Size Effect on Failure of Pre-stretched Free-Standing Nanomembranes
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Free-standing nanomembranes are two-dimensional materials with nanometer thickness but can have macroscopic lateral dimensions. We develop a fracture model to evaluate a pre-stretched free standing circular ultrathin nanomembrane and establish a relation between the energy release rate of a circumferential interface crack and the pre-strain in the membrane. Our results demonstrate that detachment cannot occur when the radius of the membrane is smaller than a critical size. This critical radius is inversely proportional to the Young’s modulus and square of the pre-strain of the membrane.
KeywordsFree standing membrane Pre-stretch Size effect Energy release rate
Free-standing ultrathin nanomembranes are a new class of two-dimensional materials that possess nanoscale thickness across macroscopic dimensions. Such nanomembranes are not only ultra-lightweight but also robust and flexible. It has been reported that elastic moduli of ultrathin nanomembranes can be 1–10 GPa with ultimate strengths of up to 100 MPa [1, 2, 3, 4, 5, 6]. These striking properties of free-standing nanomembranes have resulted in a broad spectrum of applications in separation, sensing, biomedicine and energy harvesting [7, 8, 9, 10].
Equation (3) shows why sheets over smaller holes (smaller R) is less likely to fail. This conclusion is also valid for non-circular shaped micro-holes; in this case R should be replaced by the characteristic length of the micro-hole.
will not grow.
where f*is a numerical constant which depends only on the Poisson’s ratio of the membrane.
Our experimental observations suggest that R c is in the range of 1–4 μm. The Young’s modulus E of a typical membrane is reported to be about 6.5 GPa . Assuming ν is 1/3, the pre-strain Open image in new window is estimated to be 0.12%. This estimate is based on the initial slope of the force–displacement curve of indentation tests , where we have assumed that the force–displacement curve is controlled by the pre-tension for small deflections and approximated the indenter as a point load. There is no direct measurement of W. Using the values of R c E Open image in new window and v listed above, W is estimated to be 15–50 mJ/m2, which is consistent with the strength of van der Waals interaction .
In summary, a fracture mechanics model is used to explain why small free-standing membranes are more resistant to detachment. We show that detachment can be prevented by making the membrane smaller for a given pre-strain and W, which is consistent with our experimental observations. A useful expression for critical radius of the membrane is obtained and may guide future design of free-standing membrane systems.
C.Y. Hui and R. Long are supported by a grant from the Department of Energy (DE-FG02-07ER46463). W. Cheng, M. Campolongo and D. Luo are partially supported by NYSTAR and the NSF CAREER award (grant number: 0547330).
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