Abstract
The semi-circular specimen under three-point bending loading (SCB specimen) may be used for determining mode I and mixed-mode (I and II) fracture toughness for brittle materials; this subject is covered in several references. This paper presents T-stress and stress intensity factor for SCB specimen in mode I and mixed-mode (I and II), exploring direct uses of finite element method to calculate those parameters. The commercial FE software ABAQUS was used to model the SCB specimen. Several cases including different crack lengths for investigating mode I, various crack angles for mixed-mode (I and II) and T-stress are presented. Since SCB specimen is loaded in bending, a comparison of the SCB and SE (B) specimen (ASTM E399-08 standard) was performed for mode I, discussing dimensions and amount of material involved. Finally, the result obtained from the presented finite element model are compared with results from the literature.
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References
Adamson, R.M., Dempsey, J.P., Mulmule, S.V.: Fracture analysis of semi-circular and semi-circular-bend geometries. Int. J. Fract. 77(3), 213–222 (1996)
Lim, I.L., Johnston, I.W., Choi, S.K.: Stress intensity factors for semi-circular specimens under three-point bending. Eng. Fract. Mech. 44, 363–382 (1993)
Chong, K.R., Kuruppu, M.D.: New specimen for fracture toughness determination of rock and other materials. Int. J. Fract. 13–25 (1984)
Whittaker, B.N., Singh, R.N., Sun, G.X.: Rock Fracture Mechanics-Concepts Design and Applications. Elsevier, Amsterdam (1992)
Sun, G.X., Whittaker, B.N., Singh, R.N.: Use of the Brazilian disk test for determining the mixed-mode I-II fracture toughness envelope of rock. In: Proceedings of International Conference on Mechanics of Jointed and Faulted Rocks, Austria, pp. 447–454 (1990)
Chong, K.P., Kuruppu, M.D., Kuszmaul, J.S.: Fracture toughness determination of rocks with core-based specimens SEM/RILEM. International Conference on Fracture of Concrete and Rock, Texas, pp. 13–25 (1987)
Ayatollahi, M.R., Aliha, M.R.M., Hassani, M.M.: Mixed mode brittle fracture in PMMA-an experimental study using SCB specimens. Mater. Sci. Eng. A 417(1–2), 348–356 (2006)
Aliha, M.R.M., Ayatollahi, M.R., Akbardoost, J.: Typical upper bound-lower bound mixed mode fracture resistance envelopes for rock material. Rock Mech. Rock Eng. 45(1), 65–74 (2012)
Alih, M.R.M., Ayatollahi, M.R., Smith, D.J., Pavier, M.J.: Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading. Eng. Fract. Mech. 77(11), 2200–2212 (2010)
Xie, Yousheng, Cao, Ping, Jin, Jin, Wang, Min: Mixed mode fracture analysis of semi-circular bend (SCB) specimen: a numerical study based on extended finite element method. Comput. Geotech. 82, 157–172 (2017)
“Standard Test Method for Measurement of Fracture Toughness,” ASTM E 1820, ASTM International, West Conshohocken, PA (2015)
Williams, M.L.: On the stress distribution at the base of a stationary crack. J. Appl. Mech. 24, 109–114 (1957)
Yehia, N.A.B., Shephard, M.S.: On the effect of quarter-point element size on fracture criteria. Int. J. Numer. Meth. Eng. 21, 1911–1924 (1985)
Lim, I.L., Johnston, I.W., Choi, S.K.: Comparison between various displacement-based stress intensity factor computation techniques. Int. J. Fract. 58, 193–210 (1992)
Chan, S.K., Tuba, I.S., Wilson, W.K.: On the finite element method in linear fracture mechanics. Eng. Fract. Mech. 2(1), 1–17 (1970)
Abaqus, User’s Manual 6.14, Pawtucket, RI, USA: Pawtucket, RI, USA (2016)
Davenport, J.C.W., Smith, D.J.: A study of superimposed fracture modes I, II and III on PMMA. Fatigue Fract. Eng. Mater. Struct. 16, 1125 (1993)
Chong, K.P., Kuruppu, M.D.: New method to determine the fracture toughness of rocks and oil shale. In: SME-AIME Fall Meeting Denver, Colorado, vol. 278, pp. 1853–1857 (1984)
Lim, I.L., Johnston, W.: Stress intensity factors for semi-circular specimens under three-point bending. Eng. Fract. Mech. 44(3), 363–382 (1993)
Webb, J.E., Widjaja, S.: R-curve behavior in porous cordierite honeycombs. Ceram. Eng. Sci. Proc. 7(29), 339–348 (2009)
Chong, K.P., Kuruppu, M.D.: A new specimen for mixed-mode fracture investigation of geomaterials. Eng. Fract. Mech. 30, 701–712 (1988)
Quintana-Alonso, I., Mai, S.P., Fleck, N.A., Oakes, D.C.H., Twigg, M.V.: The fracture toughness of a cordierite square lattice. Acta Mater. 58, 201–207 (2010)
Huang, J.S., Chiang, M.S.: Effects of microstructure, specimen and loading geometries on KIc of brittle honeycombs. Eng. Fract. Mech. 54(6), 813–821 (1996)
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Shahabi, E., de Castro, P.M.S.T. (2019). Analysis of the Semi-circular Bend (SCB) Specimen: Finite Element Method Determination of T-stress, KI and KII. In: Silva, L. (eds) Materials Design and Applications II. Advanced Structured Materials, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-030-02257-0_27
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DOI: https://doi.org/10.1007/978-3-030-02257-0_27
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