Slip distance model for the indentation size effect at the initiation of plasticity in ceramics and metals
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D.J. Dunstan Centre for Materials Research and Department of Physics, Queen Mary, University of London, London, E1 4NS, United Kingdom (Received 6 August 2008; accepted 28 October 2008)
The indentation size effect, in which the contact pressure increases as the size of contact decreases, has been observed for many years for both spherical and pointed indenters. The concept of strain gradient plasticity has been used to describe this phenomenon, but it is often necessary to introduce a material length scale l* to fit experimental data. Here we present a theorypbased on the concept of dislocation slip distance, which naturally ffiffiffi generates the 1/ a scaling and incorporates the material parameters that influence the size effect. We compare this model with experimental data for a range of ceramics and tungsten metal and show that the yield strain and Burgers vector are the important material parameters in the indentation size effect.
I. INTRODUCTION
The indentation size effect has been known since the early days of indentation testing but has become more prominent with the advent of micro- and nanoindentation. Improvements in measurement capability and tip shape calibration techniques have eliminated the possibility of grossly miscalculated contact areas and highlighted a genuine size effect in which materials appeared more resistant to permanent deformation for smaller contact sizes. There is now a wealth of experimental data in the literature demonstrating the indentation size effect in various materials and contact geometries.1–6 The understanding of this phenomenon is important for two reasons: firstly, in determining the difference between genuine material properties and test dependent parameters, which are vital if tensile material properties are to be predicted from an essentially nondestructive nanoindentation test, and secondly, in developing an understanding of plasticity size effects. The latter is necessary if nanotechnology is to be able to exploit “length scale engineering” to design materials and/or microstructures optimized for both strength and toughness as well as for fatigue or creep resistance. The mechanisms that drive the indentation size effect have been the subject of lively debate. For self-similar, pointed, indenters (such as the Berkovich tip geometry) an increase in measured hardness H is usually associated with a a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0104
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J. Mater. Res., Vol. 24, No. 3, Mar 2009 Downloaded: 06 Apr 2015
decreasing indenter penetration depth hp with the proportionality H / 1/hp.1,7 The concept of strain gradient plasticity has been used to describe this phenomenon, but it is often necessary to introduce a material length scale l* to fit experimental data, and the physical meaning of this length scale l* is not always clear.3,7–12 These theories fit well to data for self-similar indenter geometries.7,9 Similar strain gradient plasticity theories also predict data from spheric
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