si is quite low, equal to 0.21 for the ternary Al-0.9Mg-0.6Si and 0.29 for Al-1.0Mg-1.1Si. For the higher ageing temperature of 200 °C, a significant increase is recorded as the precipitate fraction reaches the value 0.87 for the ternary Al-0.9Mg-0.6Si and the value 1.25 for the ternary system Al-1.0Mg-1.1Si.
As illustrated by
Figure 9, the precipitate average radius records its lower values for the 180 °C ageing simulation, equal to 16.4 nm for Al-0.9Mg-0.6Si and 17 nm for Al-1.0Mg-1.1Si. For 200 °C ageing, the average radius significantly increases, reaching the value 32.2 nm for the ternary Al-0.9Mg-0.6Si and 37.9 nm for Al-1.0Mg-1.1Si system. For constant ageing temperature, the two compositions record similar values, with a slightly higher price achieved by the Al-1.0Mg-1.1Si system. From both
Figure 9 and
Figure 10, it can be seen that for the 180 and 200 °C simulations, precipitates and their average radius are rapidly grown, while their increasing rate reaches a plateau after 4 h of ageing. Given that all simulations begin with the same number of Mg
2Si grains and the same overall study surface,
Figure 10 depicts the evolution of precipitate’s density.
It can be seen that, in every simulation, a slight decrease of precipitate density is recorded as the thermodynamically unstable precipitates are dissolved providing Mg and Si content for the growth of the thermodynamically stable precipitates. It is also observed that for the lower ageing temperatures (180 °C), with the lowest precipitate fractions, precipitate density appears to have its highest values. On the other side, the 200 °C ageing simulations, attributed to the maximum precipitate fraction, have the lowest values of precipitate density. This contradiction between the precipitate fraction and density is explained by the fact that the rise of ageing temperature results in the increase of the average precipitate radius, although the overall number of precipitates is reduced.
Figure 11 depicts the variation of Mg and Si concentration in the matrix. Mg and Si concentrations in Mg
2Si are constant, 63% and 37%, respectively. The conducted simulations do not consider the iron intermetallic particles, which restrict the available Si, based on Equation (10), as long as the presence of iron intermetallic phases reduces the available Si for the Mg
2Si precipitation.
A posteriori, Equation (10) is implemented, taken the composition of Mn kai Fe from
Table 1, so as to identify if the absence of iron particles resulted in an overestimation of available Si, and consequently, an overestimation of precipitate fraction and radius.
Figure 12 presents the availability of Si for precipitation based on the restriction of Equation (10). As anticipated, Mg and Si concentrations in the matrix decreased, as the volume fraction of precipitates increased, with the most significant reduction estimated in the 200 °C ageing simulation, where the highest value of precipitates is recorded. The variation of Mg concentration in the matrix phase is most significant in comparison to Si, as Mg has higher concentration in Mg
2Si phase, rather than Si. Based on
Figure 12, it can be estimated that the absence of iron phases in simulation microstructure does not lead to overestimation of precipitate volume fraction as Si concentration has a surplus in the matrix.
Figure 13 presents the microstructure simulation by the end of each ageing simulation. It can be seen that there is a mutual distribution of precipitates, both on the bulk region of the matrix phase grains, the interfaces, and the triple junctions. At the initial ageing steps, particles precipitated primarily in the bulk region, while some precipitate free zones were present in the microstructure. Around the triple junctions, some precipitation-free zones have been noticed, as the formation of particles in the triple junctions depletes the availability of Mg and Si for further precipitation.
Figure 14 presents the interface mobility, and
Table 6 the diffusion coefficients of Mg and Si in matrix phase calculated by ThermoCalC
@. The interface mobility records its highest values for the lower temperature of 180 °C, and its lower value for the highest ageing temperature of 200 °C. On the contrary, diffusion coefficients of Mg and Si in the matrix phase are increased for higher ageing temperatures with the Si coefficient having a slightly higher value than its Mg counterpart. As the ageing temperature is increased, the diffusion mechanism is getting more important, while for lower ageing temperatures, the interface mechanism is of greater importance. Diffusion coefficients in precipitates are considered equal to zero, as Mg
2Si are stoichiometric intermetallic compounds with standard chemical composition and minimum solubility.
Figure 15 depicts the virtual EDX analysis, provided by the MICRESS® software, where the red curve represents the Si concentration and the black curve represents the Mg concentration, in both matrix phase and precipitates. The virtual EDX analysis has been considered for the horizontal line on the centre of the microstructure. The vertical axis represents the % concentration of Mg and Si, while the horizontal axis represents the position in the microstructure. For the lower ageing temperature, of 180 °C, a sparse dispersion of both Mg and Si curves has been recorded, because of the low volume fraction of precipitates. It is worth mentioning that the peak of Si curve is equal to 37% and the peak of Mg curve is equal to 63%, both attributed to Mg
2Si precipitates. For the 200 °C simulations, intense distribution is recorded, due to the increase of precipitate fraction, while some peaks have been noticed, lower than 63% and 37%. These peaks are attributed to precipitate particles, which have not received their final chemical composition of Mg
2Si.
Figure 16 and
Figure 17 depict the estimated values of yield strength and hardness, based on Equations (4)–(9), for the final ageing conditions. For the 180 °C ageing, lower values of yield strength and hardness are recorded, due to the relatively low volume fraction of precipitates. More precisely, for the ternary Al-0.9Mg-0.6Si system, the values of yield strength and hardness are equal to 139 MPa and 62 HV, respectively, while for the ternary Al-1.0Mg-1.1Si, the corresponding values are 176 MPa and 74 HV. The increase of the precipitate fraction results in the enhancement of yield strength and hardness for both ternary systems. At 200 °C, yield strength is 223 (Al-0.9Mg-0.6Si) and 291 (Al-1.0Mg-1.1Si) MPa, while hardness is 89 and 112 HV, respectively.