Effect of substrate dimensions on dynamics of ultrasonic consolidation

An FEM model is developed for a fundamental study of the time-dependent mechanical behavior of the substrate and its dimensions on ultrasonic consolidation. The simulation shows that for a given vibration condition, the amplitude of contact friction stress and displacement stabilizes to a saturated state after certain number of ultrasonic cycles. With the increased substrate height, the amplitude of contact frictional stress decreases, while that of contact interface displacement increases. The reason for the decrease in the frictional stress at the contact interface for certain substrate heights is the complicated wave interference occurring in the substrate. An analytical wave model has been built to validate the FEM model. A specific substrate geometry (height:width = 1.0) generates a minimum frictional strain state at the interface as a result of wave superposition. Such minimum strain state is believed to have produced the “lack of bonding” defect for the geometry. The energy density and transfer coefficient at the contact interface with different substrate heights is used as an indicator to correlate with the bond formation in ultrasonic bonding.