Experiments have shown that nanoindentation unloading curves obtained with Berkovich triangular pyramidal indenters are usually welldescribed by the power-law relation P = α(h − hf)m, where hf is the final depth after complete unloading and α and m are material constants. However, the power-law exponent is not fixed at an integral value, as would be the case for elastic contact by a conical indenter (m = 2) or a flat circular punch (m = 1), but varies from material to material in the range m = 1.2–1.6. A simple model is developed based on observations from finite element simulations of indentation of elastic–plastic materials by a rigid cone that provides a physical explanation for the behavior. The model, which is based on the concept of an indenter with an “effective shape” whose geometry is determined by the shape of the plastic hardness impression formed during indentation, provides a means by which the material constants in the power law relation can be related to more fundamental material properties such as the elastic modulus and hardness. Simple arguments are presented from which the effective indenter shape can be derived from the pressure distribution under the indenter.
实验表明,使用伯克维奇三角锥形压头获得的纳米压痕卸载曲线通常可以用幂律关系 P = α(h - hf)m 很好地描述,其中 hf 是完全卸载后的最终深度,α 和 m 是材料常数。然而,幂律指数并不像锥形压头(m = 2)或扁圆冲头(m = 1)的弹性接触那样固定为一个整数值,而是在 m = 1.2-1.6 的范围内因材料而异。根据对刚性锥体压入弹塑性材料的有限元模拟观察,建立了一个简单的模型,为这种行为提供了物理解释。该模型基于一个具有 "有效形状 "的压头的概念,其几何形状由压入过程中形成的塑性硬度印痕的形状决定。通过该模型,可以将幂律关系中的材料常数与弹性模量和硬度等更基本的材料特性联系起来。本文提出了一些简单的论点,根据这些论点,可以从压头下的压力分布推导出有效压头形状。