Unloading elastic modulus

Matrix cracks increase the elastic compliance. Numerical calculations indicate that the unloading elastic modulus, E, is given by21... 

Microhardness, therefore, appears to be an elastic-plastic rather elusive parameter (Marsh, 1964). Microhardness as a property is, in fact, a complex combination of other properties elastic modulus, yield strength and strain hardening capacity. One way to differentiate between the reversible and irreversible components of contact deformation is to measure the elastic recovery during unloading of the indenter (Stilwell Tabor, 1961). Extreme cases of depth recovery are best described by soft metals, where it is negligible, and fully elastic rubber, where it is complete. 

The elastic modulus (E) was calculated directly from the experimental loading-creep-unloading curve (as in Fig. 2.14) according to the procedure of Doemer Nix (1986). 

The first case (a) corresponds to a fracture that due to compression stresses is almost closed or has an initial aperture bo- Normal extension will induce aperture opening right from the beginning of stressing. As the normal stress reaches a zero value, deformation will increase under constant stress (irreversible deformations). Unloading will imply fracture closure but a residual aperture is expected due to irreversible deformations. An appropriate elastic modulus could be used if complete closure had to be achieved. 

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]. 

Both these equations require a value of the elastic modulus E. This may be obtained from a standard flexure test, or alternatively the ELS specimens may be tested as above (loaded and unloaded within the elastic region) with the specimen changed in re erse such that the starter film is not within the free length. The slope P/h of the linear P-<5 line would allow a... 

The universal hardness , is obtained from the same formula if h is inserted instead of Aplastic- The universal hardness includes both the elastic and plastic deformation. The hnear part of the unloading curve corresponds to the elastic recovery when the diamond pyramid is in a constant area contact with the material. Therefore it represents Hooke s law and allows one to calculate the corresponding elastic modulus E/ — i/) which is a complicated function of the bulk, shear, and tensile moduli is the Poisson ratio). The details of the apparatus, the measuring procedure and possible errors are given in the relevant papers to which we refer here [25-28]. If done correctly, the plastic hardness measured by the indentation agrees within about 10-15% reasonably well with that from the classical Vickers method at least in the range H < 1500kgmm [25]. 

Nanoindentation is a technique gaining increasing popularity [74-76]. Actually, the technique is sometimes abused by attempts to calculate the elastic modulus E on the basis of a model valid for fully elastic materials only [74]. While such attempts fail, a connection has been found by Fujisawa and Swain between E and the unloading strain rate [75]. As shown by Tweedie and Van Vliet [76], spherical indentation provides lower contact strains and more reliable results than conical indentation. A modification providing repetitive indenter hits perpendicular to the specimen surface at the same spot and thus nanoindentation fatigue testing (NIFT) exists also [77]. 

HaU effect measurement, 467 hardness measurement in sol-gel coatings aluminium alloy, use of, 304 antireflex coatings, 305 Berkovich indenter, 303, 304 defomation mechanisms, 302 diamond indenter, 302 elastic modulus, 303 indentation testing, 302 indium-tin-oxide coatings, 305 loading-unloading cycle, 303 pencil hardness, 305 Poisson s ratio, 303 silica, 304... 

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... 

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 ... 

---