Orientation-dependent solid solution strengthening in zirconium: a nanoindentation study
Orientation-dependent solid solution strengthening was explored through a combined microtexture plus nanoindentation study. Pure zirconium (6N purity crystal-bar Zr) and commercial Zircaloy-2 were investigated for comparison. Local mechanical properties were estimated through finite element (FE) simulations of the unloading part of the nanoindentation load–displacement response. Combinations of ‘averaging’ scheme and constitutive relationship were used to resolve uncertainty of FE-extracted mechanical properties. Comparing the two grades, non-basal oriented grains showed an overall hardening and increase in elastic modulus. In contrast, insignificant change was observed for basal (or near-basal) oriented grains. The strengthening of non-basal orientations appeared via elimination of the lowest hardness/stiffness values without a shift in the peak value. Such asymmetric development brought out the clear picture of orientation-dependent solid solution strengthening in zirconium.
Zirconium alloys are used as in-reactor structural material in the thermal nuclear reactors [1, 2, 3, 4]. Their selection is based on low-neutron-absorption cross section, excellent mechanical and corrosion properties at reactor working temperatures [3, 5, 6]. Any alloy development naturally needs to consider all these aspects. One of these is the aspect of enhancing the mechanical performance, more specifically, possibilities on enhanced strengthening. It is important to note that zirconium has a hexagonal crystal structure [7, 8]. This makes zirconium alloys anisotropic [8, 9, 10, 11]. The orientation sensitivity of the mechanical properties is naturally of both academic and applied interest.
Anisotropy of single crystal zirconium has been discussed in the literature [12, 13, 14, 15, 16, 17]. These studies were performed through conventional mechanical tests on large single crystals, hence they had experimental limitations. Nanoindentation, on the other hand, can serve as an alternative testing procedure, since precise indentations can be made within a grain. This not only eliminates the complications of generating single crystals, but allows measurements on specific microstructural features. Nanoindentation experiments typically provide load–displacement data. Experiments and practices in mechanics, however, demand the stress–strain behavior. It is possible to convert [18, 19, 20, 21, 22, 23] nanoindentation data to stress–strain plots, especially through numerical simulations. This conversion involves regression analysis, and hence the solutions may not be ‘unique’ [19, 20, 24, 25, 26, 27]. In other words, a single nanoindentation load–displacement plot may be described by multiple stress–strain behaviors.
If the above-mentioned problem of ‘non-uniqueness’ is addressed, then nanoindentation can offer interesting insights into metal physics. Of interest to the present manuscript is the effect of alloying to the strengthening behavior at grain scale of a polycrystalline material. A precise indentation made at the center of grain and away from precipitates brings out the effect of solutes present when compared to a solute-free (or negligible solute) grain and ignores the grain size effect. For example, in high-purity thin films of aluminum single crystals the reported difference in hardness, between 〈111〉 and 〈001〉 grains, is 60%. This difference scales with estimated differences in Taylor factor . Grains or orientations of aluminum alloys with a similar difference in Taylor factor, however, show a hardness difference of about 10% . Single crystals of Mg–Li alloy show an increase in the strength of basal planes with Li addition . However, prismatic and pyramidal planes are softened with Li addition . This behavior is valid for a wide range of temperature. Similar behavior is observed with Zn addition in Mg single crystals . In polycrystals, the strengthening effect increases with increase in alloying elements up to solubility limit. This increment is an overall response; however, the relative effect of alloying elements on solid solution strengthening for different orientations in a polycrystalline material remains undocumented.
A previous study  provides preliminary results on orientation sensitivity of nanohardness in crystal-bar zirconium (6N purity) and Zircaloy-2. Though a finite element-based model predicted stress–strain behavior, the problem on non-unique solutions remained. This present contribution expands on the previous work  and provides a possibility to obtain a unique/precise stress–strain behavior from nanoindentations. Covering a wide range of similar orientations for two different grades of zirconium, this study expands the possibility to have an upper limit of orientation-dependent solid solution strengthening.
Chemical composition of Zircaloy-2 (in wt% of alloying elements)
Nanoindentation and electron backscattered diffraction (EBSD)
Before nanoindentation and EBSD, all samples were electropolished using an electrolyte of 80:20 methyl alcohol and perchloric acid under 21 V at 233 K. Nanoindentation tests were performed using a Hysitron Triboindenter™ (TI 900). All nanoindents were made using a Berkovich tip in load-controlled mode to a maximum load of 5000 μN. Berkovich indenter is a three-sided pyramidal tip with half included angle of 70.3°. The contact area between indenter and material is different between spherical and Berkovich tip. Following the Oliver–Pharr analysis method  and Hertzian contact model  for nanoindentation, one needs to find appropriate contact radius. If that is considered, then stress–strain behavior for spherical or circular tips is expected to be similar. Further, using the same loading module (the so-called high-load or low-load module in a nanoindenter) strains imposed and plastic zones established are noticeably higher for Berkovich. The sharp Berkovich indenter not only provides an expanded stress–strain response, but more effectively avoids influence (if any) of grain below the indenting grains. A triangular waveform was assumed with 1000 μN/s loading and unloading rate and 10 s hold time. The maximum load was decided after a set of initial trial experiments by varying loads till projected area of indentation gets constant . To avoid having any grain size effect, indents were placed carefully close to grain center in Zircaloy-2. From the respective load–displacement plots, hardness and reduced elastic modulus were estimated using the Oliver and Pharr analysis . The indented samples were then scanned using EBSD (electron backscattered diffraction: TSL-OIM™) in a FEI™ Quanta-3D FEG (field emission gun) SEM (scanning electron microscope). Step size of 0.1 μm and identical beam/video conditions were maintained between the scans for comparison. Various precipitates may form during phase transformations in single-phase Zr alloys [3, 36]. These hard intermetallic precipitates are referred to as ‘2nd phase’ in the present work. They can be classified as: (1) Zr2(FeNi)-type intermetallic, (2) hexagonal Zr(CrFe)2 Laves phase precipitate and (3) Zr3P precipitates. Combining the inverse pole figure (IPF) and image quality (IQ) maps, near-boundary indents and indents close to the second phase were identified and subsequently omitted from the analysis.
Finite element modeling
Comparison of plastic zone size between experiment and simulation
Experimental plastic zone size (μm)
Simulated plastic zone size (μm)
Ratio of experimental plastic zone size (min/max)
Ratio of simulated plastic zone size (min/max)
This study involved orientation-dependent nanoindentation measurements in high-purity zirconium crystal-bar and in commercial Zircaloy-2. Zircaloy-2 had, on average, 25–28% higher hardness and elastic stiffness than 6N (99.9999 wt% Zr) purity crystal-bar. The shift in mechanical properties was anisotropic—elimination of lower hardness/stiffness with insignificant changes in the highest value.
The nanoindentation plots were converted to stress–strain behaviors through appropriate finite element modeling of the unloading part. The proposed scheme of ‘averaging’ and a constitutive relationship can predict toward a unique solution. This, on the other hand, helped in the effective study of the orientation-dependent solid solution strengthening. The increment in hardness due to solid solution strengthening was negligible in the hard basal/near-basal crystallographic orientations, and significant in the softer non-basal orientations.
The authors would like to express their appreciations for the support from BRNS (Board of Research on Nuclear Sciences), Nanoindentation facility at Metallurgical Engineering and Materials Science (MEMS), IIT Bombay, and National Facility of Texture and OIM (a DST-IRPHA project), IIT Bombay.
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