Skip to main content

Mode-II Fracture Response of PMMA Under Dynamic Loading Conditions

Abstract

The mode-II dynamic fracture behavior of poly(methyl methacrylate) (PMMA) was experimentally and numerically studied using ultra high-speed photography combined with digital image correlation and meshfree numerical simulations. Experiments were performed by launching a projectile from a gas gun onto pre-notched rectangular PMMA specimens. Two sample geometries were used, double edge notch specimens and single edge notch specimens. Additionally, two variations of the single edge notch specimen experiments were performed, in the first experiment the projectile directly hit the sample and in the second one a buffer was placed between the sample and projectile to ensure uniform loading. Finally, the effect of the notch sharpness was explored. The impact location was below the notch to ensure mode-II loading, which would then transition into mode-I loading once the crack starts to grow. Mode-II critical stress intensity factors were extracted and it was found that notch sharpness and loading conditions can have an effect on the path the crack follows upon fracture. All of these results were compared to numerical simulations of the crack propagation processes using a meshfree method. The numerical model successfully predicted the fracture toughness and the crack-path angle within 4% and 7% of experimental values, respectively. In addition, crack-tip speeds greater than 300 m/s were observed experimentally and numerically.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

References

  1. Theocaris P, Katsamanis P (1978) Response of cracks to impact by caustics. Eng Fract Mech 10(2):197–210. https://doi.org/10.1016/0013-7944(78)90003-6

    Article  Google Scholar 

  2. Mahajan RV, Ravi-Chandar K (1989) An experimental investigation of mixed-mode fracture. Int J Fract 41:235–252

    CAS  Article  Google Scholar 

  3. Wada H (1992) Determination of dynamic fracture toughness for PMMA. Eng Fract Mech 41(6):821–831. https://doi.org/10.1016/0013-7944(92)90234-6

    Article  Google Scholar 

  4. Wada H, Seika M, Calder CA, Kennedy TC (1993) Measurement of impact fracture toughness for PMMA with single-point bending test using an air gun. Eng Fract Mech 46(4):715–719. https://doi.org/10.1016/0013-7944(93)90178-U

    Article  Google Scholar 

  5. Kalthoff JF (2000) Modes of dynamic shear failure in solids. Int J Fract 101(1):1–31

    CAS  Article  Google Scholar 

  6. Kalthoff JF (1990) Transition in the failure behavior of dynamically shear loaded crack. Appl Mech Rev 43(5S):S247–S250

    Article  Google Scholar 

  7. Kalthoff JF (1987) The shadow optical method of caustics. Springer, Vienna

    Book  Google Scholar 

  8. Sundaram BM, Tippur HV (2017) Dynamic mixed-mode fracture behaviors of PMMA and polycarbonate. Eng Fract Mech 176:186–212

    Article  Google Scholar 

  9. Wada H, Seika M, Kennedy TC, Calder CA, Murase K (1996) Investigation of loading rate and plate thickness effects on dynamic fracture toughness of PMMA. Eng Fract Mech 54(6):805–811

    Article  Google Scholar 

  10. Delpino Gonzales O, Luong K, Homma H, Eliasson V (2016) Experimental investigation of dynamic fracture initiation in PMMA submerged in water. J Dynam Behav Mater 2(3):391–398

    Article  Google Scholar 

  11. Delpino Gonzales O, Eliasson V (2016) Influence of water uptake on dynamic fracture behavior of poly(methyl methacrylate). Exp Mech 56:59–68

    CAS  Article  Google Scholar 

  12. Chavez Morales R, Eliasson V (2020) The effect of moisture intake on the mode-II dynamic fracture behavior of carbon fiber/epoxy composites. J Dynam Behav Mater. https://doi.org/10.1007/s40870-020-00260-w

    Article  Google Scholar 

  13. Yoneyama S, Morimoto Y, Takashi M (2006) Automatic evaluation of mixed-mode stress intensity factors utilizing digital image correlation. Strain 42(1):21–29

    Article  Google Scholar 

  14. Kirugulige MS, Tippur HV (2009) 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

    Article  Google Scholar 

  15. Yates JR, Zanganeh M, Tai YH (2010) Quantifying crack tip displacement fields with DIC. Eng Fract Mech 77(11):2063–2076

    Article  Google Scholar 

  16. Gao G, Huang S, Xia K, Li Z (2015) Application of digital image correlation (DIC) in dynamic notched semi-circular bend (NSCB) tests. Exp Mech 55(1):95–104

    Article  Google Scholar 

  17. Kalthoff JF (1988) Shadow optical analysis of dynamic shear fracture. Opt Eng 27(10):835–840

    Article  Google Scholar 

  18. Ravi-Chandar K, Knauss WG (1984) An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching. Int J Fract 26(2):141–154. https://doi.org/10.1007/BF01157550

    Article  Google Scholar 

  19. Lee D, Tippur H, Kirugulige M, Bogert P (2009) Experimental study of dynamic crack growth in unidirectional graphite/epoxy composites using digital image correlation method and high-speed photography. J Compos Mater 43(19):2081–2108

    Article  Google Scholar 

  20. Zhou W, Huang J, Huang W, Liu D (2020) Dynamic fracture testing of polymethyl-methacrylate (PMMA) single-edge notched beam. Polym Test. https://doi.org/10.1016/j.polymertesting.2020.106833

    Article  Google Scholar 

  21. Rosakis AJ (1999) Cracks Faster than the Shear Wave Speed. Science 284(5418):1337–1340. https://doi.org/10.1126/science.284.5418.1337

    CAS  Article  Google Scholar 

  22. Wei H, Chen JS (2018) A damage particle method for smeared modeling of brittle fracture. Int J Multiscale Comput Eng 16(4):303–324

    Article  Google Scholar 

  23. Chen J, Baek J, Huang TH, Hillman MC (2020) Accelerated and stabilized meshfree method for impact-blast modeling. In: Soules JG (ed) Structures Congress 2020. American Society of Civil Engineers, Reston, pp 92–104

    Chapter  Google Scholar 

  24. Hillman M, Chen JS (2016) An accelerated, convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics. Int J Numer Meth Eng 107(7):603–630. https://doi.org/10.1002/nme.5183

    Article  Google Scholar 

  25. Huang TH, Wei H, Chen JS, Hillman MC (2020) Rkpm2d: an open-source implementation of nodally integrated reproducing kernel particle method for solving partial differential equations. Comput Particle Mech 7(2):393–433

    Article  Google Scholar 

  26. Chen JS, Wu CT, Yoon S, You Y (2001) A stabilized conforming nodal integration for Galerkin mesh-free methods. Int J Numer Methods Eng 50(2):435–466. https://doi.org/10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A

    Article  Google Scholar 

Download references

Acknowledgements

Authors V. Eliasson, R. Chavez Morales, D. Sharp and A. Aderounmu would like to thank the Office of Naval Research through grant number N00014-16-1-3215. Special thanks to the program manager Dr. Y.D.S. Rajapakse.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. Eliasson.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Morales, R.C., Baek, J., Sharp, D. et al. Mode-II Fracture Response of PMMA Under Dynamic Loading Conditions. J. dynamic behavior mater. 8, 104–121 (2022). https://doi.org/10.1007/s40870-021-00320-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40870-021-00320-9

Keywords

  • Dynamic fracture
  • Digital image correlation
  • PMMA
  • Mode-II
  • Ultra high-speed
  • Meshfree numerical simulation