论文标题
从力距离曲线中确定Young的任意厚度样品的模量：数值研究和简单的近似公式
Determination of Young's modulus of samples of arbitrary thickness from force distance curves: numerical investigations and simple approximate formulae
论文作者
论文摘要
我们提供了简单的表达式，以用圆锥形，抛物面或圆柱形打磨一层任意厚度所需的负载。样品下方的刚性基材导致压痕所需的负载增加。必须校正此效果，以防止高估杨的模量测量值，例如用原子力显微镜（AFM）记录的力距离曲线。轴对称打孔器和各向同性的线性弹性层的无摩擦接触问题可简化第二种的弗雷德·霍尔姆积分方程。我们通过数值解决了它们，并使用了Remez算法来获得与刚性基板无摩擦接触或与之结合的样品的负载 - 压痕关系的分段多项式近似。它们由于近似而引起的相对误差可以忽略不计，并且均匀扩散。将数值近似值与非常薄的层的渐近溶液相结合，我们获得了适用于任意厚度样品的方程式。它们是在新版本的Atomicj中实施的，Atomicj是我们的免费开放源代码应用程序，用于分析AFM录音。
We present simple expressions for load required to indent a layer of arbitrary thickness with a conical, paraboloidal or cylindrical punch. A rigid substrate underneath the sample leads to an increase of load required for indentation. This effect has to be corrected for to prevent overestimation of Young's modulus from indentation measurements, such as force - distance curves recorded with the Atomic Force Microscope (AFM). The problems of the frictionless contact of an axisymmetric punch and an isotropic, linear-elastic layer are reducible to Fredholm integral equations of the second kind. We solved them numerically and used the Remez algorithm to obtain piecewise polynomial approximations of the load - indentation relation for samples that are either in frictionless contact with the rigid substrate or bonded to it. Their relative error due to approximation is negligible and uniformly spread. Combining the numerical approximations with asymptotic solutions for very thin layers, we obtained equations appropriate for samples of arbitrary thickness. They were implemented in a new version of AtomicJ, our free, open source application for analysis of AFM recordings.
