- Email: [email protected]
Evidence that abnormal grain growth precedes fatigue crack initiation in nanocrystalline Ni-Fe
Scripta Materialia 143 (2018) 15–19
Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Evidence that abnormal grain growth precedes fatigue crack initiation in nanocrystalline Ni-Fe Timothy A. Furnish a,⁎, Daniel C. Bufford a, Fang Ren b, Apurva Mehta b, Khalid Hattar a, Brad L. Boyce a a b
Material, Physical, and Chemical Sciences Center, Sandia National Laboratories, Albuquerque, NM, United States Stanford Synchrotron Radiation Lightsource, Menlo Park, CA, United States
a r t i c l e
i n f o
Article history: Received 4 July 2017 Received in revised form 28 August 2017 Accepted 29 August 2017 Available online xxxx Keywords: Nanocrystalline Fatigue Fracture Nanostructure X-ray diffraction
a b s t r a c t Prior studies on the high-cycle fatigue behavior of nanocrystalline metals have shown that fatigue fracture is associated with abnormal grain growth (AGG). However, those previous studies have been unable to determine if AGG precedes fatigue crack initiation, or vice-versa. The present study shows that AGG indeed occurs prior to crack formation in nanocrystalline Ni-Fe by using a recently developed synchrotron X-ray diffraction modality that has been adapted for in-situ analysis. The technique allows fatigue tests to be interrupted at the initial signs of the AGG process, and subsequent microscopy reveals the precursor damage state preceding crack initiation. © 2017 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
Nanocrystalline (NC) metals with grain sizes b 100 nm exhibit remarkable mechanical properties compared to their coarse-grained counterparts including ultrahigh strength and hardness [1], wear resistance [2], and fatigue strength [3,4]. For potential structural applications, we must understand the mechanistic process by which NC metals fail under fatigue loading, whether from direct cyclic loading (e.g. aircraft turbine blades) or expansion/contraction from thermal cycling (e.g. in microelectronic devices). Review of the limited fatigue-related literature for NC metals reveals two general trends: improved fatigue strengths compared to coarsegrained counterparts [4–6] (i.e. longer lives at given cyclic stresses) and moderate-to-high crack growth rates [3,6–8] (i.e. once a crack has formed, NC metals offer limited resistance to propagation). The latter point is particularly significant as catastrophic failure in engineered NC parts would occur rapidly, with little opportunity to detect cracks and remove the component from service. Especially for materials with low resistance for crack growth, it becomes increasingly important to understand the mechanisms of crack nucleation and to recognize the warning signs, if any, of impending failure. Boyce and Padilla [4,9] observed a new mechanism for fatigue crack nucleation in NC metals involving an interdependency on abnormally large grains (ALGs) embedded in the NC matrix and they hypothesized, based on post-mortem analyses, that abnormal grain growth (AGG) is a precursor for high-cycle fatigue failure in these metals. Other researchers have also alluded to an interrelationship between grain ⁎ Corresponding author. E-mail address: [email protected] (T.A. Furnish).
http://dx.doi.org/10.1016/j.scriptamat.2017.08.047 1359-6462/© 2017 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
growth and fatigue failure in NC metals [10–17]. However, those studies never definitively concluded whether AGG preceded crack initiation, or vice-versa. To address this question, the AGG process must be detected during a fatigue test, as opposed to relying on post-mortem analyses. This is possible by modifying a recently developed synchrotron x-ray diffraction (XRD) method as described in ref. [18]. That previous work demonstrated that the signature of rare ALGs can be statistically distinguished from the ‘background’ XRD intensities from the surrounding NC grains. Our latest work adapted this method for in-situ fatigue [19], which enabled us to observe the onset and evolution of AGG in NC Ni-Fe during highcycle fatigue. In this letter, the XRD technique is adapted for rapid AGG detection during cyclic loading. With this technique, it was possible to intercept the embryonic precursor to fatigue cracking, and interrupt the test prior to crack formation. The present study investigated the high-cycle fatigue behavior of lithographically patterned freestanding thick-film Ni-40 wt%Fe tensile specimens (gage width: 0.5 mm, gage length: 2.4 mm, thickness: 25.6 μm) with a median grain size of 18.5 nm (determined by TEM [19]). Details of the electroplating conditions and resulting microstructure were described in prior development studies [19,20]. A 10 μm radius semicircular notch was machined on a single edge of the specimen using focused ion beam (FIB) milling to prescribe the location of crack initiation. Fig. 1 shows a schematic of the tensile fatigue specimens and a secondary electron microscopy (SEM) image of the FIB-milled notch. Cyclic loading was performed in tension-tension at a frequency of 3 Hz with nominal maximum and minimum stresses away from the notch of 952 MPa and 286 MPa, respectively (R = 0.3). Based on a prior study
16
T.A. Furnish et al. / Scripta Materialia 143 (2018) 15–19
intensity exceeded a set threshold above the local mean intensity, the operator was notified via a cellular text message for unattended 24 h operation. A detection limit of three standard deviations (3σ) above the local mean was used, which minimized false-alarms. Using this new adaptation, three of four samples tested were stopped after AGG but before final failure. For brevity, XRD results from only one representative sample is discussed in this letter. In this case, statistically anomalously high intensities (e.g. 3σ above the local mean) along the (111) diffraction ring were first ‘reported’ by the analysis code at 172 k cycles, at which time the fatigue test was intentionally stopped and the sample carefully removed for SEM imaging. Fig. 2 shows diffraction intensity integrated along the (111) ring at progressive cycles in the fatigue life. The x-axis is χ, the angle around the (111) diffraction ring, and the y-axis is the XRD intensity normalized by the average intensity (and shifted for visualization). While the entire 360° (111) Debye ring was collected, Fig. 2 shows only a 3° χ ‘wedge’ where the anomalous intensity spike emerged. Additional details of the analytical method and an example of a complete diffraction ring can be found in refs [18,19]. In Fig. 2, the normalized diffraction data is shown as grey solid lines while the colored points depict data above a
Fig. 1. (a) Schematic of the fatigue test specimen with a FIB-milled 10 μm radius singleedge semi-circular notch. A 100 μm × 100 μm X-ray beam was centered directly below the notch root during in-situ XRD fatigue measurements.
on notch effects in this material [20], the characteristic maximum stress under the notch is expected to be ~ 1.4 GPa, just below the material's 1.5 GPa yield strength. Elastic finite element analyses and plastic strain fields characterized by digital image correlation are provided in Supplementary Fig. S1; example tensile stress-strain curves are included in Supplementary Fig. S2. Under these cyclic stress conditions, the specimen was expected to fail after ~50–500 k cycles [20]. While other investigators have reported cyclic softening [21] and hardening [22] in nanocrystalline metals, the present study did not observe measurable macroscopic hardening or softening (Supplementary Fig. S3), perhaps because the fatigue evolution only occurred in a localized zone around the notch. A necessity of the in-situ XRD AGG detection technique is to tilt the sample with respect to the incoming X-ray beam during the fatigue test to help ensure that any growing ALGs will diffract to satisfy the Bragg condition. In this case, the specimen was repeatedly tilted from −21° to + 21° (0° defined as the specimen surface perpendicular to the incoming X-ray beam), with a diffraction pattern collected every 2.5° using an exposure time of 75 s. A square aperture defined the 100 μm × 100 μm incident beam size, which was centered on the tip of the notch where the fatigue crack initiated. A custom algorithm in Python [23] was coded to automatically, and rapidly (b1 min temporal resolution), ‘search’ the collected diffraction patterns for anomalously high intensities associated with ALGs. This was accomplished by first transforming the incoming diffraction data from polar to rectangular coordinates, integrating and averaging the data across the diffraction ring (i.e. developing a 1D representation of intensity, I, vs. angle around the diffraction ring, χ), binning the I-χ data (72 × 5° bins), calculating the standard deviation in each bin, and finally comparing each intensity value at every χ value to the local bin average. Once the diffraction
Fig. 2. XRD intensities (normalized by their averages and shifted for visualization) in the χ range that anomalous high intensities associated with ALGs were observed in-situ during cyclic loading. The fatigue was intentionally interrupted after 172 k cycles, prior to failure. The normalized XRD data is shown as grey solid lines while the colored points depict data above a certain number of standard deviations, σ, from the local mean (e.g. purple: 3 b σ b 4; blue: 4 b σ b 5; green: 5 b σ b 6; orange: 6 b σ b 7; red: σ N 7). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
T.A. Furnish et al. / Scripta Materialia 143 (2018) 15–19
certain number of standard deviations, σ, from the local mean (e.g. purple: 3 b σ b 4; blue: 4 b σ b 5; green: 5 b σ b 6; orange: 6 b σ b 7; red: σ N 7). Although the in-situ analysis performed by the Python script (using a threshold of 3σ) originally reported 172 k cycles as the first detection of ALGs, more judicious examination of the data after the fact, as presented in Fig. 2, highlighted that ALGs were present at 126 k cycles and possibly even before 55 k cycles. The fact that the Python script did not detect AGG earlier is partly an issue of threshold value calibration (e.g. the exact number of standard deviations above the local mean is very sensitive to the bin size) and can be fine-tuned for future experiments requiring higher fidelity. Additionally, although statistically anomalous data (i.e. with intensities greater than 3σ above the local mean) first appear at 48.5 k cycles, it is likely that this is the point at which the XRD signal from the ALGs begin to be distinguishable from the background intensity. Improving the signal-to-noise ratio in future attempts, such as by using a smaller beam, may help further elucidate the early stages of AGG. The anomalous peaks shift along the χ axis (i.e. shift along the diffraction ring) during cyclic loading, which indicates a slight crystal rotation of the ALGs as they evolve. Additionally, the peaks ultimately broaden across ~ 1° and multiple peaks form which span ~ 2° (e.g. as shown in the data at 172 k and 165.5 k cycles), indicating either subgrain formation in the growing ALGs or the formation of a second similarly oriented ALG within the interrogation volume. The development of low angle sub-grains has been corroborated by transmission electron microscopy (TEM) and precession electron diffraction [19]. Example TEM images of the ALG region are provided in Supplementary Fig. S4. Fig. 3 shows the total intensity (normalized by the initial total intensity) integrated in the χ range containing the anomalous high intensities (χ = 55.4° to 58.4°) as a function of cycle count. Despite scatter in the normalized data, there is a clear trend of monotonically increasing total intensity. This can be interpreted as continuous growth of the ALGs (i.e., AGG) throughout the fatigue process, assuming that this integrated intensity is roughly proportional to the volume of diffracting crystallite. Although Fig. 2 alone might suggest that AGG began suddenly, it is much more likely that AGG began much earlier in the process, but that the signal from the ALGs was below the noise floor of the current XRD technique. A line is drawn in Fig. 3 highlighting the initially slow AGG followed by a steadily increasing growth rate after ~ 120 k cycles. This trend is remarkably similar to the behavior observed in a Monte Carlo Pott's model by Rollett, Srolovitz, and Anderson (Fig. 17 in ref. [24]) evaluating thermally-driven abnormal grain growth.
Fig. 3. Total intensity across the χ range of interest (cumulative intensity from χ = 55.4° to 58.4°) as a function of the number of cycles indicating continuous growth of the ALGs during cyclic loading.
17
Fig. 4 compares oblique SEM micrographs of the notch before fatigue and after the test was interrupted at 172 k cycles. While localized surface protrusions are present at 172 k cycles, a fatigue crack had not yet formed, supporting the previous speculation [9] that AGG precedes crack formation. The surface extrusions that had formed during fatigue on the edge of the notch were approximately 500 nm in size, similar to
Fig. 4. SEM micrographs of the semi-circular notch (tilted view looking ‘inside’ the notch) before fatigue (a) and after 172 k cycles (b–c). Two immediate observations are the notable absence of any fatigue crack, despite XRD evidence of AGG, and the development of slip protrusions from the notch surface.
18
T.A. Furnish et al. / Scripta Materialia 143 (2018) 15–19
features that have been found in the vicinity of ALG/crack initiation sites in other nanocrystalline fatigue studies [9,19,20]. In other samples tested (not shown here), a small sub-micron fatigue crack was indeed found emanating from these faceted protrusions. The exact mechanism of fatigue crack initiation via these protrusions will be the subject of future work. Given that AGG begins well before crack initiation and that the fatigue-induced abnormal grain size is in the range of hundreds of nanometers to a few micrometers (see our previous work for cross-sectional analyses [9,19,20]), a comparison to crack initiation mechanisms in ultrafine grained (UFG) materials may provide additional insight. Some studies on UFG materials have highlighted macroscopic shear bands that traverse thousands of grains as a shear localization mode for crack nucleation [25,26]. Kunz and Fintová [27] also suggested crack initiation in UFG Cu to be caused by the formation of voids along shear planes. Interestingly, they also observed well-developed extrusions with characteristic sizes corresponding to their 300 nm grain size (i.e. that the extrusions were contained within individual grains). In fact, the extrusions depicted in their study (e.g. Fig. 1 in ref. [27]) are remarkably similar to those observed in this study (Fig. 4). In our current body of work, however, we have never observed long-range shear banding, nor any void nucleation inside or outside of the ALG regions. It should be noted that the current case is unique compared to UFG materials in that there is a single, highly localized region of ALGs that are surrounded by unaffected parent NC grains. This extreme bimodal material condition, with no continuity in grain structure across the ALG region deviates greatly from any relatively uniform grain distributions in the case of UFG materials. Though additional questions persist, it appears that crack initiation in these materials is directly related to these slip protrusions while other factors, such as shear banding and void nucleation, are not prevalent. In post-fracture analysis by precession electron diffraction of fatigue-induced ALGs [19], the orientations of the ALGs were found to be in accordance with maximum Schmid directions (directions within the ALGs experiencing the most shear stress), indicating that AGG is likely induced by dislocation slip processes. The protrusions observed in Fig. 4 follow the trace of a {111} plane and protrude out of the surface in a b011N direction, consistent with an FCC dislocation slip system. Though dislocation activity is thought to be largely suppressed in NC grains, once AGG occurs, the ALGs would be sufficiently large to support traditional dislocation slip mechanisms. Cheng et al. [10] performed careful TEM analysis in NC Ni-Fe that had undergone fatigue-induced grain coarsening. They found that far away from fatigue-coarsened grains, dislocation densities and distributions were comparable to the as-deposited material. Adjacent to coarsened grains, smaller NC grains (d b 20 nm) contained dislocations accumulated near grain boundaries and in some cases, adjoining NC grains exhibited a small-angle misorientation of ~6° constructed from dislocations. In the abnormally large fatigue-coarsened grains (d N 100 nm) high densities of dislocations were observed within the grain interiors. The authors postulated that grain coarsening was promoted by dislocation accumulation at the grain boundaries and that the dislocation distribution was grain size dependent. They also attributed grain growth to rotation of nano-grains, which would leave behind subgrains once they coalesced. This postulation seems consistent with our XRD evidence of grain rotation and the formation of sub-grains accompanying continuous growth of the ALGs. However, to fully elucidate the role of dislocations on AGG and slip band formation during cyclic loading, direct in-situ observation would be invaluable, e.g. via high-cycle in-situ fatigue in the TEM [28]. To conclude, this study utilized a synchrotron-based XRD method for detecting the evolution of rare ALGs in a NC matrix in-situ during highcycle fatigue. Through automated detection, the fatigue process was interrupted after the onset of AGG but before crack initiation. Additionally, slip protrusions stemming from the ALG region were found to eventually nucleate the fatigue crack. Based on these results, the
sequence of fatigue failure in NC metals appears to be quite distinct from UFG metals. The process involves cycle-dependent AGG, the formation of slip protrusions within the ALGs, and finally, crack nucleation. Additional pertinent questions persist, which will be the subject of future work. For example: What are the exact underlying mechanisms of fatigue-induced AGG? Is the process strictly governed by dislocations or are other mechanisms, e.g. grain boundary sliding, necessary? Does AGG begin immediately or is there an incubation period required? Is there a direct correlation between the ALG size and slip features? Addressing these additional questions will be paramount to understanding crack nucleation in a variety of NC metals and toward eventual reliable and predictable use of engineered NC materials. Acknowledgements The authors thank Drs. John Sharon, Cristian Arrington, and Jamin Pillars for material synthesis and Drs. Fadi Abdeljawad and Nathan Heckman for careful internal review of this manuscript. This work was funded by the United States Department of Energy, Office of Basic Energy Sciences (BES) (Grant No. 15013170), Division of Materials Science and Engineering. X-ray diffraction experiments were performed at the Stanford Synchrotron Radiation Lightsource (Proposal No. 4260). Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC0276SF00515. FIB notch preparation and electron microscopy were performed under proposal numbers C2014B0049 and U2015B0093 at the Center for Integrated Nanotechnologies, a United States Department of Energy, Office of Basic Energy Sciences User Facility. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525. Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.scriptamat.2017.08.047. References [1] C.C. Koch, K.M. Youssef, R.O. Scattergood, K.L. Murty, Adv. Eng. Mater. 7 (9) (2005) 787–794. [2] T.J. Rupert, C.A. Schuh, Acta Mater. 58 (12) (2010) 4137–4148. [3] T. Hanlon, E.D. Tabachnikova, S. Suresh, Int. J. Fatigue 27 (10 −12) (2005) 1147–1158. [4] H.A. Padilla II, B.L. Boyce, Exp. Mech. 50 (1) (2010) 5–23. [5] K. Tanaka, M. Sakakibara, H. Kimachi, Procedia Eng. 10 (0) (2011) 542–547. [6] T. Hanlon, Y.N. Kwon, S. Suresh, Scr. Mater. 49 (7) (2003) 675–680. [7] P. Cavaliere, Int. J. Fatigue 31 (10) (2009) 1476–1489. [8] R.A. Meirom, T.E. Clark, C.L. Muhlstein, Acta Mater. 60 (3) (2012) 1408–1417. [9] B.L. Boyce, H.A. Padilla, Metall. Mater. Trans. A 42A (July) (2011). [10] S. Cheng, Y. Zhao, Y. Wang, Y. Li, X.-L. Wang, P.K. Liaw, E.J. Lavernia, Phys. Rev. Lett. 104 (25) (2010) 255501. [11] A.B. Witney, P.G. Sanders, J.R. Weertman, J.A. Eastman, Scr. Metall. Mater. 33 (12) (1995) 2025–2030. [12] X.H. An, S.D. Wu, Z.G. Wang, Z.F. Zhang, Acta Mater. 74 (0) (2014) 200–214. [13] S. Cheng, S.Y. Lee, L. Li, C. Lei, J. Almer, X.-L. Want, T. Ungar, Y. Wang, P.K. Liaw, Phys. Rev. Lett. 110 (135501) (2013). [14] S. Kobayashi, A. Kamata, T. Watanabe, Acta Mater. 91 (0) (2015) 70–82. [15] X.-M. Luo, X. Li, G.-P. Zhang, Mater. Res. Lett. (2016) 1–7. [16] R.A. Meirom, D.H. Alsem, A.L. Romasco, T. Clark, R.G. Polcawich, J.S. Pulskamp, M. Dubey, R.O. Ritchie, C.L. Muhlstein, Acta Mater. 59 (3) (2011) 1141–1149. [17] X. An, Q. Lin, S. Wu, Z. Zhang, Mater. Res. Lett. 3 (3) (2015) 135–141. [18] B.L. Boyce, T.A. Furnish, H.A. Padilla II, D. Van Campen, A. Mehta, J. Mater. Sci. (2015) 1–11. [19] T.A. Furnish, A. Mehta, D. Van Campen, D.C. Bufford, K. Hattar, B.L. Boyce, J. Mater. Sci. 52 (1) (2017) 46–59. [20] T.A. Furnish, B.L. Boyce, J.A. Sharon, C.J. O'Brien, B.G. Clark, C.L. Arrington, J.R. Pillars, J. Mater. Res. 31 (06) (2016) 740–752. [21] S. Cheng, J. Xie, A.D. Stoica, X.L. Wang, J.A. Horton, D.W. Brown, H. Choo, P.K. Liaw, Acta Mater. 57 (4) (2009) 1272–1280.
T.A. Furnish et al. / Scripta Materialia 143 (2018) 15–19 [22] [23] [24] [25] [26]
B. Moser, T. Hanlon, K.S. Kumar, S. Suresh, Scr. Mater. 54 (6) (2006) 1151–1155. F. Ren, https://github.com/fang-ren/fatigue_analysis_TAF 2017. A.D. Rollett, D.J. Srolovitz, M.P. Anderson, Acta Metall. 37 (4) (1989) 1227–1240. L. Kunz, P. Lukáš, M. Svoboda, Mater. Sci. Eng. A 424 (1–2) (2006) 97–104. H. Mughrabi, H.W. Höppel, Int. J. Fatigue 32 (9) (2010) 1413–1427.
19
[27] L. Kunz, S. Fintová, Procedia Eng. 74 (2014) 2–5. [28] D.C. Bufford, D. Stauffer, W.M. Mook, S.A. Syed Asif, B.L. Boyce, K. Hattar, Nano Lett. 16 (8) (2016) 4946–4953.
Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Evidence that abnormal grain growth precedes fatigue crack initiation in nanocrystalline Ni-Fe Timothy A. Furnish a,⁎, Daniel C. Bufford a, Fang Ren b, Apurva Mehta b, Khalid Hattar a, Brad L. Boyce a a b
Material, Physical, and Chemical Sciences Center, Sandia National Laboratories, Albuquerque, NM, United States Stanford Synchrotron Radiation Lightsource, Menlo Park, CA, United States
a r t i c l e
i n f o
Article history: Received 4 July 2017 Received in revised form 28 August 2017 Accepted 29 August 2017 Available online xxxx Keywords: Nanocrystalline Fatigue Fracture Nanostructure X-ray diffraction
a b s t r a c t Prior studies on the high-cycle fatigue behavior of nanocrystalline metals have shown that fatigue fracture is associated with abnormal grain growth (AGG). However, those previous studies have been unable to determine if AGG precedes fatigue crack initiation, or vice-versa. The present study shows that AGG indeed occurs prior to crack formation in nanocrystalline Ni-Fe by using a recently developed synchrotron X-ray diffraction modality that has been adapted for in-situ analysis. The technique allows fatigue tests to be interrupted at the initial signs of the AGG process, and subsequent microscopy reveals the precursor damage state preceding crack initiation. © 2017 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
Nanocrystalline (NC) metals with grain sizes b 100 nm exhibit remarkable mechanical properties compared to their coarse-grained counterparts including ultrahigh strength and hardness [1], wear resistance [2], and fatigue strength [3,4]. For potential structural applications, we must understand the mechanistic process by which NC metals fail under fatigue loading, whether from direct cyclic loading (e.g. aircraft turbine blades) or expansion/contraction from thermal cycling (e.g. in microelectronic devices). Review of the limited fatigue-related literature for NC metals reveals two general trends: improved fatigue strengths compared to coarsegrained counterparts [4–6] (i.e. longer lives at given cyclic stresses) and moderate-to-high crack growth rates [3,6–8] (i.e. once a crack has formed, NC metals offer limited resistance to propagation). The latter point is particularly significant as catastrophic failure in engineered NC parts would occur rapidly, with little opportunity to detect cracks and remove the component from service. Especially for materials with low resistance for crack growth, it becomes increasingly important to understand the mechanisms of crack nucleation and to recognize the warning signs, if any, of impending failure. Boyce and Padilla [4,9] observed a new mechanism for fatigue crack nucleation in NC metals involving an interdependency on abnormally large grains (ALGs) embedded in the NC matrix and they hypothesized, based on post-mortem analyses, that abnormal grain growth (AGG) is a precursor for high-cycle fatigue failure in these metals. Other researchers have also alluded to an interrelationship between grain ⁎ Corresponding author. E-mail address: [email protected] (T.A. Furnish).
http://dx.doi.org/10.1016/j.scriptamat.2017.08.047 1359-6462/© 2017 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
growth and fatigue failure in NC metals [10–17]. However, those studies never definitively concluded whether AGG preceded crack initiation, or vice-versa. To address this question, the AGG process must be detected during a fatigue test, as opposed to relying on post-mortem analyses. This is possible by modifying a recently developed synchrotron x-ray diffraction (XRD) method as described in ref. [18]. That previous work demonstrated that the signature of rare ALGs can be statistically distinguished from the ‘background’ XRD intensities from the surrounding NC grains. Our latest work adapted this method for in-situ fatigue [19], which enabled us to observe the onset and evolution of AGG in NC Ni-Fe during highcycle fatigue. In this letter, the XRD technique is adapted for rapid AGG detection during cyclic loading. With this technique, it was possible to intercept the embryonic precursor to fatigue cracking, and interrupt the test prior to crack formation. The present study investigated the high-cycle fatigue behavior of lithographically patterned freestanding thick-film Ni-40 wt%Fe tensile specimens (gage width: 0.5 mm, gage length: 2.4 mm, thickness: 25.6 μm) with a median grain size of 18.5 nm (determined by TEM [19]). Details of the electroplating conditions and resulting microstructure were described in prior development studies [19,20]. A 10 μm radius semicircular notch was machined on a single edge of the specimen using focused ion beam (FIB) milling to prescribe the location of crack initiation. Fig. 1 shows a schematic of the tensile fatigue specimens and a secondary electron microscopy (SEM) image of the FIB-milled notch. Cyclic loading was performed in tension-tension at a frequency of 3 Hz with nominal maximum and minimum stresses away from the notch of 952 MPa and 286 MPa, respectively (R = 0.3). Based on a prior study
16
T.A. Furnish et al. / Scripta Materialia 143 (2018) 15–19
intensity exceeded a set threshold above the local mean intensity, the operator was notified via a cellular text message for unattended 24 h operation. A detection limit of three standard deviations (3σ) above the local mean was used, which minimized false-alarms. Using this new adaptation, three of four samples tested were stopped after AGG but before final failure. For brevity, XRD results from only one representative sample is discussed in this letter. In this case, statistically anomalously high intensities (e.g. 3σ above the local mean) along the (111) diffraction ring were first ‘reported’ by the analysis code at 172 k cycles, at which time the fatigue test was intentionally stopped and the sample carefully removed for SEM imaging. Fig. 2 shows diffraction intensity integrated along the (111) ring at progressive cycles in the fatigue life. The x-axis is χ, the angle around the (111) diffraction ring, and the y-axis is the XRD intensity normalized by the average intensity (and shifted for visualization). While the entire 360° (111) Debye ring was collected, Fig. 2 shows only a 3° χ ‘wedge’ where the anomalous intensity spike emerged. Additional details of the analytical method and an example of a complete diffraction ring can be found in refs [18,19]. In Fig. 2, the normalized diffraction data is shown as grey solid lines while the colored points depict data above a
Fig. 1. (a) Schematic of the fatigue test specimen with a FIB-milled 10 μm radius singleedge semi-circular notch. A 100 μm × 100 μm X-ray beam was centered directly below the notch root during in-situ XRD fatigue measurements.
on notch effects in this material [20], the characteristic maximum stress under the notch is expected to be ~ 1.4 GPa, just below the material's 1.5 GPa yield strength. Elastic finite element analyses and plastic strain fields characterized by digital image correlation are provided in Supplementary Fig. S1; example tensile stress-strain curves are included in Supplementary Fig. S2. Under these cyclic stress conditions, the specimen was expected to fail after ~50–500 k cycles [20]. While other investigators have reported cyclic softening [21] and hardening [22] in nanocrystalline metals, the present study did not observe measurable macroscopic hardening or softening (Supplementary Fig. S3), perhaps because the fatigue evolution only occurred in a localized zone around the notch. A necessity of the in-situ XRD AGG detection technique is to tilt the sample with respect to the incoming X-ray beam during the fatigue test to help ensure that any growing ALGs will diffract to satisfy the Bragg condition. In this case, the specimen was repeatedly tilted from −21° to + 21° (0° defined as the specimen surface perpendicular to the incoming X-ray beam), with a diffraction pattern collected every 2.5° using an exposure time of 75 s. A square aperture defined the 100 μm × 100 μm incident beam size, which was centered on the tip of the notch where the fatigue crack initiated. A custom algorithm in Python [23] was coded to automatically, and rapidly (b1 min temporal resolution), ‘search’ the collected diffraction patterns for anomalously high intensities associated with ALGs. This was accomplished by first transforming the incoming diffraction data from polar to rectangular coordinates, integrating and averaging the data across the diffraction ring (i.e. developing a 1D representation of intensity, I, vs. angle around the diffraction ring, χ), binning the I-χ data (72 × 5° bins), calculating the standard deviation in each bin, and finally comparing each intensity value at every χ value to the local bin average. Once the diffraction
Fig. 2. XRD intensities (normalized by their averages and shifted for visualization) in the χ range that anomalous high intensities associated with ALGs were observed in-situ during cyclic loading. The fatigue was intentionally interrupted after 172 k cycles, prior to failure. The normalized XRD data is shown as grey solid lines while the colored points depict data above a certain number of standard deviations, σ, from the local mean (e.g. purple: 3 b σ b 4; blue: 4 b σ b 5; green: 5 b σ b 6; orange: 6 b σ b 7; red: σ N 7). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
T.A. Furnish et al. / Scripta Materialia 143 (2018) 15–19
certain number of standard deviations, σ, from the local mean (e.g. purple: 3 b σ b 4; blue: 4 b σ b 5; green: 5 b σ b 6; orange: 6 b σ b 7; red: σ N 7). Although the in-situ analysis performed by the Python script (using a threshold of 3σ) originally reported 172 k cycles as the first detection of ALGs, more judicious examination of the data after the fact, as presented in Fig. 2, highlighted that ALGs were present at 126 k cycles and possibly even before 55 k cycles. The fact that the Python script did not detect AGG earlier is partly an issue of threshold value calibration (e.g. the exact number of standard deviations above the local mean is very sensitive to the bin size) and can be fine-tuned for future experiments requiring higher fidelity. Additionally, although statistically anomalous data (i.e. with intensities greater than 3σ above the local mean) first appear at 48.5 k cycles, it is likely that this is the point at which the XRD signal from the ALGs begin to be distinguishable from the background intensity. Improving the signal-to-noise ratio in future attempts, such as by using a smaller beam, may help further elucidate the early stages of AGG. The anomalous peaks shift along the χ axis (i.e. shift along the diffraction ring) during cyclic loading, which indicates a slight crystal rotation of the ALGs as they evolve. Additionally, the peaks ultimately broaden across ~ 1° and multiple peaks form which span ~ 2° (e.g. as shown in the data at 172 k and 165.5 k cycles), indicating either subgrain formation in the growing ALGs or the formation of a second similarly oriented ALG within the interrogation volume. The development of low angle sub-grains has been corroborated by transmission electron microscopy (TEM) and precession electron diffraction [19]. Example TEM images of the ALG region are provided in Supplementary Fig. S4. Fig. 3 shows the total intensity (normalized by the initial total intensity) integrated in the χ range containing the anomalous high intensities (χ = 55.4° to 58.4°) as a function of cycle count. Despite scatter in the normalized data, there is a clear trend of monotonically increasing total intensity. This can be interpreted as continuous growth of the ALGs (i.e., AGG) throughout the fatigue process, assuming that this integrated intensity is roughly proportional to the volume of diffracting crystallite. Although Fig. 2 alone might suggest that AGG began suddenly, it is much more likely that AGG began much earlier in the process, but that the signal from the ALGs was below the noise floor of the current XRD technique. A line is drawn in Fig. 3 highlighting the initially slow AGG followed by a steadily increasing growth rate after ~ 120 k cycles. This trend is remarkably similar to the behavior observed in a Monte Carlo Pott's model by Rollett, Srolovitz, and Anderson (Fig. 17 in ref. [24]) evaluating thermally-driven abnormal grain growth.
Fig. 3. Total intensity across the χ range of interest (cumulative intensity from χ = 55.4° to 58.4°) as a function of the number of cycles indicating continuous growth of the ALGs during cyclic loading.
17
Fig. 4 compares oblique SEM micrographs of the notch before fatigue and after the test was interrupted at 172 k cycles. While localized surface protrusions are present at 172 k cycles, a fatigue crack had not yet formed, supporting the previous speculation [9] that AGG precedes crack formation. The surface extrusions that had formed during fatigue on the edge of the notch were approximately 500 nm in size, similar to
Fig. 4. SEM micrographs of the semi-circular notch (tilted view looking ‘inside’ the notch) before fatigue (a) and after 172 k cycles (b–c). Two immediate observations are the notable absence of any fatigue crack, despite XRD evidence of AGG, and the development of slip protrusions from the notch surface.
18
T.A. Furnish et al. / Scripta Materialia 143 (2018) 15–19
features that have been found in the vicinity of ALG/crack initiation sites in other nanocrystalline fatigue studies [9,19,20]. In other samples tested (not shown here), a small sub-micron fatigue crack was indeed found emanating from these faceted protrusions. The exact mechanism of fatigue crack initiation via these protrusions will be the subject of future work. Given that AGG begins well before crack initiation and that the fatigue-induced abnormal grain size is in the range of hundreds of nanometers to a few micrometers (see our previous work for cross-sectional analyses [9,19,20]), a comparison to crack initiation mechanisms in ultrafine grained (UFG) materials may provide additional insight. Some studies on UFG materials have highlighted macroscopic shear bands that traverse thousands of grains as a shear localization mode for crack nucleation [25,26]. Kunz and Fintová [27] also suggested crack initiation in UFG Cu to be caused by the formation of voids along shear planes. Interestingly, they also observed well-developed extrusions with characteristic sizes corresponding to their 300 nm grain size (i.e. that the extrusions were contained within individual grains). In fact, the extrusions depicted in their study (e.g. Fig. 1 in ref. [27]) are remarkably similar to those observed in this study (Fig. 4). In our current body of work, however, we have never observed long-range shear banding, nor any void nucleation inside or outside of the ALG regions. It should be noted that the current case is unique compared to UFG materials in that there is a single, highly localized region of ALGs that are surrounded by unaffected parent NC grains. This extreme bimodal material condition, with no continuity in grain structure across the ALG region deviates greatly from any relatively uniform grain distributions in the case of UFG materials. Though additional questions persist, it appears that crack initiation in these materials is directly related to these slip protrusions while other factors, such as shear banding and void nucleation, are not prevalent. In post-fracture analysis by precession electron diffraction of fatigue-induced ALGs [19], the orientations of the ALGs were found to be in accordance with maximum Schmid directions (directions within the ALGs experiencing the most shear stress), indicating that AGG is likely induced by dislocation slip processes. The protrusions observed in Fig. 4 follow the trace of a {111} plane and protrude out of the surface in a b011N direction, consistent with an FCC dislocation slip system. Though dislocation activity is thought to be largely suppressed in NC grains, once AGG occurs, the ALGs would be sufficiently large to support traditional dislocation slip mechanisms. Cheng et al. [10] performed careful TEM analysis in NC Ni-Fe that had undergone fatigue-induced grain coarsening. They found that far away from fatigue-coarsened grains, dislocation densities and distributions were comparable to the as-deposited material. Adjacent to coarsened grains, smaller NC grains (d b 20 nm) contained dislocations accumulated near grain boundaries and in some cases, adjoining NC grains exhibited a small-angle misorientation of ~6° constructed from dislocations. In the abnormally large fatigue-coarsened grains (d N 100 nm) high densities of dislocations were observed within the grain interiors. The authors postulated that grain coarsening was promoted by dislocation accumulation at the grain boundaries and that the dislocation distribution was grain size dependent. They also attributed grain growth to rotation of nano-grains, which would leave behind subgrains once they coalesced. This postulation seems consistent with our XRD evidence of grain rotation and the formation of sub-grains accompanying continuous growth of the ALGs. However, to fully elucidate the role of dislocations on AGG and slip band formation during cyclic loading, direct in-situ observation would be invaluable, e.g. via high-cycle in-situ fatigue in the TEM [28]. To conclude, this study utilized a synchrotron-based XRD method for detecting the evolution of rare ALGs in a NC matrix in-situ during highcycle fatigue. Through automated detection, the fatigue process was interrupted after the onset of AGG but before crack initiation. Additionally, slip protrusions stemming from the ALG region were found to eventually nucleate the fatigue crack. Based on these results, the
sequence of fatigue failure in NC metals appears to be quite distinct from UFG metals. The process involves cycle-dependent AGG, the formation of slip protrusions within the ALGs, and finally, crack nucleation. Additional pertinent questions persist, which will be the subject of future work. For example: What are the exact underlying mechanisms of fatigue-induced AGG? Is the process strictly governed by dislocations or are other mechanisms, e.g. grain boundary sliding, necessary? Does AGG begin immediately or is there an incubation period required? Is there a direct correlation between the ALG size and slip features? Addressing these additional questions will be paramount to understanding crack nucleation in a variety of NC metals and toward eventual reliable and predictable use of engineered NC materials. Acknowledgements The authors thank Drs. John Sharon, Cristian Arrington, and Jamin Pillars for material synthesis and Drs. Fadi Abdeljawad and Nathan Heckman for careful internal review of this manuscript. This work was funded by the United States Department of Energy, Office of Basic Energy Sciences (BES) (Grant No. 15013170), Division of Materials Science and Engineering. X-ray diffraction experiments were performed at the Stanford Synchrotron Radiation Lightsource (Proposal No. 4260). Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC0276SF00515. FIB notch preparation and electron microscopy were performed under proposal numbers C2014B0049 and U2015B0093 at the Center for Integrated Nanotechnologies, a United States Department of Energy, Office of Basic Energy Sciences User Facility. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525. Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.scriptamat.2017.08.047. References [1] C.C. Koch, K.M. Youssef, R.O. Scattergood, K.L. Murty, Adv. Eng. Mater. 7 (9) (2005) 787–794. [2] T.J. Rupert, C.A. Schuh, Acta Mater. 58 (12) (2010) 4137–4148. [3] T. Hanlon, E.D. Tabachnikova, S. Suresh, Int. J. Fatigue 27 (10 −12) (2005) 1147–1158. [4] H.A. Padilla II, B.L. Boyce, Exp. Mech. 50 (1) (2010) 5–23. [5] K. Tanaka, M. Sakakibara, H. Kimachi, Procedia Eng. 10 (0) (2011) 542–547. [6] T. Hanlon, Y.N. Kwon, S. Suresh, Scr. Mater. 49 (7) (2003) 675–680. [7] P. Cavaliere, Int. J. Fatigue 31 (10) (2009) 1476–1489. [8] R.A. Meirom, T.E. Clark, C.L. Muhlstein, Acta Mater. 60 (3) (2012) 1408–1417. [9] B.L. Boyce, H.A. Padilla, Metall. Mater. Trans. A 42A (July) (2011). [10] S. Cheng, Y. Zhao, Y. Wang, Y. Li, X.-L. Wang, P.K. Liaw, E.J. Lavernia, Phys. Rev. Lett. 104 (25) (2010) 255501. [11] A.B. Witney, P.G. Sanders, J.R. Weertman, J.A. Eastman, Scr. Metall. Mater. 33 (12) (1995) 2025–2030. [12] X.H. An, S.D. Wu, Z.G. Wang, Z.F. Zhang, Acta Mater. 74 (0) (2014) 200–214. [13] S. Cheng, S.Y. Lee, L. Li, C. Lei, J. Almer, X.-L. Want, T. Ungar, Y. Wang, P.K. Liaw, Phys. Rev. Lett. 110 (135501) (2013). [14] S. Kobayashi, A. Kamata, T. Watanabe, Acta Mater. 91 (0) (2015) 70–82. [15] X.-M. Luo, X. Li, G.-P. Zhang, Mater. Res. Lett. (2016) 1–7. [16] R.A. Meirom, D.H. Alsem, A.L. Romasco, T. Clark, R.G. Polcawich, J.S. Pulskamp, M. Dubey, R.O. Ritchie, C.L. Muhlstein, Acta Mater. 59 (3) (2011) 1141–1149. [17] X. An, Q. Lin, S. Wu, Z. Zhang, Mater. Res. Lett. 3 (3) (2015) 135–141. [18] B.L. Boyce, T.A. Furnish, H.A. Padilla II, D. Van Campen, A. Mehta, J. Mater. Sci. (2015) 1–11. [19] T.A. Furnish, A. Mehta, D. Van Campen, D.C. Bufford, K. Hattar, B.L. Boyce, J. Mater. Sci. 52 (1) (2017) 46–59. [20] T.A. Furnish, B.L. Boyce, J.A. Sharon, C.J. O'Brien, B.G. Clark, C.L. Arrington, J.R. Pillars, J. Mater. Res. 31 (06) (2016) 740–752. [21] S. Cheng, J. Xie, A.D. Stoica, X.L. Wang, J.A. Horton, D.W. Brown, H. Choo, P.K. Liaw, Acta Mater. 57 (4) (2009) 1272–1280.
T.A. Furnish et al. / Scripta Materialia 143 (2018) 15–19 [22] [23] [24] [25] [26]
B. Moser, T. Hanlon, K.S. Kumar, S. Suresh, Scr. Mater. 54 (6) (2006) 1151–1155. F. Ren, https://github.com/fang-ren/fatigue_analysis_TAF 2017. A.D. Rollett, D.J. Srolovitz, M.P. Anderson, Acta Metall. 37 (4) (1989) 1227–1240. L. Kunz, P. Lukáš, M. Svoboda, Mater. Sci. Eng. A 424 (1–2) (2006) 97–104. H. Mughrabi, H.W. Höppel, Int. J. Fatigue 32 (9) (2010) 1413–1427.
19
[27] L. Kunz, S. Fintová, Procedia Eng. 74 (2014) 2–5. [28] D.C. Bufford, D. Stauffer, W.M. Mook, S.A. Syed Asif, B.L. Boyce, K. Hattar, Nano Lett. 16 (8) (2016) 4946–4953.