The thickness effect has a significant influence on the fatigue life of micro–nanometer thin films. Due to the increasing application of micro–nanometer thin films in the field of microelectronics, a suitable fatigue prediction model is urgently needed. To reveal the impact of the thickness effect on the fatigue life of a copper wire film, cyclic tension fatigue test of four groups of copper wire films were carried out. Based on the theory of continuous damage mechanics and damage homogenization method, a fatigue damage accumulation model that considered the film thickness was proposed. Based on the proposed fatigue damage prediction model, the damage evolution law and fatigue life of copper wire films with different thickness and strain range were predicted. Furthermore, the size effect of the copper films was analyzed. The results showed that the fatigue life of copper wire films will decrease with the increase of thickness and strain amplitude; the thinner the film, the more significant the thickness effect on the fatigue life is; with the increase of the film thickness, the film thickness effect will gradually decrease.

We present an exact analysis of axisymmetric bending of circular plates according to elasticity theory. On the basis of Hamiltonian state space approach, a rigorous solution of the problem is determined by means of separation of variables and symplectic eigenfunction expansion in a systematic way. The thickness effect on bending of circular plates and the applicability of the classical plate solutions for the problem are evaluated accordingly.