Influence of subsequent compression on texture

Although the twinning modes for the HCP structure have been predicted to have many types, for example, {10 1 1}<10 1 2 >, {10 1 3 }<30 3 2>, etc., depending on the c/a ratio and stress state, the main twinning mode is still the {10 1 2}<10 1 1 > system for the deformation of magnesium metal or alloys at room temperature. Symmetry conditions require that the second undistorted plane, ( 1 012) planes, be rotated. This will lead that the (0002) plane in the matrix has an angle difference of 86.3^o relative to the (0002) plane in the twinned domain.

In other words, the HCP structure in the twinned grains will have a reorientation of nearly 90^o after twinning deformation. Therefore, the (0002) planes in the stirred zone of the 4P45 modified alloy parallel to ND would be rotated to be nearly perpendicular to the ND after subsequent compression, as shown in Fig. 4-4 (a). This would make (0002) peak on the H plane of the 4P45-cp modified alloy be more intense than that the 4P45 modified alloy without compression deformation, as shown in Fig. 3-25 (b) and listed in Table 3-3.

The (10 1 0) and (11 2 0) planes of the 4P45 modified alloy roughly lying on the L-center plane still lay on the L-center plane after subsequent compression due the rotational axis perpendicular to the L-center plane, as shown in Fig. 4-4(b). Therefore, (1010) and (1120)

peaks were still most intense, no matter the 4P45 modified alloy has been subjected to subsequent compression or not, as shown in Fig. 3-25 (c) and listed in Table3-3. Similarly, the contribution of the (10 1 0) and (11 2 0) peaks of the twinned grains would contribute the weaker intensity became they become more intense in the side plane near the retreating side, as shown in Fig. 3-25(d). Moreover, the (10 1 0) and (11 2 0) peaks of the reoriented grains due to the deformation twinning and the contribution of the (0002), (10 1 3), (10 1 2), and (10 1 1) planes of the un-twinned matrix grains in the stirred zone would render the X-ray diffraction on the T plane be close to that for random Mg crystals, as shown in Fig. 3-25 (a).

It was not sufficient to obtain the completer texture data by this simple XRD experiment.

The detailed and precision volume fraction of the twinned and matrix grains and the texture of the twinned grains will need the more professional tools, such as pole figures or orientation distribution function (ODF), but the current results could still draw the basic picture for the qualitative tendency of the twinned grains by this simple XRD measurement on different planes.

4.2.3 Influence of subsequent compression on mechanical properties at room temperature

The angle between the normal of the basal plane, (0002), and tensile stress axis parallel to the WD, χ, for the twinned grains is only 3.7^o (0.021π) from 86.3^o to 90^o, as shown in Fig.

4-4 (b). The calculation method for the orient factor (S) is cited from the paper of Wang et al.

[146]. The optimally oriented slip direction, <1120>, is lying on the plane defined by the normal to the basal plane and stress axis. This will correspond to the smallest possible λangle for a given χ angle, leading to the highest value for cosλ. Therefore, the term of the λ can be expressed as cosλ = cos[(π/2)- χ] = sinχ. Taking account of the symmetry of the <1120> slip

direction rotated up to ±π/6 about the c-axis of the optimally oriented grain, the average of cosine function from –π/6 to π/6 can be weighted by the factor 3/π as cosλ = (3/π)sinχ. Therefore, the orientation factor S as a function of χ can be written as S(χ) = (3/π)cosχsinχ. The average orientation factor can be obtained as follows:

∫

. 0

1 χ χ χ

π

π . (21)

The orientation factor S for the 4P45-cp modified alloy can be expressed as S(V) = 0.3V_matix + 0.03 V_twinning, where V is the volume fraction of matrix and twinned grains for the 4P45-cp sample. Although the volume fraction of the twinned grains could not be obtained from the current XRD experiment, the orientation factor of the 4P45-cp modified alloy would be smaller than that of the 4P45 modified alloy without subsequent compression. It is well known that the relationship of the tensile stress and critical resolved shear stress (CRSS) for the basal slip system is σtension ∝ τbasal /S. From this equation, it will be speculated that yielding strength, σyielding, for the 4P45-cp modified alloy will be higher than that of the 4P45 modified alloy without subsequent compression. Therefore, the yielding strength of the 4P45-cp modified alloy could be raised from 140 MPa to 178 MPa, as shown in Fig. 3-33.

From the above results and analysis, a secondary process, namely the compressive deformation along ND, will be necessary for the FSP magnesium to lower the orientation factor, m, to raise the yielding strength. Therefore, it is suggested that multi-pass FSP and secondary process could lead to a modified magnesium alloys with a homogeneous microstructure and higher yielding strength.

4.3 Influence of FSP pass number on Mg based composties

4.3.1 Influence of FSP pass number on microstructure and interfacial reaction

It is clear and obvious that the increasing FSP pass could effectively and uniformly disperse the initial lump of SiO2 powders into the AZ61 matrix, as shown in Figs. 3-9 to 3-12.

In addition, the SiO₂ particles and magnesium undergo readily the chemical reaction of the Eqs. (7) and (8) to form the MgO and Mg2Si compounds. The 1P FSP could already disperse the initial lump of SiO₂ particle from the 6 mm x 1.25 mm grooves in the 6 mm x6 mm stirred zone to the clustering particles smaller than 1-10 μm. But the shorter heat history during 1P FSP and the smaller contact surface between the larger clustering particles and matrix might not induce all SiO2 particles to proceed the above chemical reaction. Therefore, the 1P composite samples could still be observed some amorphous SiO₂ particles in TEM micrographs, as shown in Fig. 3-18, and the XPS results for the 1P composite sample also showed that the Si-2p peak almost was still at the 100.8 eV for SiO₂, as shown in Fig. 3-22 (a).

Those larger clustered particles would be gradually broken up to smaller particles (< 1 μm) with increasing FSP passes, as shown in Fig. 3-12 (a). The larger contact surface of these smaller clustered particles and the accumulated heat history would result in more readily the occurrence of the above chemical reactions; therefore, the Si-2p peak ratio for Mg₂Si in the XPS results was gradually increasing, as shown in Fig. 3-22 (b)-(c). When the FSP pass was increased to 4P, the Si-2p peak was almost all referred to the Mg₂Si compounds, implying that most SiO2 particles have already reacted with the magnesium matrix to form Mg2Si and MgO.

The smaller clustered and more uniformly dispersed particles would result in more readily the smaller grain size after mult-passes FSP, such as the 2P, 3P or 4P composite samples, according to the estimation of Eq. (3), as shown in Table 3-2. However, the predicted grains size according to Eq. (3) was smaller than the actual grain size. Actually, some smaller clustering particles in the interior of grains could not play a role in restraining grain growth. The elevated temperatures during FSP provided sufficient energy for the matrix to overcome the drag of the smaller clustering particles, as shown in Figs. 3-14 and 3-17.

4.3.2 Texture analysis of the magnesium composites made by FSP

From the XRD results of Tables 3-4 and 3-5, basically, the texture, whose the (0002) basal planes roughly surrounded the pin column surface of the pin tool in the mainly stirred zone, of the magnesium composites samples is similar to the FSP modified alloys. It implied that the macroscopic material flow for the composites samples during FSP was still along the pin column surface of the pin tool. However, it seemed to have a tendency, that the texture intensity becomes weakened with increasing FSP pass. The smaller and smaller particles more uniformly dispersed into the magnesium matrix with FSP pass might influence the local material flow during FSP to weaken the main texture intensity. It might induce the another texture in the stirred zone, but it will need more professional tool to examine, such as, EBSD.

4.4 Comparison of mechanical properties at room temperature of the modified alloy and composites

The YS of alloy materials can be qualitatively described from the contribution of several factors. It depends on the following contributions:

z σHP: grain size contribution according to the Hall-Petch relation [9],

z σm: Schmid factor m contribution according to the critical resolved shear stress (CRSS) relation of σtension = τslip /m [9],

z σo: particle or precipitate strengthening according the Orowan mechanism [149].

The σo always depends on the volume fraction (f) of the particles or precipitates.

The 1D4P and 2D4P composite samples possessed a smaller grain size of 1.8 and 0.8 μm, respectively, as compared with the 7.8 μm grain size of the 4P45 modified alloy operated at the same FSP parameters of 800 rpm, 45 mm/min and 4 passes. This is due to the reinforcement particles restricting the rapid grain growth during FSP. The composite samples can possess stronger YS according to the Hall-Petch relation. However, Wang et al. [148]

suggested that the FSP magnesium alloys exhibited much weaker grain size dependence than the strong grain size dependence of the extruded magnesium alloys. Because the FSP magnesium alloys possess the higher Schmid factor of 0.3, it will result in the low k value (unit: MPa‧μm^1/2) in the Hall-Petch relationship, such as Eq. (1). According to the speculation of Wang et al. [148], the YS of FSP magnesium alloys with 1.8 μm and 0.8 μm should be around 130 and 190 MPa, respectively.

Because the 1D4P and 2D4P composite samples exhibited the similar texture with the 4P45 modified alloy, the comparison of σm contribution can be omitted. Subtracting the σHP

contribution for the composite samples, the excess YS is suggested to be a result of the contribution of dispersion strengthening, as shown in Fig. 3-17. However, the 4P45-cp modified alloy without particle strengthening can also gain the stronger YS than the 4P45 modified alloy due to the lower Schmid factor of the 4P45-cp modified alloy. The comparison included the considerations of σHP, σm, σo factor contributions for the modified alloys and composites is presented in the Table 4-2. The smaller grain size and particle strengthening

mechanisms for the composite samples are the main factor influencing the YS performance due to the addition of the SiO2 particles. If the similar subsequent compression processing is applied on the composites sample to lower the Schmid factor, the YS of the composite samples is also expected to be upgraded.

4.5 Analysis on deformation mechanism at elevated temperatures of magnesium based alloys and composites

It was known that the apparent ma-value for the modified alloys was calculated to be around 0.5, suggesting that the grain boundary sliding (GBS) might be the dominant deformation mechanism, in Sec. 4.1.3.2. The optimum strain rate for the modified alloys is at 1x10^-3-1x10-4 s^-1. However, the optimum strain rate for the composites is at 1x10^-2-1x10^-1 s^-1 and is superior to the modified alloys. Although the deformation mechanism of the modified alloys is GBS, the rapid grain growth at elevated temperatures for the modified alloys, as shown in Fig. 3-21, will influence the GBS to reduce the deformation potentiality. In contrast, the composite samples could maintain grain size smaller than 2 μm due to the inserted particles restraining the rapid grain growth. Therefore, the composite sample can deform at the higher strain rate and show the longer the elongation.

The superplastic deformation mechanism of the FSP composite are analyzed, using the data obtained from the 2D4P composite samples as an example. The flow stresses at a true strain of 0.3 of the 2D4P composites loaded at 250-400^oC as a function of strain rate are plotted in Fig. 4-5(a). The apparent m-value was estimated to be about 0.3-0.4 from the data presented in Fig. 4-5(a). With the consideration of the threshold stress, the true strain rate sensitivity was calculated to be around 0.5, suggesting that the grain boundary sliding might

be the dominant deformation mechanism. The apparent activation energy Q_a can be evaluated according to the equation

t cons

a R T

Q

) tan

/ 1 (

) (ln

∂ =

− ∂

=

σ

ε_&

, (22)

where _ε&, R and T are stain rate, gas constant and absolute temperature, respectively. Taking σ=20 MPa, Q_a was estimated from the slope of the plot of lnε_& against 1000/RT, as shown in Fig. 4-5(b). The apparent activation energy Q_a over 250-400^oC is 106 kJ/mol, which is between the activation energy for grain boundary self-diffusion of the Mg atoms (92 kJ/mole) and that for lattice self-diffusion of the Mg atoms (135 kJ/mole) [150]. It is suggested that the accommodation mechanism may be dislocation slip plus climb, and the latter is controlled by the mixture of grain boundary and lattice diffusion. Watanabe et al. [151] and Mabuchi et al.

[71] have also reported the same deformation and accommodation mechanism in the Mg

based composites made by other processing routes.

It is known that grain size strongly affects the optimum superplastic strain rate by the relation below [149]:

E D d b T

A ^{p n}

⎟⎠

⎜ ⎞

⎝

⎟ ⎛

⎠

⎜ ⎞

⎝

= ⎛ σ

ε_& , (23)

where A is a materials constant, σ the flow stress, E the elastic modulus, b the Burgers vector, D the diffusion coefficient, p the grain size exponent, and n the stress exponent (=1/m). The 1D4P and 2D4P composites possessed the average grain size around 1.8 and 0.8 μm, respectively. The grain size difference leads to the different optimal superplastic strain rate.

Meanwhile, at the same strain rate, the 2D4P composites show the lower flow stresses and

more smooth operation of grain boundary sliding, following the trend predicted by Eq. (23).