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Dynamic fracture instability in brittle materials: Insights from DEM simulations

  • Kou, Miaomiao (School of Civil Engineering, Qingdao University of Technology) ;
  • Han, Dongchen (School of Civil Engineering, Qingdao University of Technology) ;
  • Xiao, Congcong (China Resources Land Ltd.) ;
  • Wang, Yunteng (Cooperative Innovation Center of Engineering Construction and Safety in Shandong Blue Economic Zone)
  • Received : 2019.01.14
  • Accepted : 2019.03.20
  • Published : 2019.07.10

Abstract

In this article, the dynamic fracture instability characteristics, including dynamic crack propagation and crack branching, in PMMA brittle solids under dynamic loading are investigated using the discrete element method (DEM) simulations. The microscopic parameters in DEM are first calibrated using the comparison with the previous experimental results not only in the field of qualitative analysis, but also in the field of quantitative analysis. The calibrating process illustrates that the selected microscopic parameters in DEM are suitable to effectively and accurately simulate dynamic fracture process in PMMA brittle solids subjected to dynamic loads. The typical dynamic fracture behaviors of solids under dynamic loading are then reproduced by DEM. Compared with the previous experimental and numerical results, the present numerical results are in good agreement with the existing ones not only in the field of qualitative analysis, but also in the field of quantitative analysis. Furthermore, effects of dynamic loading magnitude, offset distance of the initial crack and initial crack length on dynamic fracture behaviors are numerically discussed.

Keywords

Acknowledgement

Supported by : Graduate Scientific Research and Innovation foundation of Chongqing

References

  1. Abraham, F. (2005), "Unstable crack motion is predictable", J. Mech. Phys. Solids, 53(5), 1071-1078. https://doi.org/10.1016/j.jmps.2004.12.005.
  2. Bazazzadeh, S., Shojaei, A., Zaccariotto, M. and Galvanetto, U. (2019a), "Application of the peridynamic differential operator to the solution of sloshing problems in tanks", Eng. Computations, 36(1), 45-83. https://doi.org/10.1108/EC-12-2017-0520.
  3. Bazazzadeh, S., Zaccariotto, M. and Galvanetto, U. (2019b), "Fatigue degradation strategies to simulate crack propagation using peridynamic based computational methods", Lat. Am. J. Solids Struct., 16(2). http://dx.doi.org/10.1590/1679-78255022.
  4. Belytschko, T., Chen, H., Xu, J. and Zi, G. (2003), "Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment", Int. J. Numer. Methods Eng., 58(12), 1873-1905. https://doi.org/10.1002/nme.941.
  5. Bowden, F.P., Brunton, J.H., Field, J.E. and Heyes, A.D. (1967), "Controlled fracture of brittle solids and interruption of electrical current", Nature, 216, 38-42. https://doi.org/10.1038/216038a0
  6. Braun, M. and Fernandez-Saez, J. (2014), "A new 2D discrete model applied to dynamic crack propagation in brittle materials", Int. J. Solids Struct., 51(21-22), 3787-3797. https://doi.org/10.1016/j.ijsolstr.2014.07.014.
  7. Buehler, M.J. and Gao, H. (2006), "Dynamic fracture instabilities due to local hyperelasticity at crack tips", Nature, 439, 307-310. https://doi.org/10.1038/nature04408
  8. Cao, R.H., Cao, P., Lin, H., Pu, C.Z. and Ou, K. (2016), "Mechanical behavior of brittle rock-like specimens with preexisting fissures under uniaxial loading: Experimental studies and particle mechanics approach", Rock Mech. Rock Eng., 49(3), 763-783. https://doi.org/10.1007/s00603-015-0779-x.
  9. Cao, R.H., Cao, P., Lin, H., Ma, G.W. and Chen, Y. (2018a), "Failure characteristics of intermittent fissures under a compressive-shear test: Experimental and numerical analyses", Theor. Appl. Fract. Mech., 96, 740-757. https://doi.org/10.1016/j.tafmec.2017.11.002.
  10. Cao, R.H., Cao, P., Lin, H., Ma, G.W., Fan, X. and Xiong, X.G. (2018b), "Mechanical behavior of an opening in a jointed rocklike specimen under uniaxial loading: Experimental studies and particle mechanics approach", Arch. Civ. Mech. Eng., 18(1), 198-214. https://doi.org/10.1016/j.acme.2017.06.010.
  11. Cao, R.H., Cao, P., Lin, H., Ma, G.W., Zhang, C.Y. and Jiang. C. (2018c), "Failure characteristics of jointed rock-like material containing multi-joints under a compressive-shear test: Experimental and numerical analyses", Arch. Civ. Mech. Eng., 18(3), 784-798. https://doi.org/10.1016/j.acme.2017.12.003.
  12. Carlsson, J. and Isaksson, P. (2019), "Crack dynamics and crack tip shielding in a material containing pores analysed by a phase field method", Eng. Fract. Mech., 206, 526-540. https://doi.org/10.1016/j.engfracmech.2018.11.013.
  13. Cho, N., Martin, C.D. and Sego, D.C. (2007), "A clumped particle model for rock", Int. J. Rock Mech. Min. Sci., 44(7), 997-1010. https://doi.org/10.1016/j.ijrmms.2007.02.002
  14. Cox, B.N., Gao, H., Gross, D. and Rittel, D. (2005), "Modern topics and challenges in dynamic fracture", J. Mech. Phys. Solids, 53(3), 565-596. https://doi.org/10.1016/j.ijrmms.2007.02.002.
  15. Emdadi, A., Fahrenholtz, W.G., Hilmas, G.E. and Zaeem, M.A. (2018), "A modified phase-field model for quantitative simulation of crack propagation in single-phase and multi-phase materials", Eng. Fract. Mech., 200, 339-354. https://doi.org/10.1016/j.engfracmech.2018.07.038.
  16. Fineberg, J., Gross, S.P., Marder, M. and Swinney, H.L. (1991), "Instability in dynamic fracture", Phys. Rev. Lett., 67(4), 457-460. https://doi.org/10.1103/PhysRevLett.67.457.
  17. Fineberg, J. and Marder, M. (1999), "Instability in dynamic fracture", Physiol. Rep., 313(1-2), 1-108. https://doi.org/10.1016/S0370-1573(98)00085-4.
  18. Fineberg, J. and Bouchbinder, E. (2015), "Recent developments in dynamic fracture: some perspectives", Int. J. Fract., 196(1-2), 33-57. https://doi.org/10.1007/s10704-015-0038-x.
  19. Haeri, H., Sarfarazi, V., Zhu, Z., Hedayat, A., Nezamabadi, M.F. and Karbala M. (2018a), "Simulation of crack initiation and propagation in three point bending test using PFC2D", Struct. Eng. Mech., 66(4), 453-463. http://dx.doi.org/10.12989/sem.2018.66.4.453.
  20. Haeri, H., Sarfarazi, V., Zhu, Z. and Lazemi, H.A. (2018b), "Investigation of the effects of particle size and model scale on the UCS and shear strength of concrete using PFC2D", Struct. Eng. Mech., 67(5), 505-516. http://dx.doi.org/10.12989/sem.2018.67.5.505.
  21. Haeri, H., Sarfarazi, V., Zhu, Z. and Marji, M.F. (2018c), "Simulation of the tensile failure behaviour of transversally bedding layers using PFC2D", Struct. Eng. Mech., 67(5), 493-504. http://dx.doi.org/10.12989/sem.2018.67.5.493.
  22. Haeri, H., Sarfarazi, V. and Zhu, Z. (2018d), "PFC3D simulation of the effect of particle size on the single edge-notched rectangle bar in bending test", Struct. Eng. Mech., 68(4), 497-505. http://dx.doi.org/10.12989/sem.2018.68.4.497.
  23. Haeri, H., Sarfarazi, V. and Zhu, Z. (2018e), "Numerical simulation of the effect of bedding layer geometrical properties on the punch shear test using PFC3D", Struct. Eng. Mech., 68(4), 507-517. http://dx.doi.org/10.12989/sem.2018.68.4.507.
  24. Hedjazi, L., Martin, C.L., Guessasma, S., Valle, G.D. and Dendievel, R. (2012), "Application of the Discrete Element Method to crack propagation and crack branching in a vitreous dense biopolymer material", Int. J. Solids Struct., 49(13), 1893-1899. https://doi.org/10.1016/j.ijsolstr.2012.03.030.
  25. Kosteski, L., D'ambra, R. and Iturrioz, I. (2012), "Crack propagation in elastic solids using the truss-like discrete element method", Int. J. Fract., 174(2), 139-161. https://doi.org/10.1007/s10704-012-9684-4.
  26. Martin, C.L., Bouvard, D. and Shima, S. (2003), "Study of particle rearrangement during powder compaction by the Discrete Element Method", J. Mech. Phys. Solids, 51, 667-693. https://doi.org/10.1016/S0022-5096(02)00101-1.
  27. Martin, C.L., Bouvard, D. and Delette, G. (2006), "Discrete element simulations of the compaction of aggregated ceramic powders", J. Am. Ceram. Soc., 89, 3379-3387. https://doi.org/10.1111/j.1551-2916.2006.01249.x.
  28. Meng, Q.H. and Wang, Z.Q. (2015), "Numerical simulation of loading edge cracks by edge impact using the extended finite element method", Acta Mech. Solida Sin., 28(2), 156-167. https://doi.org/10.1016/S0894-9166(15)30004-5.
  29. Meng, J., Cao, P., Huang, J., Lin, H., Chen, Y. and Cao, R. (2018), "Second-order cone programming formulation of discontinuous deformation analysis", Int. J. Numer. Methods Eng. https://doi.org/10.1002/nme.6006.
  30. Miehe, C., Hofacker, M. and Welschinger, F. (2010a), "A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits", Comput. Methods Appl. Mech. Engrg., 199(45-48), 2765-2778. https://doi.org/10.1016/j.cma.2010.04.011.
  31. Miehe, C., Welschinger, F. and Hofacker, M. (2010b), "Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations", Int. J. Numer. Meth. Engng., 83(10), 1273-1311. https://doi.org/10.1002/nme.2861.
  32. Mohammed, T.J., Bakar, B.H.A. and Bunnori, A.B. (2015), "Strengthening of reinforced concrete beams subjected to torsion with UHPFC composites", Struct. Eng. Mech., 56(1), 123-136. http://dx.doi.org/10.12989/sem.2015.56.1.123.
  33. Nowruzpour, M., Sarkar, S., Reddy, J.N. and Roy, D. (2019), "A derivative-free upscaled theory for analysis of defects", J. Mech. Phys. Solids, 122, 89-501. https://doi.org/10.1016/j.jmps.2018.09.018.
  34. Nowruzpour, M. and Reddy, J.N. (2018), "Unification of local and nonlocal models within a stable integral formulation for analysis of defects", Int. J. Eng. Sci., 132, 45-59. https://doi.org/10.1016/j.ijengsci.2018.06.008.
  35. Potyondy, D.O. and Cundall, P.A. (1998), "Modeling notchformation mechanisms in the URL mine-by test tunnel using bonded assemblies of circular particles", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 35(4-5), 510-511. http://dx.doi.org/10.1016/2FS0148-9062(98)00083-7.
  36. Potyondy, D.O. and Cundall, P.A. (2004), "A bonded-particle model for rock", Int. J. Rock Mech. Min. Sci., 41(8), 1329-1364. https://doi.org/10.1016/j.ijrmms.2004.09.011.
  37. Procaccia, I. and Zylberg, J. (2013), "Propagation mechanism of brittle cracks", Phys. Rev. E, 87, https://doi.org/10.1098/rspa.1964.0248.
  38. Rabczuk, T., Song, J.H. and Belytschko, T. (2009), "Simulations of instability in dynamic fracture by the cracking particles method", Eng. Fract. Mech., 76(6), 730-741. https://doi.org/10.1016/j.engfracmech.2008.06.002.
  39. Ravi-Chandar, K. and Knauss, W.G. (1984), "An experimental investigation into dynamic fracture: II. Microstructural aspects", Int. J. Fract., 26(1), 65-80. https://doi.org/10.1007/BF01152313.
  40. Rosakis, A.J., Samundrala, O. and Coker D. (1999), "Cracks faster than the shear wave speed", Science, 284, 1337-1340. https://doi.org/10.1126/science.284.5418.1337.
  41. Sarfarazi, V. and Haeri, H. (2018), "Three-dimensional numerical modeling of effect of bedding layer on the tensile failure behavior in hollow disc models using Particle Flow Code (PFC3D)", Struct. Eng. Mech., 68(5), 537-547. https://doi.org/10.12989/sem.2018.68.5.537.
  42. Sarkar, S., Nowruzpour, M., Reddy, J.N. and Srinivasa, S.A. (2017), "A discrete Lagrangian based direct approach to macroscopic modelling", J. Mech. Phys. Solids, 98, 172-180. https://doi.org/10.1016/j.jmps.2016.09.007.
  43. Sharon, E., Gross, S.P. and Fineberg, J. (1995), "Local crack branching as a mechanism for instability in dynamic fracture", Phys. Rev. Lett., 74(25), 5096-5099. https://doi.org/10.1103/PhysRevLett.74.5096.
  44. Sharon, E. and Fineberg, J. (1999), "Confirming the continuum theory of dynamic brittle fracture for fast cracks", Nature, 397(6717), 333-335. https://doi.org/10.1038/16891.
  45. Shojaei, A., Mudric, T., Zaccariotto, M. and Galvanetto, U. (2016), "A coupled meshless finite point/Peridynamic method for 2D dynamic fracture analysis", Int. J. Mech. Sci., 119, 419-431. https://doi.org/10.1016/j.ijmecsci.2016.11.003.
  46. Shojaei, A., Mossaiby, F., Zaccariotto, M. and Galvanetto, U. (2017), "The meshless finite point method for transient elastodynamic problems", Acta Mech. 228(10), 3581-3593. https://doi.org/10.1007/s00707-017-1894-4.
  47. Shojaei, A., Mossaiby F., Zaccariotto, M. and Galvanetto, U. (2018), "An adaptive multi-grid peridynamic method for dynamic fracture analysis", Int. J. Mech. Sci., 144, 600-617. https://doi.org/10.1016/j.ijmecsci.2018.06.020.
  48. Shojaei, A., Galvanetto, U., Rabczuk, T., Jenabi, A. and Zaccariotto, M. (2019), "A generalized finite difference method based on the Peridynamic differential operator for the solution of problems in bounded and unbounded domains", Comput. Methods Appl. Mech. Engrg., 343, 100-126. https://doi.org/10.1016/j.cma.2018.08.033.
  49. Song, J.H., Wang, H.W. and Belytschko, T. (2008), "A comparative study on finite element methods for dynamic fracture", Comput. Mech., 42(2), 239-250. https://doi.org/10.1007/s00466-007-0210-x.
  50. Song, J.H. and Belytschko, T. (2009), "Cracking node method for dynamic fracture with finite elements", Int. J. Numer. Methods Eng., 77(3), 360-385. https://doi.org/10.1002/nme.2415.
  51. Yang, Y.F., Li, G., Liang, Z.Z. and Tang, C.A. (2015), "Numerical investigation on crack branching during collision for rock-like material", Theor. Appl. Fract. Mech., 76, 35-49. https://doi.org/10.1016/j.tafmec.2014.12.010.
  52. Zhang, P., Hu, X., Wang, X. and Yao, W. (2018), "An iteration scheme for phase field model for cohesive fracture and its implementation in Abaqus", Eng. Fract. Mech., 204, 268-287. https://doi.org/10.1016/j.engfracmech.2018.10.006.
  53. Zhang, Z., and Chen, X. (2014), "Modeling nonlinear elastic solid with correlated lattice bond cell for dynamic fracture simulation", Comput. Methods Appl. Mech. Engrg., 279, 325-347. https://doi.org/10.1016/j.cma.2014.06.036.

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