Orientation-Dependent Nanomechanical Behavior of Pentaerythritol Tetranitrate as Probed by Multiple Nanoindentation Tip Geometries

Abstract

Nanoindentation can be leveraged to aid in the high fidelity modeling of dislocation mediated plasticity in pentaerythritol tetranitrate (PETN), an anisotropic energetic molecular crystal. Moreover, nanoindentation tip parameters such as tip geometry, size, and degree of acuity can be utilized to target anisotropic behavior. In this work, nanoindentation was conducted across a range of orientations on the (110) face of PETN to characterize resultant yield behavior, mechanical property measurements, and resultant slip behavior and fracture initiation. Three different indentation tips were utilized: a 3-sided pyramidal Berkovich tip, a 4-sided high aspect ratio Knoop tip, and a 90° conical tip. Ultimately, indenter tip radius was documented to impact yield behavior, whereas tip geometry affected larger scale processes such as slip, and tip acuity was the dominating factor that led to fracture. The axisymmetric conical tip, serving as a baseline, showed the least amount of variation in mechanical property measurements but also the largest distribution of maximum shear stress at which initial yielding occurred. Its high degree of acuity, however, was more prone to induce fracture at higher loads. The Knoop tip was shown to be suitable for average measurements, but also for elucidation of certain anisotropic features. A distinctly higher perceived hardness at 45° was measured with the Knoop tip, indicating less dislocation motion in that direction also observed in this work via scanning probe microscopy. Lastly, the commonly used Berkovich tip was a good compromise whereby it provided a representative volume element describing the average behavior of the material. These results can be utilized to target desired anisotropic behavior in a wider range of molecular crystals, as well as to inform theoretical considerations for dislocation mediated plasticity in PETN.

1. Introduction

Molecular crystals are utilized across a wide range of applications, including pharmaceuticals [1,2,3,4], energetic materials [5,6], agricultural science [7,8], and solar energy [9,10]. Due to the low symmetry, large size, and complexity of the unit cells of most organic molecular crystals, their mechanical behavior can differ markedly from those of atomic and ionic crystals [11]. Deformation, particularly the understanding of defects [12] and dislocation behavior in these materials, has been of academic and practical interest with consequences in both the yielding of energetic molecular crystals [13] as well as the packing ability of pharmaceuticals for tableting [14,15], due to their similar need to understand how the crystals compact and plastically flow. Because of this, the mechanisms for dislocation motion are important to quantify, whether it is via homogeneous nucleation or by activation of a nearby source. The maturation of nanoindentation complements this research area due to its high precision at the nanoscale and has allowed for the properties of such materials to be characterized at small volumes [16,17].

The onset of plasticity has been a topic of broader interest across the nanoindentation field. In a nanoindentation experiment where initial loading is fully elastic, the onset of plasticity can be indicated by a discontinuity in the load-displacement curve with an increase in depth without a corresponding increase in load and is often referred to as a “pop-in” [18,19]. The study of pop-ins spans the realm of materials research, and deformation mechanisms that can be studied via pop-in event include: dislocation nucleation or activation of a source [20], thin film fracture [21,22], twin formation [23], phase transformations [24,25], and flow of vacancies via diffusion [26]. The length of the pop-in is related to the number of dislocations generated under the indenter tip, which is thought to be correlated to the size of the plastic zone induced by the tip [27,28].

The correlation between the activation volume required for dislocation nucleation and tip geometry was studied by Schuh et al. in 2004, where they used nucleation theory to study the rate dependence of incipient plasticity during nanoindentation to question how the use of a blunt or sharp tip can sample different dislocation behavior [29]. Accurate prediction of dislocation nucleation under the indenter is challenging and multiple theories and criteria have been put forward in literature. Loss of ellipticity leading to an invalidation of the governing equations [30], critical value of stress gradients [31], and maximum shear stress [32] are some of the criteria used to consider dislocation nucleation under the indenter.

Even on a nearly isotropic material, the size and geometry of the indenter tip will not only impact the load-displacement behavior of the material, but also how the material elastically deforms due to varying amounts of strain localization. The role of tip geometry and degree of acuity is shown in Figure 1: when a fixed load is applied, the maximum indentation depth h will be different for each indenter tip highlighted in this paper. The impact of tip acuity, $\theta$ is also highlighted in a scenario where the indentation depth is fixed, resulting in different applied loads and different projected areas. The value of $\theta$ is standardized for each indenter tip geometry, in which the semi-angle $\theta$ is 65.3° for a Berkovich, 86.15° and 65° for the Knoop long and short axes, and 45° in the case of a 90° conical indenter tip.

Pentaerythritol tetranitrate (PETN), the material studied in this work, is an anisotropic molecular crystal with a tetragonal crystal structure. PETN is typically considered to be the most sensitive secondary explosive in the high explosives category [33]. The yield behavior of the material is of importance for compaction, with consequences in the pressing of PETN pellets for detonators [34] and for understanding the deformation during high-rate loading [35,36]. The utilization of nanoindentation to link molecular crystal defect density with yielding behavior has been studied previously [37]. It is important to rigorously investigate the indentation of molecular crystals using multiple tip geometries [38], as axisymmetric contact geometry assumptions may not always apply, in which the indented impression conforms to the tip geometry [39]. For this study, the $\left(110\right)$ face of PETN was investigated to reduce the effect on localized shear stresses that multiple crystal faces could introduce. Additionally, the $\left(110\right)$ face is easily identifiable as the largest face on the solution-grown crystals and is in the family of major slip planes [40,41].

In this paper, nanoindentation was used to quasistatically test PETN crystals using three tip geometries: a Berkovich tip, a three-cornered pyramidal shape; a Knoop tip, a four-cornered diamond-shaped pyramid with a significantly higher aspect ratio; and a 90° conical tip. Multiple tips were selected to determine which tip geometries were most effective in determining yield behavior, flow, and characterizing limited slip systems in anisotropic materials. Crystal growth as well as the sample mounting technique are first presented in Section 2, followed by the experimental parameters. Results are presented in Section 3 in three categories: yield behavior, hardness and reduced elastic modulus measurements, and slip behavior and fracture initiation. Discussion of how this may be utilized when characterizing anisotropic materials via nanoindentation is then considered through the analysis of the onset of plasticity seen at the beginning of an indentation test, along with the resulting meso-scale slip behavior around an indent impression that caused significant deformation. This paper thus aims to document the effect of both how PETN behaves under a generic spherical load point contact as a base case to compare the resultant slip behavior needed to accommodate a wider range of indenter tip geometries.

2. Materials and Methods

The PETN crystals were grown at Los Alamos National Laboratory through a solvent crystallization process and mounted for indentation at Purdue University using the method prescribed by Maughan et al. [42]. By way of this mounting process, the crystal was oriented and adhered to a 15 mm steel disk using CrystalBond adhesive by raising the crystal on a scissor jack until it made level contact with the magnetically suspended disk. This process assisted with level mounting of the crystal and ensured that the desired orientation was perpendicular to the indenter tip. An optical image of a typical PETN crystal after this process is provided in Figure 2.

Nanoindentation was conducted using a Hysitron Triboindenter 950. The Hertzian method was first used to measure the radii of the three tips by indenting Fe-3%Si at varying loads up to 12 mN to capture representative indentation depths within the elastic loading regime [44]. The respective tip radii were then determined by fitting a Hertzian elastic curve to the initial elastic loading portion, and an average of 16 indentations were used to estimate the tip radius. The radii of the Berkovich, Knoop, and conical tips were 550 nm, 850 nm, and 964 nm, respectively. These estimations showed agreement with the original manufacturer’s tip radius measurements, with gradual changes to tip radius expected over time after regular use.

To track orientation, the 0° orientation was defined based on the $\langle \overline{1}10\rangle$ direction of the PETN crystal, which can be identified visually. Because the tip orientation was fixed in the instrument, the crystal was rotated according to the corresponding orientations depicted in Figure 3, where the 0° orientation aligns with the $\langle \overline{1}10\rangle$ direction and the 90° orientation aligns with the $\langle 001\rangle$ direction. Due to the 3-fold symmetry of the Berkovich tip, the crystal was offset by 45° to align with one of its corner axes.

A total of 59 1 mN indents were done using the Berkovich tip, across 8 orientations. Similarly, a total of 108 indents were done using the Knoop tip, and 75 indents were done using the conical tip. Larger indents at 13 mN were also done to study slip behavior: a total of 32 large indents were done with the Berkovich tip across the same orientations, 27 indents with the Knoop, and 21 indents with the conical. For this work, indents were done on PETN across five different crystals to limit potential confounding parameters such as surface roughness, unlevel mounting, and potential variations in initial dislocation density. To select an area for indenting, Scanning Probe Microscopy (SPM) was conducted on a candidate region to ensure that the surface had no obstructing features, and that the slope of the surface was less than 1°. Indents were done from the 0° to 90° orientations in 15° increments. Indents were also done at 120° with the Berkovich tip, and 135° with the Knoop tip.

A quasistatic load function was applied with a 30 s loading time, 5 s holding time, and 5 s unloading time to a maximum load of 1 mN, a load at which none of the indentations showed any evidence of indentation-induced fracture. To emphasize the slip behavior and potential for cracking, indents were also done at 13 mN and followed with SPM. To image the 13 mN conical tip indents, a cube corner tip was used for SPM for improved resolution. The hardness was then calculated from the unloading curve, and the reduced elastic modulus was also calculated according to the method described by Oliver and Pharr [39].

3. Results

3.1. Yield Behavior

Representative 1 mN load-displacement data using the Berkovich, Knoop, and conical indenter tips on PETN are shown in Figure 4 at each orientation. The load-displacement curves showed a distinct difference in the yield behavior of the PETN when using different indenter tips. The elastic portion of the loading curve is correlated with tip radius, hence the conical and Knoop slopes were more closely matched. The Berkovich tip indents showed very repeatable elastic loading regimes, and a small range of loads at which the initial pop-in occurred regardless of crystal orientation. The conical tip showed similar consistency in the elastic regime, but with the highest plastic threshold of the three data sets. In comparison, the Knoop indents showed a distinctly higher sensitivity to anisotropy, with a much wider range of loads at which the initial pop-in events occurred, along with more dislocation movement after initial yielding represented by a degree of waviness of the 75° and 90° indents taken with the Knoop tip.

The initial onset of plasticity is correlated with the maximum shear stress prior to plastic deformation. The onset of plasticity occurred at contact depths less than the transition of the indenter tip from spherical to self-similar: therefore a spherical approximation of stresses at yield is appropriate. The maximum shear stress also compensates for the effect of tip radius and reduced elastic modulus, providing further insight into the distribution of yield events. The maximum shear stress was estimated using Equation (1) [45],

$${\tau }_{max}=0.31({\displaystyle \frac{6{E_r}^2}{{\pi }^3{R}^2}}{)}^{1/3}{P}^{1/3}$$

(1)

where $E_r$ is the reduced elastic modulus, R the indenter tip radius, and P the load at the first initial yield point. The cumulative fraction distribution for all indents that displayed a distinct initial yield point is shown in Figure 5, in which all indents taken at a given orientation were utilized to produce a single cumulative fraction curve.

From the cumulative fraction distribution of maximum shear stress for each tip type, on average the Berkovich indents had the lowest maximum shear stress prior to plastic deformation, and the conical indents had the highest. The slopes and variability regarding orientation also indicated that the Berkovich indents had the least amount of variability, both regarding yield behavior as well as orientation dependence. The Knoop indents showed a shallower slope and broader distribution of the cumulative fraction distribution curves, further indicating that there was a broader range of loads at which the material yielded under the Knoop tip. Finally for the conical indents, the most variability in maximum shear stress at yield occurred. The slope of the cumulative fraction distribution in Figure 5 directly scales to the activation volume. When under an applied stress, the activation volume is the difference in volume over which deformation must occur; it can also be described as the difference in volume when comparing a molecule in a nonactivated and an activated state [46]. The Schuh method, originally demonstrated on platinum using a Berkovich tip [47], was used to calculate the activation volume by linearizing the cumulative fraction distribution of initial yield load, P,

$$ln\left[ln\left({\displaystyle \frac{1}{1-F\left(P\right)}}\right)\right]=\alpha P^{1/3}+\delta$$

(2)

where $\alpha$ is the slope and $\delta$ is the intercept of the linearized data. The activation volume is given by,

$$V_{act}={\displaystyle \frac{\pi }{0.47}}{\left({\displaystyle \frac{3R}{4E_r}}\right)}^{2/3}kT·\alpha$$

(3)

where k is the Boltzmann constant, and T the temperature. The activation volume was calculated for each cumulative fraction curve, and the activation volume calculations are shown in Figure 6. Crystal orientation was not seen to significantly track with activation volume, hence the individual orientations were not differentiated in the figure. With a sample size of six, the 550 nm tip (Berkovich) indents had an average activation volume of $75.8{\mathring{\mathrm{A}}}^3$. With a sample size of eight, the 850 nm tip (Knoop) indents had an average activation volume of $60.1{\mathring{\mathrm{A}}}^3$. And with a sample size of seven, the 964 nm tip (conical) indents had an average activation volume of $48.3{\mathring{\mathrm{A}}}^3$.

Overall, an increase in tip radius resulted in a lower activation volume on average, although the spread in the activation volumes within each tip category may not provide a statistically adequate representation on its own. Nevertheless, the broader distribution of yield events observed with the Knoop and conical tips did result in a lower activation volume overall as compared to the very narrow distribution of yield events as seen with the Berkovich, which showed agreement with Schuh’s findings with regard to the statistical correlation between plasticity behavior and activation volume. This correlation indicates that when the initial onset of plasticity is variable using a particular tip geometry, the activation volume necessary for plasticity to occur is smaller as opposed to a larger activation volume with which consistent deformation mechanisms are more statistically likely to be activated. It also means that for a larger tip, there is less surrounding volume necessary to drive the surrounding area from non-plastically being under stress, to plastically deforming via dislocation nucleation or source activation. It is non-trivial to isolate the individual roles of varying tip geometries and tip radii on resultant stress profiles in this case; however, it is seen that different activation volumes are required for dislocation nucleation to occur. Other contributing factors to activation volume sensitivity also include limited slip planes, intermolecular interactions, and crystal orientation.

3.2. Hardness and Reduced Elastic Modulus

The hardness was calculated via

$$H={\displaystyle \frac{P_{max}}{A}}$$

(4)

where $P_{max}$ is the maximum applied load and A the contact area. The latter was calculated from the area function that determines the area of a calibration indent [39]. Similarly, the reduced elastic modulus, $E_r$, is given by

$$E_r={\displaystyle \frac{\sqrt{\pi }}{2\beta }}{\displaystyle \frac{S}{\sqrt{A}}}$$

(5)

where S is the contact stiffness and $\beta$ is a scaling constant based on tip geometry. Figure 4 shows the load-displacement curves from which the hardness and reduced elastic moduli were determined for the Berkovich, Knoop, and conical indenter tips. The hardness and reduced elastic modulus measurements are shown in Figure 7, where they were grouped by crystal orientation with respect to the defined tip axis, as well as the tip geometry. A summary of the hardness and reduced elastic modulus measurements for each tip geometry is provided in

Table 1. Summary of hardness and reduced elastic modulus measurements for each tip geometry, as well as their respective coefficients of variance (CoV).

Indenter Geometry	Tip Radius (nm)	Hardness, H (GPa)	CoV of H (0–90°)	Reduced Elastic Modulus, ${\mathit{E}}_{\mathit{r}}$ (GPa)	CoV of ${\mathit{E}}_{\mathit{r}}$ (0–90°)
Berkovich (n = 59)	550	0.529 ± 0.106	0.207	15.195 ± 1.078	0.071
Knoop (n = 108)	850	0.376 ± 0.099	0.259	18.782 ± 1.628	0.083
Conical (n = 75)	964	0.324 ± 0.060	0.186	12.052 ± 0.058	0.058

. The conical indents had the lowest amount of variability, in which the Berkovich and Knoop $E_r$ measurements had a 18.3% and 30.1% higher coefficient of variance (CoV) compared to the conical, respectively. Similarly, the Berkovich and Knoop hardness measurements has respective CoVs that were 10.1% and 28.2% higher than the conical CoV for hardness measurements.

Overall, the more axisymmetric the tip geometry, the lower the observed reduced elastic modulus. This difference can be attributed to plasticity and most likely due to the differences in contact area where the deformed material may not exactly conform to the tip at a given depth. The tips were calibrated in fused quartz, and when indenting aluminum, Fe-3%Si, and tungsten with all three tips to the same depths, the average reduced elastic modulus was the same regardless of indenter tip. Therefore, indenter tip selection should be intentional when indenting highly anisotropic materials with limited slip systems, as measured contact area can be impacted by the material’s ability to conform to the tip geometry, ultimately influencing the perceived reduced elastic modulus and hardness measurements.

The conical indents have the least amount of variability in mechanical property measurements. The Knoop hardness measurements showed agreement with the findings of Gallagher and Halfpenny et al., where the hardness measurements were at a relative maximum along the $\langle \overline{1}10\rangle$ and a relative minimum along the $\langle 001\rangle$ direction [40]. However, an exception was observed for the 45° orientation where the Knoop tip measured a significantly higher hardness value. This outlier at 45° was also observed using the Berkovich tip, which overall showed a pattern of a relative maxima every 90°. The conical, due to its axisymmetric geometry, served as a baseline of comparison as having the lowest coefficient of variance for both hardness and reduced elastic modulus measurements. The reduced elastic modulus measurements did not show a significant dependence on orientation. The variability in $E_r$ measurements at each orientation was observed in the Berkovich and more so with the Knoop measurements, however a clear average can be visually observed of approximately 14–16 GPa in agreement with prior studies [48].

3.3. Slip Behavior and Fracture Initiation

Images of the post-indentation impression of representative 13 mN indents at each orientation are shown in Figure 8 using all three tip geometries. The 13 mN load was selected to generate a larger volume to image and make post-indent imaging reproducible, however the properties are not reported at this load as the 13 mN indented reached a depth to which these tips were not calibrated; consequently, the potential for indentation-induced cracking would negatively influence the measured values.

Regardless of tip geometry, the slip band traces surrounding the indented region followed the ⟨001⟩ direction at each crystal orientation. It should be noted in this figure that the Berkovich scans were oriented with respect to how the tip was mounted, so the ⟨001⟩ direction was rotated 45° clockwise from the vertical direction in the Berkovich scans. Across all tip geometries it was more prevalent for groupings of small slip step traces to occur, as opposed to individual large slip steps. Surprisingly, cracking was observed consistently using the conical tip, but not in the Knoop indents. The conical tip, having more of an acute angle, has an overall higher average strain around the indenter tip, which appears to be more likely to initiate cracking than the localized stress concentrations of the corners of the Knoop and Berkovich tip geometries. This agrees with the findings of Morris et al., who asserted that more acute tips generate fracture [49]. A primary crack consistently initiated along the $\langle 001\rangle$ direction, and several smaller radial cracks were also observed in multiple directions. Any in-plane orientation effects observed with the conical indenter can otherwise be attributed to the inherent variability of the material with respect to surface roughness and defect density.

4. Discussion

The dependence of the sensitivity of single crystal PETN to pop-in events on indenter tip geometry was quantified through several nanoindentation methods with three different tip geometries. With increasing tip radius, a positive correlation to maximum shear stress, and a slightly negative correlation to activation volume was measured. Increasing tip radius was also positively linked to amount of variability in yield behavior. The onset of plasticity occurred in this material at a depth where all three tip geometries were still relatively spherical; hence, tip radii played a significant role in yield behavior [50,51,52]. The 964 nm tip (conical) had the broadest distribution of maximum shear stress at the same stress. The largest tip (conical) also had the smallest variability due to orientation effects compared to the non-axisymmetric 550 nm (Berkovich) and 850 nm (Knoop) tips.

The geometry of the indenter tip also has an impact on the resultant yield behavior of PETN, largely due to the difference in the volume of material tested. This ultimately impacts the larger scale processes such as slip and potential for fracture as the indentation depth reaches the self-similar region. More slip bands and cracking occurred in the case of the conical indents, as the larger radius of the tip enabled a higher volume of material to be tested. The findings of this work also showed agreement with the slip systems of PETN as defined by Gallagher and Halfpenny et al. [40], where considering $\left\{110\right\}$ as a major slip plane for PETN, the slip band traces on the surface of the $\left(110\right)$ plane were all aligned in the $\langle 001\rangle$ direction regardless of tip geometry and orientation. This quantification of orientation-dependent hardness anisotropy has been previously studied in cubic carbides and can be applied to other systems [53].

The Knoop hardness measurements agreed with previous literature regarding the $\left(110\right)$ in-plane orientation hardness variability of PETN; however, both the Berkovich and Knoop tip captured an increased perceived hardness when a major tip corner was 45° away from the $\langle 001\rangle$ direction, demonstrating that a non-axisymmetric indenter will show enhanced hardness when fewer slip systems are activated. The higher perceived hardness at 45° is an interesting exception to the otherwise agreed trend with Schuh et al., and indicates that it is more difficult for dislocations to move at this orientation, resulting in a higher perceived hardness and was also observed by less overall slip step traces at this orientation. Increasing the degree of axisymmetry of the indenter tip will also result in a lower observed reduced elastic modulus. This could be due to the sampling of different volumes of material, but the most likely cause would be small variations in non-conformity with the tip after plasticity occurs in these materials. No observable cracking occurred while indenting at 1 mN with the conical tip; the lower indentation depth was shallow enough such that the acuity had not yet reached 90°. In contrast, when indenting to 13 mN the depth of the conical tip was much deeper, utilizing its full acuity, which resulted in significant cracking. Hence a higher tip acuity was confirmed to track with higher likelihood of fracture at identical loads, which is in agreement with previous literature.

It is also worth distinguishing that the tip acuity dominates the strain induced rather than the tip radius. A completely vertical cumulative fraction distribution would have indicated yielding at precisely the same load every time. Schuh’s model explains the broader slope of each cumulative fraction plot by thermal activation of dislocation nucleation events. Alternatively, the broader slope can also indicate activation, rather than nucleation, of a dislocation source (e.g., cross-slip or a pre-existing defect) was more likely to occur, resulting in more variable yield behavior. Sophisticated nucleation criteria, such as Li et al. [30] and Garg et al. [31] consider all stress components, not only maximum shear value, and can potentially be sensitive to perturbations in the stress field. The perturbations in the stress field arise due to variability in test conditions, such as surface roughness and presence of defects in the sample.

It also suggests that the sampled volume was large enough for the conical indents such that a dislocation source was activated [54]. The variation in hardness measurements also indicated a sparse defect density. Across most indents regardless of tip geometry, it was shown from SPM to be more favorable for localized regions of small slip bands to form, rather than larger, sparse slip bands to nucleate new dislocation sources that would attempt to conform to the shape of the indent (see Appendix A Figure A3 for slip step height measurements as measured via SPM). Less apparent slip traces were also observed at 45° for the Knoop and Berkovich indents, further indicating less dislocation motion in that direction as measured by a higher perceived hardness. The limited slip systems were also observed to inhibit the ability of the material to perfectly conform to the shape of the conical tip. While the use of SPM in this work is isolated to qualification of slip behavior and fracture initiation, atomic force microscopy and its accessory modules such as lateral force microscopy can also be used to quantify the anisotropic behavior of molecular crystals further. As seen in the supplemental information, the comparison of tip geometries at different approaching angles to the slip steps compels the case for a tip geometry with a higher degree of acuity and axisymmetry when scanning over small surface features such as slip traces at varying orientations for consistent results.

5. Conclusions

PETN crystals were indented using three tip geometries with varying levels of axisymmetry while also varying the orientation of the crystal. The work presented offers margins of sensitivity for the commonly utilized Berkovich tip in comparison to an axisymmetric (conical) and very non-axisymmetric (Knoop) tip. It was shown that the degree of tip axisymmetry, as well as tip radius size and degree of acuity, can significantly impact nanoindentation results when studying the anisotropic behavior of PETN. This consideration of multiple tip parameters has allowed for the elucidation of a significantly higher perceived hardness on the (110) plane of PETN at 45°, indicating that it is more difficult for dislocations to move in that direction, as seen by higher perceived hardness and less overall slip step traces on the surface.

The Knoop tip can thus be leveraged for average measurements to emphasize certain anisotropic features in molecular crystals with limited slip systems. A conical tip served as a baseline of variability to study the activation of dislocation sources within the material without the effect of crystal orientation or the potential impact of a non-axisymmetric tip; however, the high acuity of the tip was shown to be more prone to fracture at higher loads. Ultimately, the Berkovich tip is a well-balanced choice for the measurement of average properties of molecular crystals.

Nanoindentation of the $\left(110\right)$ plane of PETN at varying orientations using three different tip geometries exposed sensitivity to yield behavior, mechanical property measurements, as well as slip behavior and crack initiation. By focusing on a single major slip plane within this work, the experimental results can aid high fidelity models of PETN single crystals and their onset of plasticity as they are tested in high-strain conditions where crystallographic orientation is highly influential in the bulk mechanical response.