«STRUCTURE AND PROPERTIES OF ELECTRODEPOSITED NANOCRYSTALLINE NI AND NI-FE ALLOY CONTINUOUS FOILS by Jason Derek Giallonardo A thesis submitted in ...»
In general, there is relatively good agreement with the composite model predictions as the grain size of the nanocrystalline Ni and Ni-Fe alloys decreases to below 20 nm. At average grain sizes greater than 20 nm most of the normalized average values are slightly less than Em / E0 = 1. These samples have a weak to strong (200) fibre texture. Sample no. 1 (Ni, 255 nm) has a very strong preferred (200) fibre texture and a corresponding Em / E0 value which is much lower than Em / E0 = 1. Sample no. 5 (Ni, 23 nm), which has a (111)(200) double fibre texture, is slightly greater than Em / E0 = 1. At average grain sizes less than 20 nm, the normalized values are clearly below Em / E0 = 1 and lie near or clearly below the lower bounds of the composite model predictions. These samples all have a preferred (200) fibre texture. The general trend for Em / E0 as grain size decreases is consistent with previous studies [Shen et al. (1995), Zhou et al. (2003a), Zhou et al. (2003b), Zhou et al. (2009)]; however, there is a notable variability when compared to the composite model predictions. This observation introduces a need to analyze the anisotropic elastic behaviour of these materials and consider the influence of texture together with grain size.
5.5. Effect of Texture on Young’s Modulus As noted in Chapter 4 (Section 4.5.2), the materials in this study were all observed to have some degree of texture. For the purposes of this discussion, the orientation indices for the strongest texture components ( I111 and I 200 ) are also summarized in Table 5.1. To establish an understanding of the anisotropic elastic behaviour of these materials, their dependence on crystallographic orientation is described based on three well known theoretical relationships. Firstly, the extreme situations are considered in order to illustrate
the effect of texture by calculating the values for the principal crystallographic directions in the cubic lattice using [Meyers and Chawla (1998)],
where, sij are the elastic compliances and l1, l2, and l3 are the direction cosines. In the case of the (111) direction, li l j 1 / 3, so the equation reduces to,
Given the elastic stiffnesses ( c11, c12 and c44 ) for single crystal Ni [DeKlerk and Musgrave (1955)] and single crystal Ni-Fe alloys [Kanrar and Ghosh (1983)], the values for the two
principal crystallographic directions are calculated for Ni ( E111 = 293 GPa, E100 = 130 GPa), Ni-10wt.%Fe ( E111 = 299 GPa, E100 = 131 GPa), Ni-20wt.%Fe ( E111 = 294 GPa, E100 = 122 GPa), and Ni-40wt.%Fe ( E111 = 282 GPa and E100 = 103 GPa). E111 is relatively constant up
to Ni-20wt.%Fe and only slightly decreases at Ni-40wt.%Fe. On the other hand, E100 is constant up to Ni-10wt.%Fe, but then gradually decreases at Ni-20wt.%Fe and more so at Niwt.%Fe. With the exception of sample no. 5 (Ni, 23 nm), the materials in this study have a weak to strong (200) fibre texture, and corresponding lower Young’s modulus values when compared to Em / E0 = 1 for grain sizes greater than 20 nm and when compared to the composite model predictions for grain sizes less than 20 nm. In particular, samples no. 8 (Ni-23w.%Fe, 10 nm) and 9 (Ni-32wt.%Fe, 10 nm) are clearly below the composite model predictions which may be owed to E100 ’s decreasing tendency, or sensitivity, with increasing Fe concentration. This is consistent with the findings of Fritz et al. (2003) and Torrents et al.
(2010) for Ni, and Auerswald and Fecht (2010) for Ni-W, who also observed that a preferred (200) orientation tends to produce a lower than expected Young’s modulus. In these studies, it was shown that when the orientation was changed by annealing the materials to remove the texture, there was a corresponding increase in the Young’s modulus.
Secondly, the relative degree of anisotropy is determined by calculating the elastic anisotropy factor [Zener (1948)],
For the isotropic case, = 1 but in the case of Ni, ≈ 2.53; the same can also be shown for Ni-Fe alloys: Ni-10, 20, and 40wt.%Fe, ≈ 2.57, 2.73, and 3.17, respectively. In general, these materials have a relatively high elastic anisotropy which increases with increasing Fe concentration.
Finally, the effect of texture is considered by comparing the measured values to the calculated Voigt and Reuss bounds and the Voigt-Reuss-Hill arithmetic average for polycrystalline single-phase materials which are statistically isotropic (quasi-isotropic). The bounds are determined by calculating the bulk and shear modulus using [Grimvall (1999)],
where, K is the bulk modulus and G is the shear modulus, and subscripts V and R are the Voigt and Reuss bounds, respectively. Given the elastic stiffnesses [DeKlerk and Musgrave (1955), Kanrar and Ghosh (1983)], the bounds are determined from the general relation,
Hill (1952) proposed that an arithmetic average of the elastic properties can be determined by calculating the average bulk and shear modulus given by,
where, subscript VRH refers to the Voigt-Reuss-Hill average. By using the same general relation, i.e., Eq. 5-11, EVRH can then be calculated. The measured values are then plotted as a function of Fe concentration along with the Voigt and Reuss bounds and the Voigt-ReussHill arithmetic average (see Fig. 5.5). The Voigt-Reuss-Hill average for Ni was determined to be 214 GPa. For Ni-10, 20 and 40wt.%Fe, the values were 217 GPa, 209 GPa and 192 GPa, respectively. The observed trend with the addition of Fe is a slight increase at about 10wt.% Fe followed by gradual decrease down to 40wt.% Fe. The Voigt and Reuss bounds
tend to broaden with respect to the Voigt-Reuss-Hill averages as the Fe concentration increases, which is an indicator of increasing anisotropic behaviour. The measured values tend to follow a similar trend with increasing Fe concentration, except that they are consistently lower than the Voigt-Reuss-Hill averages. In the absence of a texture, it would be expected that the measured values lie much closer to the Voigt-Reuss-Hill arithmetic average. In this particular case, sample no. 5 (Ni, 23 nm), who’s measured value is the highest or closest to the Voigt-Reuss-Hill average, has a double (111)(200) fibre texture.
Measured Young’s modulus values for the series of nanocrystalline Ni and Ni-Fe alloys compared with Voigt-Reuss-Hill average values, and Voigt and Reuss bounds.
All other samples, which have a weak to strong (200) fibre texture, are further from the Voigt-Reuss-Hill averages and lie near the Reuss bound. Thus, it is likely that texture is responsible for the lower measured values when compared to the respective Voigt-Reuss-Hill averages. At less than 20 nm, there is likely a combined grain size and texture effect.
When considering the elastic behaviour of these materials, texture is likely to have a strong influence on the normalized value Em / E0. At greater than 20 nm, the influence of grain size is minimal, so the texture can have a stronger influence. At below 20 nm, both texture and grain size can influence Young’s modulus. Another factor known to strongly influence the Young’s modulus of these materials is their magnetic state [Ledbetter and Reed (1973)]. For example, Engler (1938) demonstrated the effect of magnetic fields on the Young’s modulus of several Ni-Fe alloys. In this current study, no applied magnetic field was present during the nanoindentation measurements. However, the magnetization state of the materials was not further studied. It has also been suggested that internal or residual stresses may also affect the measured Young’s modulus [Ledbetter and Reed (1973)]. In general, electrodeposited Ni and Ni-Fe alloys are intrinsically stressed. For example, there is general agreement that increasing Fe concentration in Ni electrodeposits results in an increased deposit stress [Weil (1971), Sotirova-Chakarova and Armyanov (1990), Grimmett et al. (1993)], i.e., Fe acts as a “stress-intensifier”. The origins of this intrinsic stress in electrodeposited nanocrystalline Ni and Ni-Fe alloys will be discussed in Chapter 6.
A kinematics of polycrystal deformation study has recently predicted an increase in the Poisson ratio at very small grain sizes and shear softening at grain boundaries [Weissmuller et al. (2011)]. Experimentally, this was confirmed using a novel ultrasonic technique which showed a 30% shear softening in nanocrystalline Pd made by the inert gas condensation technique Grewer et al. (2011). It would be interesting to conduct similar experiments on electrodeposited nanocrystals to evaluate whether grain boundary shear softening also occurs in nanomaterials made by another synthesis method.
5.6. Summary The hardness and Young’s modulus values were determined for the series of nanocrystalline Ni and Ni-Fe alloys using nanoindentation. Hardness values showed a transition from regular to inverse Hall-Petch behaviour which is consistent with previous studies. The deviation from regular Hall-Petch behaviour is explained based on the influence of decreasing grain size and increasing intercrystal volume fraction resulting in the operation of deformation mechanisms other than dislocation slip. There was no significant influence of grain size on the Young’s modulus of nanocrystalline Ni and Ni-Fe alloys with grain sizes greater than 20 nm. Nanocrystalline Ni and Ni-Fe alloys with grain sizes less than 20 nm displayed slightly reduced Young’s modulus values when compared to their conventional (randomly oriented) polycrystalline counterparts. Although the general trend with grain size was consistent with the composite model predictions, there was notable variability. In order to explain this variability, the influence of texture was considered. Three theoretical relationships were used to characterize the anisotropic elastic behaviour of these materials: 1.
calculated values for the two principal crystallographic directions showed moderate sensitivity for the (111) direction and considerable sensitivity for the (100) direction as the Fe concentration increases, 2. elastic anisotropy factors were relatively high and tend to increase with increasing Fe, and 3. all measured values were below the Voigt-Reuss-Hill average values or near the Reuss bound. As a result, texture is considered to influence the measured Young’s modulus values for the entire grain size range. Moreover, at less than 20 nm, there is likely a combined grain size and texture effect.
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CHAPTER 6 Internal Stress