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Corrections to the stiffness relationship in 3-sided and conical indentation problems

机译：三方和锥形压痕问题的僵硬关系校正

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摘要

One key relationship in the depth-sensing indentation technique is the proportionality between the contact stiffness and the contact size, as can be proved from the Sneddon's solution of axisymmetric frictionless contact. However, Sneddon's solution is only accurate when the indenter approaches a half-space (e.g., for conical indenter, the half-apex angle approaches 90 degrees) and the interface is frictionless. As Hay et al. U. Mater. Res., 1999) pointed out, sharp indenters lead to a radial inward displacement on the sample surface, thus leading to extra indentation force needed to push the surface back to conform with the conical indenter. In this paper, we argue that the physical origin arises from the incorrect use of reference and deformed coordinates in the boundary conditions that define Sneddon's problem. This yields two correction factors for both load and depth solutions, which are needed for sharp pyramidal indenters and frictional contact. Approximate solutions are derived which compare favorably well with the finite element simulations. We also find that the stiffness correction factor of three-sided indenter is about 11 similar to 15% times higher than that of conical indenter, and this multiplicative factor is only a weak function of the indenter angle but does not depend on the friction coefficient and Poisson's ratio. (C) 2019 Elsevier Ltd. All rights reserved.
机译：深度传感压痕技术中的一个关键关系是接触刚度和接触尺寸之间的比例，从而可以从Sneddon的轴对称无摩擦接触溶液中证明。然而，当缩进接近半空间（例如，对于锥形压痕时，半顶点角度接近90度）并且界面是无摩擦的，Sneddon的解决方案仅准确。作为hay等人。母体。 Res。，1999）指出，尖锐的压痕导致样品表面上的径向向内位移，从而导致额外的压痕力，以便将表面推回到与锥形压头符合锥形压痕。在本文中，我们认为物理原产地产生了在限定Sneddon问题的边界条件下的引用和变形坐标的错误使用中使用的不正确使用。这为负载和深度解决方案产生了两种校正因子，这是尖锐的金字塔内压元和摩擦接触所需的。导出近似解决方案，它与有限元模拟相比好比。我们还发现三面压紧的刚度校正因子约为11比锥形压痕的15％倍增，并且该乘法因子只是压痕角度的弱功能，但不依赖于摩擦系数和泊松比。 （c）2019年elestvier有限公司保留所有权利。

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