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

[+] Author and Article Information
G. Gioia, X. Dai

Department of Theoretical and Applied Mechanics,  University of Illinois, Urbana, IL 61801

It is straightforward to show that this same size effect is valid for wires. For atomistic simulations in ultrathin wires, see, for example, Ref. 24.

J. Appl. Mech 73(2), 254-258 (Jul 19, 2005) (5 pages) doi:10.1115/1.2074767 History: Received April 30, 2005; Revised July 19, 2005

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.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

(a) A free-standing thin film. C1 and C2 are cuts performed for stress analysis. (b) The surface stress T acting on the perimeter of C1. (c) The compressive stress induced by T on the surface of C1. (d) The compressive stress induced by T on the surface of C2. (e) Applied traction that gives the same stresses as T.

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Figure 2

A plot of the dimensionless apparent yield stress σay∕σy versus the dimensionless thickness hσy∕T. See Eq. 1. The points F, R, M, and V are referred to in the text. The size effect of the apparent tensile yield stress reverses from hardening to softening at the point R.

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Figure 3

A plot of the dimensionless quantities s1, s2, and s3 versus the dimensionless thickness, hσy∕T. See Eqs. 2,3,4.

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Figure 4

A plot of the normalized plastic strain at failure in the direction of the applied stress versus the dimensionless thickness, hσy∕T. See Eq. 6.



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