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Mixed-mode I/II dynamic fracture behavior in PMMA driven by stress waves

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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

  1. 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)

    Article  Google Scholar 

  2. 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)

    Article  Google Scholar 

  3. 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)

    Google Scholar 

  4. 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)

    Google Scholar 

  5. 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)

    Article  Google Scholar 

  6. 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)

    Article  Google Scholar 

  7. 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)

    Article  Google Scholar 

  8. Anonymous. Suggested methods for determining the fracture toughness of rock. Int. J. Rock Mech. Min. Sci. Geomech Abstr. 1988;25:71–96.

  9. Guo, H., Aziz, N.I., Schmidt, L.C.: Rock fracture-toughness determination by the Brazilian test. Eng. Geol. 33(3), 177–188 (1993)

    Article  Google Scholar 

  10. 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)

    Article  Google Scholar 

  11. 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)

    Article  Google Scholar 

  12. 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)

    Article  Google Scholar 

  13. 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)

    Article  Google Scholar 

  14. 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)

    Article  Google Scholar 

  15. 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)

    Article  Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. 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))

    Google Scholar 

  18. 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))

    Google Scholar 

  19. 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))

    Google Scholar 

  20. 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))

    Google Scholar 

  21. Rege, K., Lemu, H.G.: A review of fatigue crack propagation modelling techniques using FEM and XFEM. Mater. Sci. Eng. 276, 012027 (2017)

    Google Scholar 

  22. Moes, N., Dolbow, J., Belytschko, T.: A Finite Element Method for Crack Growth without Remeshing. Int. J. Numer. Meth. Eng. 46, 131–150 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  23. 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)

    Google Scholar 

  24. Fang AP,Ye WP.Origin7.5 Science and technology mapping and data analysis. Beijing: China Machine Press, 2004:223–296.(in Chinese)

  25. 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)

    Article  MATH  Google Scholar 

  26. 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)

    Article  Google Scholar 

  27. 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)

    Article  MathSciNet  MATH  Google Scholar 

  28. 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)

    Article  Google Scholar 

  29. Westergaard, H.M.: Bearing pressure and cracks. ASME J. Appl. Mech. 6, 49–53 (1939)

    Article  Google Scholar 

  30. 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)

    Article  Google Scholar 

  31. Yoneyama, S., Morimoto, Y., Takashi, M.: Automatic evaluation of mixed-mode stress intensity factors utilizing digital image correlation. Strain 42, 21–29 (2006)

    Article  Google Scholar 

  32. Dally JW and Riley WF. Experimental Stress Analysis, 4th edn. College House Enterprises, LLC,Knoxville, TN, 2005.

  33. 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)

    Article  Google Scholar 

  34. 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)

    Article  Google Scholar 

  35. 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)

    Article  Google Scholar 

Download references

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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