Measuring Nanoscale Stress Intensity Factors with an Atomic Force Microscope

Atomic Force Microscope images of a crack intersecting the free surface of a glass specimen are taken at different stages of subcritical propagation. From the analysis of image pairs, it is shown that a novel Integrated Digital Image Correlation technique allows to measure stress intensity factors in a quantitative fashion. Image sizes as small as 200 nm can be exploited and the surface displacement fields do not show significant deviations from linear elastic solutions down to a 10 nm distance from the crack tip. Moreover, this analysis gives access to the out-of-plane displacement of the free surface at the crack tip. The mechanisms of subcritical crack propagation in silicate glasses have been the subject of extensive research (cf. [1, 2] for recent reviews). The development of advanced AFM techniques to probe in-situ crack propagation or post-mortem crack surface morphologies have recently led to explore these mechanisms at their relevant nanometric scale leading to remarkable observations on plastic crack tip damage [3, 4], stress-induced ion migration [5] and capillary condensation inside the crack tip cavity [6]. However, a proper understanding of these observations in terms of sound mechanical modeling has been hampered by the lack of a technique to measure the stress and strain fields at the crack tip with a nanometric resolution, and the proposed interpretations are still subject of debate [2]. Another weakness of the in-situ AFM observations is their limitation to access the external surface of the sample, that is intersected by the propagating crack front with a small tilt angle, thus making the local three-axial condition of stress not trivial [7]. The present letter reports a concomitant solution of all these problems. By extending the Digital Image Correlation technique to AFM topographical images of in-situ crack propagation in a silica glass it was possible (1) to characterise properly the 3D sur(a) E-mail: [email protected] (b)E-mail: [email protected] face displacement fields with nanometric resolution, (2) to show that they can be fitted by appropriate elastic solution down to a 10 nm distance from the crack tip and (3) that the locally measured surface stress-intensity factor is in agreement with the macroscopically measured value within 5% uncertainty. Digital Image Correlation (DIC) is a technique which allows one to measure displacement fields by matching a reference with a deformed image, most often an optical image. Introduced a long time ago in the field of solid mechanics by Sutton et al. [8], this technique has known a very rapid development due to the wide availability of digital imaging devices, and the increasing performance and reliability of analyses. In particular for cracks, since the pioneering work of Sutton [9], recent works [10–12] have shown that stress intensity factors can be estimated very accurately either directly through Integrated DIC (IDIC) which incorporates analytic crack fields [10], or through a tailored post-processing of the displacement field [10,11,13]. However, most applications of DIC deal with optical images, and very few with Atomic Force Microscopy (AFM) images. Among those, the most advanced published works concern thin polycrystalline silicon films [14–18]. In particular, the measurement of a uniform strain field from AFM images at different scales down to scale 1×2 μm images [17] allowed to estimate the p-1 ha l-0 04 54 09 2, v er si on 1 7 Fe b 20 10