Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Numerical Simulations of Crack Initiation and Propagation Using Cohesive Zone Elements

응집영역요소를 이용한 균열진전 모사

  • 하상렬 (포항공과대학교 기계공학과)
  • Received : 2009.09.29
  • Accepted : 2009.11.19
  • Published : 2009.12.30
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Abstract

In this study a cohesive zone model was used to simulate the delamination phenomena which occurs by a successive crack initiation and propagation in composite laminates. The cohesive zone model was incorporated to the classical finite element method via cohesive element formulation and then implemented into the user-subroutine UEL of a commercial finite element program Abaqus. To validate the formulation and implementation of the cohesive element the finite element results were compared with the experimental data of double cantilever beam and end notched flexure tests. The numerical results well agree with the experimental load-displacement curves. Also the effect of the elastic stiffness and the size of the cohesive element on the global load-displacement curves were studied numerically. To minimize the mesh-dependency of the crack propagation path and eliminate the zig-zag patterns in the load-displacement curve, cohesive elements should be refined at the crack-tip.

본 연구에서는 복합재료 적층판에서 균열 생성 및 전파로 이루어지는 계면박리 현상을 모사하기 위하여 응집영역모델을 사용하였다. 응집영역모델을 고려한 유한요소해석을 수행하기 위하여 응집요소를 수식화하였으며, 상용유한요소 프로그램인 Abaqus의 사용자 정의 서브루틴 UEL로 구현하였다. 제안된 응집요소의 타당성과 유효성을 평가하기 위하여 복합재료 적층판의 이중외팔보(double cantilever beam) 시험과 ENF(end notched flexure) 시험결과와 유한요소해석 결과를 비교하였다. 해석 결과는 거시적인 하중-변위 곡선을 비교적 잘 예측하였다. 또한 응집요소를 이용한 유한요소해석시 탄성계수와 응집요소의 크기가 구조물의 하중-변위 곡선에 미치는 영향을 수치적으로 연구하였다. 균열 전파 경로의 격자 의존성을 최소화하고 하중-변위 곡선에 나타나는 지그-재그 현상을 제거하기 위하여 균열 선단에서 충분히 작은 응집요소가 사용되어야 한다.

Keywords

References

  1. Barenblatt, G.I. (1962) Mathematical Theory of Equilibrium Crack in Brittle Fracture, Advance in Applied Mechanics, 7, pp.55-129 https://doi.org/10.1016/S0065-2156(08)70121-2
  2. Benzeggagh, M.L., Kenane, M. (1996) Measurement of Mixed-Mode Delamination Fracture Toughness of Unidirectional Glass/Epoxy Composites with Mixed-Mode Bending Apparatus, Compos. Sci. Technol., 49, pp.439-449 https://doi.org/10.1016/0266-3538(96)00005-X
  3. Camacho, G.T., Ortiz, M. (1996) Computational Modelling of Impact Damage in Brittle Materials, International Journal Solids Struc., 33, pp.2899-2938 https://doi.org/10.1016/0020-7683(95)00255-3
  4. Cox, B., Yang, Q. (2005) Cohesive Models for Damage Evolution in Laminated Composites, International Journal Fracture, 133, pp.107-137 https://doi.org/10.1007/s10704-005-4729-6
  5. Dugdale, D.S. (1960) Yielding of Steel Sheets Containing Slits, Journal Mech. Phys. Solids, 8, pp.100-108 https://doi.org/10.1016/0022-5096(60)90013-2
  6. Freund, L.B., Suresh, S. (2003) Thin Film Materials: Stress, Defect Formation, and Surface Evolution, Cambridge University Press
  7. Geubelle, P.H. (1995) Finite Deformation Effects in Homogeneous and Interfacial Fracture, International Journal Solids Struc., 36, pp.1003-1016 https://doi.org/10.1016/0020-7683(94)00174-U
  8. Goyal, S.V., Johnson, E.R., Davila, C.G. (2004) Irreversible Constitutive Law for Modeling the Delamination Process Using Interfacial Surface Discontinuities, Compos. Struct., 64, pp.91-105 https://doi.org/10.1016/j.compstruct.2003.11.005
  9. Hibbitt, Karlsson, Sorensen. (2004) ABAQUS 6.5 User's Manuals. Pawtucket, USA.
  10. Li, H., Chandra, N. (2003) Analysis of Crack Growth and Crack-tip Plasticity in Ductile Materials Using Cohesive Zone Models, International Journal Plasticity, 19, pp.849-882 https://doi.org/10.1016/S0749-6419(02)00008-6
  11. Lin, G., Geubelle, P.H., Sottos, N.R. (2001) Simulation of Fiber Debonding with Friction in a Model Composite Pushout Test, International Journal Solids Struct., 38, pp. 8547-8562 https://doi.org/10.1016/S0020-7683(01)00085-3
  12. Nittur, P.G., Maiti, S. Geubelle, P.H. (2008) Grain-Level Analysis of Dynamic Fragmentation of Ceramics under Multi-Axial Compression, Journal Mech. Phys. Solids, 56, pp. 993-1017 https://doi.org/10.1016/j.jmps.2007.06.007
  13. Ortiz, M., Pandolfi, A. (1999) Finite Deformation Irreversible Cohesive Elements for Three Dimensional Crack-Propagation Analysis, International Journal Num. Meth. Eng., 44, pp.1267-1282 https://doi.org/10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7
  14. Ruiz, G., Pandolfi, A., Ortiz, M. (2001) Three-Dimensional Cohesive Modeling of Dynamic Mixed-Mode Fracture, International Journal Numer. Methods Eng., 52, pp.97-120 https://doi.org/10.1002/nme.273
  15. Simo, J., Ju, J.W. (1987a) Strain- and Stress-Based Continuum Damage Model-I. Formulation, International Journal Solids Struct., 23, pp. 821-840 https://doi.org/10.1016/0020-7683(87)90083-7
  16. Turon, A., Camanho, P.P., Costa, J., Davila, C.G. (2006) A Damage Model for the Simulation of Delamination in Advanced Composites under Variable-Mode Loading, Mech. Mater., 38, pp.1072-1089 https://doi.org/10.1016/j.mechmat.2005.10.003
  17. Tvergaard, V., Hutchinson, J.W. (1992) The Relation Between Crack Growth Resistance and Fracture Process Parameters in Elastic-Plastic Solids, Journal Mech. Phys. Solids, 40, pp. 1377-1397 https://doi.org/10.1016/0022-5096(92)90020-3
  18. Xu, X.P., Needleman, A. (1994) Numerical Simulations of Fast Crack Growth in Brittle solids, Journal Mech. Phys. Solids, 42, pp. 1397-1434 https://doi.org/10.1016/0022-5096(94)90003-5
  19. Yang, Q., Shim, D., Spearing, S. (2004) A Cohesive Zone Model for Low Cycle Fatigue Life Prediction of Solder Joints, Microel. Eng., 75, pp.85-95 https://doi.org/10.1016/j.mee.2003.11.009