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In-Situ Measurements of Free-Standing, Ultra-Thin Film Cracking in Bending

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Abstract

Metallic thin films are widely used and relied upon for various technologies. Direct measurements of fracture toughness are rare for metallic thin films and existing methods for obtaining these measurements often do not provide characterization of the cracking process for determination of crack growth mechanisms. To rectify this, we explore a new technique which utilizes doubly clamped, in-situ three-point bend testing of micro-scale and nano-scale specimens. This is done by in-situ scanning electron microscopy (SEM) and transmission electron microscopy (TEM) mechanical testing for specimens with thicknesses of 2500 nm (SEM), 500 nm (SEM) and 100 nm (TEM). For in-situ TEM, a novel notching method is employed using the converged electron beam which achieves a notch radius of approximately 5 nm. Additionally, we present supporting characterization using Electron Backscatter Diffraction (EBSD) for 2500 nm thick specimens as a demonstration of the potential of this technique for understanding local deformation. Analysis of the acquired data presents several issues that require addressing, and recommendations for future improvements are given.

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Acknowledgments

Funding by INL (DOE) Grant #00109759 (Sub-contract to DE-AC07-951014517) and the Marshall Plan scholarship foundation via Montanuniversität Leoben. The authors would also like to thank Ruth Treml, Peter Imrich and Stefan Wurster for their help on this project. DK acknowledges funding from the Austrian Science Fund FWF (project number P25325-N20).

Author information

Correspondence to E. Hintsala.

Appendices

A1) Fabrication Details

FIB milling of a prepared lamellae was accomplished using a Zeiss LEO1540XB operating at 30 keV by multiple steps shown schematically in Fig. 7. First, the rounded electropolished edge was cut flat using a large beam current of 10 nA from the side, shown as Cut 1. The sample was then turned, reinserted into the FIB, and milled on both sides to produce lamellae of thickness appropriate for the size of samples being fabricated, typically 3× thicker than the final bending beam geometry, utilizing 10 nA current, indicated by Cut 2. At this point, the beam current was reduced to 0.5 nA to create the basic shape of the bending beams by removing material above and below the beam, see Cut 3. Next, careful reduction in size to the final dimension, smoothing the sides and removing FIB tapering was achieved by multiple cuts. This required reinsertion into the instrument to cut from both the top and from the sides. These final cuts were accomplished by using a beam current of 50pA and tilting by 2° into the side walls of the bending beam.

Fig. 7
figure7

Schematic showing the multistep process to fabricate testing specimens indicated as Cuts 1–3

A2) Notch Radius

One issue that requires some attention is whether the pre-notches realistically replicate a sharp crack. Focusing of the ion or electron beam used to produce the notches in this study is imperfect and results in a significant radius of curvature at the root of the notch. One way of viewing the problem was developed by Drory et al. [38] and is presented as equation (A.1):

$$ {K}_{Ic}^{\prime }=\left(1+\frac{\rho }{2x}\right){K}_{Ic} $$
(A.1)

where the effective stress intensity factor K Ic is modified from the ideal K Ic . The ratio of the radius of curvature, ρ, to a somewhat ambiguous length scale factor, x, determines the magnitude of this effect. This was later refined by Pugno et al. [39] and applied by Armstrong et al. to in-situ fracture testing [40], by introducing an asymptotic correction, which is presented as equation (A.2):

$$ {K}_{Ic}^{\prime }=\sqrt{1+\frac{\rho }{2{d}_0}}{K}_{Ic} $$
(A.2)

where d 0 is given by equation. (A.3)

$$ {d}_0=\frac{2}{\pi}\frac{K_{Ic}^2}{\sigma_u^2} $$
(A.3)

where σ u is the ultimate strength of the material. Considering the FIB notched 500 nm and 2500 nm bending beams, reasonable values to use are an ultimate strength of 1 GPa measured previously from pillars of Nitronic 50 of a similar size (1.5 μm diameter), a rough average measured value for K I of 10 MPa-m1/2, and a generous value for the radius of curvature of 100 nm, one gets a correction factor of 1.00039. Clearly this correction is of minor concern for such a notch in a ductile material. One should keep in mind that these concepts were initially developed for macroscopic samples and cracks, therefore they might have limitations when applied to miniaturized samples.

A3) Concerns

There are a number of currently unaddressed issues with this experimental design. First, these deeply cracked bend beams experience a rapidly increasing K I as the crack approaches the back free surface. Second, the support of the nanoindenter on the compressive side, while giving good stability to the system as previously discussed by Jaya et al. [2527], does represent a contact stress gradient. This introduces added complexity to the stress analysis, as the plastic zone from the indentation will interact with the plastic zone at the root of the notch, as described by Chen and Bull [41]. An indentation stress calculation demonstrated a substantially smaller stress from a plasticity standpoint. Using the contact cross-section to estimate the contact flow stress based upon load and imaged contact area, this was determined to be about half of the bending stress. Notably, the situation improves for smaller beams, where the reduced bending loads limit the penetration depth (Fig. 4). Additionally, clamping of the beam is a necessary feature, but this results in mechanical work being dissipated into the clamped region that is not correctly accounted for in the applied J-integral method. Given these challenges, it is clear that the use of Finite Element (FE) or other advanced computational methods will allow to more accurately determine applied stress intensity values.

Secondly, the LEFM or J-integral approach may not be the best descriptor for these very small beams. Earlier studies [42] raised questions about whether or not LEFM or LEFM-based J-integral analysis was always correct. Atluri, et al. [43] showed that a T* criteria may be more appropriate for the complete unloading and reloading format of Figs. 4, 5 and 6. Their concern was that the path-independent integral, J, could be quite different if the plastic zone was elongated to include plasticity in the crack wake, rather than just the plasticity at the front of the crack. In one of the 100 nm beams there was an indication of dislocations in the crack wake, shown in Fig. 4 iiie, where a dark contrast feature is seen along the notch flank. As this is a bright field image, this is still an open question and not a certain proof. However, it is clear in Fig. 4 that substantial dislocation plasticity was generated during the crack growth process. These observations for the first two load and re-load curves shown in Fig. 4 represent K I values according to equation (3) of 3.2 and 4.2 MPa-m1/2. Using a first-order estimate of the plastic zone diameter of π(K I ys ) 2, one evaluates plastic zone sizes at least a factor of four larger than those observed in Fig. 4. It is apparent that additional numerical approaches are required to address plasticity-based slow crack growth in such small-scale bend beams. Previously, we have shown that smaller is tougher for compression of brittle materials that are small in two or three dimensions [14].

The J-integral approach utilized here from equation (4) is standard; a possible refinement would consider the local plastic deformation at the root of the crack and the corresponding local yield stress specifically [44].

A4) Using CTOD as a Verification Technique

In order to determine the viability of the analysis in equations (3–5), they were compared against applied stress intensity factors calculated by crack tip opening displacement [45], δ c , which is given for plane stress as:

$$ {\delta}_c=\frac{K_I^2}{\sigma_{ys}E} $$
(A.5)

where K I is the opening mode applied stress intensity, σ ys is the yield strength and E is the modulus of elasticity. Given that flow stress is enhanced with reduced dimensions, estimation of a reasonable yield stress to use in conjunction with equation (1) required extrapolation of previous data. The yield strength was extrapolated from FIBed nano-pillar compression data for Nitronic 50 and from the austenitic phase of a duplex steel [46]. The data are shown in Fig. 8(a) for a range of pillar diameters ranging from 300 nm to 10 μm. The extrapolation to 100 nm gave a flow stress of approximately 1900 MPa.

Fig. 8
figure8

(a) Flow stress vs. size from micropillar compression data on Nitronic 50 extrapolated to 100 nm (b) Stress intensity values derived from equation (3) versus the measured crack opening displacement (points) and the prediction from equation (A.5) (line) for 100 nm beams

Values of δ c were measured directly from the video using the standard 90° intercept method. Values of K I calculated by equation (3) were plotted against measured δ c values as shown in Fig. 8(b), with the extrapolated flow stress of 1900 MPa inserted into equation (1) to produce the overlaying fitting line. This shows that there is good agreement between analysis using equations (1) and (3) for beams of 100 nm thickness, partially validating the analysis presented. Notably, this analysis assumes no strain hardening, which appears reasonable as repeated loading exhibits little hardening, as one would expect since the 100 nm section thickness allows easy dislocation termination at surfaces.

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Hintsala, E., Kiener, D., Jackson, J. et al. In-Situ Measurements of Free-Standing, Ultra-Thin Film Cracking in Bending. Exp Mech 55, 1681–1690 (2015). https://doi.org/10.1007/s11340-015-0069-2

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Keywords

  • Electron backscatter diffraction
  • Fracture testing
  • Electron micrscopy
  • Steel
  • Nanomechanics