Experimental determination of crack driving forces in integrated structures

For a crack in a brittle material in an integrated structure, the 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 value of 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 full-structure testing is affordable. We describe an experimental method to determine G. A crack, assisted by molecules in the environment (e.g., moisture), often extends at a velocity V increasing with the crack driving force G. The VG 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.