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method (Oliver and Pharr, 1992), where the mechanical properties are calculated based on the contact area of the probe tip to the sample, under a certain load. Since indentation measurements give us only contact depth information, the tip area function correlating the contact area and the contact depth needs to be determined/ known for the tip used in the measurements. Note that contact depth hc is defined as the vertical distance along which contact is made by the tip during loading, and is less than the maximum penetration depth (hmax) due to the elastic property of the indented surface (Oliver and Pharr, 1992). If the tip was manufactured to be perfect without any defects (which is not the case), the area function will be simply the geometrical shape function of a pre- specified tip such as, 2 Ac(hc) = 24.5 hc in the case of the Berkovich tip. However, due to tip imperfections, the area function usually takes the following polynomial form. 2 1/ 2 1/ 4 1/ 8 Ac(hc)=C0hc To determine the coefficients of the above equation, indentations at varying penetration depths (corresponding to similar depth range as the desired measurements) are performed on a standard material. Then, since the modulus of the standard material is known, the contact area corresponding to each contact depth (Ac, hc) can be calculated and plotted as in Figure 4.4, and finally, the coefficients are determined by polynomial curve-fitting. Two important elements that affect the tip calibration and thus the material property values are 1) the choice of the standard sample and 2) the contact depth range of calibration. In this study, a modified bismaleimide polymer (manufactured by BASF Corp) (Chasiotis et al., 2005) with a reduced modulus value of 5.0 GPa was used as the +C1hc +C2hc +C3hc +C4hc +···. (4.2) 55 (4.1)PDF Image | TRIBOLOGY OF POLYMERIC COATINGS FOR AGGRESSIVE BEARING APPLICATIONS
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