Modelling of Precipitation Hardening in Casting Aluminium Alloys

Precipitation hardening, or aging hardening, is one of the most widely adopted techniques for strengthening of aluminium alloys. During the precipitation process, three major mechanisms are involved: i.e. nucleation, growth and coarsening. Kampmann and Wagner have developed a powerful and flexible numerical approach (KWN model) for dealing with concomitant nucleation, growth and coarsening and thus capable of predicting the full evolution of the particle size distribution. KWN model has been successfully applied to a number of aluminium alloy systems, such as 2xxx, 6xxx and 7xxx. However, most of these modelling works were focused on the wrought aluminium alloys, few had applied to the casting aluminium alloys. In the present modelling work, the microstructure evolution is modeled based on the KWN model and then a strength model based on the well established dislocation theory is used to evaluate the resulting change in hardness or yield strength at room temperature. Then the modelling is applied to casting aluminium alloys A356 and A357. And the modelling results are validated by comparing with own experimental results and the results obtained from the open literature.


Introduction
It is convenient to divide aluminium alloys into two major categories: casting compositions and wrought compositions. In general, the principles and procedures for heat treating wrought and cast alloys are similar. Very often, the post casting heat treatments applied to a cast alloy are inspired from the developed closest wrought alloys. Since the age-hardening aluminium alloys have become the backbone of the automotive and aircraft industries, the interest in age-hardening modelling, therefore, has gained considerable momentum over past decades. During the precipitation process, three major mechanisms are involved: i.e. nucleation, growth and coarsening. These processes significantly overlap which leads to the formation of a particle population that can be described by the particle size distribution (PSD). The Kampmann and Wagner Numerical (KWN) model [1] is a powerful method for dealing with concomitant nucleation, growth and coarsening and thus capable of predicting the full evolution of the size distribution. This model has been successfully applied to a number of aluminium alloy systems, such as 2xxx, 6xxx and 7xxx [2,3]. However, most of these modelling works were focused on the wrought aluminum alloys; few had applied to the casting aluminium alloys.
In the present modelling work, the microstructure evolution is modeled based on the KWN model and then a strength model based on the well established dislocation theory is used to evaluate the resulting change in hardness or yield strength at room temperature. Then the modelling is applied to casting aluminium alloys A356 and A357. And the modelling results are validated by comparing with own experimental results and the results obtained from the open literature.

The Model
The present modelling work consists of the following two integrated components: ii) A strength model, which converts the relevant output parameters into an equivalent room temperature yield strength.

Description of the KWN Model
The essential features of this model are: • The continuous size distribution of the particles is subdivided into a large number of size classes [Rj, Rj+1] containing Nj particles respectively.
• The continuous time evolution of the particle distribution is split up into a sequence of discrete time steps.
• At each time step, the number of newly nucleated particles with the size of slightly above the critical radius is calculated using classical nucleation theory and allocated to an appropriate size class.
• The growth of existing particles is calculated by assuming growth is diffusion controlled and spherical growth morphology. The influence of the Gibbs-Thomson effect is used to calculate the modified interfacial compositions for each size class at each time step. Therefore, the existing ones grow or shrink depending on their size.
• Coarsening arises naturally in the model, and no simplifying assumptions for the shape of the particle size distribution are predesigned. When the size of a group of shrinking particles reaches zero they are removed from the size distribution • The change in matrix solute level due to precipitate formation or dissolution is calculated at each time step using the mean field approximation.
The details for the equations of nucleation, growth and coarsening refer to the Myhr and Grong's work [4].

Strength Model
The overall yield strength can be achieved by adding the various contributions:

Modelling Results and Discussion
The modelling work is applied to the casting alloys A356 and A357 with chemical composition of Al-7.0Si-0.40Mg-0.13Fe-0.03Sr and Al-7.0Si-0.62Mg-0.13Fe-0.03Sr [5] by weight percentage respectively. The experimental data used to validate the model is obtained from the literature [5] and from our own experimental data. For the own data, the yield strength is taken as approximately three times the Rockwell hardness Scale E for A356.
The modelling results are shown in Figures 1 to 3.      By choosing suitable parameters used in the microstructural and strength model, the yield strength modelling results for A356 (Fig.1) and A357 (Fig.2) are in very good agreement with the experimental data from the literature as well as own data. Because of more Mg content in A357, if ageing at the same temperature, the peak yield strength is higher and it takes shorter time to reach for A357 than that of A356. Figure 3(a). gives the particle size distribution after ageing at different temperatures for 3 hours for A356. For this time it is in over-ageing for 210°C and 230°C, peak-ageing for 190°C and underageing for 170°C. The distribution broadens significantly in going from under ageing to over ageing. When studied the evolution of PSD with time, as shown in Figure 3(b), with time evolution, the particles gradually move to a larger size and therefore the broadness of the shape of distribution becomes greater. More small particles exist in A357 than that of A356 proves why the higher yield strength is obtained in A357.

Conclusions
The Kampmann and Wagner numerical (KWN) model can be applied to not only the wrought aluminium alloys, but also the casting alloys, such as A356 and A357. By choosing suitable parameters used in the microstructural and strength model, the modelling results are in good agreement with the experimental data obtained from the literature as well as own experimental data.