(PMMA) Based Bone Cement - Tribology in Industry

great advancements in this area, micro and nanoscale optical measurements are widely availablethus leading to expansion of indentationinterpretation. Devices with depth sensingpossibilities, such as CSM Nano Indentation Tester,enable determination of hardness, elastic modulus,plastic stress-strain behavior and/or creep behaviordirectly using the tester, without the need tomeasure contact impressions.2. PRINCIPLE OF INSTRUMENTEDINDENTATION TESTING (IIT)The Nano Indentation Tester uses an alreadyestablished method where an indenter tip with aknown geometry is driven into a specific site of thematerial to be tested, by applying an increasingnormal load. When reaching a pre-set maximumvalue, the normal load is reduced until partial orcomplete relaxation occurs. This procedure isperformed repetitively; at each stage of theexperiment the position of the indenter relative tothe sample surface is precisely monitored with adifferential capacitive sensor. For eachloading/unloading cycle, the applied load value isplotted with respect to the corresponding positionof the indenter. The resulting load/displacementcurves (Fig. 2) provide data specific to themechanical nature of the material underexamination. Established models are used tocalculate quantitative hardness and elastic modulusvalues for such data.that describes the upper portion of the unloadingcurve by a power law relationship:where,F - is the test force,Fmax - is the maximum applied force,h - is the indentation depth under applied test force,hp - is the permanent indentation depth after theremoval of the test force,hmax - is the maximum indentation depth at Fmax,m - is a power law constant exponent.The power law exponent m is determined by a leastsquares fitting procedure and is a function of theindenter geometry.The contact stiffness S is given by the derivative atpeak load:And the tangent depth, hr, is thus given by:Where h r is the point of intersection of the tangentc to curve b at F max with the indentation depth-axis.The contact depth (depth of the contact of theindenter with the test piece at Fmax), h c , is then:where ε depends on the power law exponent m.The Indentation Testing Hardness H IT isdetermined from the maximum load, F max , dividedby the projected contact area A p at the contactdepth h c :Figure 2. Typical Load/displacement curveEvaluation of elastic modulus and hardness usinginstrumented indentation is realised by the methoddeveloped and proposed by Oliver and Pharr. It isthe most common approach to determine hardnessand modulus by interpretation of load - penetrationdepth (F - h) behavior during indentation (Fig. 1).Oliver and Pharr developed Power Law MethodWhere hc is the depth of the contact of the indenterwith the test piece at F max . A p (h c ) is the projectedarea of contact of the indenter at distance h c fromthe tip. A p is a function of the contact depth h c andis determined by a calibration of the indenter tip.The Vickers Hardness HV is defined by:148Tribology in industry, Volume 33, No. 4, 2011.