A New Nanoindentation Protocol for Identifying the Elasticity of Undamaged Extracellular Bone Tissue
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A New Nanoindentation Protocol for Identifying the Elasticity of Undamaged Extracellular Bone Tissue Irina Furin, Maria-Ioana Pastrama, Hawraa Kariem, Krzysztof W. Luczynski, Olaf Lahayne, Christian Hellmich1 Institute for Mechanics of Materials and Structures, TU Wien - Vienna University of Technology, Austria ABSTRACT While the quest for understanding and even mimicking biological tissue has propelled, over the last decades, more and more experimental activities at the micro and nanoscales, the appropriate evaluation and interpretation of respective test results has remained a formidable challenge. As a contribution to tackling this challenge, we here describe a new method for identifying, from nanoindentation, the elasticity of the undamaged extracellular bone matrix. The underlying premise is that the tested bovine bone sample is either initially damaged (i.e. exhibits micro-cracks a priori) or that such micro-cracks are actually induced by the nanoindentation process itself, or both. Then, (very many) indentations may relate to either an intact material phase (which is located sufficiently far away from micro-cracks), or to differently strongly damaged material phases. Corresponding elastic phase properties are identified from the statistical evaluation of the measured indentation moduli, through representation of their histogram as a weighted sum of Gaussian distribution functions. The resulting undamaged elastic modulus of bovine femoral extracellular bone matrix amounts to 31 GPa, a value agreeing strikingly well both with direct quasi-static modulus tests performed on SEM-FIB-produced micro-pillars (Luczynski et al., 2015), and with the predictions of a widely validated micromechanics model (Morin and Hellmich, 2014). Further confidence is gained through observing typical indentation imprints under Scanning Electron Microscopy (SEM), which actually confirms the existence of the two types of micro-cracks as described above. LIST OF SYMBOLS CDF I?C 7< = $1 I J J@ K
projected area of the elastic indentation contact cumulative distribution function relative error elastic modulus of undamaged, intact extracellular bone tissue material reduced elastic modulus elastic modulus of the tested substrate (i.e. damaged or undamaged extracellular bone matrix) ith experimental value of J , as determined by nanoindentation elastic modulus of the indenter tip
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Corresponding author E-mail address: [email protected] (Christian Hellmich)
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A ?MG
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8DF>?C ADF>?C FIB k m n 8 9=L FGK P R2 H SEM SPM zmn # $A %K %J 'A
weighting factor of the Gaussian cumulative distribution function (CDF) related to material phase j CDF of elastic modulus of extracellular bone matrix, determined from nanoindentation experiments CDF of elastic modulus
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