The electro-mechanical response of highly compliant substrates and thin stiff films with periodic cracks

We present results that describe the mechanical response of highly compliant substrates coated with ultra-thin stiff films, with thickness and elastic moduli differences spanning four orders of magnitude. Dimensional analysis based on shear-lag models of cracked films is used to identify key parameters that control the effective elastic properties of the cracked multi-layer, crack opening displacements, and the steady-state energy release rate for channeling crack formation. Analytical forms that describe multi-layer response in terms of film properties and crack spacing are presented and corroborated with numerical models for linear elastic materials. A key result is that the energy release rate scales with 1/ (1 a), where a is one of the Dundurs parameters describing elastic mismatch. The results can also be used to evaluate the performance of electrostrictive actuators comprised of cracked blanket electrodes and elastomer dielectrics. In this scenario, an interesting result is that ultra-thin cracked films can continue to distribute charge, since crack openings may be small enough to allow breakdown in air at typical operating voltages.