See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/253583431 Ring-on-ring strength measurements on rectangular glass slides Article in Journal of Materials Science · January 2007 DOI: 10.1007/s10853-006-1102-8 CITATIONS READS 13 1,504 4 authors , including: Jean-pierre Guin Sheldon Wiederhorn French National Centre for Scientific Research National Institute of Standards and Technology 72 PUBLICATIONS 1,221 CITATIONS 219 PUBLICATIONS 8,889 CITATIONS SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: subcritical crack growth near the fatigue limit View project ANR GLASS project: Glass behavior under laser induced shock loading conditions View project All content following this page was uploaded by Jean-pierre Guin on 14 February 2020. The user has requested enhancement of the downloaded file.
J Mater Sci (2007) 42:393–395 DOI 10.1007/s10853-006-1102-8 LETTER Ring-on-ring strength measurements on rectangular glass slides T. Fett Æ G. Rizzi Æ J. P. Guin Æ S. M. Wiederhorn Received: 30 August 2006 / Accepted: 2 October 2006 / Published online: 21 November 2006 � Springer Science+Business Media, LLC 2006 The ring-on-ring test [1–6] has been standardized and on the tensile surface are given in a normalised used extensively for strength measurements on glasses representation and ceramics. Whereas bend bars suffer from flaws at their edges that dominate the strength, the edges of r t ; r ¼ 3 F 4 p t 2 D t ; r ð m Þ ð 1 Þ carefully prepared circular disks for ring-on-ring tests almost never fail from their edges. For these speci- mens, the mechanical defects in the surface determine where F is the applied load, m is Poisson’s ratio, and t is their strength. the plate thickness. Very often, specimens are of interest which are not The results in terms of D t,r are plotted in Fig. 2a of a circular shape and yet are tested using the ring-on- along the x-axis, and in Fig. 2b along the y-axis. The ring configuration. The stress and strain distributions of stresses are almost constant in the range of x , y < r 1 these specimens can deviate strongly from that of the (for r 1 see Fig. 1b). The strong local stress peaks at the circular disk for which stress–strain relations are outer ring are caused by the concentrated contact available from literature [1]. This is the case for glass effects between ring and specimen. slides of rectangular shape. Figure 1a shows a slide of Figure 3a represents the biaxiality ratio along the 25 · 75 mm in dimension, which is loaded by two rings two symmetry axes. This ratio is found to be very close 11 mm and 22 mm in diameter. to r r / r t = 1, with maximum deviations of about 1%, i.e. In order to determine the stress distributions of such with sufficient accuracy. The test exhibits an equi- specimens, finite element computations were carried biaxial stress state within the inner ring. The influence out with 1 mm and 1.5 mm slide thickness. The of Poisson’s ratio is illustrated in Fig. 3b. resulting tangential stresses, r t , and radial stresses, r r , In the range of 0.2 £ m £ 0.25 (relevant for glass), the coefficients D t and D n (at x = y = 0) for the specially chosen geometry can be approximated as D t ffi 1 : 68 þ 1 : 12 m ð 2 Þ T. Fett � G. Rizzi ¨r Forschungszentrum Karlsruhe, Institut fu Materialforschung II, Karlsruhe, Germany D r ffi 1 : 666 þ 1 : 15 m ð 3 Þ T. Fett ( & ) Institut fu ¨r Keramik im Maschinenbau, Universita ¨t In an earlier paper [7], strength data of rectangular Karlsruhe, Haid-und-Neu-Str. 7, Karlsruhe 76131, Germany e-mail: theo.fett@ikm.uni-karlsruhe.de slides were computed with the well-known disk formula. For a disk-shaped test specimen the equi- J. P. Guin � S. M. Wiederhorn biaxial stresses in the inner ring, expressed by Eq. National Institute of Standards and Technology, (1), are [1, 2] Gaithersburg, MD, USA 123
394 J Mater Sci (2007) 42:393–395 Fig. 1 Ring-on-ring test for a) b) ( a ) rectangular glass slides (microscope slides), ( b ) y Thickness: t standard test on disks 2B=25 x 11 22 2r 1 2r 2 2W=75 2r 3 t Fig. 2 Normalised tangential 2.5 2.5 b) a) x=0 and radial stresses ( a ) along y=0 D D the x-axis, ( b ) along the y-axis 2 2 (for m = 0.25) D t D t 1.5 1.5 D r D r 1 1 0.5 0.5 0 0 ν =0.25 -0.5 -0.5 -15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15 x (mm) y (mm) D r ¼ D t ¼ ð 1 � m Þ 1 � ð r 1 = r 2 Þ 2 250 h at room temperature, while a second series of 48 � 2 ð 1 þ m Þ log ð r 1 = r 2 Þ ð 4 Þ ð r 3 = r 2 Þ 2 specimens was stored for 230 h at 90 � C. The speci- mens were cooled to room temperature and water was removed by drying the glass specimens with soft facial (for geometric data see Fig. 1b). By comparing Eq. (4) tissues. Only the polished surfaces were tested. The with the finite element results of Fig. 2, an appropriate strength data are plotted in Fig. 4 in a Weibull effective value of r 3 / r 2 can be determined for the representation. The Weibull parameters and 90% rectangular specimen. It results confidence intervals were determined according to [8, 9] (see Table 1.). Since the 90% intervals do not r 3 ; eff ¼ 1 : 57 r 2 ffi 1 : 38 B ð 5 Þ overlap, the difference in strength is significant. Possible explanations of the strength differences were discussed in [7]. Stress effects due to the gener- A commercial soda-lime glass with a high content of alkali and alkaline earth oxides was investigated in [7] ation of ion exchange layers and also crack healing (AR glass, Schott GmbH, Mainz) 1 . It consists (in wt%) effects were taken into account. Surface hydration consists of the interdiffusion of either hydrogen ions of 69% SiO 2 , 13% Na 2 O, 5% CaO, 4% Al 2 O 3 , 3% (H + ) or hydronium ions (H 3 O + ) with the Na + ions in MgO, 3% K 2 O, 2% BaO, and 1% B 2 O 3 and has a the glass. The H + /Na + exchange results in a tensile Poisson’s ratio of m = 0.22. stress in the hydration layer, because the H + ion is Specimens of 25 mm · 75 mm · 1 mm with their smaller than the Na + ion. In contrast to this, H 3 O + /Na + 25 mm · 75 mm faces polished were annealed for 5 h exchange leads to a compressive stress, because H 3 O + at 430 � C. Then, 50 specimens were stored in water for is larger than Na + . These stresses must affect the strength. 1 The use of commercial names is only for purposes of From the increased strengths of specimens stored at identification and does not imply endorsement by the National 90 � C, it can be concluded that compressive stresses Institute of Standards and Technology. 123
J Mater Sci (2007) 42:393–395 395 Fig. 3 ( a ) Ratio of the radial a) b) and tangential stresses, ( b ) 1.02 D x=y=0 x=0 D t influence of Poisson’s ratio on σ r / σ t 2 coefficients D t , D r 1 D r 0.98 y=0 D r /D t 1.95 0.96 0.94 1.9 0.92 ν =0.25 0.9 1.85 0.88 -6 -4 -2 0 2 4 6 0.18 0.2 0.22 0.24 0.26 0.28 0.3 y,x (mm) ν must be generated during ‘‘high-temperature’’ water lnln(1/(1-F)) 2 storage. In [7] the strengths were computed under the assumption of r 3, eff = B . This resulted in a compressive stress in the ion exchange layer of –2.4 GPa. From the 1 250h water 20°C evaluation of the finite element results presented before, a slightly reduced compressive stress of 0 –2.2 GPa can now be concluded. -1 230h water 90°C References -2 1. Ritter JE, Jakus K Jr, Batakis A, Bandyopadhyay N (1980) J Non-Cryst Sol 38 & 39:419 -3 2. Giovan MN, Sines G (1981) J Am Ceram Soc 64:68 3. Fessler H, Fricker DC (1984) J Am Ceram Soc 67:582 4. Solte ´sz U, Richter H, Kienzler R (1987) The concentric-ring -4 test and its application for determining the surface strength of ceramics, in High Tech Ceramics. Elsevier Science Publishers, Amsterdam, 149 -5 5. Adler, WF, Mihora, DJ (1992) Biaxial flexure testing: analysis 100 200 300 and experimental results. In: Bradt RC et al. (ed) Fracture σ c (MPa) mechanics of ceramics, vol 10. Plenum Press, New York, p 227 6. ASTM Standard C 1499–03 (2003) Monotonic equibiaxial Fig. 4 Strength data obtained from ring-on-ring tests in a flexural strength of advanced ceramics at ambient tempera- Weibull representation, squares: median values ture. American Society for Testing and Materials, West Conshohocken, PA 7. Fett T, Guin JP, Wiederhorn SM (2005) Fatigue Fract Engng Table 1 Weibull parameters and 90% confidence intervals (data Mater Struct 28:507 in brackets) of strength 8. Thoman DR, Bain LJ, Antle CE (1969) Technometrics 11:445 9. European Standard ENV 843–5, Advanced monolithic ceram- r 0 (MPa) m m corr ics - mechanical tests at room temperature - statistical analysis Water 20 � C 167.9 [156.0; 180.7] 3.43 [2.8; 4.0] 3.33 Water 90 � C 209.6 [196.8; 223.3] 4.07 [3.3; 4.8] 3.95 123 View publication stats View publication stats
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