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DOI: 10.1243/09544054JEM1887

2010 224: 1555Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering ManufactureP P Shukla, J Lawrence and H Wu

with Fibre Laser RadiationFracture Toughness of a Zirconia Engineering Ceramic and the Effects Thereon of Surface Processing

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Fracture toughness of a zirconia engineeringceramic and the effects thereon of surfaceprocessing with fibre laser radiationP P Shukla1*, J Lawrence1, and H Wu2

1Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, UK2Department of Materials, Loughborough University, Loughborough, UK

The manuscript was received on 4 November 2009 and was accepted after revision for publication on 27 January 2010.

DOI: 10.1243/09544054JEM1887

Abstract: Vickers hardness indentation tests were employed to investigate the near-surfacechanges in the hardness of a fibre laser-treated and an as-received ZrO2 engineering ceramic.Indents were created using 5, 20, and 30 kg loads to obtain the hardness. Optical microscopy,white-light interferometry, and a coordinate measuring machine were then used to observe thecrack lengths and crack geometry. Palmqvist and half-penny median crack profiles were found,which dictated the selection of the group of equations used herein. Computational and ana-lytical approaches were then adapted to determine the K1c of ZrO2. It was found that the bestapplicable equation was: K1c¼ 0.016 (E/H)1/2 (P/c3/2), which was confirmed to be 42 per centaccurate in producing K1c values within the range of 8 to 12MPam1/2 for ZrO2. Fibre lasersurface treatment reduced the surface hardness and produced smaller crack lengths in com-parison with the as-received surface. The surface crack lengths, hardness, and indentation loadswere found to be important, particularly the crack length, which significantly influenced theend K1c value when K1c¼ 0.016 (E/H)1/2 (P/c3/2) was used. This is because, the longer the cracklengths, the lower the ceramic’s resistance to indentation. This, in turn, increased the end K1c

value. Also, the hardness influences the K1c, and a softer surface was produced by the fibre lasertreatment; this resulted in higher resistance to crack propagation and enhanced the ceramic’sK1c. Increasing the indentation load also varied the end K1c value, as higher indentation loadsresulted in a bigger diamond footprint, and the ceramic exhibited longer crack lengths.

Keywords: fracture toughness (K1c), Vickers indentation technique, ZrO2 engineeringceramics

1 INTRODUCTION

Applications of ceramics have been limited owing totheir crack sensitivity and low fracture toughness(K1c). Nevertheless, the use of ceramics has increasedover the years. They are now considered to be new-age materials, used to manufacture componentsfor the aerospace, automotive, military, and power-generation sectors. Engineering ceramics offerexceptional mechanical properties, which allowsthem to replace the more conventional materials

currently used for high-demanding applications. Theengineering applications of various advanced cera-mics have been amply demonstrated [1–7]. TheVickers indentation method, applicable for calculat-ing the K1c of the Si3N4 ceramic, has been employedby Shukla [8] using the methodology derived byPonton and Rawlings [9, 10]. McColm identifiedvarious indentation techniques to determine thehardness of a variety of ceramics [11]. Strengtheningof ceramics through dislocation generation by var-ious mechanical means was conducted by Mitcjell[12], Castaing and Mazumder [13] and Rabier [14].CO2 laser treatment of Si3N4 ceramics in particularwas presented in the work of Mohanty and Mazum-der [15], showing enhancement of the flexuralstrength of the tested ceramic. Ahn et al. [16] used the

*Corresponding author: Optical Engineering, Wolfson School of

Mechanical and Manufacturing Engineering, Loughborough

University, Loughborough LE11 3TU, UK.

email: [email protected]

JEM1887 Proc. IMechE Vol. 224 Part B: J. Engineering Manufacture

1555



indentation method to investigate the residual stres-ses in machined ceramics using an X-ray diffractiontechnique. Several other investigations also usedvarious indentation methods for determining the K1c

of hard, brittle materials, using empirical equationsapplicable for radial median and Palmqvist cracksystems, as well as the influence of the ceramic’sgrain size on the K1c and elastic/plastic damage fromthe indentation method [17–38]. The British standard(ISO 6507-1) [39] demonstrates the techniques thatare required to be complied with during the Vickersindentation tests. Complying with the regulationsensured that the tests conducted on the ceramicswere valid. Moreover, other investigators furtherdemonstrated the use of a more empirical equation,further illustrated in this paper, and the accuracy andvalidation of the equation, as well as the machineaccuracy of various indentation techniques [40–48].

The K1c is a very important property of any mate-rial. This is especially so for ceramics, owing to theirbrittle nature. Materials with high K1c are much softerand more ductile. Those types of material can resistcracks at relatively higher stress levels and loading[9–13]. Materials with low K1c, such as most ceramics,are much harder and more brittle and allow crackpropagation at lower stresses and loading. Unlikewith metals, it is difficult for dislocations to propa-gate with ceramics, which makes them brittle[14–16]. Ceramics also do not yield mechanically aswell as metals, which leads to a much lower resis-tance to fracture. Ceramics, in comparison withmetals and metal alloys, have a low K1c; thus, it wouldbe an advantage if the K1c of ceramics could beimproved. This could open new avenues for ceramicsto be applicable in high-demanding applicationswhere metals and metal alloys fail owing to theirrelatively low thermal resistance, coefficient of fric-tion, wear rate, and hardness. This study investigatedthe use of empirical equations from the literature tocalculate the K1c of a ZrO2 engineering ceramic andobserved the effects thereon of fibre laser radiation toeffect surface treatment.

In comparison with a CO2 laser, the fibre laser hasa much shorter wavelength, and so it would beinteresting to investigate further the effect of short-wavelength radiation on the surface properties of aZrO2 engineering ceramic. In addition, although theNd:YAG laser wavelength is in the same region as thatof the fibre laser, the Nd:YAG laser cannot be oper-ated stably in the continuous-wave (CW) mode,which is required to minimize the thermal shockinduced in a ceramic. As one can see, this work istimely, as minimal research has been conducted intoemploying fibre lasers for the surface treatment ofmaterials, particularly engineering ceramics.

K1c is a measure of a material’s resistance to fractureor crack propagation. It is the plane strain fracture

toughness. Materials with high K1c are much softerand more ductile. Those types of material are resistantto crack generation when exposed to high stresses andloading. Themeasurement of K1cwas carried out usingthe Vickers indentation method, which calibrates thehardness of the material and induces a crack. Themeasured hardness and crack lengths were thenplaced into empirical equations to calculate thematerial’s K1c after and prior to the fibre laser surfacetreatment. The K1c of engineering materials can bedetermined using various different techniques.

2 BACKGROUND TO DETERMINETHE K1c OF CERAMICS

2.1 Vickers indentation technique

Single-edge notched beam (SENB), chevron notchedbeam (CVNB), and double-cantilever beam (DCB), aswell as the Vickers indentation method, are all con-ventionally employed for industrial applications. TheVickers indentation test can be used to determine theK1c of ceramics and glasses from empirical relation-ships, as demonstrated in references [8] to [17].Advantages of the Vickers hardness test are the cost-effectiveness and ease of set-up, and it is one of thesimplest and least time-consuming in comparisonwith the other techniques available to determine theK1c of ceramics. The Vickers indentation test methodis less responsive in comparison with other techni-ques, but minimum preparation is required, withquick and cost-effective set-up and use. There aredisadvantages to the Vickers indentation test, such asthe lack of accuracy to measure the length of thecracks, which influences the final K1c value [9, 10],the diversity of the use of the indentation equations,and its accuracy. The crack lengths are visualizedafter the test has been conducted by means of opticalmicroscopy. Change in the K1c has an influence onthe material’s functionality or the diversity of itsapplications. Improving the K1c of a material canenhance its functional capabilities, such as longerfunctional life or improved performance underhigher cyclic and mechanical loading, particularly fordemanding applications where engineering ceramicsare applicable. This paper illustrates a method todetermine the K1c by using the Vickers indentationmethod for the laser-treated, cold isostatic pressed(CIP) ZrO2 ceramics. The test samples were investi-gated for their near surface hardness, generated crackprofiles, and the surface finish, from the diamondindentations prior to and after the laser treatment.

K1c can be determined using the Vickers indenta-tion technique, which measures the hardness of thematerial by punching an indentation, with the aid ofa diamond indenter, to produce a crack in the

Proc. IMechE Vol. 224 Part B: J. Engineering Manufacture JEM1887

1556 P P Shukla, J Lawrence, and H Wu



material surface [9, 10, 18]. Measured hardness andthe crack lengths are then placed into an empiricalequation to calculate the material’s K1c [9–13, 19].The results from the Vickers indentation test can thenbe applicable to the empirical equations that werederived by Ponton [9, 10], Chicot [18], and Liang et al.[20]. The equations derived by Ponton et al. [9, 10]originate from various other authors [21–31]. How-ever, they are modified and applied specifically tohard and brittle materials, such as ceramics and glass[9, 10]. The equations have a geometrical relationshipwith various ceramics. Different ceramics have var-ious equations applicable to calculate their K1c. Pre-paration of the samples involves polishing in order tocreate a reflective surface plane (this would meanthat the surface has been well polished) [9, 10, 32, 33]prior to the Vickers indentation process. There arestill constraints with the Vickers indentation techni-ques, as reported by Gong [34], compared with themore conventional techniques applied, such as theSENB and double-torsion (DT) methods, as men-tioned elsewhere [17, 35–37]. The constraints are: (a)the dependence of the crack geometry on the appliedindentation load and the properties of the material;(b) indentation deformation (non-uniform fractureprogression or rapid fracture growth), such as lateralcracking; and (c) unsuitable consideration of theeffect of Young’s modulus and the material hardness[17].

The procedure and steps necessary to produce agenuine Vickers indentation test result and genuinelyvalid K1c values are:

1. Each indentation must be performed at a suffi-cient distance from another. This will prevent theformed cracks interconnecting and bridging withthe other diamond indentations created on theceramic surface [38, 39].

2. A minimum load of 50N must be used and isrecommended because the ceramic materials areof sufficient hardness to require enough loadingto produce an indentation.

3. It is ideal to coat the test surface with gold so thatthe performed indentations are visible. Post-indentation coating may affect the crack tip andgive an inaccurate reading.

4. The test samples should be near to 20c in thick-ness and have minimum porosity. The author alsostated that the adjacent indentations should be nocloser than 4c.

3 PROPAGATION OF THE CRACK GEOMETRYDURING THE VICKERS INDENTATION TEST

Liang et al. [20] followed an investigation into the K1c

of ceramics using the indentation method. He also

used several equations by various authors, as listed inreference [20]. It was stated by Liang et al. thatequations differ as the crack geometry changes (fromPalmqvist to median half-penny cracks). He intro-duced a new equation, stated elsewhere [20], whichwas said to be more universal than previous work.However, in order for the formula to be used, it had tobe manipulated sufficiently. Ponton and Rawling’s[9, 10] formula, in comparison, was much simplifiedand was easy to apply. Chicot [18] conducted furtherinvestigation by applying two other equations toproduce results using materials such as tungstencarbide (nickel phosphorus-treated) and pure silicon.He used the concept of a median half-penny crackand a Palmqvist crack system to determine the mostapplicable equation [18]. It was stated that highindenter loads produce a median half-penny crackwithin the material that is on the edges of the dia-mond indentation (footprint produced). This type ofcrack will always remain connected. A Palmqvistcrack is produced during low indenter loading and isof a smaller scale in comparison. The Palmqvist crackwill always appear in the initial stage of the crackgeneration during the indentation process; then, amedian half-penny crack is produced once theimpact of the indenter is exerted. It can be assumedthat a median half-penny crack may be the result, asthe ceramics are of high hardness, indicating thathigh indenter loads are required in order to inducevisible and measurable diamond footprints.

Orange et al. [35] investigated the K1c of Al2O3-ZrO2

ceramic by comparing the notched beam and theVickers indentation techniques. Cracking behaviourwas observed as Palmqvist and median half-pennycrack geometries were found. Low indentation load-ing produced Palmqvist cracks, and, with increasingloading, median half-penny cracks were found. Highmicro cracking was also found with the Vickersindentation technique when fine grain size (0–3mm)ceramics were tested, and, with increasing grain size(0–5mm), the micro cracking was reduced. With thenotched-beam technique, a higher K1c value wasachieved with increasing grain size [35]. This meansthat the ceramics with larger grain boundaries have ahigher K1c value and higher resistance to fracture.From the work of Orange et al. [35], it can be gatheredthat the notched-beam indentation technique pro-duced better results than the Vickers indentationmethod, although the reasons behind this were notwell justified.

Median half-penny-shaped cracks occur whenhigh indentation loads are applied [19, 32, 40]. Theprofile of a median half-penny-shaped crack is illu-strated in Fig. 1(a). It can be predicted that the out-come for most of the crack profiles in this studywould be of median half-penny shape. For cracksthat are of median half-penny shape, the applicable


Fracture toughness of a zirconia engineering ceramic 1557



equations differ (see equations (1) to (15)) [12, 13].The indention load at which the median half-pennycrack occurs for most ceramics is 3N [19]; this waslower than the loads applied for this investigation.Therefore, it would be reasonable to assume that thegenerated cracks would always be of a half-pennymedian type crack profile. This indicated that onlyequations particularly applicable for median half-penny cracks should be utilized for this study in orderto determine the K1c. Figure 1(b) illustrates a profileof a Palmqvist crack, which tends to occur at lowindentation loads [19, 40]. A Palmqvist crack is partof the median half-penny crack system because,when a load above 3N is applied, the indenter ‘popin’ occurs, and the already produced Palmqvist crackfurther develops into a median half-penny crack [19,40]. These cracks are shallow and lie on the axis of theindenter, as there would be a small extension at theedge of the diamond indenter [40]. Indentation loadsof up to 50N were used for this work, and so it islikely that a Palmqvist crack will occur, leading to ahalf-penny median crack geometry.

4 SELECTION OF EQUATIONS FORCALCULATING THE K1c

Equations for median half-penny-shaped crackswere used for high indenter load applications. Oneequation was selected to calculate the K1c value forthe treated and as-received samples through appli-cation of the equation to the real experimentalvalues. The equations were derived with the materi-als’ geometrical values, which were obtained byexperimental means for ceramics and glass [9, 10].Equations (1) to (15) were mentioned in the literatureto be applicable for ceramics and glass-type materi-als; however, no such equation was defined asapplicable for a certain ceramic material type; hence,the suitability of applying the various equations tothe ZrO2 was not particularly defined. This is why it

was required that an investigation be carried out inorder to determine the most suitable equation forthis study. There were ten equations selected in thisstudy, from various equations discussed in references[9], [10], and [17], to determine first the K1c of the as-received surfaces of the ZrO2 and then the laser-treated surfaces. The selected equations applicable tocalculate the K1c, using the Vickers indentationmethods, are [9]:

K1c ¼ 0:0101P=ðac1=2Þ ½38� ð1Þ

K1c ¼ 0:0515P=c3=2 ½41� ð2Þ

K1c ¼ 0:079ðP=a3=2Þ logð4:5 a=cÞ;for 0:56 c=a< 4:5 ½28� ð3Þ

K1c ¼ 0:0824P=c3=2 ½24� ð4Þ

K1c ¼ 0:4636ðP=a3=2ÞðE=HvÞ2=5ð10FÞ ½45� ð5Þ

K1c ¼ 0:0141ðP=a3=2ÞðE=HvÞ2=5 log ð8:4a=cÞ ½46�ð6Þ

K1c ¼ 0:0134ðE=HvÞ1=2ðP=c3=2Þ ½25� ð7Þ

K1c ¼ 0:0330ðE=HvÞ2=5ðP=c3=2Þfor c=a> � 2:5 ½28� ð8Þ

K1c ¼ 0:0363ðE=HvÞ2=5ðP=a1=5Þða=cÞ1:56 ½42� ð9Þ

K1c ¼ 0:016ðE=HvÞ1=2ðP=c3=2Þ ½27� ð10Þ

K1c ¼ 0:0232 ½f ðE=HvÞ�P=ðac1=2Þwhere F¼ f [log (c/a)] and is determined by the datafitting

for c=a6 � 2:8 ½47� ð11Þ

K1c ¼ 0:417 ½f ðE=HvÞ�P=ða0:42c1:08Þwhere F¼ f [log (c/a)] and is determined by the datafitting

for c=a> � 2:8 ½47� ð12Þ

K1c ¼ 0:095ðE=HvÞ2=3ðP=c3=2Þ ½43� ð13Þ

K1c ¼ 0:022ðE=HvÞ2=3ðP=c3=2Þ ½43� ð14Þ

K1c ¼ 0:035ðE=HvÞ1=4ðP=c3=2Þ ½44� ð15Þ

Fig. 1 Schematic diagram of (a) median half–penny crackand (b) Palmqvist crack system, where: l is the sur-face crack length; 2c or 2a is the length of the dia-mond indent; c is the centre of the diamond to theend of the crack tip; Pc is the load impact; and lc isan interior crack





Ponton and Rawlings [10] state that the equationgiven by Kelly et al. [31] suggested that equation (10)has an accuracy of 30–40 per cent for ceramics thatare well behaved in their indentation response.However, it is first required that the propagation ofthe crack geometry is understood from performingthe Vickers indentation test on the as-received ZrO2

ceramics, as further justified in this paper. It is notmade clear as to why this equation was particularlyused for the ceramic. It was, therefore, required thatsome of the relevant equations were applied to thetested values from this experiment to determine whatsort of results are obtained. A hardness test was per-formed on the ZrO2, assuming that the resultingcracks were of half-penny median type (as a result ofapplying a sufficient indentation load). Ten equa-tions were employed, as previously stated, to estab-lish which particular equation type produces the K1c

value that is the nearest to the known value for the as-received ZrO2 ceramics, which is normally between 8and 12MPam1/2.

5 EXPERIMENTAL METHODOLOGY

5.1 Material details

The material used for the experiment was CIP ZrO2,with 95 per cent ZrO2 and 5 per cent yttria (TenskyInternational Company Ltd). Each test piece wasobtained in a bulk of 10 · 10 · 50mm3, with a surfaceroughness of 1.58mm (as received from the manu-facturer). This was to reduce the laser beam reflec-tion, as the well-polished, shinier surfaces of theceramic would reduce beam absorption. The experi-ments were conducted in ambient conditions at aknown temperature (20 �C). All surfaces of the ZrO2 tobe treated were marked with black ink prior to thelaser treatment to enhance the absorption and allowthe laser beam to penetrate further into the surface.

5.2 Fibre laser treatment

A 200W fibre laser (SPI Ltd) was used in this work,emitting a wavelength of 1.075mm in the continuous-wave (CW) mode. Trials ranged from 75 to 150W byvarying the traverse speed for the initial experiments,to find that a traverse speed of 100mm/min was anideal constant to maintain for all trials, with only thelaser power changing. All speeds were therefore keptto 100mm/min for the main set of experiments pre-sented in Fig. 2 and Table 1. Trials below 75W for theZrO2 at 100mm/min showed no evidence of anyinfluence on the ZrO2. Focal position was kept to20mm above the workpiece to obtain a 3mm spotsize for all trials. The processing gas used was com-pressed air at a flow rate of 25 l/min. Programming ofthe laser was conducted using SPI software that

integrated with the laser machine. A 50mm line wasprogrammed using numerical control (NC) pro-gramming as a potential beam path that was trans-ferred by .dxf file. The nozzle indicated in Fig. 2 wasremoved for all experiments.

5.3 Hardness indentation test and backgroundof the Vickers indentation technique

An indenter of a specific shape, made from a dia-mond, was used to indent the surface of the ZrO2

under investigation [8–19, 35, 40]. The diamond wasinitially pressed on to the as-received surface, and theload was then released. A diamond indentation wasthus created on the surface, and its size was thenmeasured. Thereafter, the surface area of the inden-tation was placed into equation (16) to calculate thehardness value:

Fig. 2 Schematic diagram of the experimental set-up ofthe fibre laser surface treatment of the ZrO2

Table 1 Parameters used for the fibre laser treatment ofthe ZrO2

Trial no.Power(W)

Power densities(W/mm2) Comments

1 75 2083.33 no visual effect2 100 2777.77 small change in colour3 125 4372.22 small cracks apparent4 130 3611.11 small cracks on the edges5 150 4166.65 large crack apparent6 137.5 3819.44 crack-free7 143.25 3779.16 crack-free8 150 4166.66 apparent cracks





Hv ¼ 2P sin½u=2�=D2 ¼ 1:8544P=D2 ð16Þ

where P is the load applied (kg); D is the averagediagonal size of the indentation, in mm; and u is theangle between the opposite faces of the diamondindenter, being 136� with less than – 1� of tolerance.Indentation loads of 5, 20, and 30 kg were applied.The indented surface and the resulting crack lengthswere measured using the inbuilt optical microscopeof the Vickers indenter (Armstrong Engineers Ltd).This method was then implemented for the surfacesof the fibre laser-treated ZrO2. The test samples wereplaced under the macro indenter and were initiallyviewed using the built-in microscope to adjust thedistance between the surface of the workpiece andthe diamond indenter. This maintained a sufficientdistance during each indentation and allowed astandardized testing method that complies with ISO6507-1 [39].

5.4 Measurement of the crack lengths

Crack lengths generated by the Vickers diamondindentation test, as presented in Fig. 3(a), weremeasured using a contact-less, coordinate measuringmachine (CMM), Flash 200. The ceramic sampleswere placed under a traversing lens of the opticalmicroscope. The lens traverses in the y-directionand, to adjust the magnification, it is also able tomove in the z-direction. Motion in the y-direction isprovided by the bed on which the test-piece ismounted for analysis of the surface. The imageappears on the screen as the optical lens traversesabove the surface of the test-piece. The diamondindentations and the resulting crack lengths weremeasured by moving the lever in the x, y-directionsand selecting a starting point on the screen wherethe crack ends (crack tip) and stopping on the sym-metrical side of the other (symmetrical) crack tip,which produced a measurement in both the x- and y-directions.

5.5 Calculation of the fracture toughness (K1c)

The initial investigation used 15 equations to deter-mine which equation type was best suited for calcu-lating the K1c [9, 10]. The as-received surfaces of theZrO2 were first tested for their hardness. Fifty inden-tations were produced on one side of the particularsurface of the ZrO2 ceramics from various test sam-ples. Calibrated hardness was then recorded, and amean average was measured of the as-received sur-faces. Each indentation and its crack lengths werethen viewed at microscopic level with the aid of theoptical microscope, to observe the surface morphol-ogy. The crack lengths were measured using the Flash200 CMM, and crack geometry was observed by athree-dimensional surface topography using white-light interferometry (Alicona Ltd, Infinite focus, IFM2.15). The crack lengths produced by the indenta-tions were then placed into the various K1c equationswith the measured average hardness. Cracking geo-metries were then observed in order to confirm thatthe cracks generated by the diamond indentation at5 kg were of median half-penny crack profile. Thisensured that equations (1) to (15) used for the med-ian half-penny crack profile were correct. Figures 4and 5 present an example of a typical surface profileproduced from the Vickers diamond indentationusing 5 kg (see Fig. 4) and 20 kg (see Fig. 5) loads. Bothshowed evidence of median half-penny-type crackprofiles where an indenter ‘pop-in’, indicated inFigs 4 and 5, was exerted, and then a linear crack wasproduced. A Palmqvist crack profile, which tends tooccur with lower indentation loads, had occurred (asindicated from the indenter ‘pop-in’) already in thiscrack geometry. The concept was more present withhigher indentation loading, as presented in Fig. 5.

The equations used for this study were for half-penny median cracks. It was found that the cracksproduced from the Vickers indentation test were half-penny median type, and so other equations illu-strated for Palmqvist cracks were not used. Equations(1) to (10), as presented in Table 2, were used to

Fig. 3 Schematic diagram of a Vickers diamond indentation with (a) propagation of the cracks and(b) the concept of diamond indentation employed





calculate the K1c value for the as-received surface ofthe tested ZrO2. The results have been tabulated andare presented in Table 3. The equations were set upusing Microsoft Excel, which made it easy to inputparameters from the full equation. These values were

hardness, crack length, Vickers indention load, andYoung’s modulus. It can be seen that all the values,which range between 8 and 12MPam1/2 for the ZrO2,allow the equation to be accurate and useable forcalculating the K1c for the laser-treated and the as-received surfaces of the ZrO2.

Fig. 4 Topography of the Vickers diamond indentation of the as-received surface of the ZrO2 ceramicproduced by a 5 kg load, illustrating a median half-penny crack geometry

Fig. 5 Topography of the Vickers diamond indentation of the as-received surface of the ZrO2 producedby a 20 kg load, illustrating a median half-penny crack geometry

Table 2 Ten equations used to calculate the K1c for theas-received surface of the ZrO2

Equationno. Equation origin Equation

1 Lawn and Swain [38] K1c¼ 0.0101 P/(ac1/2)2 Lawn and Fuller [41] K1c¼ 0.0515 P/c3/2

3 Evans and Charles [24] K1c¼ 0.0824 P/c3/2

4 Lawn et al. [25] K1c¼ 0.0134 (E/Hv)1/2 (P/c3/2)5 Niihara et al. [28] K1c¼ 0.0330 (E/Hv)2/5 (P/c3/2)6 Lankford [42] K1c¼ 0.0363 (E/Hv)2/5(P/a1.5)

(a/c) 1.56

7 Laugier [43] K1c¼ 0.095 (E/Hv)2/3 (P/c3/2)8 Laugier [43] K1c¼ 0.022 (E/Hv)2/3 (P/c3/2)9 Tanaka [44] K1c¼ 0.035 (E/Hv)1/4 (P/c3/2)10 Anstis et al. [27] K1c¼ 0.016 (E/Hv)1/2 (P/c3/2)

Table 3 K1c value obtained from ten equations for theas-received ZrO2

Average K1c

(MPa m1/2)Percentage accuracy(K1c value within range) Status

0.90 0 Unacceptable3.25 0 Under5.20 0 Under

28.70 0 Unacceptable683.64 0 Unacceptable783.93 0 Unacceptable

2024.98 0 Unacceptable759.60 0 Unacceptable

1208.44 0 Unacceptable12.66 42 Acceptable





P¼ load (kg), N¼ load in Newton’s (N), c¼ averageflaw size, a¼ 2c, m¼ length in metres, Hv¼Vickersmaterial hardness value, E¼Young’s modulus.(Young’s modulus for all untreated samples of theZrO2 was kept to 210 GPa m1/2.) For all tested sam-ples, the indentation loads were 5 and 30 kg, andE (Young’s modulus) was 210 GPa m1/2 for the ZrO2.The range (required for equation accuracy) is 8 to12MPam1/2 – 0.40MPam1/2. The average of the K1c

was obtained by using values from 50 different Vick-ers indentation tests. This allowed more consistencyin calculating the K1c, as values were used froma bigger pool of data.

The values obtained using the equations in Table 2are presented in Table 3. The literature K1c value ofthe untreated ZrO2 is 8 to 12MPam1/2, and so thevalues that do not lie in the range given for bothceramics were not considered as acceptable, and,therefore, those equations were discarded. The K1c

values obtained using equation (10) were reasonablefor both of the materials and lie within the desiredrange, and so the equation was accurate and useable.Other equations were discarded and were not takeninto consideration for use. Each of the equations wasset up with the aid of an Excel spreadsheet. Theexperimental values obtained were input into theequation, such as the indentation load, crack lengthcreated by the Vickers diamond indentations, and themeasured hardness. The equation that generated themost accurate result was equation (10). The Vickersdiamond indenter was applied 50 times to the as-received surface plane of the ZrO2. Hardness valuesfrom the indentation test were recorded, and theresulting crack lengths were then measured, first tocalculate the K1c of the untreated surface. From this,50 K1c values were obtained from one surface plane.Thereafter, an accuracy value was determined foreach of the equations by taking values that werefound in the range between 8 and 12MPam1/2. Theaccuracy of the equation was determined by thenumber of K1c values (out of 50 indentations made onone surface plane) appearing within the rangebetween 8 and 12MPam1/2. The K1c values withinthis range were considered as accurate and were usedto calculate the accuracy of the equations. Up to 42per cent accuracy was found using the same equationwith the as-received surface of the ZrO2. Otherequations applied were discarded as they proved tobe of minimal use owing to their results from thisinvestigation. Values obtained using equation (10)were most accurate (closer to the required range forthe ZrO2) in comparison with the other equations;consequently, this equation was used for all as-received and laser-treated surfaces of the ZrO2 todetermine the K1c.

The ceramic surfaces were first treated with thefibre laser. The K1c values were then calculated using

equation (10). The reason for changing the Young’smodulus from 210 GPa to 260 GPa for the ZrO2 wasbecause of the ceramics being anisotropic (meaningthe Young’s modulus of the material was not uniformaround all orientations of the material). This mayoccur owing to certain manufacturing impurities andfurther modifications having occurred during pro-cessing of the ceramic. As the ceramic was exposed tothe fibre laser beam (thermal energy), this led to theinduction of further changes within the material fromthe induced thermal stress, indicating that theYoung’s modulus value for all laser-treated sampleswould ideally be increased when the K1c was calcu-lated. This is why the Young’s modulus was changedfor the fibre laser-treated samples when determiningthe K1c of the ZrO2 engineering ceramic.

6 RESULTS AND DISCUSSION

6.1 Analysis of the as-received surfaces:using a 30kg indentation load

The average surface hardness of the as-received sur-face was found to be 1141 Hv for ZrO2 (see Fig. 6 andTable 4). The values provided by the manufacturer forthe as-received surfaces were 800 to 1200Hv for ZrO2.The ceramics were manufactured using the CIPmethod, which may have left porosity and surfaceflaws in the ZrO2 in comparison with hot isostaticpressing (HIP). The highest value was 1129 Hv, andthe lowest was 757 Hv, when an indentation load of30 kg was applied. This fluctuation has occurredowing to several factors such as: porous structure; theceramic’s response to the diamond indentation; sur-face flaws and micro cracks pre-existing on theceramic, operator; and machine accuracy in mea-suring the sizes and footprints of the diamondindentations. Operator accuracy depends purely onthe ability of the operator to locate and measure thesize of the diamond footprint through the inbuilt lensof the Vickers indentation machine. Such errors wereminimized in the work herein, as the diamond foot-prints and the resulting crack lengths were bothmeasured using computational means. However, themachine accuracy of 875 nm for a load of 5 kg and1471.5 nm for a load of 30 kg must be taken intoconsideration when conducting the Vickers indenta-tion test [48].

The fluctuation found in the mean hardness fromthe results of this study was up to 11 per cent. This, incomparison with the values for ZrO2 given in the lit-erature, was 1 per cent higher than the – 10 per centrange (error) given in [13]. An error of 1 per centbetween the hardness values found in this study andthe literature can be excepted from being a non-conformance and may be considered to pass the





quality requirements if the hardness test was used fora (real-life) ZrO2 ceramic engineering component/product.

The average crack length produced from theVickers indentation test was 276mm for the ZrO2.Results from 50 indentations present crack lengthsthat range from 221mm as the lowest to 335mm asthe highest. The variation from its mean value waswide owing to the micro cracks pre-existing on theZrO2’s surface. If the surface were well polished, theresults of the crack lengths would be much lower, asthe surface would be less prone to cracking aftergrinding and fine polishing of the ZrO2. However, asmoother surface would prevent the laser from beingabsorbed sufficiently into the material surface andoften has the tendency to reflect more than absorb,and so the surfaces were not polished and were tes-ted as received from the manufacturer.

From applying a 30 kg load, it was found that thecracks were significantly large owing to the amountof force acting on the surface area of the ZrO2. An

example of such a crack profile is shown in Fig. 6. Itwas therefore interesting to investigate the cracklengths produced with a lower indentation load,which predictably would have a smaller effect on theend value of the K1c of the ZrO2 engineering cera-mic. As such, a 5 kg indentation load was used:owing to the force over the surface area being muchlower, it produced a smaller footprint of the dia-mond and smaller crack lengths. This would, there-fore, result in producing a lower K1c value than inthe literature and the manufacturer’s range given forthe ZrO2.

The K1c values for the as-received surfaces afterapplication of an indentation load of 30 kg, as pre-sented in Fig. 7, show that the values obtained com-plied with the values given in the literature and thevalues given by the manufacturer [1, 13]. The averageK1c for the ZrO2 was found to be 12.7MPam1/2. Thegraph in Fig. 7 indicates that there is a significantlevel of fluctuation for the values above and belowthe mean range.

Table 4 Summary of the results illustrating an increase or decrease in the parameters used for calcu-lating the K1c of the as-received and laser-treated surface of the ZrO2 ceramics

Average surface hardness,Hv

Average surface crack length(mm)

Average surface K1c

(MPa m1/2)

As-received surface using5 kg load

983 0 277 0 2.48 0

Fibre laser-treated surface 940 4% lower 177 38% lower 5.62 56% increase

Note: Values for the fibre laser-treated surface were compared with the values of the as-received surface indentedusing a 5 kg load to determine the percentage rise and decrease

Fig. 6 Example of the as-received surface of ZrO2 indented by a 30 kg load (hardness ¼ 926 Hv; cracklength ¼ 437mm; K1c ¼ 6.94MPam1/2)





The highest value above the mean was found to be18.11MPam1/2, and the lowest value below the meanwas 8.52MPam1/2. This has occurred owing to thefollowing factors:

1. A change in the material hardness influences theend K1c value. A change in hardness of – 100 Hvresulted in a change in the final K1c value of– 0.34MPam1/2 (according to equation (10)).

2. A change in the crack length (being the majorparameter in equation (10), as used in this work)by – 100mm resulted in a change in the end K1c

value of – 6.31MPam1/2, if the hardness was up to1250 Hv as a particular input parameter in thecalculation. Hence, the crack length has a biggerinfluence on the K1c value than the hardness.

3. The surface micro cracks and porosity pre-exist-ing on the ZrO2 surface make it prone to crackingand reduce the ceramic’s resistance to fracture.

4. The response of the ZrO2 to diamond indentationin some of the areas within the ZrO2 producedfluctuating values as opposed to other areas fromthe viewpoint of the crack length, porosity, andthe surface flaws.

The surface condition should also be considered,as the surface roughness for the ZrO2 was excep-tionally high for conducting the Vickers indentationtest, and this would have resulted in producinghigher crack lengths that further resulted in a reduc-tion in the ZrO2’s K1c value.

6.2 Analysis of the as-received surfaces:using a 5kg indentation load

The hardness of the ZrO2 obtained after applying a5 kg load was much lower than the hardness valuesobtained after applying a load of 30 kg. This was

because the 5 kg load applied to the material’s sur-face area resulted in lower penetration of the dia-mond indentation into the ZrO2, as well as thesurface area of the diamond footprint being smallerin dimension, which resulted in the generation of alower hardness value. The average hardness value forthe ZrO2 was 983 Hv, with the highest value being1330 Hv above the mean and the lowest being 707 Hvbelow the mean. The hardness values of the ZrO2

using a 5 kg load agree with the hardness valuesprovided by the manufacturer; however, they werefound to be towards a bottom limit. A possible causeof this vast fluctuation in the values may have beenthe ZrO2 exhibiting micro cracks, porosity, andimpurities on the near surface layer in comparisonwith the bulk hardness, which frequently producednon-uniform results.

The results showed minimal difference in thegenerated crack lengths for the ZrO2 obtained byapplying a 5 kg load in comparison with the resultsobtained by applying a 30 kg load. The average cracklength was 279mm. Despite the indentation load andthe applied force being much smaller in comparisonwith the 30 kg load, the material was still cracking inequivalent measure to the results of the trials con-ducted using a higher load. This clearly indicated thatthe surface did not exhibit a good response duringthe indentation test. This meant that a smoothersurface finish was required for the indentation test inorder to overcome this problem, so that the surfacescarring and micro cracks pre-existing on the ZrO2

were minimized, and the strength of the top surfacelayer is further enhanced for a better indentationresponse. This also has the possibility of increasingthe surface hardness and yet, at the same time, wouldreduce the resulting cracks from the Vickers diamondfootprints and avoid crack bridging between the

Fig. 7 K1c of the as-received surface of the ZrO2 after application of a 30 kg load





diamond footprints and the pre-existing surfacemicro cracks.

Ponton and Rawlings [9] suggested that a mini-mum loading of 50N must be pressed in order toproduce a diamond indentation; the minimumloading used herein agrees with the work of Pontonand Rawlings [9]. However, the loading herein was49.05N, and we still see a diamond indentation, aspresented in Fig. 8, with a median half-penny-shapeprofile. Initial experiments using lower indentationloads such as 24.5N and 9.8N also presented a suf-ficient indented footprint from the Vickers hardnesstest. The diamond indentation in Fig. 8 is smaller insize than the indentation created by the 30 kg load.

However, the average crack lengths found using a5 kg indentation load were of equal size to thosefound with the 30 kg load. The difference between theaverage values for the two test results was 3 per centand less when considering a larger pool of data. Fromthis, it can be gathered that the macro hardnessindentation test may be more stable at higherindentation loads than lower, particularly with hard,brittle materials such as ZrO2.

The results found for hardness herein whenemploying a 30 kg indentation load match the valuesprovided by the manufacturer and prove that themethod used for the hardness calculation and mea-surement of the crack lengths was valid, although the

Fig. 8 Example of the as-received surface of ZrO2 indented by a 5 kg load (hardness ¼ 1120 Hv; cracklength ¼ 425mm; K1c ¼ 1.10MPam1/2)

Fig. 9 K1c of the as-received surfaces of the ZrO2 after application of a 5 kg indentation load





values for the hardness are much smaller than thevalues provided in the manufacturer’s specificationwhen a 5 kg load was used. This was owing to the factthat the indentation load was much smaller and pro-duced smaller footprints of the diamond, which exer-ted lower force on the surface and reduced the endvalue of the K1c. The average K1c was found to be2.53MPam1/2 for the ZrO2, as presented in Fig. 9,which also shows the highest value to be 6.02MPam1/2

and the lowest to be 0.88MPam1/2. The hardnesscould be much higher if the surfaces were groundand polished prior to the Vickers indentation test, aspreviously stated. This would minimize the surfacemicro cracks and result in better consistency inachieving the hardness value and the resulting cracklengths. The surfaces were tested as received owingto the comparison made with the laser-treated sur-face, as the ground and polished surfaces wouldenhance the material’s reflectivity of the laser beamand would minimize the laser beam absorption intothe ZrO2; consequently, a compromise was requiredto be made.

6.3 Analysis of the fibre laser-treated surfaces:using a 5kg indentation load

The mean hardness found was 940 Hv on the fibrelaser-treated ZrO2 surface. The highest value abovethe mean was 1089 Hv, and the lowest was 826 Hv.There was a 4.5 per cent difference between theaverage hardness values obtained from the fibre lasertreatment and those obtained from the as-receivedsurface. The fibre laser had decreased the hardness incomparison with that of the as-received surface ofthe ZrO2. The average crack length of the fibre-trea-ted ZrO2 was 171mm. The crack length was muchreduced in comparison with the crack length of the

as-received surface, which was 277mm. The fibrelaser-treated surfaces also had much smaller cracksin comparison with the as-received surface (seeexample in Fig. 10). The reduction in the surfacehardness indicated that the laser surface treatmenthad softened the top (near) surface layer of the ZrO2.From this, it can be assumed that some degree ofmelting and solidification may have taken placeduring the laser–ceramic interaction. This wouldhave caused a localized ductile surface to haveformed, along with a change in the surface compo-sition. Further studies are being undertaken todetermine this effect.

The average K1c value for the ZrO2 after the fibrelaser treatment was 5.62MPam1/2. The highest K1c

Fig. 10 Example of the fibre laser-treated surface of theZrO2 indented by a 5 kg load, laser power ¼ 150W,100mm/min, 3mm post size (hardness ¼ 654 Hv;crack length ¼ 232mm; K1c ¼ 3.97MPam1/2)

Fig. 11 K1c of the fibre laser-treated surfaces of ZrO2 after application of 5 kg indentation load





value obtained above the mean was 9.85MPam1/2.The lowest value below the mean was 2.97MPam1/2

for the ZrO2, as presented in Fig. 11 and Table 4. TheK1c values for the fibre laser-treated ZrO2 surfacewere enhanced by 56 per cent in comparison withthose of the as-received surfaces. The values in Fig. 11fluctuate owing to the softening of the treated sur-face, which would have generated lower cracks dur-ing the indentation test. Those areas where K1c is highindicate that the localized, near-surface layer hasmore resistance to crack propagation under cyclicloads or during the onset of any tensile stresses. TheYoung’s modulus is another factor that also influ-enced this change in the ZrO2’s K1c. The Young’smodulus was increased from 210 GPa (as-receivedsurface) to 260 GPa (laser-treated surface) when theK1c was being determined. This was because the ratioof stress and strain was higher after the laser treat-ment. Owing to the way in which the Young’s mod-ulus contributing to the K1c equation was used, it waslikely that the influence of the Young’s modulus wassignificant in calculating the K1c values in this inves-tigation. The end value of the K1c would be slightlyreduced during the calculation of the K1c of the laser-treated ZrO2 in the case of the Young’s modulusbeing kept the same for the as-received surface.

7 CONCLUSIONS

Empirical equations were used on the as-receivedsurfaces of the ZrO2 to investigate the most suitableequation for calculating the K1c. Palmqvist crackswere produced, leading to half-penny median typecracks observed from the topographical investigationat indentation loads of 5, 20, and 30 kg. This con-firmed the use of the group of equations applied forthe investigation. The results from the computationalanalysis showed that equation (10) (K1c¼ 0.016(E/Hv)1/2 (P/c3/2) ) by Anstis et al. [27] was the mostaccurate. It produced 42 per cent accuracy with theK1c values that were found within the range (8 to12MPam1/2) given in the literature and by the man-ufacturer of the ZrO2.

The as-received surface analysis showed that themost influential parameter in calculating the K1c wascrack length, as it proved that longer cracks producedby the Vickers indentation led to lower resistance forthe ZrO2 to propagate a crack. Surfaces with shortercrack lengths exhibited higher resistance to indenta-tion, which further led to an improved K1c value.Hardness also influenced the ZrO2’s K1c, as the resultsshowed that surfaces with high hardness producedbigger crack lengths, which reduced the K1c, andlower surface hardness reduced the crack propaga-tion. This complied with the concept of softer (duc-tile) surfaces being less prone to cracking.

Furthermore, the changes in the hardness demon-strated that the hardness acted as an influentialparameter in changing the surface K1c value of theZrO2. The average hardness of the as-received surfacewas found to be 983 Hv, with the average crack lengthbeing 277mm using a 5 kg indentation load, which ledto an average surface K1c value of 2.48MPam1/2.

It was found that higher indentation loads pro-duced bigger diamond footprints and generatedgreater crack lengths. However, the K1c values werealso increased with the higher load, owing to theindentation load also being an important function ofthe K1c equation when the indentation method isemployed to determine the ceramic’s K1c. Theincrease in the Young’s modulus had affected the K1c

value, owing to the ratio of stress to strain possiblyincreasing after the laser treatment. The values of K1c

for the fibre laser-treated surface would be slightlylower if stress and strain were not considered.

Comparison of the as-received surface with thefibre laser-treated surface, as presented in Table 4,showed improvement in the K1c value of the top(near) surface layer of the fibre laser-treated ZrO2.The hardness was reduced by 4 per cent, whichresulted in lowering of the crack lengths to38per cent. The average hardness found with thefibre laser-treated surface was 941 Hv, with theaverage crack length being 177mm. This resulted inboosting the K1c value to 5.62MPam1/2, which was56per cent higher in comparison with the as-receivedsurface. This was owing to the hardness and thecrack lengths produced by the Vickers indentationbeing lower than those of the as-received surface.From this, it was indicative that the laser treatmenthad softened the localized surface layer as the surfacemelted and solidified. Further investigations arebeing undertaken to elaborate this effect.

Despite the advantages, the Vickers indentationmethod to calculate the ceramic’s K1c in generalcomprises of many flaws, such as the results obtainedfrom the hardness test heavily depending on theoperator’s ability to detect the crack lengths and thegeometry. Also the ceramics geometrical response tothe diamond indentation as well as the level of sur-face roughness of the ceramic, since a smoothersurface than the used in this study would result in ahigher surface strength and in fluence the hardnessand the resulting crack length values. The K1c resultscould be much more accurate if a consistent surfacehardness value was obtained, along with its crackgeometry, which could be found from employingother indentation techniques as well as various othermethods using many other existing equations, whichwould also produce variation in the K1c value.

� Authors 2010





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APPENDIX

Notation

a Twice the average flaw size (2c)c Average flaw sizeD Average diagonal sizeE Young’s modulusF f [log (c/a)]Hv HardnessK1c Fracture toughnessNC Numerical controlP Load (Kg)Pc Load impact





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