Kinetics of crack initiation and growth in organic-containing integrated structures

Organic materials are being introduced into solid-state devices to enhance performance, reduce cost, or add function. In such an integrated structure, creep in the organic material affects cracking in the adjacent inorganic material. This paper analyzes an idealized structure comprising, from top to bottom, an inorganic film, an organic underlayer, and a rigid substrate. The film is elastic, subject to a tensile stress, and susceptible to subcritical crack growth. The underlayer is viscoelastic and does not crack. A crack exists in the film. When the crack tip is stationary, as the underlayer creeps, the film stress relaxes in the crack wake, but intensifies around the crack tip, so that the crack may grow after a delay. When the crack tip moves, the underlayer creeps to a limited extent, and constrains the fresh crack opening. A nonequilibrium thermodynamic model evolves displacements, creep strains, and crack length simultaneously. Using the Laplace transform and the extended finite element method, we study delayed crack initiation, steady crack growth, and transient crack growth.