Elastic surface deformation due to indenters with arbitrary symmetry of revolution
Elastic surface deformation due to indenters with arbitrary symmetry of revolution
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具有任意旋转对称性的压头导致的弹性表面变形
DOI：
10.1088/0022-3727/37/19/023
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
N. Schwarzer
中科院分区：
文献类型：
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作者：
N. Schwarzer
四年多前，法尔提出了虚拟刚性压头的概念，以描述超出线弹性极限的压痕问题的弹性应力部分（法尔1999年《薄膜、涂层和界面材料的机械性能》（IL Chiocco，意大利，6月27日？1999年7月2日）。他建议用一个有效成形的压头和一个平坦表面的问题来代替一个作用在预变形表面上的定义良好的压头的问题。通过这种方式，他能够解释相当多种不同材料的卸载曲线，即使是使用像维氏或布氏压头这样的锋利压头。即使为了简单起见，假设的有效压头被选择为具有旋转对称性，而真实的压头不具有旋转对称性（例如，维氏压头和布氏压头分别是四面棱锥和三面棱锥），该方法也能很好地工作。为了使这个概念适用，需要得到各种不同压头形状的压力分布。作者提出了解决方案，压头与半径（r）依赖于形状描述为一系列的权力r，权力8的旋转对称。此外，为了能够完全解析地构造封闭形式的弹性场，还计算了势函数，讨论了不同压头形状对弹性压痕深度的影响，并给出了一些实例。
More than four years ago Pharr proposed the concept of the virtual rigid indenter to describe the elastic stress part of indentation problems beyond the linear elastic limit (Pharr 1999 Mechanical Properties of Films, Coatings and Interfacial Materials (IL Chiocco, Italy, June 27?July 2, 1999). He suggested substituting the problem of a well defined indenter acting on a predeformed surface with the problem of an effectively shaped indenter and a flat surface. This way he was able to explain the unloading curves of quite a variety of different materials even with sharp indenters like Vickers or Berkovich indenters. The method works well even when for the sake of simplicity the assumed effective indenter is chosen to have symmetry of revolution, which a real indenter does not (e.g. Vickers and Berkovich indenters are four and three sided pyramids, respectively).To make this concept applicable, the resulting pressure distributions of a wide range of different indenter shapes are needed. The author presents solutions for indenters with symmetry of revolution with a radius (r) dependent shape described as a series of powers of r, up to power 8. In addition, the resulting potential functions are calculated in order to be able to construct the resulting elastic field completely analytically and in closed form.The effect of the different indenter shape on the resulting elastic indentation depth is discussed, and some practical examples are considered.