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Archive of Applied Mechanics

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26-09-2022 | Original

Analytical description of unstable, rugose, circular cracks in brittle solids

Authors: Lingyue Ma, Roberto Dugnani

Published in: Archive of Applied Mechanics | Issue 12/2022

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Abstract

This manuscript presents an improvement to the analytical model for unstable, circular cracks with rugose crack-fronts propagating in infinite, brittle solids including the velocity-dependent, fracture surface energy. Extensive testing and fracture surface characterization on silicate glass, glassy carbon, single-crystal silicon, and PMMA plates were conducted, and the results were compared to the model’s predictions. For each material, the fracture surface characteristics were extracted from profilometry scans, and the crack speed was estimated from fractographic features. The estimated crack speed for the materials considered was found to be in excellent agreement with the experimental observations. The model was also used to predict the formation of the ‘mirror-mist’ boundary in silicate glasses and glass–ceramics. It was found that using the proposed theoretical framework, the mirror constants were underestimated by only approximately 15%. The formation of mist could not be investigated for PMMA and single-crystal silicon as the mechanism of mist formation was inconsistent with the assumptions made in this work.

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Fineberg’s \(\Gamma \) for SLG was plotted with the wrong magnitude, but when recalculated the magnitude was in agreement with both Miao & Tippur’s and the one in this work.

Abdel-Latif, A., Bradt, R., Tressler, R.: Dynamics of fracture mirror boundary formation in glass. Int. J. Fract 13, 349–359 (1977)CrossRef

Abrisa Technologies.: Specialty Glass Materials Products & Specifications 10/21 (2021)

Amaro, C.M.G.: Dynamic fracture in brittle amorphous materials : Dissipation mechanisms and dynamically-induced microcracking in PMMA. Ecole Polytechnique X (2009)

Bansal, G.K.: On fracture mirror formation in glass and polycrystalline ceramics. Philos. Mag. 35, 935–944 (1977). https://doi.org/10.1080/14786437708232635CrossRef

Beom, H.G., Earmme, Y.Y.: Axisymmetric crack with a slightly non-flat surface. Int J Fract 58, 115–136 (1992). https://doi.org/10.1007/BF00019972CrossRef

Bergkvist, H.: An investigation of axisymmetric crack propagation. ASTM STP 627 Fast Fracture and Crack Arrest: 312–335 (1977)

Bisoi, A.K., Mishra, J.: On calculation of fractal dimension of images. Pattern Recogn. Lett. 22, 631–637 (2001)CrossRefMATH

Bowden, F., Brunton, J., Field, J., Heyes, A.: Controlled fracture of brittle solids and interruption of electrical current. Nature 216, 38 (1967)CrossRef

Carpinteri, A., Spagnoli, A., Vantadori, S., Viappiani, D.: Influence of the crack morphology on the fatigue crack growth rate: A continuously-kinked crack model based on fractals. Eng. Fract. Mech. 75, 579–589 (2008). https://doi.org/10.1016/j.engfracmech.2007.05.007CrossRef

10.

Charkaluk, E., Bigerelle, M., Iost, A.: Fractals and fracture. Eng. Fract. Mech. 61, 119–139 (1998)CrossRef

11.

Chiarelli, M., Frediani, A.: A computation of the three-dimensional J-integral for elastic materials with a view to applications in fracture mechanics. Eng. Fract. Mech. 44, 763–788 (1993). https://doi.org/10.1016/0013-7944(93)90205-7CrossRef

12.

Congleton, J., Denton, B.K.: Dynamic fracture toughness experiment. University of Newcastle on Tyne to U. S, Army European Research Office (1975)

13.

Cotterell, B., Rice, J.: Slightly curved or kinked cracks. Int. J. Fract. 16, 155–169 (1980)CrossRef

14.

Craggs, J.: The growth of a disk-shaped crack. Int. J. Eng. Sci. 4, 113–124 (1966)CrossRefMATH

15.

Dériano, S., Jarry, A., Rouxel, T., Sangleboeuf, J.-C., Hampshire, S.: The indentation fracture toughness (KC) and its parameters: the case of silica-rich glasses. J. Non-Cryst. Solids 344, 44–50 (2004)CrossRef

16.

Dobbs, H.: Vitreous carbon and the brittle fracture of amorphous solids. J. Phys. D: Appl. Phys. 7, 24 (1974)CrossRef

17.

Dugnani, R., Ma, L.: Energy release rate of moving circular-cracks. Eng. Fract. Mech. 213, 118–130 (2019). https://doi.org/10.1016/j.engfracmech.2019.03.044CrossRef

18.

Fineberg, J.: The dynamics of rapidly moving tensile cracks in brittle amorphous material. In: Dynamic Fracture Mechanics, pp. pp 104–146. World Scientific (2006)

19.

Fineberg, J., Marder, M.: Instability in dynamic fracture. Phys. Rep. 313, 1–108 (1999)MathSciNetCrossRef

20.

Freund, L.: Crack propagation in an elastic solid subjected to general loading—I. Constant rate of extension. J. Mech. Phys. Solids 20, 129–140 (1972)CrossRefMATH

21.

Freund, L.B.: Dynamic Fracture Mechanics. Cambridge University Press (1998)MATH

22.

Hakimelahi, B., Soltani, N.: 3D J-integral evaluation using the computation of line and surface integrals. Fatigue Fract. Eng. Mater. Struct. 33, 661–672 (2010). https://doi.org/10.1111/j.1460-2695.2010.01478.xCrossRef

23.

Harding, D.S., Oliver, W.C., Pharr, G.M.: Cracking During Nanoindentation and its Use in the Measurement of Fracture Toughness. MRS Proc. 356, 663 (1994). https://doi.org/10.1557/PROC-356-663CrossRef

24.

Hutchinson, J.W.: Crack tip shielding by micro-cracking in brittle solids. Acta Metall 35, 1605–1619 (1987). https://doi.org/10.1016/0001-6160(87)90108-8CrossRef

25.

Jiao, D., Qu, R.T., Zhang, Z.F.: Macroscopic bifurcation and fracture mechanism of polymethyl methacrylate. Adv Eng Mater 17, 1454–1464 (2015). https://doi.org/10.1002/adem.201500021CrossRef

26.

Kerkhof, F.: Bruchvorgange in glasern, verlag der deutschen glastech. Gesellsch, Frankfurt (1970)

27.

Kostrov, B.: The axisymmetric problem of propagation of a tension crack. J. Appl. Math. Mech. 28, 793–803 (1964)MathSciNetCrossRefMATH

28.

Lo, C.Y., Nakamura, T.: Computational analysis of dynamically propagating cracks in axisymmetric solids. Int. J. Fract. 70, 217–235 (1995)CrossRef

29.

Ma, L., Djurdjanovic, D., Dugnani, R.: Statistical accuracy of fractographic estimation in silicate glasses with design of experiments and pairwise T-tests. Eng. Failure Anal. 116, 104699 (2020). https://doi.org/10.1016/j.engfailanal.2020.104699CrossRef

30.

Ma, L., Dugnani, R., Zednik, R.: Quantifying the accuracy of fractographic strength estimates in silicate glasses. J. Eur. Ceram Soc. 38, 3643–3649 (2018)CrossRef

31.

Ma, L., Moulins, A., Dugnani, R.: Analytical description of fracture features in single crystal silicon. Eur. J. Mech. A. Solids 87, 104203 (2021). https://doi.org/10.1016/j.euromechsol.2020.104203MathSciNetCrossRefMATH

32.

Ma, L., Sun, H., Dugnani, R.: Shape evolution of unstable, flexural cracks in brittle materials. J. Mater. Eng. Perform. 29, 1311–1320 (2020). https://doi.org/10.1007/s11665-020-04657-5CrossRef

33.

Mandelbrot, B.B., Passoja, D.E., Paullay, A.J.: Fractal character of fracture surfaces of metals. Nature 308, 721–722 (1984). https://doi.org/10.1038/308721a0CrossRef

34.

Mecholsky, J., Rice, R., Freiman, S.: Prediction of fracture energy and flaw size in glasses from measurements of mirror size. J. Am. Ceram. Soc. 57, 440–443 (1974)CrossRef

35.

Mecholsky, J.J., Freimam, S.W., Rice, R.W.: Fracture surface analysis of ceramics. J. Mater. Sci. 11, 1310–1319 (1976)CrossRef

36.

Mecholsky, J.J., Freiman, S.W.: Relationship between fractal geometry and fractography. J. Am. Ceram Soc. 74, 3136–3138 (1991)CrossRef

37.

Mecholsky, J.J., Plaia, J.R.: Fractal analysis on fracture surfaces of glass using replication techniques. J. Non-Cryst. Solids 146, 249–255 (1992). https://doi.org/10.1016/S0022-3093(05)80498-3CrossRef

38.

Mecholsky, J.J. Jr.: Fractal analysis and fractography: What can we learn that’s new? In: Key Engineering Materials, pp. 145–153. Trans Tech Publ (2009)

39.

Miao, C., Tippur, H.V.: Dynamic fracture of soda-lime glass plates studied using two modified Digital Gradient Sensing techniques. Eng. Fract. Mech. 232, 107048 (2020)CrossRef

40.

Moulins, A., Ma, L., Dugnani, R., Zednik, R.J.: Dynamic crack modeling and analytical stress field analysis in single-crystal silicon using quantitative fractography. Theor. Appl. Fract. Mech. 102693 (2020)

41.

Newman, J., Raju, I.: Stress-intensity factor equations for cracks in three-dimensional finite bodies. In: Fracture Mechanics: Fourteenth Symposium—Volume I: Theory and Analysis. ASTM International (1983)

42.

Omer, N., Yosibash, Z.: On the path independency of the point-wise J integral in three-dimensions. Int. J. Fract. 136, 1–36 (2005). https://doi.org/10.1007/s10704-005-3934-7CrossRefMATH

43.

Rabinovitch, A., Frid, V., Bahat, D.: Wallner lines revisited. AIP (2006)

44.

Richter, H., Kerkhof, F.: Stress wave fractography. In: Fractography of glass, pp. 75–109. Springer (1994)

45.

Rigby, R.H., Aliabadi, M.H.: Decomposition of the mixed-mode J-integral—revisited. Int. J. Solids Struct. 35, 2073–2099 (1998). https://doi.org/10.1016/S0020-7683(97)00171-6CrossRefMATH

46.

Schardin, H.: Velocity effects in fracture. In: Averbach, B.L. (ed.) Fracture, pp. 297–330. Wiley (1959)

47.

Sharon, E., Gross, S.P., Fineberg, J.: Energy dissipation in dynamic fracture. Phys. Rev. Lett. 76, 2117 (1996)CrossRef

48.

Silling, S., Bobaru, F., Wang, Y.: Three-dimensional simulation of fractographic features with multiscale peridynamics. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States) (2015)

49.

Smith, R., Mecholsky, J., Jr.: Application of atomic force microscopy in determining the fractal dimension of the mirror, mist, and hackle region of silica glass. Mater. Charact. 62, 457–462 (2011)CrossRef

50.

Standard test methods for strength of glass by flexure (determination of modulus of rupture). ASTM International (2017)

51.

Swenson, D.: Derivation of the near-tip stress and displacement fields for a moving crack without using complex functions. Eng. Fract. Mech. 24, 315–321 (1986)CrossRef

52.

Tsai, Y.M.: Exact stress distribution, crack shape and energy for a running penny-shaped crack in an infinite elastic solid. Int. J. Fract. 9, 157–169 (1973)CrossRef

53.

Weerasooriya, T., Moy, P., Casem, D., Cheng, M., Chen, W.: Fracture toughness for PMMA as a function of loading rate. In: Proceedings of the 2006 SEM Annual Conference & Exposition on Experimental and Applied Mechanics (2006)

54.

Winkler, S., Senf, H., Rothenhausler, H.: High velocity fracture investigation in alumina. Ceram. Trans. 17, 165–183 (1990)

55.

Xie, H., Sanderson, D.J.: Fractal effects of crack propagation on dynamic stress intensity factors and crack velocities. Int. J. Fract. 74, 29–42 (1996). https://doi.org/10.1007/BF00018573CrossRef

56.

Zhang, Z., Zheng, S., Zhou, F.: Dynamic crack propagation experiment in brittle PMMA. Optoelectron. Adv. Mater.-Rap. Commun. 8, 937–942 (2014)

57.

Zhao, J., Bradt, R., Walker, P., Jr.: The fracture toughness of glassy carbons at elevated temperatures. Carbon 23, 15–18 (1985)CrossRef

58.

Zimmermann, C., Schönert, K.: Microscopic observation of the tips of fast running cracks in PMMA. J. Mech. Phys. Solids 34, 319–331 (1986). https://doi.org/10.1016/0022-5096(86)90023-2CrossRef

Title: Analytical description of unstable, rugose, circular cracks in brittle solids
Authors: Lingyue Ma
Roberto Dugnani
Publication date: 26-09-2022
Publisher: Springer Berlin Heidelberg
Published in: Archive of Applied Mechanics / Issue 12/2022
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI: https://doi.org/10.1007/s00419-022-02272-5

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