Contribution of Residual Stress to the Strength
of Abrasive Ground Alumina
W. H. Tuan* and J. C. Kuo
Institute of Materials Science and Engineering, National Taiwan University, Taipei, 10764, Taiwan, Republic of China
(Received 14 July 1998; accepted 16 October 1998)
Abstract
Residual stresses are introduced into the surface region of ceramics during abrasive grinding. The presence of the residual stresses can aect the strength of the ground specimens. In the present study, a methodology is proposed to determine the contribution of the residual stresses to the strength of the ground specimens. The method uses Weibull sta-tistics to evaluate the crack size distribution before and after annealing. If the crack size distribution is not changed after annealing, the amount of the strength reduction is attributed to the eect of resi-dual stresses as veri®ed by direct measurements of the residual stress at the surface. # 1999 Elsevier Science Limited. All rights reserved
Keywords: residual stresses, ®nishing, surfaces, strength, Al2O3,
1 Introduction
Dimensional tolerance has to be tightly controlled for many structural applications. Abrasive grind-ing is therefore frequently used to meet the requirement. During abrasive grinding, material together with the ¯aws in the surface region are removed, while residual stresses are introduced into the newly formed surface region. The magni-tude of the residual stress has been determined by a
X-ray topography technique on diamond,1 a
pho-toelastic technique on MgO,2 an indentation
tech-nique on a glass-ceramic3 and Si
3N4,4 an X-ray
diraction technique on Al2O3,5 and a bending
technique on many ceramics.6 Typically, these
techniques only reveal the residual stress in a shal-low surface region. For example, a compressive
stress of 350 MPa was detected in the 10 m sur-face region of Si3N4.6
The magnitude of the residual stress in a deeper surface region can also be detected by modifying the previous techniques. For example, the surface region can be removed by polishing to expose the region beneath the surface.6The distribution of the
residual stress as a function of depth can then be determined. However, this technique can lead to biased results, mainly because the polishing tech-nique can also induce residual stress in the surface region.6,7 Other techniques such as neutron
dif-fraction and acoustic scattering which have deeper penetration depth than that of X-rays were used to determine the residual stress pro®le in SiC±Al2O3
composites8 and Si 3N4.4
The distribution of the residual stress beneath the surface after abrasive grinding has therefore been established. The residual stress is compressive on the surface and tensile underneath.4 However,
the reported values of the residual stress dier sig-ni®cantly from one report to another. The varia-tion may be due to the strong dependence of the magnitude of the residual stress on the grinding conditions. For example, the residual stress induced in a Si3N4 and a ferrite by a dressed
dia-mond wheel is twice that induced by an undressed wheel.6 The contribution of the residual stress to
the resulting strength of the ground specimens is also unclear. For example, one report stated that the strength of a Si3N4 is not changed despite a
compressive surface stress as high as 350 MPa.6
However, another report claimed that the strength of a machined Si3N4 specimen was nearly twice
that of the polished one.4
There is not only residual stress introduced into the newly exposed surface region, but machining ¯aws are also formed.4,9,10The size of the
machin-ing ¯aws depends strongly on the microstructure of the machined specimens. However, many proces-sing ¯aws exist in the ceramic components before
Printed in Great Britain. All rights reserved P I I : S 0 9 5 5 - 2 2 1 9 ( 9 8 ) 0 0 2 6 0 - X 0955-2219/99/$ - see front matter
1593 *To whom correspondence should be addressed. Fax: +886 223634562; e-mail: tuan@ccms.ntu.edu.tw
the components are ground. The residual stresses can be reduced by an annealing treatment.9
How-ever, the size of ¯aws may also change during annealing. The contribution from residual stresses to the strength is therefore dicult to be quanti®ed
by annealing treatment alone.11 In the present
study, the magnitude of residual stress in the ground specimens is manipulated by using an annealing treatment. In addition, the crack size distribution is monitored by using Weibull statis-tics. The contribution of residual stress to strength is determined by combining the annealing treat-ment and Weibull statistics.
2 Experimental
A commercial alumina powder (CH-92A, 92% Al2O3, Marusu Co., Japan) was used in the present
study. The specimens were prepared by die-press-ing the powder into rectangular bars. The pressdie-press-ing pressure employed was 140 MPa. The powder compacts were sintered at 1480C for 1 h. After sintering, the size of the rectangular bars is 3.24.044 mm.
Grinding was performed using a surface grinder with a resin bonded 325 grit diamond wheel. The diameter of the wheel was 175 mm. Truing and dressing of the diamond wheel had a dramatic eect on the grinding quality.6,12 The wheel was
®rst trued by grinding a low carbon steel and then dressed with a porous alumina dressing stick before grinding the specimens. A water-based oil emulsion grinding ¯uid was used for cooling. The specimens were ground longitudinally at a table speed of 0.17 m/s and a wheel surface speed of 27.5 m/s. The depth of cut was 10 m/pass. Only the tensile surface of the ¯exural specimens was ground. The depth of cut was kept constant until 200 m in thickness of the specimen was removed. The specimens were not beveled.
Some specimens were annealed to remove the residual stresses. These specimens were ®rst ground at 10 m/pass to remove a thickness of 200 m. The specimens were then annealed at 1190C for 1 or 10 h. The extent of residual stresses in surface region was quanti®ed by the X-ray diraction (XRD) method (30 KV, 20 mA). A thin layer of silicon slurry was ®rst coated on the surface of the XRD specimens. The silicon layer was used as an internal standard to determine the shift of 2 of the (110) peak of Al2O3. The ®nal density was
deter-mined by the water displacement method. The grain boundaries were revealed by thermal etching the polished specimens. The microstructure was observed with scanning electron microscopy (SEM). The grain size was determined using the
line intercept technique, with more than 300 grains counted. Four-point bending was used to deter-mine the ¯exural strength of the specimens. The four-point span was 10 mm30 mm. The rate of loading was 0.083 mm/s. The surface roughness of the ground specimens was measured with a stylus surface pro®lometer.
3 Results and Discussion
The absolute density of the alumina specimens is 3.65 g/cm3. The density is lower than the
theore-tical density for pure Al2O3, indicating the presence
of a glassy phase in the specimens. The micro-structure of the specimen is shown in Fig. 1. The
average size of Al2O3 grains is 1.7 m. From
microstructural observation, the porosity in the specimen is less than 2%. The ground surface of the specimen is shown in Fig. 2. Many grains have pulled out and a small amount of smooth area is observed on the surface. Despite the presence of a glassy phase, the microstructural features of the spe-cimens after grinding are very similar to those of
high-purity alumina specimens.10 The material
removal mechanism is suggested as grain disintegra-tion resulting from intergranular microfractures.
Fig. 1. The microstructure of the alumina specimen.
The average surface roughness, Ra, and the
max-imum roughness, Rmax, of the ground specimens
are 0.26 m and 5.8 m, respectively.
The average strength of the specimens is shown in Table 1. The strength of the as-sintered speci-mens is increased by 92 MPa after abrasive grind-ing. As the ground specimens are annealed at 1190C for 1 h, the strength decreased by 40 MPa. By increasing the annealing time from 1 to 10 h, the strength is decreased slightly by 13 MPa.
The variation of strength can be characterized with Weibull statistics. The Weibull statistics treats the probability of failure, F, based on a weakest-link theory as13
F 1 ÿ expÿ ÿ u o
mV 1
where is the strength of the specimen, u the threshold strength below which fracture can not occur, o the characteristic strength which corre-sponds to 63.2% probability of failure, m the Wei-bull modulus and V the stressed volume. Equation (1) can be re-arranged as follows,
lnfln1= 1ÿFgm ln ÿ u ÿ m ln o constant 2 The above equation has been frequently termed as the 3-parameter Weibull equation. The probability of failure, F, is calculated as
F n ÿ 05=N 3
where n is the nth specimen as the experimental data are ranked in order, N the total number of the specimens.
When the threshold strength, u, is assumed as zero, eqn (2) simpli®es as
lnfln1= 1ÿFgm ln ÿ m ln o constant 4
The above equation is termed as the 2-parameter Weibull equation. Using both the 2-parameter and 3-parameter statistics to evaluate the data can shed more light on the data distribution.14 The value of
Weibull modulus is determined by least-square regression analysis. The 2-parameter Weibull dis-tribution for the as-sintered, ground and annealed specimens is shown in Fig. 3. The ®gure suggests that the threshold strength, u, is not zero. By using the regression ®t to determine the value of u, the 3-parameter Weibull distribution can be deter-mined. The 2-parameter Weibull distribution and 3-parameter Weibull distribution for the as-sin-tered specimens are shown in Fig. 4. The correla-tion factor for the 2-parameter and 3-parameter equations is 0.96 and 0.97, respectively. Both equations give reasonably good ®t to the data. The values of the Weibull modulus determined by the Weibull 2-parameter and 3-parameter equations are shown in Table 1. The values of the Weibull modulus calculated by the 2-parameter and 3-parameter equations given in Table 1 show a simi-lar trend; the two analyses are consistent to each other.
The grain size of the annealed specimens was measured and no signi®cant grain growth after
Table 1. The number of specimens used, strength and Weibull modulus of the as-sintered, ground and annealed specimens.
As-sintered Ground Annealed,
119C/1h 119Annealed,C/10h Number of specimens used 30 30 29 29 Average strength/MPa 199 291 251 238 Standard deviation of strength 41 21 17 23 2-parameter Weibull modulus 5.6 16.6 18.1 12.4 3-parameter Weibull modulus 1.3 2.4 2.3 1.5
Fig. 3. Weibull plots calculated using the 2-parameter statistics.
Fig. 4. Comparison of the 2-parameter and 3-parameter Weibull distribution for the as-sintered specimens.
annealing was noted. However, the size of cracks may be modi®ed during annealing through crack opening15 or crack healing.16,17 Previous study
suggested that the size of cracks in alumina can be altered by heat treating at a temperature as low as 1100C.17 The change in strength after annealing
which should therefore result from either a change in the critical crack size or a reduction in the dual stress. To evaluate the contribution of resi-dual stress to strength, the change of crack size distribution is monitored by using the Weibull sta-tistics (Fig. 3 and Table 1).
From Table 1, the Weibull modulus increases signi®cantly after abrasive grinding and is then virtually unchanged as the specimens are annealed at 1190C for 1 h. This indicates that the crack size distribution is not altered by annealing at 1190C for 1 h. The Weibull modulus decreases as the annealing time is increased to 10 h, which indicates that the size of cracks is modi®ed by the 10 h anneal. The strength reduction after 1 h annealing (40 MPa) can be attributed to the release of resi-dual stress, for the crack size is not changed after annealing at 1190C for 1 h. This can be further con®rmed by the XRD analysis. The shift of dif-fraction angle, 2, of ground specimens is 0.052. This value is decreased to 0.005 after annealing at 1190C for 1 h, indicating that most residual stres-ses are relieved after annealing.
The surface residual stress after abrasive
grind-ing can be much higher than 40 MPa.6 However,
the strength of brittle ceramics is controlled by the stress acting on the critical crack. The residual stress that surrounds the tip of critical crack is dif-ferent from the surface stress. However, the size of the critical crack varies from one specimen to another. Therefore, direct measurement of the residual stress can shed little light on the contribu-tion of residual stress to strength. In the present study, it is not intended to indicate that a residual stress of 40 MPa existed at a certain depth from the surface. However, it demonstrates that the metho-dology of using both the annealing treatment and Weibull statistics can determine the contribution of residual stress to strength.
The strength increased by 92 MPa after abrasive grinding. Since there is a 40 MPa contribution from the residual stress, the additional 50 MPa must arise from the removal of large cracks by grinding. These assumptions can be veri®ed with Weibull statistics (Fig. 5). The Weibull modulus of the as-sintered specimens increased signi®cantly after abrasive grinding, which removed the mate-rial from the surface region. The depth of the materials removed in the present study is about 200 m, which is likely larger than the size of ¯aws produced during the processing stages. Due to the
average strength increase, the large cracks in sur-face region must be either removed or reduced in size and further indicates that large cracks tend to form in the surface region of the specimens used in the present study during powder processing and ®ring. Due to the presence of residual stress and removal of large cracks, the Weibull modulus is signi®cantly enhanced (Fig. 5).
A recent study suggested that the strength of the alumina specimens with high purity (>99% Al2O3)
was increased by 40 MPa after abrasive grinding.10
A 30 MPa strength increase is attributed to the introduction of residual stress during grinding. This value is close to the strength increase for the present system. It implies that the residual stress induced by grinding is mainly stored in the alumina phase. The contribution of the removal of large crack from the surface region for the present sys-tem is as large as 50 MPa. It suggests that large cracks are likely formed in the impure system dur-ing processdur-ing. The removal of the surface region can thus enhance the strength signi®cantly.
4 Conclusions
In the present study, alumina was used to investi-gate the contribution of residual stress induced
Fig. 5. (a) The strength distribution of the as-sintered mens. (b) The Weibull distribution of the as-sintered speci-mens is shifted to its right by introducing residual stress. (c) The large cracks in surface region are removed by grinding. (d) The strength and Weibull modulus of the ground specimens is therefore much higher than those of the as-sintered specimens.
during abrasive grinding on strength. The strength of the as-sintered specimens is increased by 92 MPa by abrasive grinding. The strength of the ground specimens is reduced by 40 MPa as a suitable annealing pro®le is applied. The annealing treat-ment can easily reduce the residual stress and can also change the size of cracks. By employing the Weibull 2-parameter and 3-parameter statistics, the crack size after annealing at 1190C for 1 h is found unchanged, whereas XRD analysis reveals little residual stress in the surface region of the annealed specimens. The strength reduction after annealing results primarily from the removal of residual stress. The contribution of residual stress to the strength after grinding can thus be determined.
The present study demonstrates that abrasive grinding in¯uences the strength of machined cera-mics in two ways. One feature is that the grinding introduces residual stresses into the surface region. The presence of the residual stresses is compressive and hence bene®cial to the strength. Another fea-ture is that large cracks are frequently formed in the surface region during processing. These large cracks can be removed or reduced in size by a sui-table grinding process. Therefore, both the magni-tude and variation in strength can be signi®cantly improved by applying abrasive grinding.
Acknowledgements
The present study was supported by the National Science Council, Republic of China, through con-tract number NSC86-2216-E002-031.
References
1. Frank, F. C., Lawn, B. R. and Lang, A. R., A study of strains in abraded diamond surfaces. Proc. R. Soc. Lon-don, Ser. A., 1967, 310, 239±252.
2. Bernal, E. and Koepke, B. G., Residual stresses in machined MgO crystals. J. Am. Ceram. Soc., 1973, 56, 634±639.
3. Cook, R. F., Lawn, B. R., Dabbs, T. P. and Chantikul, P., Eect of machining damage on the strength of a glass ceramic. J. Am. Ceram. Soc., 1981, 64, c121±c122. 4. Marshall, D. B., Evans, A. G., Khuri-Yakub, B. T., Tien,
J. W. and Kino, G. S., The nature of machining damage in brittle materials. Proc. R. Soc. London, Ser. A, 1983, 385, 461±475.
5. Lange, F. F., James, M. R. and Green, D. J., Determination of residual surface stresses caused by grinding in poly-crystalline Al2O3. J. Am. Ceram. Soc., 1983, 66, c16±c17.
6. Johnson-Walls, D., Evans, A. G., Marshall, D. B. and James, M. R., Residual stresses in machined ceramics. J. Am. Ceram. Soc., 1986, 69, 44±47.
7. Hockey, B. J., Plastic deformation on aluminum oxide by indentation and abrasion. J. Am. Ceram. Soc., 1971, 54, 223±231.
8. Majumdar, S., Kupperman, D. and Singh, J., Determina-tion of residual stresses in a SiC-Al2O3 composite using
neutron diraction. J. Am. Ceram. Soc., 1988, 71, 858± 863.
9. Matsuo, Y., Ogasawara, T., Kimura, S., Sato, S. and Yasuda, E., The eect of annealing on surface machining damage of alumina ceramics. J. Ceram. Soc. Jpn, Int. Ed., 1991, 99, 371±376.
10. Tuan, W. H. and Kuo, J. C., Eect of abrasive grinding on the strength and reliability of alumina. J. Euro. Ceram. Soc., 1998, 18, 799±806.
11. Samuel, S., Chandrasekar, S., Farris, T. N. and Licht, R. H., Eect of residual stresses on the fracture of ground ceramics. J. Am. Ceram. Soc., 1986, 72, 1960±1966. 12. Tuan, W. H. and Kuo, J. C., Eect of truing of diamond
wheel on the strength of alumina after abrasive grinding. J. Mater. Sci. Letter, 1997, 16, 806±808.
13. Weibull, W., A statistical distribution function of wide applicability. J. Appl. Mech., 1951, 18, 293±297.
14. Quirmbach, P., Wolf, M., Brook, R. J. and Hennicke, H. W., Development of microstructure during pressureless sintering of alumina. J. European Ceram. Soc., 1992, 10, 51±57.
15. Thompson, A. M., Chan, H. M. and Harmer, M. P., Crack healing and stress relaxation in Al2O3. J. Am.
Ceram. Soc., 1995, 78, 567±571.
16. Lange, F. F. and Radford, K. C., Healing of surface cracks in polycrystalline Al2O3. J. Am. Ceram. Soc., 1970,
53, 420±421.
17. Moatt, J. E., Plumbridge, W. J. and Hermann, R., High temperature crack annealing eects on fracture toughness of alumina and alumina-SiC composite. Brit. Ceram.-Trans., 1996, 95, 23±29.
