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Buckling behavior of metal film/substrate structure under pure bending
2.J. W. Hutchinson and Z. Suo, Adv. Appl. Mech. 29, 63 (1992).
17.As the Cu substrate is under the pure bending, the strain in the Cu substrate is assumed as the linear function of the . The strain of the neutral axial is zero. Therefore, the strain at the interface between the Cu film and Cu substrate is about . As the thickness of Cu film is much smaller than that of Cu substrate, the strain is the Cu film should be near to for the comparability of deformation.
21.Although Eq. (2) is derived for elastic film, it used here just for approximately evaluating the critical buckling strain for the Cu film on the Cu substrate. As the Cu film was under the plastic deformation, Eq. (2) could be not proper for obtaining the exactly critical strain. According to the theory of elastic stability by Timoshenko and Gere [Theory of Elastic Stability, 2nd Ed. (McGraw-Hill, New York, 1963)] and the copper characterized by the power law (Refs. 3–6), the critical strain of the Cu film could be slightly larger than the obtained by Eq. (2). However, the shrink strain in the Cu film is still larger than the critical buckling strain and also could induce the buckling of Cu film.
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