On the Vickers Indentation Fracture Toughness Test

On the Vickers Indentation Fracture Toughness Test

George D. Quinnw

National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8529

Richard C. Bradt

Department ofMetal. & Mater. Science, College of Engineering, University of Alabama, Tuscaloosa, Albama 35487-0202

The Vickers indentation fracture toughness test, or VIF, is ad-dressed by considering its origins and the numerous equationsthat have been applied along with the technique to estimate thefracture resistance, or the KIc of ceramics. Initiation and prop-agation of cracks during the VIF test are described and contrast-ed with the pre-cracking and crack growth for internationallystandardized fracture toughness tests. It is concluded that theVIF test technique is fundamentally different than standard frac-ture toughness tests. The VIF test has a complex three-dimen-sional crack system with substantial deformation residual stressesand damage around the cracks. The VIF test relates to an ill-defined crack arrest condition as opposed to the rapid crackpropagation of the standardized fracture toughness tests.

Previously published fracture toughness results employing theVIF technique are reviewed. These reveal serious discrepanciesin reported VIF fracture toughness values. Finally, recent frac-ture resistance measurements by the VIF technique for theStandard Reference Material SRM 2100 are presented. Theseare compared with standardized test results for the same mate-rial. It is concluded that the VIF technique is not reliable as afracture toughness test for ceramics or for other brittle materi-als. What the VIF actually measures in terms of fracture re-sistance cannot be readily defined. It is recommended that theVIF technique no longer be acceptable for the fracture toughnesstesting of ceramic materials.

I. Introduction

THE Vickers indentation fracture (VIF) test has been a pop-ular experimental technique for the estimate of the fracture

resistance of brittle ceramics for the past three decades. Theconcept of monitoring cracks created by hardness indentationsoriginated with Palmqvist1 in the 1950s, half a century ago, butthe concept was first advocated as a fracture toughness test by

Evans and Charles2 in the mid-1970s. Evans and Charles appliedthe VIF to materials from single crystal oxides to cemented car-bides, all of which seemed amenable to the test. The techniquerapidly achieved popularity because of its expediency. It seemedto be a convenient way to determine KIc. It requires only a smallvolume of material and the actual measurements can be quicklycompleted with only a short sample preparation time and at aminimum financial cost. In nearly all respects the VIF methodseemed to be practically ideal, although it is admittedly a rathernon-conventional approach for determining the fracture tough-ness.

The VIF technique has been thoroughly described in two in-dependent, comprehensive reviews of the fracture toughnesstesting of brittle materials.3,4 Recently, a third review, that byMorrell5 categorizes the VIF as ‘‘not meeting fracture mechanicscriteria,’’ a stunning indictment. The present authors believe afair assessment of the VIF is that most currently active research-ers do not consider the VIF to be an accurate, nor a reliablemethod for determining KIc or any other fracture resistance pa-rameter. These concerns were amplified when the VIF test ex-perienced difficulties in three international round robinexercises.6,7 Unfortunately, the VIF method is being consideredin some quarters as a possible method for evaluating fracturetoughness for materials specifications. These combined issueshave prompted this re-examination of the validity of the VIFtechnique for the fracture resistance testing of ceramics.

This paper first reviews the origin of the VIF technique andthen considers the crack initiation and crack propagation duringa VIF measurement. The VIF multiple cracks are then com-pared with the single crack of approved standardized fracturetoughness tests. This paper considers the numerous equationsthat are applied in the VIF method. The fundamental originsand the accuracies of these equations are questioned. Next, theresults are addressed from the numerous equations which havebeen applied to the VIF technique as they have been summar-ized in several comprehensive archival papers. Finally, recentVIF data were obtained and compared with similar measure-ments by approved international standard fracture toughnesstests for a NIST Standard Reference Material developed espe-cially for standardized fracture toughness testing of ceramics. Incombination, these considerations have lead to the conclusionthat the VIF technique should be discontinued for the measure-ment of the fracture toughness of brittle materials.

Feature

D. Green—contributing editor

This work was supported by the U. S. Department of Energy, Heavy Vehicle MaterialsProgram with Oak Ridge National Laboratory.

wAuthor to whom correspondence should be addressed. e-mail: [email protected]

Manuscript No. 22201. Received September 1, 2006; approved November 22, 2006.

Journal

J. Am. Ceram. Soc., 90 [3] 673–680 (2007)

DOI: 10.1111/j.1551-2916.2006.01482.x

r 2007 The American Ceramic Society

No claim to original US government works

II. Origin of the VIF Technique

The Vickers indentation technique was introduced to the ce-ramic fracture community by Evans and Charles2 in a briefcommunication note approximately 30 years ago. It appearedduring a period when considerable attention was focused on thenature of deformation and cracking around Vickers indenta-tions,8–13 a field that became known as indentation mechanics.z

The Evans and Charles note was not very extensive by anymeasure, but it undeniably suggested that one might utilize thecracks which emanate from the corners of a high testing loadVickers microhardness indentation to determine the fracturetoughness of brittle materials. Evans and Charles presented ageneralized equation and a normalized calibration curve thatappeared to apply to many different materials, some withPalmqvist cracks and some with median cracks. It appearedthat this technique might be a universal fracture toughness test.It certainly was a very convenient one.

Subsequently, numerous other authors have used similarcurve fitting methods and dimensional analyses to relate the ex-tending crack lengths from a Vickers indentation impression tothe fracture toughness for both mixtures of Palmqvist and me-dian cracks and for each type of crack independently. Many ofthe researchers have been puzzled with their results from theVIF measurements, which has lead to a proliferation of numer-ous equation modifications to satisfy those researchers in theirquest for a satisfactory value of the fracture toughness. At lastcount, more than 30 equations have been presented in the liter-ature. Not surprising, only rarely do any two of them producethe same result for the fracture toughness for the same test con-ditions.

Fracture toughness determination by the VIF technique pro-ceeds by first preparing a high-quality smoothly polished testspecimen surface. The specimen is not precracked. The polishedspecimen surface is then indented by a Vickers pyramidal mi-crohardness indenter. Usually a conventional hardness testingmachine is used to gradually apply load to the indenter to peakload, hold the load constant for a set dwell period, and thenunload the indenter. The sample is indented at a high testingload to create a deformed region beneath and in the vicinity ofthe impression, which leads to the generation of four cracksemanating from the corners of the square Vickers diamond im-pression. Figure 1 illustrates a Vickers indentation with foursuch cracks radiating from the impression corners. Not all in-dentations and their cracks are as ideal as those shown in Fig. 1,as Fig. 2 illustrates. The lengths of the cracks, along with theindentation load, the impression size, the hardness and elasticmodulus of the material, and an empirical calibration constantare used to compute the fracture toughness of the material.Considerable care must be used to measure the length of thecracks. Variations in microscopic techniques and equipment aswell as observer skill and subjectivity can cause considerableuncertainty. Although the result is not a valid fracture tough-ness, most papers call the resulting value KIc.

During Vickers indentation, with increasing indentationloads, one observes a transition during the development of thecracks about the impression. For low test loads, the indentationbegins as a crack-free pyramidal microhardness impression. Itthen evolves or transforms to an impression with individualcracks emanating from the four corners of the impression at thesurface, but also containing an extensive crack pattern beneaththe surface. Finally, it experiences extensive lateral cracking andoften considerable spalling about the impression for the higherindentation test loads as shown in Fig. 2. These crack-type in-dentation transitions occur at different applied test load levelsfor different ceramic materials. The material surrounding theimpression is left with a complex residual stress state dependenton the indentation load and the multiple cracking.

There are many questions as to the exact sequence of crackgrowth from the Vickers indentation corners for different ce-

ramic materials.14–16 For example, it may be that the cracks firstform as Palmqvist cracks that later extend to form mediancracks, or median cracks may form directly from the deform-ation beneath the indenter. The cracks may form either duringindenter loading or unloading. The environment may also play arole. It is not easy to ascertain the sequence from the end resultthat is visible only on the sample surface, but in all cases thecracks extending from the four corners of the pyramidal Vickersindentation are measured, as is the size of the indentation itself.The latter point, the size of the indentation, is often a quitechallenging measurement for the higher test loads especiallywhere there has been considerable spalling about the indentationimpression such as shown in Fig. 2.

III. Equations for Fracture Resistance from the VIF Technique

As previously noted, numerous VIF equations by different au-thors have been summarized in various forms in different jour-nal and proceedings publications. It is not sufficient to simplystate that none of them are based on exact theory. Many equa-tions are the products of dimensional analyses modified withexperimentally derived calibration factors with occasional vague

Fig. 1. A 98 N Vickers indentation with cracks in a NIST StandardReference Material 2100 test piece.

Fig. 2. A 98 N Vickers indentation in a boron carbide. Note the severespalling.

zLawn and Fuller9 suggested as early as 1975 that: ‘‘Indentation fracture presents itselfas a useful addition to the mechanical testing repertoire of materials scientists.’’

674 Journal of the American Ceramic Society—Quinn and Bradt Vol. 90, No. 3

allusions to a theoretical basis. Many are just the manipulationof previous equations with new calibration constants in an at-tempt to achieve reasonably correct values of the fracture tough-ness for the material under investigation. Most, if not all, ofthese equations and their empirical derivations are highly ques-tionable for none of them are the product of an accurate stressintensity factor solution. The complex crack network and re-sidual stress damage zone around indentations are not amenableto a straightforward analysis as in most traditional fracture me-chanics test configurations. Yet, the equations for the VIF havebeen attractive for they sometimes yield, fortuitously, what ap-pear to be reasonable values for the fracture toughness. This hasencouraged the continued use of the VIF technique for the de-termination of the fracture toughness of brittle materials in nu-merous academic and industrial laboratories. This continued usehas persisted in spite of the suspect reputation of the VIF tech-nique and a general skepticism and mistrust by the traditionalfracture mechanics community.

Following the original Evans and Charles note, Marshall andEvans17 refined the original equation and published a simplifiedformula. This was followed by two papers by Anstis et al.18

Chantikul et al.19 that presented further refinements to theproposed equations. Two additional papers by Niihara20,21

followed, the latter specifically addressing Palmqvist cracks.An equation by Miyoshi22 for median cracks that is an adap-tation of Anstis et al.’s18 has also been used. It is the equationsfrom these papers that seem to be the most frequentlyquoted and the most often applied. However, a plethora of ad-ditional equations in other publications has followed. A list ofequations will not be presented here. Many of them have beentabulated in the series of four papers by Li et al.,23 Ponton andRawlings,24,25 and Ghosh et al.26 which are discussed in somedetail later.

Many derivations make assumptions about the plasticallydeformed damage zone underneath the indentation. The dam-age zone is commonly modeled by an expanding cavity in thesolid. The stress distribution from the expanding cavity is in turnconverted to an equivalent force that acts to open the median orPalmqvist cracks. Other models have the plastic zone acting as awedge or a spring. There are numerous assumptions about de-formation and fracture built into these models. It appears thatmany of the equations are manipulations of previous equationswith new calibration constants in an attempt to achieve reason-ably correct values of the fracture toughness for the materialunder investigation. Ponton and Rawlings24,25 have summarizedmany of the equations along with the assumptions and the in-consistencies in their 1989 review papers.

It is important to note a couple of features of many of theseequations, features which cast considerable doubt on their fun-damental nature and, ultimately, their value. All of the equa-tions contain the indentation test load, the crack length, theindentation size, the elastic modulus, and the hardness of thematerial in one form, or another. Often these parameters areraised to peculiar non-integer exponents that consist of fractionsor decimals, such as 0.4, 0.6, and 0.7. In other applicable equa-tions, the same parameters are raised to 0.5, 1.5, or 2.0 powers.These aspects of the multitude of equations do not inspire con-fidence in their utilization. The peculiar power quantities are notsurprising when it is considered that the equations are neitherthe result of a closed-form analytical solution, nor a formalstress intensity analysis of the cracks that result, but rather arejust sort of an informal adjustment of previous equations. Inaddition to, or perhaps because of the above inconsistencies,various geometrical effects and other factors are often collectedinto a dimensionless calibration factor at the beginning of theequation. In most instances, it is a formidable, if not impossible,challenge for any scholar to obtain that calibration factor fromfirst principles. This factor has often been adjusted or ‘‘tuned’’ tofit expected results for a particular material. To simply state thatthese equations are highly suspect would be an understatementfor there is really little, if any, defensible basis for their justifi-cation from a fundamental perspective.

IV. Concept of Fracture Toughness

Almost all of the publications employing the VIF techniquerefer to the resulting measurement as the fracture toughness, orKIc. For that reason, it is important to consider the definition ofthe concept of fracture toughness before further considering thecrack initiation and growth situation in the VIF technique andcontrast it with that of a single crack in the accepted standard-ized tests. For a basic definition of KIc, a quote from the recenttext of Munz and Fett27 suffices: ‘‘If a component or a testspecimen with a crack is loaded, KI increases with increasingload until unstable crack propagation occurs at a critical valueof KI. This critical value is the fracture toughness, KIc.’’ Perhapsit is the specificity of this precise definition that led Morrell5 toclassify the VIF as one of the ‘‘Test methods not meeting frac-ture mechanics criteria.’’ Although undetected slow crackgrowth and R-curves have created some problems with fracturetoughness testing of ceramics in the past, it is now generally ac-cepted that many brittle materials actually do have a definitevalue of the fracture toughness in the classical sense. These in-clude many fine-grained polycrystalline ceramics as well ascoarse-grained ceramics that fracture transgranularly withoutbridging. For example, sintered a silicon carbide with smallamounts of boron and carbon sintering aids and no boundaryphase has a specific fracture toughness, KIc.

23,26,28

The concept of KI is derived from linear elastic fracture me-chanics, LEFM. It is a measure of the magnitude of the stressfield in the crack tip region. When the Roman numeral I is af-fixed to K as a subscript, it refers to the tensile or opening modecondition of failure, as opposed to a shear mode such as speci-fied by a II or a III. Thus the quantity known as the fracturetoughness, KIc, refers to the critical value of the stress intensityfactor in the opening mode when fracture initiates and unstablecrack propagation occurs. A part of that definition is the sub-script c for it is considered to refer to critical or catastrophiccrack propagation. As such it is usually referred to the particularcondition of crack growth that proceeds rapidly and completelythrough the test specimen. In fact, several standardized fracturetoughness tests experience just that: a catastrophic fracture withthe single pre-crack propagating completely through the testspecimen once KIc is reached at the crack tip during loading.One exception is the chevron notch in bending method, a stand-ardized test method in which the crack is propagated stablythrough a triangular cross sectional area.3–5,y

Because of the complexity of interacting stress fields frommultiple cracks, the standardized tests for the measurement ofthe fracture toughness or KIc consist of only a single well-definedcrack in a geometrically simple test specimen that is subjected toa well-defined loading configuration. These points are reflectedin the makeup of the internationally accepted standardized frac-ture toughness tests for KIc, such as those that have been ap-proved for ceramics and other brittle materials including thechevron-notched beam, (CNB), single-edge pre-cracked beam(SEPB), and the surface crack in flexure (SCF) methods.29–35

Although fracture toughness is believed to be a material con-stant, like all other engineering parameters, experimental KIc

measurements are subject to statistical scatter. In principle, allvalid techniques for fracture toughness measurement shouldyield the same value for a material within the normal statistic-al uncertainties of the test itself. To achieve such accuracy, sev-eral criteria for a standard KIc test have been established by theinternational fracture testing standards community. The testmust consist of a well-defined simple specimen geometry forwhich the state of stress of the test piece is known during load-ing. For simplicity, there must be a sharp single pre-crack in thespecimen for which the alteration of the uncracked stress field isknown, so that KI is well-defined with an accurate stress inten-sity solution for the particular test specimen. There must not be

yThere are other configurations, such as the double cleavage-drilled compression methodand Obreimoff’s wedge-loaded mica flake arrangement, that rely on special geometries topromote stable crack extension. Configurations that promote stable extension may be valu-able for studying R-curve behavior. Nevertheless, mostKIcmethods are intended to measurethe critical value of the stress intensity by initiating fracture with unstable crack extension.

March 2007 On the Vickers Indentation Fracture Toughness Test 675

any ambiguity relative to the value of KIc at the crack tip duringloading when the test specimen achieves the critical conditionand fails catastrophically. These criteria demand a definitemathematical expression for the fracture toughness, an expres-sion for KIc that involves the specimen geometry, the descriptivepre-crack parameters and the maximum load at failure duringthe test. All of the accepted standardized tests for ceramic ma-terials meet these stringent criteria.29–34 This is the reason whythe standardized tests have been demonstrated to yield the samevalue of the fracture toughness for a NIST Standard ReferenceMaterial as will be discussed later.

V. VIF in Contrast to Standardized Fracture Toughness Tests

Having described both the non-conventional VIF technique andthe standard fracture toughness tests, it is necessary to comparethe two on the critical points. First is the specimen geometry.For the standard tests, it is a simple, well-defined geometry forwhich the loading conditions and the state of stress are well-known during the loading process. The geometry is usually onefor which a closed-form solution of the stress state is available inmany standard mechanics texts. For the VIF technique, anyshape or chunk of material is adequate so long as it can bemounted and polished. The standard tests employ pre-crackedspecimens with a single well-defined crack for which there existsa formal stress intensity solution. There is no pre-crack in theVIF specimen: multiple cracks are generated during the actualtest when the indenter is forced into the polished specimen sur-face. Despite allusions to the contrary, the VIF cracks do nothave an applicable stress intensity solution.

In the standard tests, loading is applied in a universal me-chanical testing machine, but in the VIF technique the specimenis loaded through a hardness indenter. During loading in thestandard tests, the pre-crack extends in an accelerating cata-strophic manner through the entire test specimen. In the VIFmethod, deformation occurs below and around the indentation,cracks form and propagate beneath the indenter and then inter-sect the surface. The cracks decelerate to an arrest conditionaway from the indentation. The VIF leaves a multiple crackcondition about the indentation. At the end of a standardizedfracture toughness test, the single crack has halved the specimen,but in the VIF method multiple cracks have arrested in a post-test configuration and material environment that consists ofmultiple cracking and residual stresses of considerable complex-ity. Often major spalling occurs about the indentation, especiallyfor the higher test loads in the VIF technique. The multiplecracks in a VIF test do not remotely ascribe to the definition offracture toughness in the text of Munz and Fett,27 nor the manyother similar definitions for fracture toughness that appear invarious other textbooks.

VI. Published Summary Results for the VIF Technique

There are numerous publications involving the use of the VIFmethod, but four papers with similar thrusts highlight the basicproblems of the VIF. They extensively summarize the VIFmethod by evaluating the results of the technique using manyof the equations which have been suggested for the VIF.23–26

Although these publications are now more than a decade old,when the four are considered together, they are quite revealingand demonstrate the failings of the VIF technique. The papersof Li et al.,23 Ponton and Rawlings,24,25 and Ghosh et al.26

summarize a large number of VIF results using the numerousdifferent equations for the same materials. Their compilationsalone are impressive. The sintered alpha silicon carbide used byLi et al.23 and Ghosh et al.26 was a candidate for a NIST KIc

Standard Reference Material. The paper’s listings of fracturetoughness numbers will not be duplicated here, only the mostimportant results will be summarized. The three most criticalconclusions of these four publications relative to the credibilityof the VIF method are as follows:

(1) When the many different proposed equations are ap-plied to calculate the fracture resistance at the same, or at verynearly the same crack lengths in a ceramic material, then widelyrangingz values of KIc result.

(2) None of the equations are able to generate accurate re-sults for different materials. An equation may, by chance or byforce fitting the calibration factors, produce plausible results forone specific material, but usually gives poor results for otherseven within a single material class.

(3) When the different equations are applied to estimate thefracture resistance as it varies with the crack length from theindentations, as determined for different indentation test loads,then sometimes the fracture resistance appears to increase andsometimes it decreases with crack length for the same material.The ‘‘R-curve like’’ results are frequently contradictory for thesame material when determined by the different fracture resist-ance equations for the VIF.

These conclusions from four different, but closely related pa-pers clearly illustrate the basic deficiencies of the VIF method.The first is that the VIF method is not consistent. The techniquejust does not produce a unique value for KIc, which is not sur-prising. This suggests that the VIF technique does not andprobably cannot measure the value of KIc for brittle materialssuch as ceramics. The range of fracture resistance values cer-tainly points out the unreliability of the VIF method. A funda-mental problem with the VIF method is that brittle materials donot deform and fracture underneath an indentation in a self-similar manner as many have assumed. Covalently-bonded hardceramics (e.g., silicon carbide) deform and fracture very differ-ently than ionically-bonded cubic ceramics (e.g., magnesium ox-ide) or glasses. Fine-grained and coarse-grained ceramics oftendo not deform and fracture the same way. Furthermore, thecracks often are not the idealized semicircular median or Palmq-vist cracks assumed in the models. The VIF crack system is ac-tually a three-dimensional network of intersecting orthogonaland interacting cracks. Hence, it should not be surprising thatthe quest for the universal indentation fracture equation or cal-ibration constant has been in vain.

The observation that fracture resistance appears to vary withdifferent length VIF cracks is equally disturbing when one con-siders the contradictory nature of the results in light of the otherreported R-curve trends for brittle ceramics. R-curves are eitherflat, as for glass and some fine-grain size ceramics, or they havean increasing resistance trend with increasing crack length as forcoarse-grain size polycrystalline ceramic materials and ceramiccomposites. R-curves should not be decreasing with increasingcrack length. This makes the VIF results even more confusingand problematical if one wishes to consider that the VIF tech-nique actually measures some form of crack arrest phenomenon,or a value for KIa somewhere along the R-curve of the test ma-terial.

The R-curve, KIa interpretation of the crack arrest situation inthe VIF actually has considerable intrinsic appeal, for the cracksfrom the indentation corners obviously become arrested in theVIF test. Unfortunately, the VIF condition of crack arrest isvirtually impossible to specify with any degree of certainty be-cause of the auxiliary multiple cracking and spalling about theindentations at higher test loads. In addition there are substantialresidual stresses from the indentation deformation and the pileup of flowed material about the impression.36,37 This extremelycomplicated situation no doubt results in crack opening displace-ments (COD) for the VIF cracks that are very different from theCOD values that occur in the typical double cantilever beam orchevron V-notched specimens which are commonly utilized forceramic R-curve determinations. Furthermore, the VIF cracksarrest in a multiple crack environment, where the multitude ofcracks varies, dependent on the auxiliary cracking and spalling.In spite of its ‘‘R-curve like’’ appeal, the contradictory results

zPonton and Rawlings25 showed that for identical indentation data the computed frac-ture toughness varied by as much as a factor of 7 for the 19 different VIF equations theytabulated. Variations of almost a factor of 2 were obtained with some of the commonly usedVIF equations.


from the different VIF equations indicate that this is probablynot a valid interpretation. The many equations for the VIF donot consistently predict the expected trends of increasing crackgrowth resistance with increasing crack length and they mostcertainly do not all predict the same R-curve trends.

The collective results in the four quoted papers23–26 clearlysignaled a serious problem with the VIF technique over a decadeago. Unfortunately, many researchers have continued to use theVIF method in spite of these red flag warnings in the archivalliterature. It is puzzling to say the least. It is no doubt the con-sequence of the expediency of the VIF technique to obtain aresult, even though the result is probably not a correct one. Ofcourse, it is also possible that a VIF toughness result may for-tuitously appear to be reasonable, another point which has leadto its continued application.

VII. New VIF Results for the NIST SRM 2100 and Sintered aSilicon Carbide

The general state of fracture toughness testing has improvedconsiderably in the past 30 years since the appearance of the VIF

method. In the 1970s only a few academic laboratories and evenfewer industrial and government laboratories were active in themeasurement of fracture resistance. Today, standards organiza-tions in Europe, Japan, and the US have refined and optimizedfracture testing techniques.29–31 The International Organizationfor Standards (ISO) approved standard test methods are nowavailable for the SEPB,32 the CNB,34 and SCF33 tests. In the late1990s, SRM 2100, was prepared by NIST.38–40 It is a commer-cial hot-pressed fine-grain size silicon nitride that has been dem-onstrated to yield the same KIc value irrespective of the testmethod. The certified value for the fracture toughness, KIc, ofSRM 2100 is 4.57 MPa �m1/2 with an uncertainty of 0.11MPa �m1/2 for the average of five test outcomes at the 95%confidence level. Thus, if one makes five measurements of thefracture toughness, 95% of the time the result should be between4.46 and 4.68 MPa �m1/2. The uncertainty is remarkably smalland attests to the consistency of the SRM. Almost identical re-sults were obtained by SEPB, CNB, and SCF methods despitethe dramatic difference in the precrack types and sizes as shownin Fig. 3.

For VIF measurements of SRM 2100, test bar halves (3mm� 4 mm� 23 mm) which had previously been used to es-tablish the certified value for SRM 2100 were mounted and pol-ished. Indentations were put into surfaces with differentorientations in order to account for possible preferred orienta-tion effects in this hot-pressed material. Indentations were madewith a diamond Vickers indenter in a conventional hardnesstester that was checked with a NIST SRM 2831 reference disk.41

Dwell time was 15 s. Ten indentations were made at each of fourindentation loads: 9.8, 19.6, 49, and 98 N. Indentations at 196 Nwere made in one specimen. One interesting observation madeduring all these experiments was that the crack lengths for asingle indentation often differed by 2%–11%. Some indenta-tions had cracks with similar sizes. The crack length differencesfor a single indentation were greater in the first test piece (Fig. 4aand Table I). The longer cracks were in the hot pressing plane,which is expected to have lower fracture toughness. The secondspecimen with the cracks running perpendicular to the hotpressing plane had much less variability in crack lengths. Anaverage crack length size was used in all of our calculations.Wilantewicz16 has observed that one median or radial cracksystem often forms before the perpendicular crack system andcould interfere with the latter. Further details of these tests aredescribed elsewhere.7

Values of the fracture toughness were calculated using threedifferent popular equations: Anstis et al.’s equation,18 Niihara’sequation20,21 as used in a ceramic ball bearing specification,42

Fig. 3. Fracture surfaces of two silicon nitride Standard Reference Ma-terial 2100 specimens. The single-edge precracked beam test piece on theleft had a �2 mm deep precrack (arrows), whereas the surface crack inflexure test piece on the right had a 50 mm deep semielliptical precrack(arrow). Virtually identical fracture toughnesses were obtained despitethe dramatic difference in precrack sizes and shapes.

Fig. 4. Representation of the Vickers indentation fracture results for two Standard Reference Material 2100 test pieces with different orientations.Miyoshi’s equation seems to fortuitously match in one case.


and Miyoshi’s equation22 as used in Japanese IndustrialStandard (JIS) R 1607.30 These equations have been discussedin detail by Quinn.7 The latter two equations were deve-loped and calibration constants adjusted with silicon nitridespecifically in mind. The results of the VIF measurementsare summarized in Tables I and II and are presented inFigs. 4 and 5 along with the certified value for KIc. There aresmall differences in the VIF results for the two test pieces at lowindentation loads. These diminish to less than 5% at 49 and98 N.

It is evident from the results in the Tables and Fig. 4 that noneof these three popular equations consistently yields the correct,certified value of fracture toughness of 4.57 MPa �m1/2 for SRM2100. The VIF results from Anstis et al.’s and Niihara’s equa-tions are incorrect at all loads. In fact, the standard value doesnot even fall within their error bars. Results from Miyoshi’sequation do not match when the indentations were made in the 4mm� 25 mm specimen surface (Table I and Fig. 4(a)) and thedata do not fall within the error bars. The data do match for theother case (Table II and Fig. 4(b)). All three equations suggest aslightly rising R-curve with about a 10% increase of the averagefracture resistance over the range of indentation loads that wereapplied in the testing.

Miyoshi’s equation produces a match in one instance, but theagreement should not come as a surprise. Miyoshi’s VIF equa-tion calibration factor was empirically force fitted to match validdata from other methods for a fine-grained equiaxed silicon ni-tride.22

How well does Miyoshi’s equation fare with sintered a siliconcarbide? This homogenous fine-grained material was the backup material for the NIST fracture toughness SRM. It has a flatR-curve and no sensitivity to slow crack growth at room tem-perature. Ghosh et al.’s26 original data were re-analyzed usingMiyoshi’s equation. The results are shown in Fig. 5. Analysesand testing28,29,35 of the sintered a silicon carbide have refinedthe KIc values to 2.6 MPa �m1/2 to 2.8 MPa �m1/2 dependingupon plate density. Figure 5 shows that Miyoshi’s equationsubstantially overestimates the actual fracture toughnessof the silicon carbide by nearly 20%. The standard test KIc

values do not even fall within the VIF error bars. The other twoequations do not fit the standard KIc values very well either at25–35 N.

VIII. Discussion

One primary conclusion that must be drawn from all of theearlier studies23–26 is that even if one equation does match ex-pected fracture toughness results for a particular material, itoften does not produce reliable results for another material. Theoutcomes in the present study confirm this beyond any doubt.Ponton and Rawlings’ analyses24,25 for 16 materials devotedmuch energy and space seeking the one equation that gave thebest fit to the available data, but their search was fruitless. Noneof the numerous equations were satisfactory even for simpleranking of materials between classes. It should be clear thatthere never will be a universal VIF equation that will be reliablefor all brittle materials.

Is it surprising that the VIF technique is incapable of con-sistently producing results that yield the correct results? Notreally, for the previous technical discussions and the aforemen-tioned publications23–26 indicate that the VIF method is dis-tinctly different than a fracture toughness test. The VIF does notproduce a reliable KIc value. The crack initiation and propaga-tion in the VIF test is not the same as the sequence of crackprocesses in the standardized fracture toughness tests. Whyshould the VIF technique be expected to yield the correct frac-ture toughness value?

The toughness versus indentation test load curves presentedin Fig. 4 closely resemble similar curves in the four earlier pub-lications23–26 of over 10 years ago that were discussed previous-ly. These recent results simply reconfirm the conclusions of thosearchival papers regarding the VIF technique for fracture tough-ness measurements. Those conclusions are that the VIF is not asuitable fracture toughness measurement method. The VIFshould not be used for fracture toughness testing, even if justfor a comparative basis. The VIF does not provide legitimatetoughness values.

IX. A Word of Caution about Nanoindentation FractureToughnesses

Recently there has been an escalating interest in applying someof the VIF technique concepts to the nanomeasurement of thefracture toughness of materials by measuring the crack lengthsemanating from the three corners of sharp nanoindenters.43,44

Table II. Vickers Indentation Fracture Resistance Results for a Standard Reference Material (SRM) 2100 Silicon Nitride Test Piecewith Indentations in a 3 mm� 25 mm Face

Indentation

load (N)

Average diagonal

half length a (mm)

Average crack half

length c (mm)

SRM 2100w certified KIc

(MPa �m1/2)

Anstisz Kc

(MPa �m1/2)

Niiharay Kc

(MPa �m1/2)

Miyoshiz Kc

(MPa �m1/2)

9.8 16.770.3 30.970.5 4.57 3.8970.13 5.7870.18 4.5570.1519.6 23.770.3 49.670.9 4.57 3.8470.10 5.7070.14 4.4970.1249 37.970.4 91.771.4 4.57 3.8670.10 5.7270.15 4.5170.1298 53.670.4 145.673.7 4.57 3.8770.15 5.7370.22 4.5270.17196 76.570.7 222.076.4 4.57 4.1570.18 6.1370.27 4.8570.21

wThe uncertainty of SRM 2100 is 0.11 MPa .m1/2 for the average of five test outcomes at the 95% confidence level. At a 1 standard deviation confidence level, the

uncertainty would be 70.06 MPaOm. zAnstis et al. equation.18 yNiihara’s median crack equation,20,21 with a constant value of 10.4 as per ref.42 zMiyoshi’s equation 22 as

used in JIS R 1607.30 Uncertainties are 1 standard deviation unless otherwise noted. The notes are the same as for Table I.

Table I. Vickers Indentation Fracture Resistance Results for a Standard Reference Material (SRM) 2100 Silicon Nitride Test Piecewith Indentations in a 4 mm� 25 mm Face

Indentation

load (N)

Average diagonal

half length a (mm)

Average crack

half length c (mm)

SRM 2100w certified

KIc (MPa �m1/2)

Anstisz Kc

(MPa �m1/2)

Niiharay Kc

(MPa �m1/2)

Miyoshiz Kc

(MPa �m1/2)

9.8 16.270.3 33.071.4 4.57 3.4470.20 5.1470.30 4.0270.2319.6 23.570.1 52.071.0 4.57 3.5670.11 5.2970.16 4.1670.1349 37.570.2 94.071.5 4.57 3.6970.09 5.4770.13 4.3170.1098 53.370.3 148.971.9 4.57 3.7270.08 5.5170.11 4.3470.09

wThe uncertainty of SRM 2100 is 0.11 MPa .m1/2 for the average of 5 test outcomes at the 95% confidence level. At a 1 standard deviation confidence level, the uncertainty

would be70.06 MPa .m1/2. zAnstis et al. equation.18 yNiihara’s median crack equation,20,21 with a constant value of 10.4 as per ref.42 zMiyoshi’s equation 22 as used in JIS R

1607.30 Uncertainties are 1 standard deviation unless otherwise noted. Kc designates the apparent fracture toughness using the equation from the listed source.


Interest has been particularly high for characterizing thinfilms.45 It can be called the NIF test technique. The triangularBerkovich nanoindenter geometry and that of cube corner in-denters is even more sharply pointed than the Vickers diamondpyramid and they readily produce cracks. These sharp three-sided indenters may be expected to create extensive impressioncorner cracking at even lower comparable indentation test loadsthan a Vickers indenter. They will also create complex multiplecrack configurations and residual stresses.

In view of the above collective observations and conclusionsabout the VIF technique for fracture toughness testing, onemust consider the nanoindentation fracture toughnesses, or theNIF technique, with similar reservations as have been expressedfor the VIF determined toughness values. In other words, solong as there is an obvious lack of a definite formal solution forthe stress intensity factor at the crack tip and the applicableequations are no more than dimensional analyses with calibra-tion factors, the validity of any results of nanoindentation frac-ture toughness measurements must be considered highly suspect.Nanoindentation or NIF toughnesses should be seriously ques-tioned and probably should never be used, even with extremecaution. Similar to the VIF toughnesses, NIF toughnesses areunlikely to be accurate or valid, except fortuitously. There clear-ly is a need to develop fracture toughness test methods at thevery small scale that have the same accuracy and precision as ispossible for micro- and macroscale tests.

X. Summary and Conclusions

The VIF for the determination of fracture resistance has beenreviewed. Its history and origin have been discussed along withthe numerous equations which different authors have proposedto apply to the VIF test. The cracking processes have been de-scribed and were contrasted with those of standardized fracturetoughness tests with reference to the basic definition of fracturetoughness. Extensive compilations of VIF test results previouslysummarized in the literature were also reviewed and considered.Finally, additional VIF experiments were performed on a Stand-ard Reference Material to establish whether the VIF test had theability to determine a valid KIc. One equation produced resultsthat came close, but only because it had an empirical calibration

constant force fitted to a similar silicon nitride. The same equa-tion did not procedure accurate results for sintered a siliconcarbide, another well-characterized ceramic. It undoubtedly failsfor many others as well.

What then does the VIF test actually do or measure? It doesnot appear to correctly measure any crack propagation param-eter. The VIF does appear to represent some form of a complexcrack arrest phenomenon. That crack arrest process occurs inthe presence of a multiple-cracked material environment and ina highly complex residual stress condition, often accompaniedby extensive spalling of material from around the indentation.These features create an incredibly complex crack tip arrest en-vironment, one that is impossible to describe. The crack arrestsituation of the VIF defies meaningful description.

It must be concluded that the VIF technique is not suitablefor the measurement of the fracture toughness, KIc, or any otherform of the fracture resistance of ceramics or other brittle ma-terials. Any agreement with accepted fracture toughness, KIc

data is either fortuitous or due to force fitting the VIF calibra-tion constants. It is recommended that use of the VIF be dis-continued for all ceramic materials. It is not a reliable fracturetest method. It should not be applied to or be acceptable for anybasic fracture resistance measurements of ceramics or any othermaterials. It should never be used for determination of theproperty KIc in materials specifications.

Acknowledgments

The first author (G. D. Q.) thanks his colleagues who have so painstakinglyhelped refine fracture toughness test methods and help prepare the NIST SRM2100 including R. Gettings, K. Xu, Dr. J. Swab, Dr. J. Salem, Prof. M. Jenkins,and Prof. I. Bar-On. We also thank M. Sakai, Z. Li, A. Kobayashi, A. Ghosh, C.Henager, and K. W. White for consultations and advice.

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Fig. 5. Fracture toughness of sintered alpha silicon carbide using thedata from Ghosh et al.26 The average KIc from all standard test methodsis very consistent and falls between 2.6 and 2.8 MPa �m1/2 as shown bythe band. Note that the Vickers indentation fracture data withMiyoshi’sequation falls well outside the correct range.


18G. R. Anstis, P. Chantikul, B. R. Lawn, and D. B. Marshall, ‘‘A CriticalEvaluation of Indentation Techniques for Measuring Fracture Toughness: I, Dir-ect Crack Measurements,’’ J. Am. Ceram. Soc., 64 [9] 533–8 (1981).

19P. Chantikul, G. R. Anstis, B. R. Lawn, and D. B. Marshall, ‘‘A CriticalEvaluation of Indentation Techniques for Measuring Fracture Toughness: II,Strength Methods,’’ J. Am. Ceram. Soc., 64 [9] 539–43 (1981).

20K. Niihara, ‘‘Indentation Fracture Toughness of Brittle Materials for Palmq-vist Cracks’’; pp. 97–105 in Fracture Mechanics of Ceramics, Vol. 5, Edited byR. C. Bradt., et al. Plenum Publishing Co., NewYork, 1983.

21K. Niihara, ‘‘A Fracture Mechanics Analysis of Indentation-Induced Palmq-vist Cracks in Ceramics,’’ J. Mater. Sci. Lett., 2, 221–3 (1983).

22T. Miyoshi, ‘‘A Study on Evaluation of KIc for Structural Ceramics,’’ Trans.Jap. Soc. Mech. Eng., Ser. A., 51A, 2489–97 (1985).

23Z. Li, A. Ghosh, A. S. Kobayashi, and R. C. Bradt, ‘‘Indentation FractureToughness of Sintered Silicon Carbide in the Palmqvist Crack Regime,’’ J. Am.Ceram. Soc., 72 [6] 904–11 (1989).

24C. B. Ponton and R. D. Rawlings, ‘‘Vickers Indentation Fracture Test. Part 1:Review of Literature and Formulation of Standardised Indentation ToughnessEquations,’’ Mater. Sci. Tech., 5 [9] 865–72 (1989).

25C. B. Ponton and R. D. Rawlings, ‘‘Indentation Fracture Toughness Test.Part 2, Application and Critical Evaluation of Standardised Indentation Tough-ness Equations,’’ Mater. Sci. Tech., 5 [10] 961–76 (1989).

26A. Ghosh, Z. Li, C. H. Henager, A. S. Kobayashi, and R. C. Bradt, ‘‘VickersMicroindentation Toughness of a Sintered SiC in the Median Crack Regime’’; pp.219–32 in Fracture Mechanics of Ceramics, Vol. 12, Edited by R. C. Bradt., et al.Plenum Publishing Co., NewYork, 1996.

27Munz D. and T. Fett, Ceramics: Mechanical Properties, Failure Behavior, andMaterials Selection, pp. 20. Springer Verlag, NewYork, 1999.

28G. D. Quinn and J. A. Salem, ‘‘Effect of Lateral Cracks Upon FractureToughness Determined by the Surface Crack in Flexure Method,’’ J. Am. Ceram.Soc., 85 [4] 873–80 (2002).

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Richard ‘‘Dick’’ Bradt is a profes-sor of materials engineering at theUniversity of Alabama, Tusca-loosa, AL, USA, where he is theAlton N. Scott Professor of En-gineering. Dick is a graduate ofMIT and RPI and has previouslyheld faculty positions at PennState University, the Universityof Nevada and the University ofWashington, the latter wherehe held the endowed Kyocera

Professorship. Prof. Bradt has directed over 100 graduatetheses and coauthored nearly 400 papers with students andcolleagues. More than 100 of these manuscripts have appearedin the Journal and Bulletin of the American Ceramic Society.Dr. Bradt has served as coeditor of over 20 proceedings ofinternational conferences that primarily address fracture andthe mechanical properties of ceramic and glass materials. Prof.Bradt is a Fellow of the American Ceramic Society and alsoASM-International, as well as Distinguished Life Member ofUNITECR, the international refractories organization.

George Quinn is a Ceramic En-gineer in the Ceramics Division atthe National Institute of Stan-dards and Technology. A gradu-ate of Northeastern University inBoston, Mr. Quinn worked for 21years at the U.S. Army MaterialsResearch Laboratory in Water-town, MA, before coming toNIST in 1990. He spent 1 year in1987 as an exchange scientist atthe German Aerospace Research

Establishment in Cologne. He works on mechanical testing,reliability analysis, and fractography, with emphases on re-finements to and standardization of test methods. He is amaster fractographer and has analyzed many commercial,military, and research fracture problems. He has led manynational and international standardization programs includ-ing six successful international round robin projects on flex-ural strength, fracture toughness, hardness, and fractography.He has authored or coauthored 18 standards and preparedthree standard reference materials. He is a fellow of theAmerican Ceramic Society and also the American Societyfor Testing and Materials.


On the Vickers Indentation Fracture Toughness Test

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