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Effects of adhesive and frictional contacts on the nanoindentation of two-dimensional material drumheads
Journal of the Mechanics and Physics of Solids ( IF 5.0 ) Pub Date : 2024-08-22 , DOI: 10.1016/j.jmps.2024.105828 Yifan Rao , Nanshu Lu
Journal of the Mechanics and Physics of Solids ( IF 5.0 ) Pub Date : 2024-08-22 , DOI: 10.1016/j.jmps.2024.105828 Yifan Rao , Nanshu Lu
Nanoindentation of suspended circular thin films, dubbed drumhead nanoindentation, is a widely adopted technique for characterizing the mechanical properties of micro- or nano-membranes, including atomically thin two-dimensional (2D) materials. This method involves suspending an ultrathin specimen over a circular microhole and applying a precise indenting force at the center using an atomic force microscope (AFM) probe. Classical solutions assuming a point load and a fixed edge, which are referred to as Schwerin-type solutions, are commonly used to estimate Young’s modulus of the membrane material out of load–deflection measurements. However, given the widespread experimental evidence for adhesive and frictional contacts between the probe tip and the membrane, as well as sliding between the membrane and its supporting substrate, quantitative investigations of the effects of these interactions are required. In this paper, we formulate a boundary value problem to rigorously model such effects, ensuring relevance to experimental operations. Our numerical analyses reveal that the adhesive effect at the tip-membrane interface diminishes as the indentation depth increases or the tip size decreases. Furthermore, frictional interactions at this interface shift the maximum membrane stress from the center to the tip-membrane contact line with increasing indentation depth and interfacial shear stress. At large indentation depths, the size of the indenter tip and the sliding of the membrane-substrate are found to have a large effect on the indentation load–deflection relationship. Thus, we propose a new approximate formula for this relationship assuming a non-adhesive and frictionless spherical tip of a finite radius and a slippery contact with the supporting substrate. This formula is more accurate than the widely used Schwerin-type solution. It can be used to simultaneously extract the in-plane stiffness of the membrane and the shear strength at the membrane-substrate interface.
中文翻译:
粘合和摩擦接触对二维材料鼓面纳米压痕的影响
悬浮圆形薄膜的纳米压痕(称为鼓面纳米压痕)是一种广泛采用的技术,用于表征微米或纳米膜(包括原子薄的二维(2D)材料)的机械性能。该方法包括将超薄样品悬挂在圆形微孔上,并使用原子力显微镜 (AFM) 探针在中心施加精确的压入力。假设点载荷和固定边缘的经典解决方案(称为 Schwerin 型解决方案)通常用于根据载荷偏转测量来估计膜材料的杨氏模量。然而,考虑到探针尖端与膜之间的粘合和摩擦接触以及膜与其支撑基底之间的滑动的广泛实验证据,需要对这些相互作用的影响进行定量研究。在本文中,我们制定了一个边值问题来严格模拟此类效应,确保与实验操作的相关性。我们的数值分析表明,随着压痕深度的增加或尖端尺寸的减小,尖端-膜界面处的粘合效果会减弱。此外,随着压痕深度和界面剪切应力的增加,该界面处的摩擦相互作用将最大膜应力从中心转移到尖端膜接触线。在大压痕深度时,压头尖端的尺寸和膜-基底的滑动被发现对压痕载荷-挠度关系有很大影响。因此,我们为这种关系提出了一个新的近似公式,假设有限半径的非粘性和无摩擦的球形尖端以及与支撑基底的光滑接触。 该公式比广泛使用的 Schwerin 型解决方案更准确。它可用于同时提取膜的面内刚度和膜-基材界面的剪切强度。
更新日期:2024-08-22
中文翻译:
粘合和摩擦接触对二维材料鼓面纳米压痕的影响
悬浮圆形薄膜的纳米压痕(称为鼓面纳米压痕)是一种广泛采用的技术,用于表征微米或纳米膜(包括原子薄的二维(2D)材料)的机械性能。该方法包括将超薄样品悬挂在圆形微孔上,并使用原子力显微镜 (AFM) 探针在中心施加精确的压入力。假设点载荷和固定边缘的经典解决方案(称为 Schwerin 型解决方案)通常用于根据载荷偏转测量来估计膜材料的杨氏模量。然而,考虑到探针尖端与膜之间的粘合和摩擦接触以及膜与其支撑基底之间的滑动的广泛实验证据,需要对这些相互作用的影响进行定量研究。在本文中,我们制定了一个边值问题来严格模拟此类效应,确保与实验操作的相关性。我们的数值分析表明,随着压痕深度的增加或尖端尺寸的减小,尖端-膜界面处的粘合效果会减弱。此外,随着压痕深度和界面剪切应力的增加,该界面处的摩擦相互作用将最大膜应力从中心转移到尖端膜接触线。在大压痕深度时,压头尖端的尺寸和膜-基底的滑动被发现对压痕载荷-挠度关系有很大影响。因此,我们为这种关系提出了一个新的近似公式,假设有限半径的非粘性和无摩擦的球形尖端以及与支撑基底的光滑接触。 该公式比广泛使用的 Schwerin 型解决方案更准确。它可用于同时提取膜的面内刚度和膜-基材界面的剪切强度。