Colloids and Surfaces B: Biointerfaces 38 (2004) 77–82

Effect of defect size on fracture strength of dental low fusion porcelain

Toshio Satoa,∗, Kiichi Tsujia, Norimichi Kawashimaa, Hideaki Satob, Yoshiharu Nakamurac

a Department of Biomedical Engineering, Toin University of Yokohama, 1614 Kurogane-cho, Aoba-ku, Yokohama 225-8502, Kanagawa, Japanb Department of Mechanical Engineering, Musashi Institute of Technology, Setagaya-ku, Tokyo, Japan

c Department of Fixed Prosthodontics, Tsurumi University School of Dental Medicine, Yokohama, Kanagawa, Japan

Received 15 June 2004; accepted 29 July 2004

Abstract

Various grinding defects were produced on the surface of specimen dental low fusion porcelain in an attempt to establish the relationshipbetween defect size and fracture strength. In addition, the applicability of the process zone size-fracture criterion in assessing the materialproperties of dental low fusion porcelain was examined.

Super porcelain AAA E3 (Noritake Co., Japan) was used as dental low fusion porcelain. The bending strength and fracture toughness valuew ive paperso crack usinga grinding wase

at ckl©

K

1

octtittoptefl

cro-uringf thes-theen-

ed ine lin-acturemall.prop-on-

e fac-

a ma-pen-

0d

ere estimated by the three-point bending test. After glazing, grinding flaws were introduced by grinding the specimen with abrasf various mesh sizes. In order to calculate the fracture toughness value of dental low fusion porcelain, we introduced a surfaceVickers indenter. The results were discussed based on the process zone size-fracture criterion. The size of cracks caused by

stimated with the process zone size-fracture criterion and Newman–Raju formula.As the defect size decreased, the fracture stress approached the strength for smooth specimen without defect. TheKc value showed

endency to approach theKlc value when the defect size increased. The relationship between the fracture stress,σF, and the equivalent craength,ae, was in good agreement with the theoretical relations deduced from the criterion in dental low fusion porcelain.

2004 Elsevier B.V. All rights reserved.

eywords: Dental low fusion porcelain; Fracture toughness; Fracture criterion; Process zone; Bending strength

. Introduction

In general, dental porcelains that are biocompatible withral tissues are excellent materials with respect to aestheti-ism, corrosion resistance and abrasion resistance. In addi-ion, they are also widely used in the reproduction of colorone and aesthetic restoration. However, since they are ceram-cs, they are very brittle. Therefore, it is important to maintainhe hardness of dental porcelains without compromising aes-hetics their qualities[1]. While grinding corrects the formf dental porcelains, surface cracks caused by the grindingrocess decrease the strength. Glazing and firing then follow

he form production. However, if occlusal adjustment is nec-ssary, grinding is carried out again so that the processingaws sometimes decrease the strength.

∗ Corresponding author. Tel.: +81 45 974 5115; fax: +81 45 974 5115.E-mail address:toshio@cc.toin.ac.jp (T. Sato).

Depending on the grinding conditions, numerous miscopic fractures appear on the surface of ceramics dthe grinding process. Thus, fracture strength reduction ogrinding material can occur[2]. Several studies have invetigated the relationship between grinding conditions andrate of fracture strength reduction. Furthermore, the dimsion of fractures produced in grinding has been examinseveral linear fracture mechanical studies. However, thear fracture mechanics cannot adequately assess the frstrength properties when the dimension of cracks is sConsequently, in order to evaluate the fracture strengtherties of fractures resulting from grinding, the use of nlinear fracture mechanical methods is necessary. Somtors to consider include:

(1) Fracture toughness, which can be considered to beterial property value, is not constant but rather is dedent on defect size.

927-7765/$ – see front matter © 2004 Elsevier B.V. All rights reserved.oi:10.1016/j.colsurfb.2004.07.015

78 T. Sato et al. / Colloids and Surfaces B: Biointerfaces 38 (2004) 77–82

(2) The fracture strength (σF) of smooth experimental ce-ramic specimens shows a significant association with de-fect size.

(3) Fracture strength (σF) and fracture toughness value varywidely.

Although important findings on structural ceramics havebeen obtained in investigations related to the observationsmentioned above, little data is available regarding dentalporcelains.

In the present paper, grinding was performed in order tomake cracks of various sizes on the surface of a low fusionporcelain. In addition, the effect of defect size on the strengthof low fusion porcelain was investigated using the three-pointbending test. Next, the authors proposed a criterion for frac-ture based on the process zone size[3–6]. The feasibilityof the fracture criterion as applied to low fusion porcelainwas then examined. The effect of defect size on the frac-ture stress of low fusion porcelain was also systematicallyinvestigated. The size of cracks produced by grinding wasestimated using the process zone size-fracture criterion andthe Newman–Raju formula[7].

2. Materials and methods

2e

seda wasS ),C ).Mp lled

water. The slurry was poured into a 5 mm× 6 mm× 40 mmmetal mold, which was vibrated until no moisture and bubbleappeared in the surface. The specimen was removed from themetal mold and sintered in a vacuum furnace. Thus, rectangu-lar specimens of 3 mm× 4 mm× 40 mm size (JIS R1601[8])were prepared and glazing was carried out on them. Firingand glazing conditions of the low fusion porcelain were as fol-lows: drying time: 7 min, starting firing temperature: 600◦Cfiring temperature: 930◦C, programming rate: 50◦C/min,cooling time: 10 s, holding time: 0 min, vacuum tempera-ture in the firing: 600◦C, degree of vacuum: 72 cm/Hg andvacuum solution exception temperature: 920◦C.

The bending strength and fracture toughness value wereestimated by the three-point bending test. After glazing,grinding flaws were longitudinally introduced into the spec-imen at a right angle by grinding the specimen with abrasivepapers of various mesh sizes (#40, #150, #600, #1000 and#2000). The flaw depth was varied from 0.9 to 22�m. Nexta machined notch was introduced using a band saw (BS-3000, Iguzakuto Co., Japan). The band width was 0.2 mmand the depth was varied from 0.23 to 1.42 mm. The de-fect was positioned at the center of the tension surface ofthe specimen. All tests were made using a three-point load-ing system. The cross-head speed in the monotonic testeswas 0.5 mm/min at room temperature. The fracture tough-n ength( thes rfacer pth ofg anda d byS

2z

s ass mi-c lt ofas rocesszi imesc O orX pec-t ssσ nt(i nfs

σ

W resss Z =

.1. Production method of test specimen andxperimental procedure

Super porcelain AAA E3 (Noritake Co., Japan) was us a low fusion porcelain. The chemical compositioniO2 (64.5 mass%), Al2O3 (14.4 mass%), K2O (8.7 mass%aO (0.7 mass%), MgO (0.6 mass%) and Li2O (0.4 mass%anufacturing process is shown inFig. 1. The low fusionorcelain powder (3 g) was dispersed in 1.2 mL of disti

Fig. 1. Manufacturing process of dental low fusion porcelain.

ess value was calculated from the measured crack lJIS R1607[9]). Young’s modulus and Poisson’s ratio ofpecimen were 64.3 GPa and 0.22, respectively. A suoughness meter and SEM were used to measure the derinding flaw and machined notch, respectively. Beforefter fracturing the surface of the specimen was observeEM.

.2. Evaluation of fracture stress, based on the processone model[3–6]

A process zone develops at the crack tip of ceramichown inFig. 2 [3–6]. In this process zone, innumerablerocracks occur[10–14]or the volume increases as a resuphase transformation induced by stress like ZrO2 [10]. Thetress in the area therefore decreases to the level of pone forming stressσp and ceases to show the 1/

√r singular-

ty. The stress distribution in the process zone is sometonsidered to show characteristics similar to those in YO due to work hardening or softening materials, res

ively, as shown inFig. 2. However, in this paper, the strep expressed by BO shown inFig. 2is assumed to be consta

�yy = σp) for simplicity. The process zone forming stressσps almost equal to the fracture stressσF of the plain specimeor static fracture or static fatigue limit stressσth of the plainpecimen for static fatigue[3–6]:

p = σF or σth (1)

hen the sizeD of the process zone is so small that a sttate similar to small scale yielding is established (SSP

T. Sato et al. / Colloids and Surfaces B: Biointerfaces 38 (2004) 77–82 79

Fig. 2. Process zone and stress distribution ahead of crack tip.

the small scale process zone), the fracture condition of con-stantKlc is established. If the process zone sizeD is so largeand the SSPZ condition is not met, then the fracture condi-tion of constantKlc is not established. The limit conditionis expressed as follows based on the ASTM Standard E399[15]:

W-a, B, a≥- 2.5

(Klc

σp

)2

(2)

whereW is the specimen width,a the crack length andB theplate thickness. In the case of cracked materials, the processzone sizeD is expressed as follows when it is sufficientlysmall to meet the SSPZ condition:

D = π

8

(K

σF

)2

(3)

If the process zone sizeD is relatively large in comparisonwith the crack length and does not meet the SSPZ condi-tion, the process zone sizeD based on the Dugdale model isexpressed as follows[16]:

D = a

{sec

(πσ

2σF

)− 1

}(4)

For this case, the fracture condition of constantKlc is note ocessz canb

D

w on-d ere-f

crack equivalent lengthae of cracked materials is expressedas follows based on the expressions (3)–(5)[3–6]:

π

8

(Klc

σF

)2

= ae

{sec

(πσc

2σF

)− 1

}(6)

3. Results

3.1. Vickers hardness and introduction of pre-crack byindentation

In order to calculate the fracture toughness value of lowfusion porcelain, we introduced a surface crack using a Vick-ers indenter. The applied Vickers load was between 9.8 and98 N. The length of the surface crack ranged from about 0.18to 1 mm.Fig. 3a shows a typical SEM photo of a surface crackintroduced by the Vickers indenter. In this case, as shown inFig. 3b, a median crack of about 210�m in length was formedon the surface by a Vickers load of 9.8 N. It is apparent thatcrack length 2c varies according to indentation loadPv.

Fig. 3. Indentation and semi-elliptical crack: (a) indentation crack; (b) semi-elliptical (median/radial) crack.

stablished. Assuming that fracture occurs when the prone sizeD reaches a certain limit, the fracture conditione expressed as follows:

= Dc (5)

hereDc is the critical process zone size. This fracture cition criterion is the process zone fracture criterion. Th

ore, the relationship between the fracture stressσc and the

80 T. Sato et al. / Colloids and Surfaces B: Biointerfaces 38 (2004) 77–82

Fig. 4. Load of Vickers indentation effects: (a) half length of crack andindenter size; (b) Vickers hardness; (c) fracture toughness.

Fig. 4a shows the relationships betweenPv and the halflengthaof the indentation length and half lengthcof the cracklength using logarithms for both. According to JIS standardR1607[9], assuming thatHv is fixed, the gradient betweenPv anda should be 2.0. Based on the results of the test, thegradient is calculated to be 2.15, and the test values are linear.The Vickers hardness was calculated asHv(reg) = 1.50 GPafrom the regression curve of the indentation length in thefigure. If theKlc value is fixed, the gradient betweenPv andc becomes 1.5. From these results, it can be seen that therelationshipPv ∝ c1.4 is generally correct in the range ofPv9.8–100 N. Accordingly, it can be said that these cracks arenot Palmqvist-type surface cracks but fully developed median

cracks. This is supported also by the results of the fractureobservation indicated inFig. 3b.

Fig. 4b and c show the relationships between theHv valueandPv and the relationship between theKlc value andPv,respectively, to investigate whether or not the assumed con-dition Hv and theKlc value described above are fixed. Inthe relationship betweenHv andPv, theHv value increasesslightly asPv increases; maximumHv is reached at 49 N;Hvlies mainly in the range of 1.20–1.90 GPa; and the discrep-ancy is of the same degree without being greatly dependenton the load. Moreover, in the relationship between theKlcvalue andPv, the tendency for theKlc value to decrease asPv increases was not observed, and we consider that the av-erage value of eachKlc value was on the whole fixed andnot dependent onPv despite a certain amount of discrepancy.Incidentally, the average value ofKlc was 1.06 MPam1/2.

Next, we considered that residual stress from compres-sion exists at the crack edge when the specimen is indentedwith the Vickers indenter. When we investigated this by theindenter press-in method (JSMS-SD-4-01)[17] to study theinfluence of residual stress, the residual stress was found tobe−18.9 to 0.94 MPa, and considered a value in this rangeto have only slight influence.

3.2. Effect of crack length on the fracture stress

thes saww dt sid-e efect.T asf

a

w .v

T ck

ress.

Defects introduced in the specimen by both polishingpecimen with abrasive papers and by using the bandere replaced by the lengthae. The lengthae was introduce

o represent the crack in an infinite plate taking into conration the width of the specimen and the shape of the dhe parameterae (equivalent crack length) is expressed

ollows:

e = 1

π

(Kc

σc

)2

(7)

hereKc is the fracture toughness value for the defectKcalue was taken from JIS R1607[9].

The relationship betweenae andσc is shown inFig. 5.he dashed line (Klc) represents the point at which the cra

Fig. 5. Relationship between equivalent crack length and fracture st

T. Sato et al. / Colloids and Surfaces B: Biointerfaces 38 (2004) 77–82 81

Fig. 6. Relationship between equivalent crack length and fracture toughness.

length and fracture stress reach a constant fracture condition.The solid line represents the process zone curve forσc andae obtained using the process zone size-fracture criterion.The fracture strength deviated from the constantKlc line asthe defect size became smaller, approaching the strength ofthe smooth experimental ceramic specimen. The four dots, atwhich theae value is 10−4, indicate the fracture strength ofthe smooth experimental ceramic sample. These results showthat the relationship between ae andσc, as determined bythe process zone size-fracture criterion, correlate well withexperimental values. The ISO 6872[18] bending strengthrequirement for porcelain is over 50 MPa. Theae for thisbending strength is calculated to 0.1 mm, which means thatthe standard is satisfied if the defect is less than 0.1 mm.

Fig. 6 shows the relationship betweenKc andae. Whenae is less than approximately 0.3 mm, the data indicated thatKc decreased asae became smaller. On the other hand, asthe defect size increased,Kc also increased untilKc becameequivalent toKlc. The solid line inFig. 6 indicates the asso-ciation betweenKc andae as determined by the process zonesize-fracture criterion. As predicted by the process zone size-fracture criterion, the relationship betweenKc andae corre-lates well with the experimental data.

These results show that the fracture toughness of ceramics,a typical example of a brittle material, is not uniform, andt se asc ed int

4

n,t ed byt tc redf thao es bea

Fig. 7. Estimation of semi-elliptical crack size due to grinding by processzone size-fracture criterion.

the same value ofKc, are easily obtained as reverse problem ofthe Newman–Raju formula[7]. Fig. 7shows the relationshipbetweenb andc. In this case, the average fracture stress of74.2 MPa and the minimum stress of 59.1 MPa for smooth

Fig. 8. Fracture surface of ground specimen: (a) state near the crack initiationsite; (b) microphotograph of semi-elliptical crack shape from which crackinitiated (2c = 198.0�m, b = 92.3�m).

hat the tendency for the fracture toughness to decrearack length decreases holds for the samples examinhis investigation[19].

. Discussion

If the fracture stressσc of a ground specimen is knowhe size of the crack caused by grinding can be estimathe process zone size-fracture criterion[20]. The equivalenrack lengthae is easily obtained by substituting the measuracture stress intoEq. (6). Next, the equivalent crack lenge and the fracture stressσc are substituted intoEq. (7) inrder to obtain the fracture toughnessKc. The depth and thurface length of a semi-elliptical crack are assumed tobnd 2c, respectively. The values ofbandc, both of which give

82 T. Sato et al. / Colloids and Surfaces B: Biointerfaces 38 (2004) 77–82

specimens were used asσc. Region A inFig. 7is for the casein which fracture occurs at the surface (point A), and region Bis for the case in which fracture occurs at the deepest position(point B).

In order to examine the validity of fracture dimensions pro-jected by the methods used in this study, the fractured surfaceof specimens under investigation was observed. Although itwas difficult to identify surface defects resulting from grind-ing, examples of cracks that were on experimental specimensduring the grinding process are shown inFig. 8a and b. Here,these SEM images show the fracture plane for which a #40abrasive paper was used to form grinding flaws. A chevronpattern on the fracture plane can be seen inFig. 8a. The cir-cle in this figure indicates the initiation point of the fracturewhich was determined by tracing backwards along the ob-served surface pattern.Fig. 8b shows the SEM of the samplefragment tilted 6◦ and enlarged. From this figure, the length ofthe defect 2c is 198.0�m and the depthb is 92.3�m, formingan almost semi-elliptical crack. The circles inFig. 7 are forexamplesb andc, which were obtained in a similar manner.Although the number of examples, as shown inb andc, werefew, these results matched the results predicted in this figurecomparatively well. These results suggest that employing theprocess zone size-fracture criterion enables quantitative esti-mation of fracture dimensions formed by grinding.

5

e ofs stab-l ngth.I turec fu-s zonese aledt

( spec

( e

(he

process zone size-fracture criterion by applying it to den-tal low fusion porcelain.

(4) Various sizes of surface cracks caused by grinding couldbe estimated based on the critical process zone size-fracture criterion usingσF, ae and the Newman–Rajuformula[7].

References

[1] R. Morena, P.E. Lockwood, C.W. Fairhurst, Dent. Mater. 2 (1986)58–62.

[2] S. Ban, K.J. Anusavice, J. Dent. Res. 69 (12) (1990) 1791–1799.

[3] K. Tsuji, K. Iwase, K. Ando, Fatigue Fract. Eng. Mater. Struct. 22(1999) 509–517.

[4] K. Ando, B.A. Kim, M. Iwase, N. Ogura, Fatigue Fract. Eng. Mater.Struct. 15 (2) (1992) 139–149.

[5] M.C. Chu, K. Ando, Fatigue Fract. Eng. Mater. Struct. 16 (3) (1993)335–350.

[6] K. Ando, M. Iwase, B.A. Kim, M.C. Chu, S. Sato, Fatigue Fract.Eng. Mater. Struct. 16 (9) (1993) 995–1006.

[7] J.C. Newman, I.S. Raju, Eng. Fract. Mech. 15 (1) (1981) 2185–2192.[8] JIS R1601, Testing Method for Flexural Strength of High Perfor-

mance Ceramics, Japan Standards Association, 1993.[9] JIS R1607, Testing Methods for Fracture Toughness of High Perfor-

mance Ceramics, Japan Standards Association, 1990.[10] A.G. Evans, K.T. Faber, J. Am. Ceram. Soc. 67 (4) (1984) 255–

260.[[ 983)

[ ringce, F.F., New

[ . 54

[ ctureand

[[ idual

acture

[[ 91)

[ . 17

. Conclusions

Various grinding defects were produced on the surfacpecimen dental low fusion porcelain in an attempt to eish the relationship between defect size and fracture stren addition, the applicability of the process zone size-fracriterion in assessing the material properties of dental lowion porcelain was examined. By employing the processize-fracture criterion and the Newman–Raju formula[7], anxamination of the size of cracks formed by grinding revehe following:

1) Fracture stress approached the strength for smoothimen without defect with decreasing defect size.

2) TheKc value tended to approach theKlc value when thdefect size increased.

3) The relationship between the fracture stressσF and theequivalent crack lengthae could be arranged to give t

-

11] W. Kreher, W. Pompe, J. Mater. Sci. 16 (1981) 694–706.12] R.G. Hoagland, J.D. Embury, J. Am. Ceram. Soc. 63 (7–8) (1

404–410.13] T. Kishi, S. Wakayama, S. Kohara, Microfracture process du

fracture toughness testing in Al2O3 ceramics evaluated by AE sourcharacterization, in: R.C. Bradt, A.G. Evans, D.P.H. HasselmanLangr (Eds.), Fracture Mechanics of Ceramics, Plenum PressYork, 1986, pp. 85–100.

14] S. Wakayama, H. Nishimura, T. Kishi, Jpn. Soc. Mech. Eng(508) (1988) 2143–2150 (in Japanese).

15] ASTM E399-81, Standard Test Method for Plane-strain FraToughness of Metallic Material, American Society for TestingMaterials, Philadelphia, PA, 1981.

16] D.S. Dugdale, J. Mech. Phys. Solids 8 (1960) 100–108.17] JSMS Committee on Fatigue of Materials, JSMS-SD-4-01, Res

stress measurement for engineering ceramics by indentation frmethod, 2001.

18] ISO 6872, Dental Ceramic, 2nd ed., 1995.19] B.A. Kim, T. Seki, K. Ando, Jpn. Soc. Mech. Eng. 57 (541) (19

288–294 (in Japanese).20] B.A. Kim, K. Ando, S. Sato, Fatigue Fract. Eng. Mater. Struct

(2) (1994) 187–200.