UNCORRECTED PROOF UNCORRECTED PROOF Ž . Surface and Coatings Technology 00 2000 0000 On the application of the work-of-indentation approach to depth-sensing indentation experiments in coated systems Jonathan R. Tuck ,1 , Alexander M. Korsunsky 1 , Steve J. Bull, Rob I. Davidson Materials Di  ision, Department of Mechanical, Materials and Manufacturing Engineering, Uni  ersity of Newcastle, Newcastle upon Tyne, NE1 7RU, UK Received 16 June 2000; received in revised form 30 August 2000; accepted 30 August 2000 Abstract The work-of-indentation approach is developed and applied for hardness calculations in soft or hard materials, and also for a range of coated systems. The method appears to be less sensitive than other definitions to the effects of pile-up observed in soft materials. Work-of-indentation hardness is calculated directly from the energy of indentation without the need for estimating penetration depths, areas or volumes, which can be time consuming and inaccurate. In particular, using the plastic component of the work-of-indentation yields consistent results across the range of materials studied. The method breaks down, however, at very low loads and small penetration depths, which is likely to be due to deviations from the ideal tip geometry.  2000 Elsevier Science S.A. All rights reserved. Keywords: PLEASE SUPPLY 1. Introduction The concept of work-of-indentation arises naturally in the study of hardness. Similarly to the way in which toughness was introduced by Griffith to describe the energy expenditure per unit area during fracture, hard- ness can be understood in terms of energy expenditure per unit volume during indentation. However, a sig- nificant difference exists between the two cases. In the case of brittle fracture, the area concerned has a clear physical meaning of the crack surface. In the case of indentation, however, the volume in question cannot be simply equated to that displaced by the indenter. Not only is this volume poorly defined, but also it is difficult to measure. Depth sensing indentation offers remarkable oppor-  Corresponding author. Tel.: 44-191-222-7913; fax: 44-191- 222-8563. 1 Present address: Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK. tunities of analysis and interpretation. The detailed and accurate record of the applied load and the tip dis- placement during both the loading and unloading phases of the experiment allows the energetic charac- teristics of the process to be computed. It is then possible to choose as a basis for a hardness definition a combination of any two or more from the following parameters: maximum load P and depth , total work- of-indentation W, or its elastic W and plastic W parts. e p In the present study, a family of possible hardness definitions was systematically applied to the results of nanoindentation experiments in various bulk materials and coated systems. The purpose of this study was to identify the most suitable formulations appropriate to each case and class of materials. The viability of the work-of-indentation approach for estimation of mate- rial hardness was investigated. The performance of this approach for soft materials at low loads was compared with the Oliver and Pharr method of hardness calcula- tion from nanoindentation data. The results suggest that the approach affords several improvements in 0257-897200$ - see front matter  2000 Elsevier Science S.A. All rights reserved. Ž . PII: S 0 2 5 7 - 8 9 7 2 00 01063-X