University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.
ACS Nano. 2011 Jul 26;5(7):5400-7. doi: 10.1021/nn200461g. Epub 2011 Jun 6.
We investigate the effective mechanical response of a layered system consisting of a thin crystalline sheet (nanomembrane) on a bulk substrate, with a high elastic mismatch (in the range of 5 to 9 orders of magnitude) between the stiff sheet and the compliant substrate. Using finite-element mechanics models and indentation experiments ranging from micro to nano, we show that the mismatch between the sheet and substrate elastic moduli, the length scale of deformation, and the sheet thickness all play a significant role in defining the effective stiffness of the layered system. For a wide range of indenter sizes, the mechanical response of the composite system is indistinguishable from that of the compliant substrate. In particular, at large indenter sizes, the mechanical response of the layered system is dominated by that of the compliant substrate. For decreasing indenter sizes, the effective stiffness of the layered structure reaches a finite value different from either the one expected for the compliant substrate or for a bulk crystal of the same material as the stiff top membrane.
我们研究了由一个薄的晶体片（纳米膜）在一个大块基底上组成的层状系统的有效力学响应，其中刚性片和柔性基底之间的弹性失配非常高（在 5 到 9 个数量级之间）。通过使用从微观到纳米的有限元力学模型和压痕实验，我们表明，片和基底弹性模量之间的失配、变形的尺度和片的厚度都在确定层状系统的有效刚度方面起着重要作用。对于广泛的压头尺寸，复合系统的力学响应与柔性基底的力学响应无法区分。特别是在大压头尺寸下，层状系统的力学响应由柔性基底主导。随着压头尺寸的减小，层状结构的有效刚度达到一个不同于柔性基底或相同材料的块状晶体的有限值。
