Surface Stress and Reversing Size Effect in the Initial Yielding of Ultrathin Films

Very recent experiments indicate that in free-standing metallic films of constant grain size the initial yield stress increases as the film becomes thinner, it peaks for a thickness on the order of $100nm$⁠, and then starts to decrease. This reversing size effect poses two challenges: (1) It cannot be explained using currently available models and (2) it appears to contradict the classical experimental results due to J. W. Beams [1959, “Mechanical Properties of Thin Films of Gold and Silver,” in Structure and Properties of Thin Films, Wiley, New York, pp. 183–198]. Here we show that the reversing size effect can be explained and the contradiction dispelled by taking into account how the initial yielding is affected by the surface stress. We also predict that the mode of failure of a film changes from ductile to brittle for a thickness on the order of $100nm$⁠, in accord with experiments.