DOI QR코드

DOI QR Code

Peridynamic analysis of dynamic fracture behaviors in FGMs with different gradient directions

  • Kou, Miaomiao (School of Civil Engineering, Qingdao University of Technology) ;
  • Bi, Jing (School of Civil Engineering, Guizhou University) ;
  • Yuan, Binhang (Computer Science Department, Rice University) ;
  • Wang, Yunteng (Chongqing University)
  • 투고 : 2019.11.22
  • 심사 : 2020.02.21
  • 발행 : 2020.08.10

초록

In this article, a developed bond-based peridynamic model for functionally graded materials (FGMs) is proposed to simulate the dynamic fracture behaviors in FGMs. In the developed bond-based peridynamic model for FGMs, bonds are categorized into three different types, including transverse directionally peridynamic bond, gradient directionally peridynamic bond and arbitrary directionally peridynamic bond, according to the geometrical relationship between directions of peridynamic bonds and gradient bonds in FGMs. The peridynamic micromodulus in the gradient directionally and arbitrary directionally peridynamic bonds can be determined using the weighted projection method. Firstly, the standard bond-based peridynamic simulations of crack propagation and branching in the homogeneous PMMA plate are performed for validations, and the results are in good agreement with the previous experimental observations and the previous phase-field numerical results. Then, the numerical study of crack initiation, propagation and branching in FGMs are conducted using the developed bond-based peridynamic model, and the influence of gradient direction on the dynamic fracture behaviors, such as crack patterns and crack tip propagation speed, in FGMs is systematically studied. Finally, numerical results reveal that crack branching in FGMs under dynamic loading conditions is easier to occur as the gradient angle decreases, which is measured by the gradient direction and direction of the initial crack.

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참고문헌

  1. Abanto-Bueno, J. and Lambros, J. (2006), "An experimental study of mixed model crack initiation and growth in functionally graded materials", Exp. Mech., 46(2), 179-186. https://doi.org/10.1007/s11340-006-6416-6.
  2. Aizikovich, S.M., Galybin, A.N. and Krenev, L.I. (2015), "Semi-analytical solution for mode I penny-shaped crack in a soft inhomogeneous layer", Int. J. Solids Struct., 53, 129-137. https://doi.org/10.1016/j.ijsolstr.2014.10.010.
  3. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., 18(3), 659-672. https://doi.org/10.12989/scs.2015.18.3.659.
  4. Areias, P., Rabczuk T. and Dias-da -Costa, D. (2013), "Element-wise fracture algorithm based on rotation of edges", Eng. Fract. Mech., 110, 113-137. https://doi.org/10.1016/j.engfracmech.2013.06.006.
  5. Areias, P., Msekh M. and Rabczuk, T. (2016), "Damage and fracture algorithm using the screened poisson equation and local remeshing", Eng. Fract. Mech., 158, 116-143. https://doi.org/10.1016/j.engfracmech.2015.10.042.
  6. Areias, P., Reinoso, J., Camanho, P., Cesar de Sa, J. and Rabczuk T. (2018), "Effective 2D and 3D crack propagation with local mesh refinement and the screened Poisson equation", Eng. Fract. Mech., 189, 339-360. https://doi.org/10.1016/j.engfracmech.2017.11.017.
  7. Arioui, O., Belakhdar, K., Kaci, A. and Tounsi, A. (2018), "Thermal buckling of FGM beams having parabolic thickness variation and temperature dependent materials", Steel Compos. Struct., 27(6), 777-788. https://doi.org/10.12989/scs.2018.27.6.777.
  8. Bazazzadeh, S., Shojaei, A., Zaccariotto, M. and Galvanetto, U. (2018), "Application of the Peridynamic differential operator to the solution of sloshing problems in tanks", Eng. Comput., 36(1), 45-83. https://doi.org/10.1108/EC-12-2017-0520.
  9. Bazazzadeh, S., Mossaiby, F. and Shojaei, A. (2020), "An adaptive thermo-mechanical peridynamic model for fracture analysis in ceramics", Eng. Fract. Mech., 223, 106708. https://doi.org/10.1016/j.engfracmech.2019.106708.
  10. Bobaru, F. and Duangpanya, M. (2010), "The peridynamic formulation for transient heat conduction", Int. J. Mass Transf., 53(19), 4047-4059. https://doi.org/10.1016/j.ijheatmasstransfer.2010.05.024.
  11. Bobaru, F. and Hu, W. (2012), "The meaning selection and use of the peridynamic horizon and its relation to crack branching in brittle materials", Int. J. Fract., 176(2), 215-222. https://doi.org/10.1007/s10704-012-9725-z.
  12. Bobaru, F. and Duangpanya, M. (2012), "A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities", J. Comput. Phys., 231(7), 2764-2785. https://doi.org/10.1016/j.jcp.2011.12.017.
  13. Bourdin, B., Francfort, G. and Marigo, J.J. (2000), "Numerical experiments in revisited brittle fracture", J. Mech. Phys. Solids, 48(4), 797-826. https://doi.org/10.1016/s0022-5096(99)00028-9.
  14. Bouiadjra, R.B., Mahmoudi, A., Benyoucef, S., Tounsi, A. and Bernard, F. (2018), "Analytical investigation of bend ing response of FGM plate using a new quasi 3D shear deformation theory: Effect of the micromechanical models", Struct. Eng. Mech., 66(3), 317-328. https://doi.org/10.12989/sem.2018.66.3.317
  15. Carlsson, J. and Isaksson, P. (2019), "Crack dynamics and crack tip shielding in a material containing pores ana lysed by a phase field method", Eng. Fract. Mech., 206, 526-540. https://doi.org/10.1016/j.engfracmech.2018.11.013.
  16. Cheng, Z.Q., Gao, D.Y. and Zhong, Z. (2012), "Interface crack of two dissimilar bonded functionally graded strips with arbitrary distributed properties under plane deformations", Int. J. Mech. Sci., 54(1), 287-293. https://doi.org/10.1016/j.ijmecsci.2011.11.009.
  17. Cheng, Z., Liu, Y., Zhao, J., Feng, H. and Wu, Y. (2018), "Numerical simulation of crack propagation and branching in functionally graded materials using peridynamic modeling", Eng. Fract. Mech., 191, 13-32. https://doi.org/10.1016/j.engfracmech.2018.01.016.
  18. Cheng, Z.Q., Sui, Z.B., Cheng, H., Yuan, C.F. and Chu, L.S. (2019), "Studies of dynamic fracture in functionally graded materials usingperidynamic modeling with composite weighted bond", Theor. Appl. Fract. Mech., 103, 102242. https://doi.org/10.1016/j.tafmec.2019.102242.
  19. Cheng, Z., Zhang, G., Wang, Y. and Bobaru, F. (2015), "A peridynamic model for dynamic fracture in functionally graded materials", Compos. Struct., 133, 529-546. https://doi.org/10.1016/j.compstruct.2015.07.047.
  20. Chen, Z., Niazi, S. and Bobaru, F. (2019), "A peridynamic model for brittle damage and fracture in porous materi als", Int. J. Rock Mech. Min. Sci., 122, 104059. https://doi.org/10.1016/j.ijrmms.2019.104059.
  21. Chen, Z. and Bobaru, F. (2015), "Peridynamic modeling of pitting corrosion damage", J. Mech. Phys. Solids, 78, 352-381. https://doi.org/10.1016/j.jmps.2015.02.015.
  22. Chen, Z., Bakenhus, D. and Bobaru F. (2016), "A constructive peridynamic kernel for elasticity", Comput. Methods Appl. Mech. Engrg., 311, 356-373. https://doi.org/10.1016/j.cma.2016.08.012.
  23. Diana, V. and Casolo, S. (2019), "A bond-based micropolar peridynamic model with shear deformability: Elasticity, failure properties and initial yield domains", Int. J Solids Struct., 160, 201-231. https://doi.org/10.1016/j.ijsolstr.2018.10.026.
  24. Fallahnejad, M., Bagheri, R. and Noroozi, M. (2018), "Transient analysis of two dissimilar FGM layers with mul tiple interface cracks", Struct. Eng. Mech., 67(3), 277-281. https://doi.org/10.12989/sem.2018.67.3.277.
  25. Francfort, G.A. and Marigo, J.J. (1998), "Revisiting brittle fracture as an energy minimization problem", J. Mech. Phys. Solids, 46(8), 1319-1342. https://doi.org/10.1016/s0022-5096(98)00034-9.
  26. Galeban, M.R., Mojahedin, A., Taghavi, Y. and Jabbari, M. (2016), "Free vibration of functionally graded thin beams made of saturated porous materials", Steel Compos. Struct., 21(5), 999-1016. https://doi.org/10.12989/scs.2016.21.5.999.
  27. Gu, P. and Asaro, R.J. (1997), "Cracks in functionally graded materials", Int. J. Solids Struct., 34(1), 1-17. https://doi.org/10.1016/0020-7683(95)00289-8.
  28. Gupta, A., Jain, N.K., Salhotra, R. and Joshi, P.V. (2018), "Effect of crack location on vibration analysis of partially cracked isotropic and FGM micro-plate with non-uniform thickness: An analytical approach", Int. J. Mech. Sci., 145, 410-429. https://doi.org/10.1016/j.ijmecsci.2018.07.015.
  29. Gu, X., Zhang, Q., Huang, D. and Yv, Y. (2016), "Wave dispersion analysis and simulation method for concrete SHPB test in peridynamics", Eng. Fract. Mech., 160, 124-137. https://doi.org/10.1016/j.engfracmech.2016.04.005.
  30. Ha, Y.D. and Bobaru, F. (2010), "Studies of dynamic crack propagation and crack branching with peridynamics", Int. J. Fract., 162(1-2), 229-244. https://doi.org/10.1007/s10704-010-9442-4.
  31. Ha, Y.D. and Bobaru F. (2011), "Characteristics of dynamic brittle fracture captured with peridynamics", Eng. Fract. Mech., 78(6), 1156-1168. https://doi.org/10.1016/j.engfracmech.2010.11.020.
  32. Ha, Y.D., Lee J. and Hong J.W. (2015), "Fracturing patterns of rock-like materials in compression captured with peridynamics", Eng. Fract. Mech., 144, 176-193. https://doi.org/10.1016/j.engfracmech.2015.06.064.
  33. Huang, D., Lu, G., Wang, C. and Qiao, P. (2015), "An extended peridynamic approach for deformation and fracture analysis", Eng. Fract. Mech., 141, 196-211. https://doi.org/10.1016/j.engfracmech.2015.04.036.
  34. Huang, D., Lu, G. and Qiao, P. (2015), "An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis", Int. J. Mech. Sci., 94-95, 111-122. https://doi.org/10.1016/j.ijmecsci.2015.02.018.
  35. Hu, Y.L. and Madenci, E. (2016), "Bond-based peridynamic modeling of composite laminates with arbitrary fiber orientation and stacking sequence", Compos. Struct., 153, 139-175. https://doi.org/10.1016/j.compstruct.2016.05.063.
  36. Hu, Y.L. and Madenci, E. (2017), "Peridynamics for fatigue life and residual strength prediction of composite lam inates", Compos. Struct., 160, 169-184. https://doi.org/10.1016/j.compstruct.2016.10.010.
  37. Hu, Y.L., Madenci, E. and Phan, N. (2017), "Peridynamics for predicting damage and its growth in composites", Fatigue Fract. Eng. Mater. Struct., 40(8), 1214-1226. https://doi.org/10.1111/ffe.12618.
  38. Jin, X., Wu, L.Z., Guo, L.C., Yu H.J. and Sun Y.G. (2009), "Experimental investigation of the mixed-mode crack propagation in ZrO2/NiCr functionally graded materials", Eng. Fract. Mech., 76(12), 1800-1810. https://doi.org/10.1016/j.engfracmech.2009.04.003.
  39. Kirugulige, M.S. and Tippur H.V. (2006), "Mixed-mode dynamic crack growth in functionally graded glass-filled epoxy", Exp. Mech., 46(2), 269-281. https://doi.org/10.1007/s11340-006-5863-4.
  40. Kou, M., Han, D., Xiao, C. and Wang Y. (2019a), "Dynamic fracture instability in brittle materials: Insights from DEM simulations", Struct. Eng. Mech., 71(1), 65-75. https://doi.org/10.12989/sem.2019.71.1.065.
  41. Kou, M.M., Lian, Y.J. and Wang, Y.T. (2019b), "Numerical investigations on crack propagation and crack branching in brittle solids under dynamic loading using bond-particle model", Eng. Fract. Mech., 212, 41-56. https://doi.org/10.1016/j.engfracmech.2019.03.012.
  42. Kou, M., Liu, X., Tang, S., and Wang, Y. (2019c), "3-D X-ray computed tomography on failure characteristics of rock-like materials under coupled hydro-mechanical loading", Theor. Appl. Fract. Mech., 104, 102396. https://doi.org/10.1016/j.tafmec.2019.102396.
  43. Lee, J., Hong, J.W. and Jung, J.W. (2017), "The mechanism of fracture coalescence in pre-cracked rock-type mate rial with three flaws", Eng. Geol., 223, 31-47. https://doi.org/10.1016/j.enggeo.2017.04.014.
  44. Le, Q.V., Chan, W.K. and Schwartz, J. (2014), "A two-dimensional ordinary, state based peridynamic model for linearly elastic solids", Int. J. Numer. Meth. Engng., 98(8), 547-561. https://doi.org/10.1002/nme.4642.
  45. Luo, J., Ramazani, A. and Sundararaghavan, V. (2018), "Simulation of micro-scale shear bands using peridynamics with an adaptive dynamic relaxation method", Int. J. Solids Struct., 130-131, 36-48. https://doi.org/10.1016/j.ijsolstr.2017.10.019
  46. Luo, J. and Sundararaghavan, V. (2018), "Stress-point method for stabilizing zero-energy modes in non-ordinary state-based peridynamics", Int. J. Solids Struct., 150, 197-207. https://doi.org/10.1016/j.ijsolstr.2018.06.015.
  47. Messaoudi, K., Boukhalfa, A. and Beldjelili, Y. (2018), "Three dimensional finite elements modeling of FGM plate bending using UMAT", Struct. Eng. Mech., 66(4), 487-494. https://doi.org/10.12989/sem.2018.66.4.487.
  48. Moes, N., Dolbow, J. and Belytschko, T. (1999), "A finite element method for crack growth without remeshing", Int. J. Numer. Meth. Engng., 46(1), 131-150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J.
  49. Moes, N. and Belytschko, T. (2002), "Extended finite element method for cohesive crack growth", Eng. Fract. Mech., 69(7), 813-833. https://doi.org/10.1016/s0013-7944(01)00128-x.
  50. Miehe, C., Hofacker, M. and Welschinger, F. (2010), "A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits", Comput. Methods Appl. Mech. Engrg., 199, 2765-2778. https://doi.org/10.1016/j.cma.2010.04.011.
  51. Nabil, B., Abdelkader, B., Miloud, A. and Noureddine, B. (2017), "On the mixed-mode crack propagation in FGMs plates: comparison of different criteria", Struct. Eng. Mech., 61(3), 371-379. https://doi.org/10.12989/sem.2017.61.3.371.
  52. Nguyen, D.K. and Tran, T.T. (2018), "Free vibration of tapered BFGM beams using an efficient shear deformable finite element model", Steel Compos. Struct., 29(3), 363-377. https://doi.org/10.12989/scs.2018.29.3.363.
  53. Ni, T., Zhu, Q.Z., Zhao, L.Y. and Li, P.F. (2018), "Peridynamic simulation of fracture in quasi brittle solids using irregular finite element mesh", Eng. Fract. Mech., 188, 320-343. https://doi.org/10.1016/j.cma.2018.11.028.
  54. Ni, T., Zaccariotto, M., Zhu, Q.Z. and Galvanetto, U.(2019), "Static solution of crack propagation problems in peri dynamics", Comput. Methods Appl. Mech. Engrg., 346, 126-151. https://doi.org/10.1016/j.cma.2018.11.028.
  55. Pan, H.Z., Song, T.S. and Wang, Z.H. (2015), "An analytical model for collinear cracks in functionally graded materials with general mechanical properties", Compos. Struct., 132, 359-371. https://doi.org/10.1016/j.compstruct.2015.05.055.
  56. Park, W.T., Han, S.C. and Jung, W.Y. (2016), "Dynamic instability analysis for S-FGM plates embedded in Paster nak elastic medium using the modified couple stress theory", Steel Compos. Struct., 22(6), 1239-1259. https://doi.org/10.12989/scs.2016.22.6.1239.
  57. Rabczuk, T. and Belytschko, T. (2004), "Cracking particles: a simplified meshfree method for arbitrary evolving cracks", Int. J. Numer. Meth. Engng., 61(13), 2316-2343. https://doi.org/10.1002/nme.1151.
  58. Rabczuk, T. and Belytschko, T. (2007), "A three-dimensional large deformation meshfree method for arbitrary evolving cracks", Comput. Methods Appl. Mech. Engrg., 196(29-30), 2777-2799. https://doi.org/10.1016/j.cma.2006.06.020.
  59. Rabczuk, T. and Zi, G. (2007), "A meshfree method based on the local partition of unity for cohesive cracks", Comput. Mech., 39(6), 743-760. https://doi.org/10.1007/s00466-006-0067-4.
  60. Ren, H.L., Zhuang, X.Y., Cai, Y.C. and Rabczuk T. (2016), "Dual-horizon peridynamics", Int. J. Numer. Meth. Engng., 108(12), 1451-1476. https://doi.org/10.1002/nme.5257.
  61. Ren, H.L., Zhuang, X.Y. and Rabczuk, T. (2017), "Dual-horizon peridynamics: A stable solution to varying hori zons", Comput. Methods Appl. Mech. Engrg., 318, 762-782. https://doi.org/10.1016/j.cma.2016.12.031.
  62. Rousseau, C.E. and Tippur H.V. (2001), "Dynamic fracture of compositionally graded materials with cracks along the elastic gradient: experiments and analysis", Mech. Mater., 33(7), 403-421. https://doi.org/10.1016/s0167-6636(01)00065-5.
  63. Shojaei, A., 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.
  64. 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.
  65. Shojaei, A., Galvanetto, U., Rabczuk, T., Jenabi, A. and Zaccariotto, M. (2019a), "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.
  66. Shojaei, A., Mossaiby, F., Zaccariotto, M. and Galvanetto, U., (2019b), "A local collocation method to construct Dirichlet-type absorbing boundary conditions for transient scalar wave propagation problems", Comput. Methods Appl. Mech. Engrg., 356, 629-651. https://doi.org/10.1016/j.cma.2019.07.033.
  67. Mossaiby, F., Shojaei, A., Boroomand, B., Zaccariotto, M. and Galvanetto, U. (2020), "Local Dirichlet-type absorbing boundary conditions for transient elastic wave propagation problems", Comput. Methods Appl. Mech. Engrg., 362, 112856. https://doi.org/10.1016/j.cma.2020.112856.
  68. Silling, S.A. (2000), "Reformulation of elasticity theory discontinuities and long range force", J. Mech. Phys. Solids, 48(1), 175-209. https://doi.org/10.1016/s0022-5096(99)00029-0.
  69. Silling, S.A. and Askari, E. (2005), "A meshfree method based on the peridynamic model of solid mechanics", Comput. Struct., 83(17), 1526-1535. https://doi.org/10.1016/j.compstruc.2004.11.026.
  70. Silling, S.A., Epton, M., Weckne, O., Xu, J. and Askari, E. (2007), "Peridynamic states and constitutive modeling", J. Elast., 88(2), 151-184. https://doi.org/10.1007/s10659-007-9125-1.
  71. Silling, S.A. (2014), "Origin and effect of nonlocality in a composite", J. Mech. Mater. Struct., 9(2), 245-258. https://doi.org/10.2140/jomms.2014.9.245.
  72. Wang, Y., Zhou, X. and Xu, X. (2016), "Numerical simulation of propagation and coalescence of flaws in rock materials under compressive loads using the extended non-ordinary state-based peridynamics", Eng. Fract. Mech., 163, 248-273. https://doi.org/10.1016/j.engfracmech.2016.06.013.
  73. Wang, Y., Zhou, X. and Shou, Y. (2017), "The modeling of crack propagation and coalescence in rocks under uni axial compression using the novel conjugated bond-based peridynamics", Int. J. Mech. Sci., 128-129, 614-643. https://doi.org/10.1016/j.ijmecsci.2017.05.019.
  74. Wang, Y., Zhou, X., Wang, Y. and Shou, Y. (2018a), "A 3-D conjugated bond-pair-based peridynamic formulation for initiation and propagation of cracks in brittle solids", Int. J. Solid Struct., 134, 89-115. https://doi.org/10.1016/j.ijsolstr.2017.10.022.
  75. Wang, Y., Zhou, X. and Kou, M. (2018b), "A coupled thermo-mechanical bond-based peridynamics for simulating thermal cracking in rocks", Int. J. Fract., 211(1-2), 13-42. https://doi.org/10.1007/s10704-018-0273-z.
  76. Wang, Y., Zhou, X. and Kou, M. (2018c), "Peridynamic investigation on thermal fracturing behavior of ceramic nuclear fuel pellets under power cycles", Ceram. Int., 44(10), 11512-11542. https://doi.org/10.1016/j.ceramint.2018.03.214.
  77. Wang, L., Xu, J. and Wang, J. (2018d), "A peridynamic framework and simulation of non-Fourier and nonlocal heat conduction", Int. J. Mass Transf., 118, 1284-1292. https://doi.org/10.1016/j.ijheatmasstransfer.2017.11.074.
  78. Wang, L., Xu, J., Wang, J. and Karihaloo J. B. (2019a), "A mechanism-based spatiotemporal non-local constitutive formulation for elastodynamics of composites", Mech. Mater., 128, 105-116. https://doi.org/10.1016/j.mechmat.2018.07.013
  79. Wang, L., Xu, J. and Wang, J. (2019b), "The elastodynamics in linearized isotropic stated-based peridynamic material", J. Elast., 137(2), 157-176. https://doi.org/10.1007/s10659-018-09723-7.
  80. Wang Y., Zhou X. and Kou M. (2019c), "An improved coupled thermo-mechanic bond-based peridynamic model for cracking behaviors in brittle solids subjected to thermal shocks", Eur. J. Mech. A-Solid, 73, 282-305. https://doi.org/10.1016/j.euromechsol.2018.09.007.
  81. Wang, Y.T., Zhou, X.P. and Kou, M.M. (2019d), "Three-dimensional numerical study on the failure characteristics of intermittent fissures under compressive-shear loads", Acta Geotech., 14(4), 1161-1193. https://doi.org/10.1007/s11440-018-0709-7.
  82. Wang, L. and Wang, J. (2019), "On the invariance of governing equations of current nonlocal theories of elasticity under coordinate and gauge transformations", J. Elast., 137(2), 237-246. https://doi.org/10.1007/s10659-018-09715-7.
  83. Wang, Y.T. and Zhou, X.P. (2019), "Peridynamic simulation of thermal failure behaviors in rocks subjected to heating from boreholes", Int. J. Rock Mech. Min. Sci., 117, 31-48. https://doi.org/10.1016/j.ijrmms.2019.03.007.

피인용 문헌

  1. Dynamic Fracture Analysis of Functionally Graded Material Structures - A Critical Review vol.7, 2020, https://doi.org/10.1016/j.jcomc.2021.100227