Length scales for the fracture of nanostructures

Length scales are essential to the understanding of small volume deformation and fracture in emerging technologies. Recent analysis by two groups at the atomistic (Horstmeyer and Baskes, 1999) and mesoscopic (Gerberich et al., 2002) levels have shown the importance of the volume to surface ratio to the indentation size effect (ISE) at small depths of penetration. We have interpreted this in terms of the plastic work under the contact and the surface work associated with the creation of new surface or the excess surface stress. Treating this as a modified Griffith criterion the case is made that this same length scale should apply to the delamination of thin films. By making this simple equivalency in length scales, an R-curve analysis for crack growth resistance, GR, in thin film delamination emerges. This recovers the classic σ2ysh/E term as well as the fact that interfacial toughness should scale with the square root of incremental crack growth. Here σys is yield strength, h is thickness and E is modulus of the film. As applied to thin Cu and Au films bonded to silicon substrates, the model is in good agreement.