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http://dx.doi.org/10.12989/cac.2017.20.1.039

Direct and indirect methods for determination of mode I fracture toughness using PFC2D  

Sarfarazi, Vahab (Department of Mining Engineering, Hamedan University of Technology)
Haeri, Hadi (Department of Civil Engineering, Aria University of Sciences and Sustainability)
Shemirani, Alireza Bagher (Department of Civil Engineering, SADRA Institute of Higher Education)
Publication Information
Computers and Concrete / v.20, no.1, 2017 , pp. 39-47 More about this Journal
Abstract
In this paper, mode I fracture toughness of rock was determined by direct and indirect methods using Particle Flow Code simulation. Direct methods are compaction tension (CT) test and hollow centre cracked quadratic sample (HCCQS). Indirect methods are notched Brazilian disk (NBD) specimen, the semi-circular bend (SCB) specimen, hollow centre cracked disc (HCCD), the single edge-notched round bar in bending (SENRBB) specimen and edge notched disk (END). It was determined that which one of indirect fracture toughness values is close to direct one. For this purpose, initially calibration of PFC was undertaken with respect to data obtained from Brazilian laboratory tests to ensure the conformity of the simulated numerical models response. Furthermore, the simulated models in five introduced indirect tests were cross checked with the results from direct tests. By using numerical testing, the failure process was visually observed. Discrete element simulations demonstrated that the macro fractures in models are caused by microscopic tensile breakages on large numbers of bonded discs. Mode I fracture toughness of rock in direct test was less than other tests results. Fracture toughness resulted from semi-circular bend specimen test was close to direct test results. Therefore semi-circular bend specimen can be a proper test for determination of Mode I fracture toughness of rock in absence of direct test.
Keywords
tensile strength; direct test; flexural test; double punch tensile test and ring test;
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1 Rajabi, M., Soltani, N. and Eshraghi, I. (2016), "Effects of temperature dependent material properties on mixed mode crack tip parameters of functionally graded materials", Struct. Eng. Mech., 58(2), 144-156.
2 Ramadoss, P. and Nagamani, K. (2013), "Stress-strain behavior and toughness of high-performance steel fiber reinforced concrete in compression", Comput. Concrete, 11(2), 55-65.
3 Sato, K. (2006), "Fracture toughness evaluation based on tensionsoftening model and its application to hydraulic fracturing", Pure Appl. Geophys., 163(5), 1073-1089.   DOI
4 Shiryaev, A.M. and Kotkis, A.M. (1982), "Methods for determining fracture toughness of brittle porous materials", Industr. Labor., 48(9), 917-918.
5 Singh, R.N. and Sun, G.X. (1990), "A numerical and experimental investigation for determining fracture toughness of welsh limestone", Min. Sci. Technol., 10(1), 61-70.   DOI
6 Suresh, S. and Shih, C.F., Morrone, A. and O'Dowd, N.P. (1990), "Mixed-mode fracture toughness of ceramic materials", J. Am. Ceram. Soc., 73(5), 1257-1267.   DOI
7 Tutluoglu, L. and Keles, C. (2011), "Mode I fracture toughness determination with straight notched disk bending method", J. Rock Mech. Min. Sci., 48(8), 1248-1261.   DOI
8 Zhou, Y.X., Xia, K., Li, X.B., Li, H.B., Ma, G.W., Zhao, J., Zhou, Z.L. and Dai, F. (2012), "Suggested methods for determining the dynamic strength parameters and mode-I fracture toughness of rock materials", J. Rock Mech. Min. Sci., 49, 105-112.   DOI
9 Potyondy, D.O., Cundall, P.A. and Lee, C. (1996), "Modeling of rock using bonded assemblies of circular particles", Proceedings of 2nd North American Rock Mechanics Symposium, Montreal, Vancouver.
10 Mohammad, A. (2016), "Statistical flexural toughness modeling of ultra high performance concrete using response surface method", Comput. Concrete, 17(4), 33-39.
11 Molenar, A.A.A., Scarpas, A., Liu, X. and Erkens, S.M.J.G. (2002), "Semi-circular bending test: Simple but useful?", J. Assoc. Asph. Pav. Technol., 71, 794-815.
12 Obara, Y., Kuruppu, M. and Kataoka, M. (2010), "Determination of fracture toughness of anisotropic rocks under water vapour pressure by semi-circular bend test", Proceedings of the Mine Planning and Equipment Selection, Victoria, Australia.
13 Ouchterlony, F. (1981), Extension of the Compliance and Stress Intensity Formulas for the Single Edge Crack Round Bar in Bending, ASTM STP 745.
14 Obara, Y., Sasaki, K. and Yoshinaga, T. (2007), "Estimation of fracture toughness of rocks under water vapour pressure by semi-circular bend (SCB) test", J. MMIJ, 123(4-5), 145-151.   DOI
15 Obara, Y., Yoshinaga, T. and Hirata, A. (2009), "Fracture toughness in mode I and II of rock under water vapour pressure", Proceedings of the ISRM Regional Symposium EUROCK, Cavtat, Italy.
16 Ouchterlony, F. (1980), A New Core Specimen for the Fracture Toughness Testing of Rock, Swedish Detonic Research Foundation Report, Stockholm, Sweden.
17 Ouchterlony, F. (1986), "Suggested methods for determining the fracture toughness of rock", J. Rock Mech. Min. Sci. Geo-Mech. Abstr., 25(1), 71-96.
18 Ouchterlony, F. (1988), "Suggested methods for determining the fracture toughness of rock", J. Rock Mech. Min. Sci. Geomech. Abstr., 25(2), 71-96.
19 Pan, B., Gao, Y. and Zhong, Y. (2014), "Theoretical analysis of overlay resisting crack propagation in old cement concrete pavement", Struct. Eng. Mech., 52(4), 167-181.
20 Potyondy DO, Cundall PA (2004), "A bonded-particle model for rock", J. Rock Mech. Min. Sci., 41(8), 1329-1364.   DOI
21 Lee, S. and Chang, Y. (2015), "Evaluation of RPV according to alternative fracture toughness requirements", Struct. Eng. Mech., 53(6), 1271-1286.   DOI
22 Kataoka, M., Hashimoto, A., Sato, A. and Obara, Y. (2012), "Fracture toughness of anisotropic rocks by semi-circular bend (SCB) test under water vapor pressure", Proceedings of the 7th ARMS, Seoul, Korea, October.
23 Kataoka, M., Obara, Y. and Kuruppu, M. (2011), "Estimation of fracture toughness of anisotropic rocks by SCB test and visualization of fracture by means of X-ray CT", Proceedings of the 12th ISRM International Congress, Beijing, China, October.
24 Kequan, Y.U. and Zhoudao, L.U. (2015), "Influence of softening curves on the residual fracture toughness of post-fire normalstrength concrete", Comput. Concrete, 15(2), 102-111.
25 Khan, K. and Al-Shayea, N.A. (2000), "Effect of specimen geometry and testing method on mixed I-II fracture toughness of a limestone rock from Saudi Arabia", Rock Mech. Rock Eng., 33(3), 179-206.   DOI
26 Kuruppu, M.D., Obara, Y., Ayatollahi, M.R., Chong, K.P. and Funatsu, T. (2014), "ISRM-suggested method for determining the mode I static fracture toughness using semi-circular bend specimen", Rock Mech. Rock Eng., 47, 267-274.   DOI
27 Lim, I.L., Johnston, I.W. and Choi, S.K. (1993), "Stress intensity factors for semi-circular specimens under three-point bending", Eng. Fract. Mech., 44(3), 363-382.   DOI
28 Lim, I.L., Johnston, I.W., Choi, S.K. and Boland, J.N. (1994), "Fracture testing of a soft rock with semi-circular specimens under three-point loading, part 1-mode I", J. Rock Mech. Min. Sci., 31(3), 185-197.
29 Maccagno, T.M. and Knott, J.F. (1989), "The fracture behaviour of PMMA in mixed modes I and II", Eng. Fract. Mech., 34(1), 65-86.   DOI
30 Mahajan, R.V. and Ravi-Chandar, K. (1989), "An experimental investigation of mixed-mode fracture", J. Fract., 41(4), 235-252.   DOI
31 Aliha, M.R., Ayatollahi, M.R. and Akbardoost, M.R.J. (2012b), "Typical upper bound-lower bound mixed mode fracture resistance envelopes for rock material", Rock Mech. Rock Eng., 45(1), 65-74.   DOI
32 Akbas, S. (2016), "Analytical solutions for static bending of edge cracked micro beams", Struct. Eng. Mech., 59(3), 66-78.
33 Aliha, M.R. and Ayatollahi, M.R. (2013), "Two-parameter fracture analysis of SCB rock specimen under mixed mode loading", Eng. Fract. Mech., 103, 115-123.   DOI
34 Aliha, M.R. and Ayatollahi, M.R. (2014b), "Rock fracture toughness study using cracked chevron notched Brazilian disc specimen under pure modes I and II loading-a statistical approach", Theor. Appl. Fract. Mech., 69, 17-25.   DOI
35 Aliha, M.R., Ayatollahi, M.R. and Pakzad, R. (2008), "Brittle fracture analysis using a ring-shape specimen containing two angled cracks", J. Fract., 153(1), 63-68.   DOI
36 Aliha, M.R., Bahmani, A. and Akhondi, S. (2015a), "Determination of mode III fracture toughness for different materials using a new designed test configuration", Mater. Des., 86, 863-871.   DOI
37 Aliha, M.R., Bahmani, A. and Akhondi, S. (2015b), "Numerical analysis of a new mixed mode I/III fracture test specimen", Eng. Fract. Mech., 134, 95-110.   DOI
38 Aliha, M.R.M., Sistaninia, M., Smith, D.J., Pavier, M.J., Ayatollahi, M.R. (2012a), "Geometry effects and statistical analysis of mode I fracture in guiting limestone", J. Rock Mech. Min. Sci., 51, 128-135.   DOI
39 Aliha, M.R., Hosseinpour, G.R. and Ayatollahi, M.R. (2013), "Application of cracked triangular specimen subjected to threepoint bending for investigating fracture behavior of rock materials", Rock Mech. Rock Eng., 46(5), 1023-1034.   DOI
40 Aliha, M.R., Pakzad, R. and Ayaollahi, M.R. (2014a), "Numerical analyses of a cracked straight-through flattened Brazilian disk specimen under mixed-mode loading", J. Eng. Mech., 140(1), 219-224.   DOI
41 Amrollahi, H., Baghbanan, A. and Hashemolhosseini, H. (2011), "Measuring fracture toughness of crystalline marbles under modes I and II and mixed mode I-II loading conditions using CCNBD and HCCD specimens", J. Rock Mech. Min. Sci., 48(7), 1123-1134.   DOI
42 Atkinson, B.K. (1987), Fracture Mechanics of Rock, Academic Press, London, U.K.
43 Atkinson, C., Smelser, R.E. and Sanchez, J. (1982), "Combined mode fracture via the cracked Brazilian disc test", J. Fract., 18(4), 279-291.
44 Ayatollahi, M.R. and Alborzi, M.J. (2013), "Rock fracture toughness testing using SCB specimen", Proceedings of the 13th International Conference on Fracture, Beijing, China, June.
45 Banks-Sills, L. and Bortman, Y. (1986), "A mixed mode fracture specimen: Analysis and testing", J. Fract., 30(3), 181-201.   DOI
46 Barker, L.M. (1977), "A simplified method for measuring plane strain fracture toughness", Eng. Fract. Mech., 9(2), 361-369.   DOI
47 Chong, K.P., Kuruppu, M.D. and Kuszmaul, J.S. (1987), "Fracture toughness determination of layered materials", Eng. Fract. Mech., 28(1), 43-54.   DOI
48 Buchholz, F.G., Pirro, P.J.M., Richard, H.A. and Dreyer, K.H. (1987), "Numerical and experimental mixed-mode analysis of a compact tension-shear-specimen", Proceedings of the 4th International Conference Numerical Methods in Fracture Mechanics, Pineridge Press.
49 Chang, S.H., Lee, C.I. and Jeon, S. (2002), "Measurement of rock fracture toughness under modes I and II and mixed-mode conditions by using disc- type specimen", Eng. Geol., 66(1), 9-97.
50 Chong, K.P. and Kuruppu, M.D. (1984), "New specimen for fracture toughness determination for rock and other materials", J. Fract., 26(2), 59-62.   DOI
51 Cundall, P.A. and Strack, O. (1979), "A discrete element model for granular assemblies", Geotech., 29(1), 47-65.   DOI
52 Dai, F., Chen, R., Iqbal, M.J. and Xia, K. (2010), "Dynamic cracked chevron notched Brazilian disc method for measuring rock fracture parameters", J. Rock Mech. Min. Sci., 47(4), 606-613.   DOI
53 Fayed, A.S. (2017), "Numerical analysis of mixed mode I/II stress intensity factors of edge slant cracked plates", Eng. Sol. Mech., 5(1), 61-70.
54 Hadei1, R. and Kemeny, J. (2016), "New development to measure mode I fracture toughness in rock", Period. Polytech. Civil Eng., 61(1), 51.
55 Haeri, H. and Sarfarazi, V. (2016a), "The effect of micro pore on the characteristics of crack tip plastic zone in concrete", Comput. Concrete, 17(1), 107-112.   DOI
56 Haeri, H. (2015d), "Propagation mechanism of neighboring cracks in rock-like cylindrical specimens under uniaxial compression", J. Min. Sci., 51(3), 487-496.   DOI
57 Haeri, H. (2015e), "Influence of the inclined edge notches on the shear-fracture behavior in edge-notched beam specimens", Comput. Concrete, 16(4), 605-623.   DOI
58 Haeri, H. (2015f), "Experimental crack analysis of rock-like CSCBD specimens using a higher order DDM", Comput. Concrete, 16(6), 881-896.   DOI
59 Haeri, H., Khaloo, K. and Marji, M.F. (2015b), "Experimental and numerical analysis of Brazilian discs with multiple parallel cracks", Arab. J. Geosci., 8(8), 5897-5908   DOI
60 Haeri, H., Marji, M.F. and Shahriar, K. (2015a), "Simulating the effect of disc erosion in TBM disc cutters by a semi-infinite DDM", Arab. J. Geosci., 8(6), 3915-3927.   DOI
61 Huang, J. and Wang, S. (1985), "An experimental investigation concerning the comprehensive fracture toughness of some brittle rocks", J. Rock Mech. Min. Sci. Geomech. Abstr., 22(2), 99-104.   DOI
62 Haeri, H., Shahriar, K., Marji, M.F. and Moarefvand, P. (2014), "Investigating the fracturing process of rock-like Brazilian discs containing three parallel cracks under compressive line loading", Str. Mater., 46(3), 133-148.
63 Haeri, H., Shahriar, K., Marji, M.F. and Moarefvand, P. (2015c), "The HDD analysis of micro cracks initiation, propagation and coalescence in brittle substances", Arab. J. Geosci., 8, 2841-2852.   DOI
64 He, M.Y., Cao, H.C. and Evans, A.G. (1990), "Mixed-mode fracture: The four point shear specimen", Acta Metal Mater., 38(5), 839-846.   DOI
65 Karfakis, M.G. and Akram, M. (1993), "Effects of chemical solutions on rockm fracturing", J. Rock Mech. Min. Sci. Geomech. Abstr., 30(7), 1253-1259.   DOI
66 Isida, M., Imai, R. and Tsuru, H. (1979), "Symmetric plane problems of arbitrarily shaped plates with an edge crack", Trans. Jap. Soc. Mech. Eng., 45(395A), 743-749.   DOI
67 ISRM (2007), The Complete ISRM Suggested Methods for Rock Characterization Testing and Monitoring: 1974-2006, International Society for Rock Mechanics, Kozan Ofset, Ankara, Turkey.
68 Itasca PFC2D (1999), Particle Flow Code in 2 Dimensions, Theory and Background, Itasca Consulting Group, Minneapolis, U.S.A.
69 Kataoka, M. and Obara, Y. (2013), "Estimation of fracture toughness of different kinds of rocks under water vapor pressure by SCB test", J. MMIJ, 129, 425-432.   DOI
70 Haeri, H., Sarfarazi, V. and Lazemi, H. (2016b), "Experimental study of shear behavior of planar non-persistent joint", Comput. Concrete, 17(5), 639-653.   DOI