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Size effect on fracture behavior of quasi-brittle materials during uniaxial compression tests

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Abstract

Understanding the size dependence of quasi-brittle materials' fracture behavior is useful in assessing the safety of flawed rock engineering structures. In this study, a set of uniaxial compression tests were conducted to scrutinize the mechanical properties and crack morphology of cubic specimens with sizes of 75 mm, 100 mm, 125 mm and 150 mm. The results showed that the specimens had significant size dependence in terms of strength and crack initiation angle. The crack type and fracture pattern were not affected by the specimen size and were mainly controlled by the pre-existing crack inclination angle. Next, the test results were compared with the maximum tangential stress criterion considering the T-stress. The results also showed that the crack initiation angles of specimens with different sizes were in good agreement with the theoretical calculations. The non-singular compressive stress perpendicular to the crack surface inhibited the generation of the fracture process zone (FPZ). In addition, the stress required for tensile failure was smaller for large-size specimens, leading to a decrease in the length of the FPZ with increasing specimen size. The FPZ variation law of the uniaxial compression tests was greatly different from that of the mode I loading.

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References

  1. Ayatollahi, M.R., Akbardoost, J.: Size effects in mode II brittle fracture of rocks. Eng. Fract. Mech. 112–113, 165–180 (2013). https://doi.org/10.1016/j.engfracmech.2013.10.011

    Article  Google Scholar 

  2. Petit, J.-P., Barquins, M.: Can natural faults propagate under Mode II conditions? Tectonics 7, 1243–1256 (1988). https://doi.org/10.1029/TC007i006p01243

    Article  Google Scholar 

  3. Ozbolt, J., Eligehausen, R., Petrangeli, M.: Size Effect in Concrete Structures. University of Stuttgart, Stuttgart (1994)

    Google Scholar 

  4. ASTM Standard E399-12. Standard test method for linear-elastic plane-strain fracture toughness KIC of metallic materials. Annual book of ASTM standards. West Conshohocken, PA: ASTM International; 2013.

  5. Kuruppu, M.D., Obara, Y., Ayatollahi, M.R., et al.: ISRM-suggested method for determining the Mode I static fracture toughness using semi-circular bend specimen. Rock Mech. Rock Eng. 47, 267–274 (2014). https://doi.org/10.1007/s00603-013-0422-7

    Article  Google Scholar 

  6. Aliha, M.R.M., Ashtari, R., Ayatollahi, M.R.: Mode I and Mode II fracture toughness testing for a coarse grain marble. Appl. Mech. Mater. 5–6, 181–188 (2006). https://doi.org/10.4028/www.scientific.net/AMM.5-6.181

    Article  Google Scholar 

  7. Wang, J.-J., Huang, S.-Y., Hu, J.-F.: Limit of crack depth in KIC testing for a clay. Eng. Fract. Mech. 164, 19–23 (2016). https://doi.org/10.1016/j.engfracmech.2016.08.006

    Article  Google Scholar 

  8. Suits, L.D., Sheahan, T.C., Wang, J.-J., et al.: Experimental study on fracture behavior of a silty clay. Geotech. Test. J. 30, 100715 (2007). https://doi.org/10.1520/GTJ100715

    Article  Google Scholar 

  9. Wang, J., Huang, S., Guo, W., et al.: Experimental study on fracture toughness of a compacted clay using semi-circular bend specimen. Eng. Fract. Mech. 224, 106814 (2020). https://doi.org/10.1016/j.engfracmech.2019.106814

    Article  Google Scholar 

  10. Chong, K.P., Kuruppu, M.D.: New specimen for fracture toughness determination for rock and other materials. Int. J. Fract. 26, R59–R62 (1984). https://doi.org/10.1007/BF01157555

    Article  Google Scholar 

  11. Aliha, M.R.M., Ayatollahi, M.R., Smith, D.J., et al.: Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading. Eng. Fract. Mech. 77, 2200–2212 (2010). https://doi.org/10.1016/j.engfracmech.2010.03.009

    Article  Google Scholar 

  12. Zhang, S., An, D., Zhang, X., et al.: Research on size effect of fracture toughness of sandstone using the center-cracked circular disc samples. Eng. Fract. Mech. 251, 107777 (2021). https://doi.org/10.1016/j.engfracmech.2021.107777

    Article  Google Scholar 

  13. Bažant, Z.P., Gettu, R., Kazemi, M.T.: Identification of nonlinear fracture properties from size effect tests and structural analysis based on geometry-dependent R-curves. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 28, 43–51 (1991). https://doi.org/10.1016/0148-9062(91)93232-U

    Article  Google Scholar 

  14. Ayatollahi, M.R., Akbardoost, J.: Size and geometry effects on rock fracture toughness: mode I fracture. Rock Mech. Rock Eng. 47, 677–687 (2014). https://doi.org/10.1007/s00603-013-0430-7

    Article  Google Scholar 

  15. Ayatollahi, M.R., Akbardoost, J.: Size effects on fracture toughness of quasi-brittle materials—a new approach. Eng. Fract. Mech. 92, 89–100 (2012). https://doi.org/10.1016/j.engfracmech.2012.06.005

    Article  Google Scholar 

  16. Hoover, C.G., Bažant, Z.P.: Universal size-shape effect law based on comprehensive concrete fracture tests. J. Eng. Mech. 140, 473–479 (2014). https://doi.org/10.1061/(ASCE)EM.1943-7889.0000627

    Article  Google Scholar 

  17. Bažant, Z.P.: Size effect in blunt fracture: concrete, rock, metal. J. Eng. Mech. 110, 518–535 (1984). https://doi.org/10.1061/(ASCE)0733-9399(1984)110:4(518)

    Article  Google Scholar 

  18. Karamloo, M., Mazloom, M.: An efficient algorithm for scaling problem of notched beam specimens with various notch to depth ratios. Comput. Concr. 22, 39–51 (2018). https://doi.org/10.12989/CAC.2018.22.1.039

    Article  Google Scholar 

  19. Erarslan, N.: Microstructural investigation of subcritical crack propagation and Fracture Process Zone (FPZ) by the reduction of rock fracture toughness under cyclic loading. Eng. Geol. 208, 181–190 (2016). https://doi.org/10.1016/j.enggeo.2016.04.035

    Article  Google Scholar 

  20. Hillerborg, A., Modéer, M., Petersson, P.E.: Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem. Concr. Res. 6, 773–781 (1976). https://doi.org/10.1016/0008-8846(76)90007-7

    Article  Google Scholar 

  21. Akbardoost, J., Ayatollahi, M.R.: Experimental analysis of mixed mode crack propagation in brittle rocks: the effect of non-singular terms. Eng. Fract. Mech. 129, 77–89 (2014). https://doi.org/10.1016/j.engfracmech.2014.05.016

    Article  Google Scholar 

  22. Karihaloo, L.B.: Size effect in shallow and deep notched quasi-brittle structures. Int. J. Fract. (1999). https://doi.org/10.1023/A:1018633208621

    Article  Google Scholar 

  23. Awaji, H., Sato, S.: Combined mode fracture toughness measurement by the disk test. J. Eng. Mater. Technol. 100, 175–182 (1978). https://doi.org/10.1115/1.3443468

    Article  Google Scholar 

  24. Chang, S.H., Lee, C.I., Jeon, S.: Measurement of rock fracture toughness under modes I and II and mixed-mode conditions by using disc-type specimens. Eng. Geol. 66, 79–97 (2002). https://doi.org/10.1016/S0013-7952(02)00033-9

    Article  Google Scholar 

  25. Bazant, Z., Planas, J.: Fracture Size Effect in Concrete and Other Quasi-brittle Materials. Epfl (1997)

    Google Scholar 

  26. Xing, Y., Huang, B., Ning, E., Zhao, L., et al.: Quasi-static loading rate effects on fracture process zone development of mixed-mode (I-II) fractures in rock-like materials. Eng. Fract. Mech. 240, 107365 (2020). https://doi.org/10.1016/j.engfracmech.2020.107365

    Article  Google Scholar 

  27. Yang, S.Q., Jing, H.W.: Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression. Int. J. Fract. 168, 227–250 (2011). https://doi.org/10.1007/s10704-010-9576-4

    Article  Google Scholar 

  28. Miao, S., Pan, P.Z., Wu, Z., et al.: Fracture analysis of sandstone with a single filled flaw under uniaxial compression. Eng. Fract. Mech. 204, 319–343 (2018). https://doi.org/10.1016/j.engfracmech.2018.10.009

    Article  Google Scholar 

  29. Li, H., Wong, L.: Influence of flaw inclination angle and loading condition on crack initiation and propagation. Int. J. Solids Struct. 49(18), 2482–2499 (2012). https://doi.org/10.1016/j.ijsolstr.2012.05.012

    Article  Google Scholar 

  30. Yang, S.Q., Dai, Y.H., Han, L.J., et al.: Experimental study on mechanical behavior of brittle marble samples containing different flaws under uniaxial compression. Eng. Fract. Mech. 76(12), 1833–1845 (2009). https://doi.org/10.1016/j.engfracmech.2009.04.005

    Article  Google Scholar 

  31. Marji, M.F.: A bonded particle model for analysis of the flaw orientation effect on crack propagation mechanism in brittle materials under compression. Arch. Civ. Mech. Eng. 14(1), 40–52 (2014). https://doi.org/10.1016/j.acme.2013.05.008

    Article  Google Scholar 

  32. Cheng, H., Zhou, X., Zhu, J., et al.: The effects of crack openings on crack initiation, propagation and coalescence behavior in rock-like materials under uniaxial compression. Rock Mech. Rock Eng. 49(9), 1–14 (2016). https://doi.org/10.1007/s00603-016-0998-9

    Article  Google Scholar 

  33. Gratchev, I., Kim, D.H., Yeung, C.K.: Strength of rock-like specimens with pre-existing cracks of different length and width. Rock Mech. Rock Eng. 49(11), 1–6 (2016). https://doi.org/10.1007/s00603-016-1013-1

    Article  Google Scholar 

  34. Xu, J., Li, Z., et al.: Damage evolution and crack propagation in rocks with dual elliptic flaws in compression. Acta Mech. Solida Sin. (2017). https://doi.org/10.1016/j.camss.2017.11.001

    Article  Google Scholar 

  35. Zhang, J.-Z., Zhou, X.-P.: Fracture process zone (FPZ) in quasi-brittle materials: review and new insights from flawed granite subjected to uniaxial stress. Eng. Fract. Mech. 274, 108795 (2022). https://doi.org/10.1016/j.engfracmech.2022.108795

    Article  Google Scholar 

  36. Erdogan, F., Sih, G.C.: On the crack extension in plates under plane loading and transverse shear. J. Basic Eng. 85, 519–525 (1963). https://doi.org/10.1115/1.3656897

    Article  Google Scholar 

  37. Williams, M.L.: On the stress distribution at the base of a stationary crack. J. Appl. Mech. 24, 109–114 (1957). https://doi.org/10.1115/1.4011454

    Article  MathSciNet  MATH  Google Scholar 

  38. Ren, L., Zhu, Z., Wang, M., Zheng, T., Ai, T.: Mixed-mode elastic-plastic fractures: improved R-criterion. J. Eng. Mech. 140, 04014033 (2014). https://doi.org/10.1061/(ASCE)EM.1943-7889.0000755

    Article  Google Scholar 

  39. Zhang, X.-P., Wong, L.N.Y.: Cracking processes in rock-like material containing a single flaw under uniaxial compression: a numerical study based on parallel bonded-particle model approach. Rock Mech. Rock Eng. (2011). https://doi.org/10.1007/s00603-011-0176-z

    Article  Google Scholar 

  40. Williams, J.G., Ewing, P.D.: Fracture under complex stress—the angled crack problem. Int. J. Fract. 26, 346–351 (1984). https://doi.org/10.1007/BF00962967

    Article  Google Scholar 

  41. Gupta, M., Alderliesten, R.C., Benedictus, R.: A review of T-stress and its effects in fracture mechanics. Eng. Fract. Mech. 134, 218–241 (2015). https://doi.org/10.1016/j.engfracmech.2014.10.013

    Article  Google Scholar 

  42. Smith, D.J., Ayatollahi, M.R., Pavier, M.J.: The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading: BRITTLE FRACTURE IN MIXED MODE CONDITIONS. Fatigue Fract. Eng. Mater. Struct. 24, 137–150 (2001). https://doi.org/10.1046/j.1460-2695.2001.00377.x

    Article  Google Scholar 

  43. Tang, S.B., Bao, C.Y., Liu, H.Y.: Brittle fracture of rock under combined tensile and compressive loading conditions. Can. Geotech. J. 54, 88–101 (2017). https://doi.org/10.1139/cgj-2016-0214

    Article  Google Scholar 

  44. Zheng, T., Zhu, Z., Wang, B., Zeng, L.: Stress intensity factor for an infinite plane containing three collinear cracks under compression: an infinite plane containing three collinear cracks. ZAMM-J. Appl. Math. Mech. Z. Für Angew. Math. Mech. 94, 853–861 (2014). https://doi.org/10.1002/zamm.201300001

    Article  MATH  Google Scholar 

  45. Ayatollahi, M.R., Aliha, M.R.M.: H, Saghafi, An improved semi-circular bend specimen for investigating mixed mode brittle fracture. Eng. Fract. Mech. 78, 110–123 (2011). https://doi.org/10.1016/j.engfracmech.2010.10.001

    Article  Google Scholar 

  46. Aliha, M.R.M., Bahmani, A., Akhondi, Sh.: Mixed mode fracture toughness testing of PMMA with different three-point bend type specimens. Eur. J. Mech. ASolids. 58, 148–162 (2016). https://doi.org/10.1016/j.euromechsol.2016.01.012

    Article  Google Scholar 

  47. Aliha, M.R.M., JafariHaghighatpour, P., Tavana, A.: Application of asymmetric semi-circular bend test for determining mixed mode I+II fracture toughness of compacted soil material. Eng. Fract. Mech. 262, 108268 (2022). https://doi.org/10.1016/j.engfracmech.2022.108268

    Article  Google Scholar 

  48. Zhang, J., Zhou, X.: Forecasting catastrophic rupture in brittle rocks using precursory AE time series. J. Geophys. Res. Solid Earth (2020). https://doi.org/10.1029/2019JB019276

    Article  Google Scholar 

  49. Zhang, J.-Z., Zhou, X.-P.: AE event rate characteristics of flawed granite: from damage stress to ultimate failure. Geophys. J. Int. 222, 795–814 (2020). https://doi.org/10.1093/gji/ggaa207

    Article  Google Scholar 

  50. Zhang, J., Zhou, X., Zhou, L., Berto, F.: Progressive failure of brittle rocks with non-isometric flaws: insights from acousto-optic-mechanical (AOM) data. Fatigue Fract. Eng. Mater. Struct. 42, 1787–1802 (2019). https://doi.org/10.1111/ffe.13019

    Article  Google Scholar 

  51. Zhou, X.-P., Zhang, J.-Z., Wong, L.N.Y.: Experimental study on the growth, coalescence and wrapping behaviors of 3D cross-embedded flaws under uniaxial compression. Rock Mech. Rock Eng. 51, 1379–1400 (2018). https://doi.org/10.1007/s00603-018-1406-4

    Article  Google Scholar 

  52. Wong, L., Einstein, H.H.: Systematic evaluation of cracking behavior in specimens containing single flaws under uniaxial compression. Int. J. Rock Mech. Min. Sci. 46, 239–249 (2009). https://doi.org/10.1016/j.ijrmms.2008.03.006

    Article  Google Scholar 

  53. Zhou, X.-P., Zhang, J.-Z.: Damage progression and acoustic emission in brittle failure of granite and sandstone. Int. J. Rock Mech. Min. Sci. 143, 104789 (2021). https://doi.org/10.1016/j.ijrmms.2021.104789

    Article  Google Scholar 

  54. Fan, Y., Zhu, Z., Zhao, Y., et al.: Analytical solution of T-stresses for an inclined crack in compression. Int. J. Rock Mech. Min. Sci. 138, 104433 (2021). https://doi.org/10.1016/j.ijrmms.2020.104433

    Article  Google Scholar 

  55. Cotterell, B.: Brittle fracture in compression. Int. J. Fract. Mech. 8, 195–208 (1972). https://doi.org/10.1007/BF00703881

    Article  Google Scholar 

  56. Chaker, C., Barquins, M.: Sliding effect on branch crack. Phys. Chem. Earth 21, 319–323 (1996). https://doi.org/10.1016/S0079-1946(97)00055-4

    Article  Google Scholar 

  57. Huang, S.Y., Wang, J.J., Wang, A.G., et al.: Fracture failure mechanism and fracture criterion of compacted clay under compression and shear action. Chin. J. Geotech. Eng. 43(3), 492–501 (2021). https://doi.org/10.11779/CJGE202103012

    Article  Google Scholar 

  58. Thiercelin, M., Roegiers, J.C.: Fracture toughness determination with the modified ring test. In: Proceedings of the International Symposium on Engineering in Complex Rock Formations, pp. 284–290. Elsevier (1988). https://doi.org/10.1016/B978-0-08-035894-9.50041-X

  59. Zhou, X.P., Cheng, H., Feng, Y.F.: An experimental study of crack coalescence behaviour in rock-like materials containing multiple flaws under uniaxial compression. Rock Mech. Rock Eng. 47, 1961–1986 (2014). https://doi.org/10.1007/s00603-013-0511-7

    Article  Google Scholar 

  60. Zhang, S., Wang, H., Li, X., et al.: Experimental study on development characteristics and size effect of rock fracture process zone. Eng. Fract. Mech. 241, 107377 (2021). https://doi.org/10.1016/j.engfracmech.2020.107377

    Article  Google Scholar 

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Acknowledgements

This work was supported by the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJZD-K202000705), the A Project of Innovation and Development Joint Fund of Chongqing Natural Science Foundation (Municipal Education Commission) (CSTB2022NSCQ-LZX0049), the National Natural Science Foundation of China (52109113), the Natural Science Foundation on the project of Chongqing (cstc2021jcyj-msxmX1114), and the Ministry of Water Conservancy Embankment Safety and Disease Prevention Engineering Technology Research Center Open Subject Fund Funded Projects (LSDP202101).

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  1. School of Materials Science and Engineering, Chongqing Jiaotong University, Chongqing, 400074, China

    Junjie Wang

  2. Engineering Research Center of Diagnosis Technology and Instruments of Hydro-Construction, Chongqing Jiaotong University, Chongqing, 400074, China

    Chuan Lv & Zhenfeng Qiu

  3. National and Local Engineering Laboratory of Civil Engineering Materials for Transportation, Chongqing Jiaotong University, Chongqing, 400074, China

    Shiyuan Huang

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Wang, J., Lv, C., Huang, S. et al. Size effect on fracture behavior of quasi-brittle materials during uniaxial compression tests. Arch Appl Mech 93, 3171–3188 (2023). https://doi.org/10.1007/s00419-023-02431-2

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