Ultrasonic attenuation and velocity changes in multilayer structures containing multiple delaminations

Delaminations between ceramic and electrode layers in multilayer capacitors and multilayer actuators are common discontinuities that are difficult to detect using ultrasonic imaging if the diameter is smaller than 50 μm. Detailed theoretical analysis has been performed for the propagation of ultrasonic waves in multilayer structures containing multiple delaminations. The T-matrix approach is used to treat wave attenuation in periodic structures with alternating ceramic and electrode layers. Multiple penny-shaped delaminations are assumed perpendicular to the incidence wave and the forward scattering amplitude of the wave from delaminations is calculated by substituting the average effective crack opening displacement into the scattered wave displacement. The effective phase velocity, wave amplitude and attenuation coefficient have been calculated for different crack densities. The results provide a theoretical base for attenuation based nondestructive testing (NDT) to assess the degree of delaminations in multilayer structures.