Molecular Dynamics approach for Fracture Simulation along a Weakly Bonded Interface

Molecular Dynamics approach for Fracture Simulation along a Weakly Bonded Interface

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Author(s)

Author(s): Seyed Bijan Mahbaz, Milad Mosharafi, Maurice B. Dusseault

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DOI: 10.18483/ijSci.2019 56 269 148-158 Volume 8 - May 2019

Abstract

Opening mechanisms for fractures (joints) characterized by weak bonding (nano-micro scale cracks) in low-porosity rock play a key role in shale oil and shale gas development through staged hydraulic fracturing. We explore the cohesive interface strength of two weakly bonded slabs of Polymethylmethacrylate (PMMA) with nano-scale Molecular Dynamics (MD) methods, calibrated to experimental data and simulated by the Finite Element Method (FEM). The proper stress/strain state at the weakly bonded interface is determined because it is required for MD simulation. Then, we develop a representative PMMA structure as an input for LAMMPS© software to simulate a tensile strength test. Results including per-atom stress values and pressures in different components are extracted, and we note that the fracture location and its behavior deduced from MD simulations follows experimental results. The total force for this simulation is close to 80 × 106 N, and we can use this parameter to reflect the fracture behavior of the weakly bonded PMMA slabs with an acceptable accuracy, considering the levels of uncertainty.

Keywords

Fracture Opening, Molecular Dynamics (MD), Finite Element Method (FEM), Polymethylmethacrylate, PMMA

References

  1. Abraham, F.F., Brodbeck, D., Rudge, W.E. & Xu, X. 1997. A molecular dynamics investigation of rapid fracture mechanics. Journal of the Mechanics and Physics of Solids, 45 (9): 1595–1619.
  2. Adams, G.C., Bender, R.G., Crouch, B.A. & Williams, J.G. 1990. Impact Fracture Toughness Tests on Polymers, Polym. Eng. Sci., 30, 241.
  3. Ahmed, J.K., Amer, Z. J. A. & Al-Bahate, M.J.M. 2014. Effect of chlorophyll and anthocyanin on the secondary bonds of poly methyl methacrylate (PMMA). International Journal of Technical Research and Applications, 2(6): 73–80.
  4. Alpern, J., Marone, C., Elsworth, D., Belmonte, A. & Connelly, P. 2012. Exploring the physicochemical processes that govern hydraulic fracture through laboratory experiments. 46th US Rock Mechanics / Geomechanics Symposium, 24-27 June 2012. Chicago, Illinois, 2958–2963.
  5. Arndt, M. 2004. Upscaling from Atomistic Models to Higher Order Gradient Continuum Models for Crystalline Solids, PhD. thesis, University of Bonn, Germany.
  6. Baker, T. 2017. Molecular computer simulations of graphene oxide intercalated with methanol: swelling properties and interlayer structure. Masters’ Thesis, Umea University, Sweden.
  7. Barisik, M. & Beskok, A. 2011. Equilibrium molecular dynamics studies on nanoscale-confined fluids. Microfluidics and Nanofluidics, 11(3): 269–282.
  8. Belak, J., Glosli, J.N., Boercker, D.B. & Sowers, I.F. 1995. Molecular dynamics simulation of mechanical deformation of ultra-thin metal and ceramic films. In Proceedings of the spring meeting of the Materials Research Society (MRS), Cambridge University Press, San Francisco.
  9. Cheng, H. & Dusseault, M.B. 2004. A continuum damage model for geomaterials. International Journal of Rock Mechanics and Mining Sciences, 41(3): 375–375.
  10. Cui, S.T., Cummings, P.T. & Cochranoe, H. D. 1996. The calculation of the viscosity from the autocorrelation function using molecular and atomic stress tensors. Molecular Physics, 88(6): 1657–1664.
  11. Dalmas, D., Guerra, C., Scheibert, J. & Bonamy, D. 2013. Damage mechanisms in the dynamic fracture of nominally brittle polymers. International Journal of Fracture, 184(1–2): 93–111.
  12. Dehghan, A. N., Goshtasbi, K., Ahangari, K. & Jin, Y. 2015. Experimental investigation of hydraulic fracture propagation in fractured blocks. Bulletin of Engineering Geology and the Environment, 74(3): 887–895.
  13. Dmour, H.N. & Shokir, E.M. 2010. Pre-post FRAC test data analysis for hydraulically fractured vertical tight gas well-field case study. Petroleum Science and Technology, 28(2): 155–175.
  14. Elmo, D., Stead, D., Eberhardt, E. & Vyazmensky, A. 2013. Applications of finite/discrete element modeling to rock engineering problems. International Journal of Geomechanics, 13(5): 565-580.
  15. Faye, A., Parameswaran, V. & Basu, S. 2016. Dynamic fracture initiation toughness of PMMA: a critical evaluation. Mechanics of Materials, 94: 156–169.
  16. Fenley, A.T., Muddana, H.S. & Gilson, M.K. 2014. Calculation and visualization of atomistic mechanical stresses in nanomaterials and biomolecules. PLoS ONE, 9(12): e113119.
  17. Gomez R. D. M., Dusseault, M.B. & Gracie, R. 2016. Cohesion and fracturing in a transparent jointed rock analogue. 50th US Rock Mechanics/ Geomechanics Symposium, 26-29 June 2016, Houston, Texas.
  18. Hart, R. 2003. Enhancing Rock Stress Understanding through numerical modeling. International Journal of Rock Mechanics & Mining Sciences, 40(2003): 1089-1097.
  19. Hashemi, S. A., Hashemi, S. H., Pirjamadi, M. R. & Niknam, A. 2016. Study of oil recovery method through chemical injection in order to improve oil exploitation. International Academic Journal of Science and Engineering, 3(3): 144-152.
  20. Heinz, H., Paul, W. & Binder, K. 2005. Calculation of Local Pressure Tensors in Systems with Many-Body Interactions. Physical Review E, 72: 066704-1–066704-10.
  21. Hoover, W.G. 1985. Canonical Dynamics: Equilibrium Phase-Space Distributions. Physical Review A, 31(3):1695–1697.
  22. Huang, D., Wang, M. & Lu, G. 2014. Continuum fracture analysis and molecular dynamic study on crack initiation and propagation in nanofilms. Journal of Nanomaterials, Article ID: 732434, 2014: 1–7.
  23. Huang, D. & Zhuo, J. S. 2006. Molecular Dynamics Simulation of Size Effect on Mechanical Properties of Nano-Metals. Computational Methods in Engineering and Science, 21-23 August 2006, Sanya, Hainan, China.Jeffrey, R.G., Chen, Z.R., Zhang, X., Bunger, A.P. & Mills, K.W. 2015. Measurement and analysis of full-scale hydraulic fracture initiation and fracture reorientation. Rock Mechanics and Rock Engineering. 48(6): 2497–2512.
  24. Jing, L. & Hudson, J.A. 2002. Numerical methods in rock mechanics. International Journal of Rock Mechanics & Mining Sciences, 39(4): 409–427.
  25. Keshavarzi, R. & Jalili, S. 2014. Building a mechanical earth model and its application in a geomechanical analysis of hydraulic fracture behaviour in naturally fractured reservoirs. European Journal of Environmental and Civil Engineering, 18(3): 336–357.
  26. Kim, Y.S., Choi, D.Y. & Won, S.Y. 2001. Molecular dynamics simulation for grain boundary deformation under tensile loading condition. Journal of Materials Science & Technology, 17 (01): 145–146.
  27. Kim, J H. & Lee, S.H. 2002. Molecular dynamics simulation studies of benzene, toluene, and p-xylene in a canonical ensemble. Bulletin-Korean Chemical Society, 23(3): 441–446.
  28. Li, M., Kang, Z., Li, R., Meng, X. & Lu, Y. 2013. A molecular dynamics study on tensile strength and failure modes of carbon nanotube junctions. Journal of Physics D: Applied Physics, 46(49): 495301.
  29. Li, W., Li, G., Yang, X., Liu, Lisheng, & Zhai, P. 2015. Influence of Nanopores on the Tensile/Compressive Mechanical Behavior of Crystalline CoSb3: A Molecular Dynamics Study. Journal of Electronic Materials, 44(6): 1477–1482.
  30. Large, M. C. J., Moran, J. & Ye, L. 2009. The role of viscoelastic properties in strain testing using microstructured polymer optical fibres (mPOF), Meas. Sci. Technol., 20(3): 034014-034014.
  31. Mahbaz, S. B., Goddard, A. & Dusseault, M. B. 2013. Scanning electron microscopy (SEM) and profilometer scanning microscopy to estimate in situ stresses in a dolomite core specimen. In proceedings of7th U.S. Rock Mechanics/Geomechanics Symposium, San Francisco.
  32. Makke, A. 2011. Mechanical properties of homogenous polymers and block copolymers: a molecular dynamics simulation approach. PhD. Thesis, Université Claude Bernard - Lyon I, France.
  33. Mayo, S.L., Olafson, B.D. & Goddard, W.A. 1990. DREIDING: A generic force field for molecular simulations. Journal of Physical Chemistry, 94(26): 8897–8909.
  34. Miguel, E.D. & Jackson, G. 2006. The nature of the calculation of the pressure in molecular simulations of continuous models from volume perturbations. Journal of Chemical Physics, 125(16): 164109-1–164109-11
  35. Mitra, R. 2006. Imaging of Stress in rock samples using numerical modeling and laboratory tomography. PhD. Thesis, Virginia Polytechnic Institute and State University, USA.
  36. Monasse, B. & Boussinot F. 2014. Determination of forces from a potential in molecular dynamics. Condensed Matter/ Statistical Mechanics, arXiv:1401.1181v1.
  37. Mosharafi, M., Mahbaz, S. B. & Dusseault, M. B. 2017. Molecular dynamic model applications in reservoir geomechanics and fracture propagation in pure calcium carbonate. 51st U.S. Rock Mechanics/Geomechanics Symposium, 25-28 June, San Francisco, California, USA.
  38. Murray, S.J., Subramani, V.J., Selvam, R.P. & Hall, K.D. 2010. Molecular dynamics to understand the mechanical behavior of cement paste. Transportation Research Record, 2142: 75–82.
  39. Nose, S. 1984. A molecular dynamics method for simulations in the canonical ensemble. Journal of Molecular Physics, 52(2): 255–268.
  40. Okada, O., Oka, K., Kuwajima, S., Toyoda, S. & Tanabe, K. 2000. Molecular simulation of an amorphous poly (methyl methacrylate) – poly (tetrafluoroethylene) interface. Computational and Theoretical Polymer Science, 10(3–4): 371–381.
  41. Pei, L., Lu, C., Tieu, K., Zhu, H. & Zhao, X. 2013. A molecular dynamics simulation of fracture in nanocrystalline copper. Journal of Nano Research, 23: 50–56.
  42. Rountree, C. L., Kalia, R. K., Lidorikis, E., Nakano, A., Brutzel, L.V. & Vashishta, P. 2002. Atomistic aspects of crack propagation in brittlematerials: multimillion atom molecular dynamics simulations. Annual Review of Materials Research, 32: 377–400.
  43. Rottler, J., Barsky, S. & Robbins, M.O. 2002. Cracks and crazes: on calculating the macroscopic fracture energy of glassy polymers from molecular simulations. Physical Review Letters, 89(14): (148304-1–148304-4).
  44. Saitoh, K-I., Sameshima, Y. & Daira, S., 2014. Nano-Scale Modelling and Simulation of Metal Wiredrawing by Using Molecular Dynamics Method. World Journal of Nano Science and Engineering, 4(2): 70–83.
  45. Sivakumar, G. & Maji, V.B. 2014. Finite element simulation of crack initiation and propagation in rocks. Rock Engineering and Rock Mechanics: Structures in and on Rock Masses - Proceedings of EUROCK 2014, ISRM European Regional Symposium, 829-834.
  46. Shaw, A. Tian, L. & Russell, A. 2016. Tensile Properties of High-purity Ca Metal. British Journal of Applied Science & Technology, 15(6): 1–6.
  47. Shen, Sh. & Atluri, S. N. 2004. Atomic-level stress calculation and continuum-molecular system equivalence. Computer Modeling in Engineering and Sciences, 6(1): 91–104.
  48. Shokir, E.M. & Al-Quraishi, A.A. 2009. Experimental and numerical investigation of proppant placement in hydraulic fractures. Petroleum Science and Technology, 27(15): 1690–1703.
  49. Suarez-Rivera, R., Burghardt, J., Edelman, E., Stanchits, S. & Surdi, A. 2013. Geomechanics considerations for hydraulic fracture productivity. 47th US Rock Mechanics / Geomechanics Symposium, 23-26 June 2013. San Francisco, California, 1140–1148.
  50. Sutmann, G. 2002. Classical Molecular Dynamics. John von Neumann Institute for Computing, 10: 211–254.
  51. Thiercelin, M.J. & Lemanczyk, Z.R. 1986. Stress gradient affects the height of vertical hydraulic fractures. SPE Production Engineering, 1(4): 245–254.
  52. Thompson, A. P., Plimpton, S. & Mattson, W. 2009. General formulation of pressure and stress tensor for arbitrary many-body interaction potentials under periodic boundary conditions. Journal of Chemical Physics, 131(15): 154107-1–154107-6
  53. Van Gunsteren, W.F. & Mark, A.E. 1998. Validation of molecular dynamics simulation. Journal of Chemical Physics, 108(15): 6109–6116.
  54. Veeranjaneyulu, J. & Rao, H.R. 2012. Simulation of the crack propagation using fracture mechanics techniques in aero structures. International Journal of Engineering Research and Applications, 2(5): 1168–1173.
  55. Viswambaran, M., Kapri, A., D'Souza, D. & Kumar M.R. 2011. An evaluation of fracture resistance of interim fixed partial denture fabricated using poly methyl methacrylate and reinforced by different fibres for its optimal placement: an in vitro study. Medical Journal Armed Forces India, 67(4): 343–347.
  56. VMD version 1.9.1, 2012, User’s Guide, Beckman Institute for Advanced Science and Technology University of Illinois at Urbana-Champaign 405 N. Mathews Urbana, IL 61801.
  57. Wu, X., Moon, R.J. & Martini, A. 2014. Tensile strength of Iβ crystalline cellulose predicted by molecular dynamics simulation. Cellulose, 21(4): 2233–2245.
  58. Yang, S., Gao, F. & Qu, J. 2013. A molecular dynamics study of tensile strength between a highly-crosslinked epoxy molding compound and a copper substrate. Polymer (United Kingdom). 54(18): 5064–5074.
  59. Yetisir, M., Gracie, R. & Dusseault, M. B. 2016. Up-scaling DEM simulations. 50th US Rock Mechanics / Geomechanics Symposium 2016, 3, 1971-1979.
  60. Yu, H., Chong, Z. Z., Beng Tor, Sh. & Loh, N. H. 2015. Low temperature and deformation-free bonding of PMMA microfluidic devices with stable hydrophilicity via oxygen plasma treatment and PVA coating. RSC Advances, 5(11): 8377-8388.
  61. Zhao, Z., Liu, J. & Soh, A.K. 2018. On the da Vinci size effect in tensile strengths of nanowires: A molecular dynamics study. AIP Advances, 8(1),015315.
  62. Zhang, Z-X. 2016. Rock Fracture and Blasting: Theory and Applications. Butterworth-Heinemann, Oxford, United Kingdom.

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