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Journal of Shanghai Jiaotong University(Science) >

2018 , Vol. 23 >Issue 1: 182 - 189

DOI: https://doi.org/10.1007/s12204-018-1924-y

Non-Linearity of the Mirror Constant for Glasses Fractured in Flexure

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  • (1. University of Michigan - Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China; 2. ′ Ecole de Technologie Sup′erieure, Montreal, Canada)

Online published: 2018-02-01

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Abstract

Fractography relies on topographic features on the fracture surfaces to deduce the stress state of the failed component. Traditionally, fractographers assumed that the fracture strength of brittle materials was related to the reciprocal of the square root of the mirror radius linearly, in accordance with the empirical equation formally postulated by Orr in 1972. In this manuscript a novel analytical model to describe the dynamic behavior of elliptical cracks was derived on the basis of thermodynamic principles. Unlike Orr’s equation, the proposed model considered the effects of the plate thickness and it could be used to improve the strength prediction based on the plate’s geometry and material properties. To verify the validity of the model, 39 annealed, 2mm thick, soda-lime silicate glass plates were fractured by four-points bending test and the fracture surfaces were imaged by confocal laser microscope and carefully studied. Excellent agreement was observed between the experimental data and the proposed theoretical framework.

Key words： fractography; flexural strength; brittle; soda-lime silicate glass; mirror constant

Cite this article

MA Lingyue1 (马凌越), DUGNANI Roberto1*, MOULINS Anthony2 . Non-Linearity of the Mirror Constant for Glasses Fractured in Flexure[J]. Journal of Shanghai Jiaotong University(Science), 2018 , 23(1) : 182 -189 . DOI: 10.1007/s12204-018-1924-y

References

[1] ORR L. Practical analysis of fractures in glass windows[J]. Materials Research and Standards, 1972, 12(1):21-23. [2] American Society for Testing and Materials. Standardpractice for fractographic analysis of fracture mirrorsizes in ceramics and glasses: ASTM C1678-10 [S].West Conshohocken, PA: American Society for Testingand Materials, 2015. [3] QUINN G D. Guidelines for measuring fracture mirrors[J]. Fractography of Glasses and Ceramics V: CeramicTransactions, 2007, 199: 163-187. [4] JOSEPH C C, JOHN J M. Use of crack branchingdata for measuring near-surface residual stresses intempered glass [J]. Journal of the American CeramicSociety, 1989, 72(9): 1584-1587. [5] QUINN G D. NIST recommended practice guide: fractographyof ceramics and glasses: NIST SP-960-16 [S].Gaithersburg, MD: Nat. Inst. of Stand. Technol., 2007. [6] ABDEL-LATIF A, BRADT R, TRESSLER R. Dynamicsof fracture mirror boundary formation in glass[J]. International Journal of Fracture, 1977, 13(3):349-359. [7] AGNETTI S. Strength on cut edge and ground edgeglass beams with the failure analysis method [J]. FratturaEd Integrita??trutturale, 2013, 7(26): 31-40 (inItalian). [8] ALARC′ON O E, MEDRANO R E, GILLIS P P. Fractureof glass in tensile and bending tests [J]. Metallurgicaland Materials Transactions A, 1994, 25(5): 961-968. [9] ANSELMI F, MERLO A, BRUSCO G. Methodologiadi analisi frattografica dei parabrezza e caratterizzazionedella costante di sepecchio [C]//Proceeding ofConvegno IGF XIII Cassino 1997. 2008. [10] BALL M, LANDINI D, BRADT R, et al. Fracture mistregion in a soda-lime-silica float glass [J]. Fractographyof Ceramic and Metal Failures, 1984: 110-120. [11] BRITTON M. Glass as an engineering material. II.,1981, 12(6): 258-268. [12] CHOI S R, GYEKENYESI J P. Crack branching andfracture mirror data of glasses and advanced ceramics[J]. NASA/TM, 1998. [13] DUCKWORTH W, SHETTY D, ROSENFIELD A.Influence of stress gradients on the relationship betweenfracture stress and mirror size for float glass [J].Glass Technology, 1983, 24(5): 263-273. [14] DUGNANI R, ZEDNIK R. Flexural strength by fractographyin modern brittle materials [J]. Journal of theAmerican Ceramic Society, 2013, 96(12): 3908-3914. [15] GAUME O, PELLETIER S. Analysis of fracture featuresfor uni-axial bent glass plates [J]. Saint-GobainRecherche, Technical Document, 2013. [16] GULATI S, BAYNE J, POWELLW, et al. Mirror constantfor AMLCD glass [J]. American Ceramic SocietyBulletin, 2004, 83(5): 14-15. [17] HAN W T, TOMOZAWA M. Fractographic analysisof hydrothermally treated silica glass [J]. Journal ofnon-crystalline solids, 1993, 163(3): 309-314. [18] KERPER M, SCUDERI T. Relation of fracture stressto fracture pattern for glass rods of various diameters[J]. American Ceramic Society Bulletin, 1966, 45(12):1065-1066. [19] KIMS J, CHOI S J. AMLCD glass mirror constant andcrack flaw size in non-crack LCD panels [J]. Journal ofInformation Display, 2017, 18(1): 19-24. [20] KIRCHNER H P, CONWAY J. Comparison of theStress-Intensity and Johnson-and-Holloway Criteriafor Crack Branching in Rectangular Bars [J]. Journalof the American Ceramic Society, 1987, 70(8): 565-569. [21] KIRCHNER H P, KIRCHNER J W. Fracture mechanicsof fracture mirrors [J]. Journal of the American CeramicSociety, 1979, 62(3-4): 198-202. [22] KULP A B. Analysis of strength variation in glass dueto ion exchange [D]. Blacksburg: Department of MaterialsScience and Engineering, Virginia PolytechnicInstitute and State University, 2012. [23] LIN M H, PAN W W, CHENG P J, et al. The mirrorconstant of glass substrates by 4PB test [J]. SIDSymposium Digest of Technical Papers, 2014, 45(1):697-700. [24] LINDQVIST M, LEBET J P. Strength of glass determinedby the relation of the critical flaw to the fracturemirror [J]. Engineering Fracture Mechanics, 2014,119(3): 43-52. [25] MECHOLSKY J, GONZALEZ A, FREIMAN S. Fractographicanalysis of delayed failure in soda-lime glass[J]. Journal of the American Ceramic Society, 1979,62(11-12): 577-580. [26] MECHOLSKY J, RICE R. Fractographic analysis ofbiaxial failure in ceramics [J]. Fractography of Ceramicand Metal Failures, 1984, 185-193. [27] MECHOLSKY J, RICE R, FREIMAN S. Predictionof fracture energy and flaw size in glasses from measurementsof mirror size [J]. Journal of the AmericanCeramic Society, 1974, 57(10): 440-443. [28] NORTON M, ATKINSON B. Stress-dependent morphologicalfeatures on fracture surfaces of quartz andglass [J]. Tectonophysics, 1981, 77(3-4): 283-295. [29] PISARENKO G, KOZUB Y I, SOLUYANOV V, et al.Determining the strength of brittle materials by meansof fracture-surface studies [J]. Strength of Materials,1975, 7(7): 793-797. [30] QUINN J B. Extrapolation of fracture mirror andcrack-branch sizes to large dimensions in biaxialstrength tests of glass [J]. Journal of the American CeramicSociety, 1999, 82(8): 2126-2132. [31] RUGGERO S A. Quantitative fracture analysis ofetched soda-lime silica glass: Evaluation of theblunt crack hypothesis [D]. Gainesville: University ofFlorida, 2003. [32] SCHWARTZ T A. The fractography of inorganic glass[D]. Cambridge: Department of Materials Science andEngineering, Massachusetts Institute of Technology,1977. [33] SHAND E. Breaking stress of glass determined fromdimensions of fracture mirrors [J]. Journal of theAmerican Ceramic Society, 1959, 42(10): 474-477. [34] SHAND E B. Strength of glass—the Griffith methodrevised [J]. Journal of the American Ceramic Society,1965, 48(1): 43-49. [35] TERAO N. Sur une relation entre la r′esistance `a larupture et le foyer d’eclatement du verre [J]. Journalof the Physical Society of Japan, 1953, 8(4): 545-549(in French). [36] ZACCARIA M, OVEREND M. Validation of a simplerelationship between the fracture pattern and the fracturestress of glass [C]//Proceedings of the EngineeredTransparency International Conference at Glasstec.D¨usseldorf, Germany: Mendeley, 2012: 1-9. [37] FREUND L B. Dynamic fracture mechanics [M]. Cambridge:Cambridge university press, 1998. [38] ABDEL-LATIF A I A, TRESSLER R E, BRADT RC. Fracture mirror formation in single crystal alumina[J]. Applications and Non-metals, 1977, 3: 933-939. [39] MOTT N. Fracture of metals: some theoretical considerations[J]. Engineering, 1948, 165: 16-18. [40] BANSAL G K. On fracture mirror formation in glassand polycrystalline ceramics [J]. Philosophical Magazine,1977, 35(4): 935-944. [41] American Society for Testing and Materials. Standardtest methods for strength of glass by flexure (determinationof modulus of rupture): ASTM C158-02 [S].West Conshohocken, PA: American Society for Testingand Materials, 2012. [42] HULL D. Fractography: observing, measuring andinterpreting fracture surface topography [M]. Cambridge:Cambridge University Press, 1999. [43] LOPEZ-CEPERO J, DE ARELLANO-LOPEZ A,QUISPE-CANCAPA J, et al. Confocal microscopy forfractographical surface characterization of ceramics [J].Microscopy and Analysis, 2005, 19(5): 13-15. [44] DUGNANI R, ZEDNIK R J. Geometric description offracture surface features in isotropic brittle solids [J].Engineering Fracture Mechanics, 2016, 165: 87-97. [45] NEWMAN J C, RAJU I S. Stress Intensity FactorEquations for Cracks in Three-Dimensional FiniteBodies Subjected to Tension and Bending Loads [J].Astm Stp, 1983. [46] WIEDERHORN S M. Fracture surface energy of glass[J]. Journal of the American Ceramic Society, 2010,52(2): 99-105. [47] DWIVEDI P, GREEN D J. Indentation crack - shapeevolution during subcritical crack growth [J]. Journalof the American Ceramic Society, 1995, 78(5): 1240-1246. [48] SHERMAN D, BE’ERY I. Shape and energies of a dynamicallypropagating crack under bending [J]. Journalof Materials Research, 2003, 18(10): 2379-2386. [49] SNEDDON I N. Fourier transformations [M]. NewYork: McGraw-Hill, 1951. [50] FINEBERG J, MARDER M. Instability in dynamicfracture [J]. Physical Review Letters, 1991, 67(4): 457-460. [51] YOFFE E H. The moving Griffith crack [J]. The PhilosophicalMagazine, 1951, 42(7): 739-750. [52] MECHOLSKY J J, FREIMAM SW, RICE RW. Fracturesurface analysis of ceramics [J]. Journal of MaterialsScience, 1976, 11(7): 1310-1319.
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