Crystal Indentation Hardness
Total Page：16
File Type：pdf, Size：1020Kb
crystals Editorial Crystal Indentation Hardness Ronald W. Armstrong 1,*, Stephen M. Walley 2,† and Wayne L. Elban 3,† 1 Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA 2 Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, UK; [email protected] 3 Department of Engineering, Loyola University Maryland, Baltimore, MD 21210, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-410-723-4616 † These authors contributed equally to this work. Academic Editor: Sławomir Grabowski Received: 5 January 2017; Accepted: 6 January 2017; Published: 12 January 2017 Abstract: There is expanded interest in the long-standing subject of the hardness properties of materials. A major part of such interest is due to the advent of nanoindentation hardness testing systems which have made available orders of magnitude increases in load and displacement measuring capabilities achieved in a continuously recorded test procedure. The new results have been smoothly merged with other advances in conventional hardness testing and with parallel developments in improved model descriptions of both elastic contact mechanics and dislocation mechanisms operative in the understanding of crystal plasticity and fracturing behaviors. No crystal is either too soft or too hard to prevent the determination of its elastic, plastic and cracking properties under a suitable probing indenter. A sampling of the wealth of measurements and reported analyses associated with the topic on a wide variety of materials are presented in the current Special Issue. Keywords: crystal hardness; nanoindentations; dislocations; contact mechanics; indentation plasticity; plastic anisotropy; stress–strain characterizations; indentation fracture mechanics 1. Introduction The concept of material hardness has been tracked historically by Walley starting from biblical time and proceeding until the 1950s, with pictorial emphasis given to the earliest 19th century design of testing machines and accumulated measurements [1]. Walley’s review leads up to David Tabor setting a new course via science connection with his seminal 1951 book The Hardness of Metals [2] and further leading, for example, to a later 1973 conference proceedings on The Science of Hardness Testing and Its Research Applications [3]. The subject has gained increased importance with the relatively recent advent of orders of magnitude greater force and displacement measuring capabilities available with modern nano-indentation test systems. A review was presented in 2013 of the complete elastic, plastic and, when appropriate, cracking behaviors that can be monitored for crystals, polycrystals, composites and amorphous materials under suitable probing indentation [4]. A substantial reference list was included in the review of conferences and books produced until that time. As will be seen in the current updated collection of research and review articles, no crystal can be too soft or too hard within its environment to escape measurement with a suitable probing indenter applied using appropriate test conditions. 2. Continuous Indentation Testing The original application of the hardness test corresponded to the obtainment of a single reference point for measurement of an applied load and resultant plastic deformation. Much has been made, and continues to be made, of correlating the measurement with some aspect of the same material unidirectional stress–strain behavior beginning from historical association with the ultimate Crystals 2017, 7, 21; doi:10.3390/cryst7010021 www.mdpi.com/journal/crystals Crystals 2017, 7, 21 2 of 9 Crystals 2017, 7, 21 2 of 9 material unidirectional stress–strain behavior beginning from historical association with the ultimate tensile stress. In like manner, current achievements of continuous indentation load– tensiledeformation stress. measurements, In like manner, particularly current achievements obtained with of nanoindentation continuous indentation test instruments, load–deformation are being measurements,developed to describe particularly the full obtained material with indentation-b nanoindentationased stress–strain test instruments, behavior. are Figure being developed1 provides toan describeexample thein which full material a number indentation-based of measurements stress–strain are compared. behavior. The hardness Figure1 providesstress is load an example divided inby whichcontact a numberarea; and, of the measurements hardness strain are compared.is based on The a spherica hardnessl-tipped stress indenter is load divided and evaluated by contact in area;terms and,of the the surface-projec hardness strainted isindentation based ona diameter, spherical-tipped d, divided indenter by the and actual evaluated or effective in terms ball of thediameter, surface-projected D [5]. The terminal indentation open diameter, circle pointsd, divided on the by dashed the actual and or solid effective elastic ball loading diameter, linesD are[5]. Thecomputed terminal for open indicated circle pointsD values on the on dashedthe basis and of solid an indentation elastic loading fracture lines aremechanics computed description, for indicated as Dwillvalues be described. on the basis Pathak of an and indentation Kalidindi fracturehave give mechanicsn an updated description, description as will of such be described. nanoindentation Pathak andstress–strain Kalidindi curves have given[6]. Here, an updated a brief descriptionpreview is ofgiven such of nanoindentation information currently stress–strain available curves from [6]. Here,point-by-point a brief preview measurements is given of informationmade conventionally currently available or from from continuous point-by-point load/penetration measurements mademeasurements. conventionally or from continuous load/penetration measurements. Figure 1. Hardness-based stress–strain description of indentation test measurements. The hardness Figure 1. Hardness-based stress–strain description of indentation test measurements. The hardness stress is load divided by the projected area of contact; and, the hardness strain is the projected contact stress is load divided by the projected area of contact; and, the hardness strain is the projected contact diameter divided by the actual or effective ball diameter of the indenter tip [5]. The solid experimental diameter divided by the actual or effective ball diameter of the indenter tip [5]. The solid (ball test) and dashed linear dependencies are computed in accordance with a Hertzian description; experimental (ball test) and dashed linear dependencies are computed in accordance with a Hertzian and, the Vickers hardness numbers are plotted on the abscissa scale at a position corresponding to the description; and, the Vickers hardness numbers are plotted on the abscissa scale at a position indenter diagonal, d = 0.375D. corresponding to the indenter diagonal, d = 0.375D. 2.1. Continuous Load–Deformation Measurements 2.1. Continuous Load–Deformation Measurements The NaCl crystal (solid curve) hardness stress–strainstress–strain measurement shown in Figure 11 was was obtained on on indenting indenting an an {001} {001} crystal crystal surface surface wi withth a 6.35 a 6.35 mm mm ball ball in ain standard a standard compression compression test. test.Such Suchmeasurments measurments are made are made much much easier easier with with the the naturally-rounded naturally-rounded tips tips of of nanometer- nanometer- or micrometer-scale indenter tips in nano-test indentationindentation systems. Figure 22 showsshows anan exampleexample elasticelastic loading/unloading behavior behavior recorded recorded for for nanoindenta nanoindentationtion of of a a {0001} {0001} sapphire sapphire crystal crystal surface surface [7]. [7]. The nonlinearnonlinear dependence dependence on on penetration penetration depth, depth,h, mayh, may be employed be employed to determine to determine the effective the effective elastic moduluselastic modulus for a known for a known tip diameter tip diameter in accordance in accordance with the with Hertzian the Hertzian relationship: relationship: CrystalsCrystals 20172017,,7 7,, 2121 33 ofof 99 Crystals 2017, 7, 21 3 of 9 E* = [{(1 − νB)/EB} + {(1 − νS)/ES}]−1 = (3√2/4)(P/D1/2)h−3/2 (1) E* = [{(1 − νB)/EB} + {(1 − νS)/ES}]−1 = (3√2/4)(P/D1/2)h−3/2 (1) −1 p 1/2 −3/2 In Equation (1),E* ν =B [{(1,EB and− ν Bν)/S,EESB are} + {(1Poisson’s− νS)/ ratioES}] and=(3 Young’s2/4)(P modulus/D )h for ball and specimen,(1) respectively,In Equation P is (1),load, νB and,EB and again, νS, EDS areis (effective) Poisson’s ball ratio diameter. and Young’s As indicated modulus in for Figure ball and2, the specimen, value of In Equation (1), νB, EB and νS, ES are Poisson’s ratio and Young’s modulus for ball and specimen, respectively,E* can be determined P is load, fromand again, fit to theD is indentation (effective) ball loading diameter. curve As if indicatedD for the inrounded Figure indenter2, the value tip ofis respectively, P is load, and again, D is (effective) ball diameter. As indicated in Figure2, the value of Eknown.* can be Dub, determined Brazhkin, from Novikov, fit to the Tolmachovaindentation loadinget al. have curve reported if D for thesimilar rounded measurements indenter tip on is E* can be determined from fit to the indentation loading curve if D for the rounded indenter tip is known.sapphire Dub,and stishoviteBrazhkin, single Novikov, crystals Tolmachova [8]. Elastic moduluset al. have determinations reported similar for aluminum measurements have been on