Oliver-Pharr method

Van Landigham et al. reviewed nanoindentation of polymers, [40, 41] including a summary of the most common analyses of load-indentation data. Chief among these methods is an analysis of indentation load-penetration curves according to the Oliver-Pharr method. [42] This method is based on relationships developed by Sneddon for the penetration of a flat elastic half space by different probes with particular axisymmetric shapes (e.g., aflat-ended cylindrical punch, a paraboloid of revolution, or a cone) [43], More recently, Withers and Aston discussed indentation in the context of plasticity and viscoelasticity [44]. 

The unloading was conducted with the same rate as loading. In the given experiment the Berkovich indentor was used with the angle at the top of 65.3° and rounding radius of 200 nm. Indentations were carried out in the checked load regime with preload of 0.001 mN. For elasticity modulus calculation the obtained result in the experiment by nanoindentation course dependences of load on indentation depth (strain) in 10 points for each sample at loads of 0.01, 0.02, 0.03, 0.05, 0.10, 0.50, 1.0, and 2.0 mN were processed according to Oliver-Pharr method [18]. 

According to the Oliver-Pharr method, the elastic modulus Eo of the sample are given by the following equation based on the load (P) versus indentation depth (h) test curve ... 

Often the soft films deposited on hard substrates have the possibility to pile-up upon indentation due to the change of the films plastic deformation behaviour attributed to the constraint stress enforced by the relatively harder substrate, whereas in the opposite case the films tend to sink-in. As a result, the former case could erroneously increase the mechanical properties calculated using Oliver-Pharr method because according to the method E oc where A is extracted from nanoindentation load-depth data and not from direct measurement, while the piled-up material would accommodate an extra amount of load but causes underestimation of the real contact depth and hence the contact area. On the other hand, the sink-in effect accounts for the overestimation of the real contact area and hence decrease of the calculated mechanical properties. Both of these cases would cause problems in the calculation using Oliver-Pharr method, which was first established for monolithic materials use only, as the calculated mechanical properties deviate from the true values. Therefore, in the absence of the pile-up and sink-in effects, the calculation in this study using Oliver-Pharr method could generate more accurate estimation towards the real mechanical properties of the film. 

Maitra et al. determined the hardness of PVA with 0.6 wt% oxidized NDs using nanoindentation and the Oliver-Pharr method addition of nanofiller enhanced the hardness 80% of the neat polymer [48]. Hardness and modulus of FG/epoxy composites increased steadily with the incorporation of up to 1.5 wt% nanofiller. An increased amount of agglomerates was obtained at a loading of 2 wt% amino FGs as observed by the dramatic drop in the modulus this behavior also affected the nanocomposite hardness, as depicted in Figure 10.20 [113], The microhardness of amino FGs/PI nanocomposites showed a dependence on nanofiller content, although the dependence diminishes at loadings > 1 wt%, where the effect starts to saturate [115]. Covalently bonded amino NDs/epoxy composites showed a 200 times higher hardness compared to the neat... 

Berkovich indentor nanoshungite Oliver-pharr method quadrates method superreinforcing... 

Characterization of the mechanical properties of these thin silica layers, unreinforced or reinforced, is usually conducted by using the nanoindentation technique [33-37] to determine the hardness (H) of the layer and the elastic modulus ( ) using the Oliver-Pharr method [38]. In these tests, a Berkovich indenter is used and low maximum loads are applied (in the range of mN) to avoid the influence of the mechanical response of the substrate. A complete review of how to calculate different key mechanical parameters ( , H, fracture toughness, residual stresses, and adhesion) of thin sol-gel coatings using nanoindentation tests and scratch testing with nanoindenter equipment can be found in the work of Malzbender et al. [39]. 

The Oliver Pharr method [10], which proposes the estimation of the slope of the unloading curve by first fitting the entire unloading data, was employed to determine reduced elastic modulus E and the hardness (//) of the materials. The reduced elastic modulus is related to the elastic modulus of the sample E) and the contact stifBiess S) by the following equations ... 

Pharr, G.M., Harding, D.S. and Oliver, W.C., Measurement of fracture toughness in thin films and small volumes using nanoindentation methods. MRS, 1995, pp. 663-675. 

Figure 10.35 Methods of measuring the mechanical properties of thin films (a) Nano-indentation, (b) beam deflection and (c) disc deflection. (Adapted from G.M. Pharr and W.C. Oliver, 1992, Measurement of Thin Film Mechanical Properties Using Nanoindentation , Materials Research Society Bulletin XVII (July) 28...

The nanoindentation experiments were conducted at room temperature with a Nano Indenter XP system (MTS Nanoinstruments, Knoxville, TN) using a Berkovich-type diamond tip. Before each test, the system was calibrated using a fused silica. The continuous stiffness mode (CSM) was used in the tests. Thirty randomly selected different fiber and CVI matrix locations were indented for each component of C/C composites. The method of Oliver and Pharr was employed for the elastic modulus calculations. ... 

Kriese, M.D., Gerberich, W.W. and Moody, N.R., Quantitative adhesion measures of multilayer films Part 1. Indentation mechanics. J. Mater. Res., 14(7), 3007-3018 (1999). Pharr, G.M., Harding, D.S. and Oliver, W.C., Measurement of fracture toughness in thin films and small volumes using nanoindentation methods. MRS, 1995, pp. 663-675. Pethica, J.B. and Oliver, W.C., Tip surface interactions in STM and AFM. Phys. Scripta, T19A, 61-66 (1987). 

Du and co-workers (256) analyzed SFM force indentation curves according to the method by Oliver and Pharr (104). For PS and PC thin films, good agreement between theory and experiment required the introduction of a correction factor that accounts for the asymmetry to the SFM indentation (256). 

Nanoindentation experiments were performed using two different nanoindentation systems to make indents at peak loads from 100 pN to 500 mN. Hardness and Young s Modulus were extracted from the load-displacment curves using the method of Oliver and Pharr. All load displacement curves were corrected for thermal drift and the indenter area functions were carefully calibrated following the Oliver and Pharr approach using a fused silica standard sample prior to testing the coated samples. 

The determination of mechanical properties of periodically re-crystallized Pt thin films has been performed using a nanoindentation test. The sample surface was subjected to a loading — unloading cycle with a Berkovich diamond tip. Using the calculation method developed by Oliver and Pharr,local measurements of both hardness H) and Young modulus E) of the thin Pt films have been carried out. 

Conventionally, the compliance method proposed by Oliver and Pharr [153] has been used to determine the hardness (H) and elastic modulus ( ) by means of nanoindentation from the analysis of the load-displacement curve. In this method, the unloading segment of the curve is fitted to a power law function to obtain the contact depth and thus the contact area (A) at the peak load (Pmax) required to determine H H= A typical load-unload displacement curve for a... 

Swain methods, named after their respective authors (Oliver and Pharr, 1992 Field and Swain, 1993). These methods have several limitations. Firstly, one major assumption of both methods is that only elastic recovery happens while unloading this might not be strictly the case as revealed for very light indents and when films show viscoelastic response (Le Bourhis and Patriarche, 2003). Secondly, the methodology was derived from the solution to elastic contact problems, while prior to unloading the contact conditions involve plastic deformation. Thirdly, the material around the contact may exhibit substantial pile-up or sink-in, the projected contact area being then either underestimated or overestimated, yielding errors in the hardness values (Oliver and Pharr, 1992 Field and Swain, 1993). 

Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7(4) 1564 Oroshnik J, Croll WK (1978) Threshold adhesion failure an approach to aluminum thin-film adhesion measurement using the stylus method. In Mittal KL (ed) Adhesion measurement of thin films, thick films and bulk coatings, ASTM STP 640. American Society for Testing and Materials, West Conshohocken, p 158... 

The most widely used method for calculating the contact area is developed by Oliver and Pharr. It has been developed for elastic materials only a fact that needs to be remembered applying their approach to any other materials [12-13]. One fits depth vs. load unloading data to a power law function ... 

Property measurements are based on the contact mechanics of an axisymmetric indenter with an elastically isotropic half space, using the method developed by Oliver and Pharr. Hardness values (H) are calculated as ... 

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