Instrumented indentation of fused silica by Berkovich indenter

Abstract Scaling relationships among indentation variables such as the maximum indentation displacement, contact depth, the ratio of load over contact stiffness, and the ratio of permanent displacement over the maximum displacement were investigated via Berkovich indentation of fused silica. Load-displacement curves were characterized by power-law functions for both loading and unloading. The power exponents can be assumed to be constant for loading and unloading. Hardness, elastic modulus, and yield stress were measured to be 9.8 GPa, 73.3 GPa, and 5.5 GPa, respectively, for fused silica that can be assumed to be elastic-perfectly plastic. The empirical algorithm for estimating yield stress was verified for fused silica. The experimental results accorded well with theoretical prediction and dimensional analysis. The expressions obtained can be used to check indentation data, and general implications of the relations are discussed.

[1]  Brian R. Lawn,et al.  Elastic recovery at hardness indentations , 1981 .

[2]  Alexei Bolshakov,et al.  A critical examination of the fundamental relations used in the analysis of nanoindentation data , 1999 .

[3]  Fuqian Yang,et al.  Finite element simulation of the effect of electric boundary conditions on the spherical indentation of transversely isotropic piezoelectric films , 2012 .

[4]  Ming Liu,et al.  Finite element analysis of large contact deformation of an elastic–plastic sinusoidal asperity and a rigid flat , 2014 .

[5]  John C. Lambropoulos,et al.  Nanoindentation technique for measuring residual stress field around a laser-induced crack in fused silica , 1998 .

[6]  M. Troyon,et al.  A critical examination of the P–h2 relationship in nanoindentation , 2003 .

[7]  M. Tarfaoui,et al.  Mechanical characterization of carbon nanotubes based polymer composites using indentation tests , 2017 .

[8]  Ian M. Hutchings,et al.  Analysis of nano-indentation measurements on carbon nitride films , 2003 .

[9]  Seung-Eock Kim,et al.  Determination of equi-biaxial residual stress and plastic properties in structural steel using instrumented indentation , 2017 .

[10]  George Constantinides,et al.  On the conical indentation response of elastic auxetic materials: Effects of Poisson's ratio, contact friction and cone angle , 2016 .

[11]  G. Pharr,et al.  A critical examination of the Berkovich vs. conical indentation based on 3D finite element calculation , 2004 .

[12]  A. Matthews,et al.  On the significance of the H/E ratio in wear control: a nanocomposite coating approach to optimised tribological behaviour , 2000 .

[13]  Xiaodong Li,et al.  Effect of sample tilt on nanoindentation behaviour of materials , 2007 .

[14]  Alain Iost,et al.  Fracture toughness of glasses and hydroxyapatite: a comparative study of 7 methods by using Vickers indenter , 2016 .

[15]  M. Troyon,et al.  Fundamental relations used in nanoindentation: Critical examination based on experimental measurements , 2002 .

[16]  Yun-Hee Lee,et al.  Assessment of surface-local strains from remnant microindents on a Zr-based metallic glass , 2014, Metals and Materials International.

[17]  Fuqian Yang,et al.  Analysis for the Indentation with a Flat Indenter on an Elastic-Perfectly Plastic Thin Film , 2014 .

[18]  D. Chicot,et al.  Mechanical characterization of brittle materials using instrumented indentation with Knoop indenter , 2017 .

[19]  Yang-Tse Cheng,et al.  An energy-based method for analyzing instrumented spherical indentation experiments , 2004 .

[20]  G. Pharr,et al.  Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology , 2004 .

[21]  Morten Mattrup Smedskjær,et al.  Indentation deformation mechanism of isostatically compressed mixed alkali aluminosilicate glasses , 2015 .

[22]  M. Sakai,et al.  Energy principle of the indentation-induced inelastic surface deformation and hardness of brittle materials , 1993 .

[23]  D. Tabor.  A simple theory of static and dynamic hardness , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[24]  Zvi Rosenberg,et al.  Deep indentation and terminal ballistics of polycarbonate , 2017 .

[25]  Alex A. Volinsky,et al.  Nanoindentaion techniques for assessing mechanical reliability at the nanoscale , 2003 .

[26]  A Oila,et al.  Extracting mechanical properties of copper coatings on oxidized silicon substrates by nanoindentation , 2014 .

[27]  J. Georges,et al.  Vickers Indentation Curves of Magnesium Oxide (MgO) , 1984 .

[28]  Liang Meng,et al.  An objective meta-modeling approach for indentation-based material characterization , 2017 .

[29]  Konstanty Skalski,et al.  Stress–strain characteristic of human trabecular bone based on depth sensing indentation measurements , 2017 .

[30]  Luquan Ren,et al.  Effects of Indenter Tilt on Nanoindentation Results of Fused Silica : an Investigation by Finite Element Analysis , 2013 .

[31]  Yang-Tse Cheng,et al.  Effects of 'sinking in' and 'piling up' on estimating the contact area under load in indentation , 1998 .

[32]  Kong Boon Yeap,et al.  Nanoindentation for reliability assessment of ULK films and interconnects structures , 2013 .

[33]  Marcel Potuzak,et al.  Thermal history dependence of indentation induced densification in an aluminosilicate glass , 2016 .

[34]  Meysam Haghshenas,et al.  Multi-cycling instrumented nanoindentation of a Ti-23Nb-0.7Ta-2Zr-1.2O alloy in annealed condition , 2017 .

[35]  Fuqian Yang,et al.  Finite element analysis of the spherical indentation of transversely isotropic piezoelectric materials , 2012 .

[36]  M. Sakai,et al.  Elastoplastic load–depth hysteresis in pyramidal indentation , 2002 .

[37]  F. A. Khalid,et al.  Indentation fracture toughness behavior of FeCo-based bulk metallic glass intrinsic composites , 2017 .

[38]  Alexei Bolshakov,et al.  Influences of pileup on the measurement of mechanical properties by load and depth sensing indentation techniques , 1998 .

[39]  Tanguy Rouxel,et al.  Densification of window glass under very high pressure and its relevance to Vickers indentation , 2006 .

[40]  Subra Suresh,et al.  DETERMINATION OF ELASTOPLASTIC PROPERTIES BY INSTRUMENTED SHARP INDENTATION , 1999 .

[41]  Jinju Chen,et al.  Relation between the ratio of elastic work to the total work of indentation and the ratio of hardness to Young’s modulus for a perfect conical tip , 2009 .

[42]  Cher Ming Tan,et al.  Intrinsic mechanical properties of diamond-like carbon thin films deposited by filtered cathodic vacuum arc , 2004 .

[43]  Abdulaziz S. Alaboodi,et al.  Finite element modeling of nano-indentation technique to characterize thin film coatings , 2017, Journal of King Saud University - Engineering Sciences.

[44]  Song Li,et al.  A Technique for Hi-speed Indentation Experiment Based on Hopkinson Bar , 2017 .

[45]  Xiaodong Zhu,et al.  Quantitative evaluation of bonding strength for hard coatings by interfacial fatigue strength under cyclic indentation , 2017 .

[46]  Zhang Chunyu,et al.  Understanding indentation-induced elastic modulus degradation of ductile metallic materials , 2017 .

[47]  Matteo Chiesa,et al.  Densification modeling of fused silica under nanoindentation , 2012 .

[48]  Ian M. Hutchings,et al.  Influence of inert gases on ionized magnetron plasma deposition of carbon nitride thin films , 2003 .

[49]  T. Clyne,et al.  Extraction of plasticity parameters from a single test using a spherical indenter and FEM modelling , 2017 .

[50]  D. J. Ma,et al.  Method for Identifying Vickers Hardness by Instrumented Indentation Curves with Berkovich/Vickers Indenter , 2016 .

[51]  Amir K. Miri,et al.  Mechanical characterization of nanoclay-filled PDMS thin films , 2016 .

[52]  Yang-Tse Cheng,et al.  Scaling relationships for indentation measurements , 2002 .

[53]  Alex A. Volinsky,et al.  Nanoindentation of Au and Pt/Cu thin films at elevated temperatures , 2004 .

[54]  Fuqian Yang,et al.  Three-dimensional finite element simulation of the Berkovich indentation of a transversely isotropic piezoelectric material: effect of material orientation , 2013 .

[55]  D. M. Marsh,et al.  Plastic flow in glass , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[56]  Jae Ryoun Youn,et al.  Measurement of residual stresses in polymeric parts by indentation method , 2013 .

[57]  C. Muhlstein,et al.  Correlations between free volume and pile-up behavior in nanoindentation reference glasses , 2008 .

[58]  D. Ozevin,et al.  Acoustoelastic Coefficients in Thick Steel Plates under Normal and Shear Stresses , 2016 .

[59]  Y. Tokovyy,et al.  Axisymmetric problem on the indentation of a hot circular punch into an arbitrarily nonhomogeneous half-space , 2015 .

[60]  Yang-Tse Cheng,et al.  Relationships between hardness, elastic modulus, and the work of indentation , 1998 .

[61]  Danko Ćorić,et al.  Vickers indentation fracture toughness of Y-TZP dental ceramics , 2017 .

[62]  John C. Lambropoulos,et al.  Surface effects on Young’s modulus and hardness of fused silica by nanoindentation study , 2007 .

[63]  N. Mott,et al.  The theory of indentation and hardness tests , 1945 .

[64]  H. Ishikawa,et al.  Indentation method to measure the residual stress induced by ion implantation , 2006 .

[65]  Ajit Achuthan,et al.  The effect of work-hardening and pile-up on nanoindentation measurements , 2014, Journal of Materials Science.

[66]  Yang-Tse Cheng,et al.  Scaling, dimensional analysis, and indentation measurements , 2004 .

[67]  I. Ashcroft,et al.  A combined inverse finite element – elastoplastic modelling method to simulate the size-effect in nanoindentation and characterise materials from the nano to micro-scale , 2017 .

[68]  D. A. Dietrich,et al.  Depth-sensing indentation measurements with Vickers and Berkovich indenters , 1998 .

[69]  Ali Hassanpour,et al.  Ball Indentation on Powder Beds for Assessing Powder Flowability: Analysis of Operation Window , 2017 .

[70]  Fuqian Yang,et al.  Orientation effect on the Boussinesq indentation of a transversely isotropic piezoelectric material , 2013 .

[71]  Michael V. Swain,et al.  Geometry and bluntness tip effects on elastic–plastic behaviour during nanoindentation of fused silica: experimental and FE simulation , 2010 .

[72]  R. King,et al.  Elastic analysis of some punch problems for a layered medium , 1987 .

[73]  D. Jarzabek,et al.  Decrease of Nano-hardness at Ultra-low Indentation Depths in Copper Single Crystal , 2016 .

[74]  G. Kermouche,et al.  Mechanical modelling of indentation-induced densification in amorphous silica , 2008 .

[75]  J. M. Alvarado-Orozco,et al.  Inter Laboratory Comparison and Analysis on Mechanical Properties by Nanoindentation , 2009 .

[76]  R. Hill.  The mathematical theory of plasticity , 1950 .

[77]  Donald S. Gardner,et al.  Plastic properties of thin films on substrates as measured by submicron indentation hardness and substrate curvature techniques , 1986 .

[78]  Alexei Bolshakov,et al.  Using the Ratio of Loading Slope and Elastic Stiffness to Predict Pile-Up and Constraint Factor During Indentation , 1998 .

[79]  D. Tabor.  Hardness of Metals , 1937, Nature.

[80]  J. Malzbender.  Comment on hardness definitions , 2003 .

[81]  G. Pharr,et al.  An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments , 1992 .

[82]  Q. Qin,et al.  Indentation of Metal Foam Core Sandwich Beams: Experimental and Theoretical Investigations , 2016 .

[83]  C. Tromas,et al.  A new technology for nanohardness measurements: principle and applications , 1998 .

[84]  Yang-Tse Cheng,et al.  Further analysis of indentation loading curves: Effects of tip rounding on mechanical property measurements , 1998 .

[85]  Yang-Tse Cheng,et al.  Scaling approach to conical indentation in elastic-plastic solids with work hardening , 1998 .