DOI QR코드

DOI QR Code

Estimation of a mixed-mode cohesive law for an interface crack between dissimilar materials

  • Song, Sung-Il (Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology) ;
  • Kim, Kwang-Soo (Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology) ;
  • Kim, Hyun-Gyu (Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology)
  • Received : 2015.04.03
  • Accepted : 2015.10.22
  • Published : 2016.01.25

Abstract

In this paper, a mixed-mode cohesive law for an interface crack between epoxy and TR (transparent thermoplastic) resin is inversely estimated by the field projection method using numerical solutions and experimentally measured displacements. Displacements in a region far away from the crack tip are measured by digital image correlation technique. An inverse analysis, the field projection method formulated from the interaction J- and M-integrals with numerical auxiliary fields, is carried out to estimate a mixed-mode cohesive law for an interface crack between dissimilar materials. In the present approach, nonlinear deformations and damage near the crack tip are converted into the relationships of tractions and separations on crack surfaces behind the crack tip. The phase angle of mixed-mode singularities of the interface crack is also obtained from measured displacements in this study.

Keywords

Acknowledgement

Grant : Launching Plug-in Digital Analysis Framework for Modular system Design

Supported by : Ministry of Trade, Industry & Energy (MI)

References

  1. Williams, M.L. (1959), "The stresses around a fault or crack in dissimilar media", Bull. Seismol. Soc. Am., 49(2), 199-204.
  2. Rice, J.R. (1988), "Elastic fracture mechanics concepts for interfacial cracks", J. Appl. Mech., ASME, 55(1), 98-103. https://doi.org/10.1115/1.3173668
  3. Erdogan, F. (1965), "Stress distribution in bonded dissimilar materials with cracks", J. Appl. Mech., ASME 32(2), 403-10. https://doi.org/10.1115/1.3625814
  4. England, A.H. (1965), "A crack between dissimilar media", J. Appl. Mech., ASME, 32(2), 400-402. https://doi.org/10.1115/1.3625813
  5. Rice, J.R. and Sih, G.C. (1965), "Plane problems of cracks in dissimilar media", J. Appl. Mech., ASME, 32(2), 418-423. https://doi.org/10.1115/1.3625816
  6. Matos, P.P.L., Mcmeeking, R.M., Charalambides, P.G. and Drory, M.D. (1989), "A method for calculating stress intensities in bimaterial fracture", Int. J. Fract., 40(4), 235-254. https://doi.org/10.1007/BF00963659
  7. Hutchinson, J.W. and Suo, Z. (1992), "Mixed mode cracking in layered materials", J. Appl. Mech., 29(63), 191.
  8. Xu, X.P. and Needleman, A. (1994), "Numerical simulations of fast crack growth in brittle solids", J. Mech. Phys. Solids., 42(9), 1397-1434. https://doi.org/10.1016/0022-5096(94)90003-5
  9. Camacho, G.T. and Ortiz, M. (1996), "Computational modeling of impact damage in brittle materials", Int. J. Solid. Struct., 33(20), 2899-2938. https://doi.org/10.1016/0020-7683(95)00255-3
  10. Ortiz, M. and Pandolfi, A. (1999), "Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis", Int. J. Numer. Method. Eng., 44, 1267-1282. https://doi.org/10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7
  11. Mergheim, J., Kuhl, E. and Steinmann, P. (2005), "A finite element method for the computational modeling of cohesive cracks", Int. J. Numer. Meth. Eng., 63(2), 276-289. https://doi.org/10.1002/nme.1286
  12. Xu, L. and Tippur, H.V. (1995), "Fracture parameters for interface cracks: an experimental-finite element study of crack tip fields and crack initiation toughness", Int. J. Fract., 71(4), 345-363. https://doi.org/10.1007/BF00037814
  13. Ikeda, T., Miyazaki, N. and Soda, T. (1998), "Mixed mode fracture criterion of interface crack between dissimilar materials", Eng. Fract. Mech., 59(6), 725-735. https://doi.org/10.1016/S0013-7944(97)00177-X
  14. Liechti, K.M. and Chai, Y.S. (1992), "Asymmetric shielding in interfacial fracture under in-plane shear", J. Appl. Mech., ASME, 59(2), 295-304. https://doi.org/10.1115/1.2899520
  15. Yuuki, R., Liu, J., Xu, Q., Ohira, J.Q. and Ono, T. (1994), "Mixed mode fracture criteria for an interface crack", Eng. Fract. Mech., 47(3), 367-377. https://doi.org/10.1016/0013-7944(94)90094-9
  16. Tan, H., Liu, C., Huang, Y. and Geubelle, P.H. (2005), "The cohesive law for the particle/matrix interfaces in high explosives", J. Mech. Phys. Solid., 53(8), 1892-1917. https://doi.org/10.1016/j.jmps.2005.01.009
  17. Zhu, Y., Liechti, K.M. and Ravi-Chandar, K. (2009), "Direct extraction of rate-dependent tractionseparation laws for polyurea/steel interfaces", Int. J. Solid. Struct., 46(1), 31-51. https://doi.org/10.1016/j.ijsolstr.2008.08.019
  18. Guo, Z.K., Kobayashi, A.S., Hay, J.C. and White, K.W. (1999), "Fracture process zone modeling of monolithic Al2O3", Eng. Fract. Mech., 63(2), 115-129. https://doi.org/10.1016/S0013-7944(99)00030-2
  19. Shen, B. and Paulino, G.H. (2011), "Direct extraction of cohesive fracture properties from digital image correlation: A hybrid inverse technique", Exp. Mech., 51(2), 143-163. https://doi.org/10.1007/s11340-010-9342-6
  20. Gain, A.L., Carroll, J., Paulino, G.H. and Lambros, J. (2011), "A hybrid experimental/numerical technique to extract cohesive fracture properties for mode-I fracture of quasi-brittle materials", Int. J. Fract., 169(2), 113-131. https://doi.org/10.1007/s10704-010-9578-2
  21. Kim, H.G. and Lee, K.W. (2009), "A study on the influence of measurement location and regularization on the evaluation of boundary tractions by inverse finite element method", Finite Elem. Anal. Des., 45(8), 569-582. https://doi.org/10.1016/j.finel.2009.03.006
  22. Hong, S. and Kim, K.S. (2003), "Extraction of cohesive-zone laws from elastic far-fields of a cohesive crack tip: a field projection method", J. Mech. Phys. Solid., 51(7), 1267-1286. https://doi.org/10.1016/S0022-5096(03)00023-1
  23. Hong, S., Chew, H.B. and Kim, K.S. (2009), "Cohesive-zone laws for void growth - I. Experimental field projection of crack-tip crazing in glassy polymers", J. Mech. Phys. Solid., 57(8), 1357-1373. https://doi.org/10.1016/j.jmps.2009.04.003
  24. Chew, H.B., Hong, S. and Kim, K.S. (2009), "Cohesive zone laws for void growth - II. Numerical field projection of elasto-plastic fracture processes with vapor pressure", J. Mech. Phys. Solid., 57(8), 1374- 1390. https://doi.org/10.1016/j.jmps.2009.04.001
  25. Chalivendra, V.B., Hong, S., Arias, I., Knap, J., Rosakis, A. and Ortiz, M. (2009), "Experimental validation of large-scale simulations of dynamic fracture along weak planes", Int. J. Impact Eng., 36(7), 888-898. https://doi.org/10.1016/j.ijimpeng.2008.11.009
  26. Kim, H.G., Chew, H.B. and Kim, K.S. (2012), "Inverse extraction of cohesive zone laws by field projection method using numerical auxiliary fields", Int. J. Numer. Meth. Eng., 91(5), 516-530. https://doi.org/10.1002/nme.4281
  27. Oh, J.C. and Kim, H.G. (2013), "Inverse estimation of cohesive zone laws from experimentally measured displacements for the quasi-static mode I fracture of PMMA", Eng. Fract. Mech., 99, 118-131. https://doi.org/10.1016/j.engfracmech.2012.11.002
  28. Shih, C.F., Moran, B. and Nakamura, T. (1986), "Energy release rate along a three-dimensional crack front in a thermally stresses body", Int. J. Fract., 30(2), 79-102. https://doi.org/10.1007/BF00034019
  29. Jin, Z-.H. and Sun, C.T. (2005), "Cohesive zone modeling of interface fracture in elastic bi-materials", Eng. Fract. Mech., 72(12), 1805-1817. https://doi.org/10.1016/j.engfracmech.2004.09.011
  30. Rice, J.R. (1988), "Elastic fracture mechanics concepts for interface cracks", J. Appl. Mech., ASME, 55(1), 98-103. https://doi.org/10.1115/1.3173668
  31. Matos, P.P.L., McMeeking, R.M., Charalambides, P.G. and Drory, M.D. (1989), "A method for calculating stress intensities in biomaterial fracture", Int. J. Fract., 40(4), 235-254. https://doi.org/10.1007/BF00963659
  32. Stern, M., Becker, E.B. and Dunham, R.S. (1976), "A contour integral computation of mixed-mode stress intensity factors", Int. J. Fract., 12(3), 359-368. https://doi.org/10.1007/BF00032831
  33. Rice, J.R. (1968), "A path independent integral and the approximate analysis of strain concentration by notches and cracks", J. Appl. Mech., ASME, 35(2), 379-386. https://doi.org/10.1115/1.3601206
  34. Barenblatt, G.I. (1962), "The mathematical theory of equilibrium cracks in brittle fracture", Adv. Appl. Mech., 7(1), 55-129. https://doi.org/10.1016/S0065-2156(08)70121-2
  35. Xu, X.P. and Needleman, A. (1993), "Void nucleation by inclusion debonding in a crystal matrix", Model. Simul. Mater. Sci. Eng., 1(2), 111-132. https://doi.org/10.1088/0965-0393/1/2/001
  36. Tvergaard, V. (1990), "Effect of fibre debonding in a whisker-reinforced metal", Mater. Sci. Eng., 125(2), 203-213. https://doi.org/10.1016/0921-5093(90)90170-8
  37. Needleman, A. (1987), "A continuum model for void nucleation by inclusion debonding", J. Appl. Mech., ASME, 54(3), 525-531. https://doi.org/10.1115/1.3173064
  38. Freed, Y. and Banks-Sills, L. (2008), "A new cohesive zone model for mixed mode interface fracture in biomaterials", Eng. Fract. Mech., 75(15), 4583-4593. https://doi.org/10.1016/j.engfracmech.2008.04.013
  39. Park, K.S., Paulino, G.H. and Roesler, J.R. (2009), "A unified potential-based cohesive model of mixedmode fracture", J. Mech. Phys. Solid., 57(6), 891-908. https://doi.org/10.1016/j.jmps.2008.10.003

Cited by

  1. Mixed-mode fracture analysis of composite bonded joints considering adhesives of different ductility vol.207, pp.1, 2017, https://doi.org/10.1007/s10704-017-0219-x
  2. Using CZM and XFEM to predict the damage to aluminum notched plates reinforced with a composite patch vol.15, pp.2, 2020, https://doi.org/10.2140/jomms.2020.15.185
  3. Adhesive thickness effects on the mixed-mode fracture toughness of bonded joints vol.96, pp.1, 2016, https://doi.org/10.1080/00218464.2019.1681269
  4. Selected Aspects of Cohesive Zone Modeling in Fracture Mechanics vol.11, pp.2, 2016, https://doi.org/10.3390/met11020302