An indentation fatigue depth propagation law Baoxing Xu, a Zhufeng Yue b and Xi Chen a, * a Columbia Nanomechanics Research Center, Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027-6699, USA b Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China Received 7 November 2008; revised 8 January 2009; accepted 19 January 2009 Available online 29 January 2009 Using both experimental and numerical studies, we show that, upon cyclic indentation with a flat cylindrical indenter, the steady- state rate of indentation depth propagation can be well characterized by a simple power-law function of the stress intensity range and the maximum stress intensity, which is qualitatively similar to the steady-state growth of a fatigue crack. The simple law of indentation fatigue has the potential to extract the fatigue properties of materials with small volumes and clarify the fatigue crack mechanisms. Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Indentation fatigue experiment; Finite element analyses; Indentation depth propagation; Fatigue crack growth; Stress intensity When a metal is subjected to cyclic uniaxial load- ing, a fatigue crack initiates and grows with the number of cycles. The intermediate region of the fatigue crack growth of many metallic materials can be described by the well-known Paris equation [1,2], where the crack growth rate is a power-law function of the nominal stress intensity factor range, DK = K max  K min , with K max and K min denoting the maximum and minimum stress intensity factors, respectively. Recent studies have shown that another important driving force for fatigue crack propagation is K max , especially for the relatively more brittle materials. For example, Liu and Chen [3] and Dauskardt et al. [4] explored the competition be- tween the intrinsic mechanism of crack advance ahead of the crack tip and the extrinsic mechanism of crack tip shielding behind the tip. From extensive experiments, they proposed the following phenomenological law for the fatigue crack growth rate: da=dN ¼ CðK max Þ n ðDK Þ m ð1Þ Here, DK and K max represent the intrinsic and extrinsic mechanisms of fatigue crack growth, the dominances of which are denoted by the power indices m and n, respec- tively. m, n and C are empirical constants that depend on the material and microstructure, fatigue frequency, loading mode and environment, etc. In other words, there are various intrinsic and extrinsic factors that could either promote or impede the fatigue crack growth in ductile or brittle materials, yet their fundamental roles are still not yet sufficiently understood [5,6]. Meanwhile, with the wide applications of small mate- rial structures, including nano-/micro-electromechanical systems (N/MEMS) and thin films [7,8], there is an increasing practical need to understand the fatigue proper- ties of materials of very small volumes. Note that these small material structures often exhibit properties distinct from their bulk counterparts, and it is challenging to mea- sure their fatigue characteristics using conventional uniax- ial testing methods. The development of an alternative testing technique could help to address both the funda- mental and the practical challenges described above. Instrumented indentation is widely used to measure the mechanical properties of material structures at various nanoscopic, microscopic and macroscopic scales [9–11]. Its popularity arises in that it is easy to conduct, only minor preparation (if any) of the tested material is needed, and the tests are inherently simple, fast and pre- cise. The tests can be conducted at various working tem- peratures and in a range of environments, and measurements close to in situ conditions are possible thanks to the small penetration needed in most cases. Therefore, it is a very attractive alternative testing tech- nique for small material structures [12–14]. Upon cyclic indentation loading, also known as the indentation fatigue test, an early study by Li and Chu 1359-6462/$ - see front matter Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2009.01.027 * Corresponding author. Tel.:+1 212 854 3787; fax: +1 212 854 6267; e-mail: xichen@civil.columbia.edu Available online at www.sciencedirect.com Scripta Materialia 60 (2009) 854–857 www.elsevier.com/locate/scriptamat