The hardening mechanism of Mg based nano-ZrO 2 and nano-SiO 2 particles

Predicting the overall mechanical properties of the composite is very important for material designs and applications. There have been many attempts to correlate the overall composite mechanical properties with the properties of the composite constitutes, for example, the self-consistent variation methods [176], mean-field theories [177], shear-lag theory [178], finite element method (FEM) [179] and the rule of mixtures (ROM) [180].

Among them, the simplest and intuitive method for estimating the effective mechanical properties in terms of constitutes is the ROM. Although the FEM gives satisfactory results for problems with the complex geometry and the nonlinearity of the materials properties, the ROM as a simple and fast solution for the simplified model is also useful, in which, the Voigt model based on the equal stain assumption and the Reuss model based on the equal stress assumption have been widely used.

However, most of the models are derived for elastic properties. In addition, the correlation between the effective hardness of the composite, which is the easiest mechanical property obtained by simple testing, and the hardness values of its constituent phases are not

well established. Therefore, there is still argument about the validity of the ROM for composites with hard particles, especially for plastic properties.

Figure 4-3 shows a schematic diagram showing (a) the iso-stress (Reuss) model and (b) the iso-strain (Voigt) model. The ROMs, such as the equal strain treatment which is an upper bound, Eq. (8) below, and the equal stress treatment which is a lower bound, Eq. (9) below, can be used for estimating the effective hardness H of the composite:

s s h

up fhH f H

H = + , (8) ) 1

/ /

( + ⁻

= h h s s

low f H f H

H , (9)

where, Hh and Hs are the hardness values of the hard and soft phases, and fh and fs are the volume fractions of the hard and soft phases, respectively. The subscripts up and low in H represent the upper and the lower bounds of hardness, respectively.

More recently, the elastio-plastic finite element analysis (FEA) for the conventional unit cell model of the uniaxial compression of the composites with homogeneously distributed second particles has been carried out by Kim [181]. Combined with experimental results, the validity of the ROM in composites with hard particles had been confirmed. The FEA results fit better with the iso-strain model except for low volume fractions (<30%) of hard particles where the FEA results fit closely the iso-stress curve. This can be explained by the fact that the deformation of the soft matrix is larger than that of the hard particle. That is, as the compression proceeds on a composite with a high volume fraction of the hard particles, the distance between the particles is getting closer, the load is transferred to the adjacent particles along the loading direction and the hard particles can be deformed. On the other hand, for a low volume fraction of the hard particles, the deformation occurred mainly in the soft matrix

with little deformation of the hard particles. Such inhomogeneous deformation with the main deformation occurring in the soft matrix is much more apparent under the indentation of the composite than under the uniaxial compression. Figure 4-4 shows a schematic drawing of the load transfer direction in the indentation test. Because the loading direction is mainly normal to the indenter surface, the stress state might be similar to the ‘iso-stress’ condition rather than the ‘iso-strain’ condition.

The extreme case of this inhomogeneous deformation is the ‘wet sand effect’ [182], which means that only the soft matrix surrounding the hard particles deforms. In this case, it might be considered that the effective hardness of the particle reinforced composite is mainly related to the hardness of the soft matrix. This situation can be analyzed by using the following approximation of the ‘iso-stress’ case,

s s h s s h s h

low H H f H f H H f

H = /( + )≈ / , (10)

where Hh>> Hs and fh<<fs.

Equation (10) indicates that the effective hardness of the particle reinforced composite can be approximated to that of the soft matrix only when the hardness of the hard particle is much higher than that of the soft matrix (Hh>> Hs) and the volume fraction of the particles is much lower than that of the matrix (fh<<f^s). Otherwise, this approximation, Eq. (10), is not satisfied and should be modified.

In the present ZrO2 and SiO2 particle reinforced Mg-AZ31 composites fabricated by FSP, it is hardly possible to prepare the same state of the matrix in the real samples, regardless of the volume fraction of the same-sized particles. However, the hardness of the matrix without any particle can be roughly deduced from previous hardness results (d, in μm):

2 /

72 1

40+ ⁻

= g

v d

H . (11)

The comparison of the hardness of the AZ31 matrix deduced from Eq. (10) is given in Table 4-1. The hardness Hv of the ZrO2 and SiO2 particles is ~900 and ~1000, respectively, much higher than that of the AZ31 matrix after FSP (Hv~76-90, depending on the refined grain size).

The maximal volume fraction of the particles is ~20%. Therefore, it is considered that the approximation of Eq. (10) is satisfied for the present case. The prediction results, as shown in Table 4-1, approximately match the experimental ones, especially in the case of lower volume fractions. Our present results confirm that the effective hardness of the particle reinforced composite can be approximated to that of the soft matrix when the hardness of the hard particle is much higher than that of the soft matrix and the volume fraction of the particles is much lower than that of the matrix.

As can be seen in Table 3-5, the average grain size of the FSP composites is smaller than that of the un-reinforced FSP Mg-AZ31 alloy. The finer grain structure in the composites could result from the SiO2 or ZrO2 particle addition. It is well recognized that the second phase particles will influence the stress and strain distribution during plastic deformation, and thus particles will strongly affect the dynamic recrystallization (DRX) process. Generally, particles could be classified into two size groups according to their effects on RX. Particles larger than 0.1-1 μm will stimulate the RX process, while particles smaller than 0.1 μm will hinder DRX process [183].

As for the present composites, the behavior of the second phases might be much more complex since their size and distribution will change during FSP. During the first FSP, the particles will be dispersed inhomogeneously, some large size particle clusters will occur unavoidably. However, the particles will be dispersed more and more homogeneously with

increasing FSP passes, and the large size particle clusters will change into smaller ones gradually (to an average size of 180-300 nm, as listed in Table 3-5). Simultaneously, stress concentration around the second phases (particle clusters) will produce a large strain gradient in the adjacent magnesium matrix because of the dislocation pile-up against the second phases during the FSP deformation. Nucleation of dynamic recrystallization is stimulated in these zones. While the nuclei grows, small second phases will hinder grain boundary migration due to the Zener pinning. The second phase pinning on grain boundaries could be observed clearly in Figs. 3-29, 3-30 and 3-50. In other words, the second phases play a different role in DRX during FSP according to their changing size. At the beginning of FSP, while the second phase is large, the strain energy in the matrix around it is high. These kinds of places are preferential sites for nucleation of DRX. While the second phase changes into small particles due to the mechanical breaking with increasing FSP passes, the new nuclei has already been produced in the matrix. Then, the small particles act as obstacles for grain growth. Therefore, relatively fine magnesium grains are generated in the present composites during the multiple FSP passes. If the FSP heat input is lowered by lowering the pin rotation and raising the advancing speed, the resulting grain size can be further lowered.

In this study, it is clear that the softest AZ31 Mg alloy can be hardened by the inclusion of nano fillers through FSP, from Hv~50 up to Hv~105. If the harder AZ91 alloy is in use, Hv

is expected to be raised from the original 65 to over 120, based on the prediction of Hs/fs in Eq. (10). The hardened bulk section or surface layer would greatly improve the wear resistance that is vital for practical applications.