Abstract
To investigate the dynamic behavior of mixed-mode I/II cracks under stress wave loading, such as crack initiation and propagation, an experimental system that combines the split Hopkinson pressure bar (SHPB) with digital image correlation (DIC) was established. The dynamic fracture experiments for pure mode I and mixed mode I/II were conducted using the single cleavage drilled compression (SCDC) specimen of polymethyl methacrylate (PMMA) with different impact velocities. The displacement and strain field histories of the crack tip from impact to complete fracture were obtained by the DIC method. Then, the dynamic stress intensity factors (DSIFs) were calculated by least-squares analysis of the crack tip displacement field. Moreover, the extended finite element method (XFEM) was used to simulate the crack propagation, and the crack propagation paths were acquired under pure mode I and mixed-mode I/II loadings, which were basically consistent with the experimental results. Combined with the analysis of energy evolution, the characteristics of fracture and crack propagation of the brittle rock-like materials caused by stress waves were revealed.
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References
Chai, S.B., Li, J.C., Zhang, Q.B., Li, H.B., Li, N.N.: Stress wave propagation across a rock mass with two non-parallel joints. Rock Mech. Rock Eng. 49(10), 1–10 (2016)
Zhu, Z.M., Xu, W.T., Feng, R.Q.: A new method for measuring mode-i dynamic fracture toughness of rock under blasting loads. Exp. Tech. 40(3), 889–905 (2016)
Xu, W.T., Zhu, Z.M., Zeng, L.G.: Testing method study of mode-I dynamic fracture toughness under blasting loads. Chin. J. Rock Mech. Eng. 34(S1), 2767–2772 (2015)
Hu, R., Zhu, Z.M., Hu, Z.: Experimental study of regularity of crack propagation under blasting dynamic loads. Chin. J. Rock Mech. Eng. 32(7), 1476–1481 (2013)
Li, Q.M., Lu, Y.B., Meng, H.: Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests Part II: Numerical simulations. Int. J. Impact Eng. 36(12), 1327–1334 (2009)
Wang, Q.Z., Yang, J.R., Zhang, C.G., et al.: Sequential determination of dynamic initiation and propagation toughness of rock using an experimental–numerical–analytical method. Eng. Fract. Mech. 141, 78–94 (2015)
Reddish, D.J., Stace, L.R., Vanichkobchinda, P., et al.: Numerical simulation of the dynamic impact breakage testing of rock. Int. J. Rock Mech. Min. Sci. 42(2), 167–176 (2005)
Anonymous. Suggested methods for determining the fracture toughness of rock. Int. J. Rock Mech. Min. Sci. Geomech Abstr. 1988;25:71–96.
Guo, H., Aziz, N.I., Schmidt, L.C.: Rock fracture-toughness determination by the Brazilian test. Eng. Geol. 33(3), 177–188 (1993)
Tang, T., Bažant, Z.P., Yang, S., et al.: Variable-notch one-size test method for fracture energy and process zone length. Eng. Fract. Mech. 55(3), 383–404 (1996)
Yang, S., Tang, T., Dan, G.Z., et al.: Splitting tension tests to determine concrete fracture parameters by peak-load method. Adv. Cem. Bas. Mat. 5(1), 18–28 (1997)
Wang, Q.Z., Xing, L.: Determination of fracture toughness KIC by using the flattened Brazilian disk specimen for rocks. Eng. Fract. Mech. 64(2), 193–201 (1999)
Ayatollahi, M.R., Aliha, M.R.M.: Wide range data for crack tip parameters in two disc-type specimens under mixed mode loading. Comput. Mater. Sci. 38(4), 660–670 (2007)
Aliha, M.R.M., Ayatollahi, M.R.: 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 (2014)
Surendra, K.V.N., Simha, K.R.Y.: Analysis of cracked and un-cracked semicircular rings under symmetric loading. Eng. Fract. Mech. 128, 69–90 (2014)
Mirsayar, M.M., Razmi, A., Berto, F.: Tangential strain-based criteria for mixed-mode I/II fracture toughness of cement concrete. Fatigue Fract Eng Mater Struct. 41(1), 129–137 (2018)
Wang, K., Wang, Q.Z.: Experimental study of mixed mode dynamic fracture for cracked straight through flattened Brazilian disc. J Exp. Mech. 05, 417–426 (2008). ((in Chinese))
Wang, M., Zhu, Z.M., Xie, J.: Experimental and numerical studies of the mixed-mode I and II crack propagation under dynamic loading using SHPB. Chin. J. Rock Mech. Eng. 34(12), 2474–2485 (2015). ((in Chinese))
Ni, M., Gou, X.P., Wang, Q.Z.: Test method for rock dynamic fracture toughness using single cleavage drilled compression specimen impacted by split Hopkinson pressure bar. Eng. Mech. 30(1), 365–372 (2013). ((in Chinese))
Yang, J.R., Zhang, C.G., Zhou, Y., et al.: A new method for determining dynamic fracture toughness of rock using SCDC specimens. Chin. J. Rock Mech. Eng. 34(2), 279–292 (2015). ((in Chinese))
Rege, K., Lemu, H.G.: A review of fatigue crack propagation modelling techniques using FEM and XFEM. Mater. Sci. Eng. 276, 012027 (2017)
Moes, N., Dolbow, J., Belytschko, T.: A Finite Element Method for Crack Growth without Remeshing. Int. J. Numer. Meth. Eng. 46, 131–150 (1999)
Dong, L.T., Atluri, S.N.: Fracture & fatigue analyses: SGBEM-FEM or XFEM? Part 1: 2D structures. Comput. Model. Eng. Sci. 90, 379–413 (2013)
Fang AP,Ye WP.Origin7.5 Science and technology mapping and data analysis. Beijing: China Machine Press, 2004:223–296.(in Chinese)
Gregoire, D., Maigre, H., Rethore, J., et al.: Dynamic crack propagation under mixed-mode loading=Comparison between experiments and X-FEM simulations. Int. J. Solids Struct.. 44, 6517–6534 (2007)
Gregoire, D., Maigre, H., Combescure, A.: New experimental and numerical techniques to study the arrest and the restart of a crack under impact in transparent materials. Int. J. Solids Struct.. 46, 3480–3491 (2009)
Zhao, H., Gary, G.A.: Three dimensional analytical solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar application to experimental techniques. J. Mech. Phys. Solids. 43(8), 1335–1348 (1995)
Wang, M., Wang, F., Zhu, Z.M., et al.: Modelling of crack propagation in rocks under SHPB impacts using a damage method. Fatigue Fract. Eng. Mater. Struct. 42(8), 1699–1710 (2019)
Westergaard, H.M.: Bearing pressure and cracks. ASME J. Appl. Mech. 6, 49–53 (1939)
Nishioka, T., Atluri, S.N.: Path independent integrals, energy release rates, and general solutions of near-tip fields in mixed-mode dynamic fracture mechanics. Eng. Fracture Mech. 18, 1–22 (1983)
Yoneyama, S., Morimoto, Y., Takashi, M.: Automatic evaluation of mixed-mode stress intensity factors utilizing digital image correlation. Strain 42, 21–29 (2006)
Dally JW and Riley WF. Experimental Stress Analysis, 4th edn. College House Enterprises, LLC,Knoxville, TN, 2005.
Ayatollahi, M.R., Nejati, M.: An over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis. Fatigue&Fract. Eng. Mater. Struct.. 34(3), 159–176 (2011)
Kirugulige, M.S., Tippur, H.V.: Measurement of fracture parameters for a mixed-mode crack driven by stress waves using image correlation Technique and high-speed digital photography. Strain 45(2), 108–122 (2010)
Zhang, Q.B., Zhao, J.: A review of dynamic experimental techniques and mechanical behaviour of rock materials. Rock Mech. Rock Eng. 47(4), 1411–1478 (2014)
Acknowledgements
This research was supported by the National Natural Science Foundation of China (No. 51974316) and the Fundamental Research Funds for Central Universities (No. 2022JCCXLJ01 and 2022YJSLJ04).
Funding
This research was supported by the National Natural Science Foundation of China (No. 51974316) and the Fundamental Research Funds for Central Universities (No. 2022JCCXLJ01 and 2022YJSLJ04). Awards were granted to the author Liyun Yang.
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Liu, H., Yang, L., Xie, H. et al. Mixed-mode I/II dynamic fracture behavior in PMMA driven by stress waves. Arch Appl Mech 93, 3113–3129 (2023). https://doi.org/10.1007/s00419-023-02428-x
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DOI: https://doi.org/10.1007/s00419-023-02428-x