含褶皱二维材料弯曲压痕响应分析模型  

Analysis Model of Bending Indentation Response of Two⁃Dimensional Materials with Buckles

作　　者：郭亮 曹国鑫 GUO Liang;CAO Guoxin(School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《力学季刊》2024年第4期931-940,共10页Chinese Quarterly of Mechanics

摘　　要：悬空二维材料由于其纳米级的厚度,在制备过程中极易产生拉伸失稳褶皱,然而褶皱对二维材料的压痕响应影响通常被忽略.本研究采用理论分析方法,研究二维材料所含褶皱对其弯曲压痕响应的影响,并进一步提出了含褶皱二维材料弯曲压痕响应分析模型.研究发现,在中心集中力作用下,含褶皱二维材料的弯曲挠度和载荷呈线性关系,其线性斜率与褶皱幅值与波长的比值A/λ成正比,当A/λ=0.01~0.05时,其斜率为无褶皱薄膜结果的1.32~3.21倍,因此,忽略薄膜褶皱的影响,将导致通过弯曲压痕测试获得的二维材料弹性模量明显高估(达3.21倍).二维材料弹性模量被高估的原因为褶皱增强了二维材料的整体抗弯刚度,进而提高了用来拟合弹性模量的压痕载荷位移关系斜率.Due to the nanoscale thickness of suspended two-dimensional(2D)materials,stretching instability wrinkles are prone to be introduced during the preparation process.However,the influence of wrinkles on the indentation response of twodimensional materials is usually ignored.In this paper,the influence of wrinkles on the bending indentation response of 2D materials is investigated through theoretical analysis,and a model for the bending indentation response of 2D materials with wrinkles is proposed.It is found that under the action of central concentrated force,the bending deflection of 2D materials with wrinkles is linearly related to the load,and the relation slope is proportional to the ratio of wrinkle amplitude to wavelength A/λ.When A/λ=0.01~0.05,the slope is 1.32~3.21 times that of the case without wrinkles.This results in a significant overestimation(up to 3.21 times)of the elastic modulus of the 2D material obtained by the bending indentation test.The mechanism of overestimating the elastic modulus of 2D materials is that the wrinkles enhance the overall flexural stiffness of 2D materials,and thus increase the slope of the indentation load displacement relationship used to fit the elastic modulus.

关 键 词：薄膜褶皱 二维材料 弯曲压痕响应 弹性模量 

分 类 号：O34[理学—固体力学]