Understanding nanoindentation unloading curves
- PDF / 290,418 Bytes
- 12 Pages / 612 x 792 pts (letter) Page_size
- 54 Downloads / 217 Views
A. Bolshakov Houston Technology Center, Baker Atlas/INTEQ, Houston, Texas (Received 17 June 2002; accepted 24 July 2002)
Experiments have shown that nanoindentation unloading curves obtained with Berkovich triangular pyramidal indenters are usually well-described by the power-law relation P ⳱ ␣(h − hf)m, where hf is the final depth after complete unloading and ␣ 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.
I. INTRODUCTION
Load and depth-sensing indentation, also referred to as nanoindentation, has been developed over the past two decades as a technologically important tool for measuring the mechanical properties of materials, especially at small scales.1–7 The technique relies on high-resolution instruments that continuously monitor the loads and displacements of an indenter as it is pushed into and withdrawn from a material. The load–displacement data obtained during one or more cycles of loading and unloading can be analyzed to derive a variety of mechanical properties, most commonly, the hardness and elastic modulus.3,4 Such analyses are frequently based on solutions to the problem of indentation of an elastic halfspace by a rigid, axially symmetric punch.8,9 Accurate measurement of mechanical properties by nanoindentation methods requires a detailed understanding of the information contained in the indentation loading and unloading curves.4,9 Obtaining such an understanding is not an easy task due to the complex elastic and plastic deformation processes that occur during indentation, as well as the nonuniformity of the stress and deformation fields in the vicinity of the contact. For a)
Address all correspondence to this author. e-mail: [email protected]
2660
http://journals.cambridge.org
J. Mater. Res., Vol. 17, No. 10, Oct 2002 Downloaded: 02 Jun 2014
this reason, many methods for measuring properties by nanoindentation rely heavily on empirical observations that do not have solid theoretical underpinnings.3,4,7 In this work, a conceptual framework is developed to explain the experimentally observed mathematical form of nanoindentation unloading curves obtained with sharp, geometrically self-similar indenters l
Data Loading...
