Int J Fract (2009) 158:15–26 DOI 10.1007/s10704-009-9362-3 ORIGINAL PAPER Indentation-induced subsurface tunneling cracks as a means for evaluating fracture toughness of brittle coatings Herzl Chai Received: 20 January 2009 / Accepted: 11 May 2009 / Published online: 10 June 2009 © Springer Science+Business Media B.V. 2009 Abstract When a plate glued to a compliant substrate is subject to indentation, cracks may initiate from its subsurface due to flexure. Upon increasing the load, the damage develops into a set of tunnel radial cracks which propagate stably under a diminishing stress field. This phenomenon is utilized here to extract fracture toughness K C for brittle materials in the form of thin plates or films. Experiments show that the SIF at the tip of the subsurface radial cracks is well approximated as K ∼ P /c 3/2 , where P is the indentation load and c the mean length of the crack fragments. Using a transparent substrate, c can be easily determined after unloading, from which K C is found. This simple and economic concept is applied to a wide variety of thin ceramic coat- ings, yielding toughness data consistent with literature values. Because the tip of the tunneling cracks are well removed from the contact site, the method circumvents certain complications encountered in common top-sur- face radial cracking techniques such as the effect of plastic deformation, residual stresses and crack exten- sion after unloading. Although the present tests are lim- ited to coating thicknesses >150 μm, it is believed that thinner coatings may be studied as well provided that the indenter radius is kept sufficiently small to insure that subsurface radial cracking dominates over all other failure modes. H. Chai (B ) School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel e-mail: herzl@eng.tau.ac.il Keywords Indentation · Brittle coating · Thin-film · Fracture toughness · Radial cracks · Channel/tunnel cracks 1 Introduction Fracture of a stiff layer on a compliant substrate from indentation (Fig. 1) is a subject of basic and practi- cal interest. Due to flexure, cracks may initiate from flaws on the lower surface (subsurface) of the coat- ing. Because of the diminishing nature of the contact stresses, these cracks proliferate and propagate stably in the radial direction with increasing load (Chai et al. 1999). The onset of fracture is of interest in safety designs as well as a means for extracting critical failure stress in thin (Chai et al. 1999; Chai 2005) or ultra thin (Kim et al. 2006; Borrero-López et al. 2008) coatings. The propagation phase of the subsurface radial cracks has been studied with the aid of 3D FEM analyses (Cao 2002; Rudas et al. 2005) or analytic models which sim- plifies the damage to a semi-circular (Kim et al. 2001) or semi-elliptical (Chai 2006) subsurface crack. While the original goal of this work was to establish a sim- ple yet accurate growth law for this crack system, as the work has progressed it became apparent that such growth law may serve as a simple means for assessing fracture toughness K C in thin brittle materials. It is this aspect which is of main interest here. Evaluating K C in hard materials using standard spec- imens such as compact tension or four-point bending 123