A four-point bending technique for studying subcritical crack growth in thin films and at interfaces

Abstract

A technique was developed to obtain the subcritical crack growth velocity in a 4-point bending sample by analyzing the load-displacement curve. This was based on the observation that the compliance of a beam increases as the crack grows. Beam theory was used to analyze the general configuration where two cracks propagated in the opposite directions. A simple equation relating the crack velocity to the load and displacement was established, taking advantage of the fact that the compliance was linearly proportional to the crack lengths; thus the absolute crack length was not important. Two methods of obtaining crack velocity as a function of load were demonstrated. First, by analyzing a load-displacement curve, a corresponding velocity curve was obtained. Second, by changing the displacement rate and measuring the corresponding plateau load, a velocity value was calculated for each plateau load. While the former was capable of obtaining the dependence of crack velocity versus load from a single test, the latter was found to be simpler and more consistent. Applications were made to a CVD SiO₂ system. In both cases of crack propagation either inside the SiO₂ layer or along its interface with a TiN layer, the crack growth velocity changed with the stress intensity at the crack tip exponentially. As a result, a small crack will grow larger under essentially any tensile stresses typically existing in devices, provided that chemical agents facilitating stress corrosion mechanisms are also present.