Experimental Determination of Crack Driving Forces in Integrated Structures

For a crack in a structure, the crack driving force G is the reduction of the elastic energy in the structure, associated with the crack extending per unit area. In principle, G can be calculated by solving a boundary value problem. In practice, however, such a calculation is prohibitively difficult for integrated structures of complex architectures, diverse materials and small features. The calculated G is suspect when deformation properties and residual stress fields are poorly characterized. On the other hand, it costs little to make many replicates of an integrated structure, so that massive testing is affordable. We describe an experimental method to measure G. A crack, assisted by molecules (e.g., moisture) in the environment, often extends at a velocity V increasing with the crack driving force G. The V-G function is specific to a given material and its environment. Once determined, the same function applies when this material is integrated in a structure with other materials, provided environmental molecules reach the crack front. In the integrated structure, an observed crack velocity, together with the known V-G function, provides a reading of the crack driving force. The observed crack velocity can be used to measure deformation properties of ultrathin films. We also describe a procedure to measure the crack driving force GR due to the residual stress field in the integrated structures, even when GR by itself is too low for the crack to extend at a measurable velocity.