A Cohesive Zone Model for Crack Growth Simulation in AISI 304 Steel

Document Type : Research Paper


Center for Postgraduate Studies, Aeronautical University of Science and Technology, Tehran


Stable ductile crack growth in 3 mm thick AISI 304 stainless steel specimens has been investigated experimentally and numerically. Multi-linear Isotropic Hardening method coupled with the Von-Mises yield criterion was adopted for modeling elasto-plastic behavior of the material. Mode-I CT fracture specimens have been tested to generate experimental load-displacement-crack growth data during stable crack growth. The critical fracture energy (JIc) was then determined using the finite elements results in conjunction with the experimental data. The effect of in-plane constraints on the numerical-experimental JIc calculation was then investigated. The results of finite element solution were used to tailor an exponential CZM model for simulation of mode-I stable crack growth in CT specimens. It is found that the adopted CZM is generally insensitive to the applied constraints to the crack tip stress state and thus it can effectively be used for simulating crack growth in this material.                                      


[1] Kim J., Gao X., Srivatsan T.S., 2003, Modeling of crack growth in ductile solids: a three-dimensional analysis, International Journal of Solids and Structures 40(26): 7357-7374.
[2] Wei Z., Deng X., Sutton M.A., Yang J., Cheng C. S., Zavattieri P., 2011, Modeling of mixed-mode crack growth in ductile thin sheets under combined in-plane and out-of-plane loading, Engineering Fracture Mechanics 78(17): 3082-3101.
[3] Zhu X.K., Joyce J.A., 2012, Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization, Engineering Fracture Mechanics 85(1): 1-46.
[4] Pirondi A., Fersini D., 2009, Simulation of ductile crack growth in thin panels using the crack tip opening angle, Engineering Fracture Mechanics 76(1): 88-100.
[5] Li H., Fu M.W., Lu J., Yang H., 2011, Ductile fracture: experiments and computations, International Journal of Plasticity 27( 2): 147-180.
[6] Jackiewicz J., Kuna M., 2003, Non-local reqularization for FE simulation of damage in ductile materials, Computational Materials Science 28(3-4): 784-695.
[7] Barenblatt G.I., 1959, Equilibrium cracks formed during brittle fracture, Journal of Applied Mathematics and Mechanics 23: 1273-1282.
[8] Dugdale D.S., 1960, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids 8: 100-104.
[9] Rahulkumar P., Jagota A., Bennison S.J., Saigal S., 2000, Cohesive element modeling of viscoelastic fracture: application to peel testing of polymers, International Journal of Solids and Structures 37: 1873-1897.
[10] Siegmund T., Brocks W., 2000, A numerical study on the correlation between the work of separation and the dissipation rate in ductile fracture, Engineering Fracture Mechanics 67: 139-154.
[11] Camacho G.T., Ortiz, M., 1996, Computational modeling of impact damage in brittle materials, International Journal of Solids and Structures 33: 2899-2938.
[12] Mohammed I., Liechti K.M., 2000, Cohesive zone modeling of crack nucleation at bimaterial corners, Journal of the Mechanics and Physics of Solids 48: 735-764.
[13] Roesler J., Paulino G.H., Park K., Gaedicke C., 2007, Concrete fracture prediction using bilinear softening, Cement and Concrete Composites 29: 300-312.
[14] Shim D. J., Paulino G.H., Dodds Jr. R.H., 2006, J resistance behavior in functionally graded materials using cohesive zone and modified boundary layer models, International Journal of Fracture 13: 91-117.
[15] Aronsson C.G., Backlund J., 1986, Tensile fracture of laminates with cracks, Journal of Composite Materials 20: 287-307.
[16] Espinosa H.D., Dwivedi S., Lu H.C., 2000, Modeling impact induced delamination of woven fiber reinforced composites with contact/cohesive laws, Computer Methods in Applied Mechanics and Engineering 183: 259-290.
[17] Song S.J., Wass A.M., 1995, Energy-based mechanical model for mixed-mode failure of laminated composites, AIAA Journal 33: 739-745.
[18] Kubair D.V., Geubelle P.H., Huang Y.Y., 2003, Analysis of rate –dependent cohesive model for dynamic crack propagation, Engineering Fracture Mechanics 70: 685-704.
[19] Liong R. T., 2011, Application of the Cohesive Zone Model to the Analysis of Rotors with a Transverse Crack, Karlsruher Institut Fur Technologie, KIT Scientific Publishing, Karlsruhe, Germany.
[20] Wang J.T., 2010, Relating Cohesive Zone Models to Linear Elastic Fracture Mechanics, NASA/TM-2010-216692, National Aeronautics and Space Administration, USA.
[21] Scheider I., Brocks W., 2003, Simulation of cup-cone fracture using the cohesive model, Engineering Fracture Mechanics 70: 1943-1961.
[22] Cornec A., Schonfeld W., Schwalbe K. H., Scheider I., 2009, Application of the cohesive model for predicting the residual strength of a large scale fuselage structure with a two-bay crack, Engineering Failure Analysis 16: 2541-2558.
[23] Li W., Siegmund T., 2002, An analysis of crack growth in thin-sheet metal via a cohesive zone model, Engineering Fracture Mechanics 69: 2073-2093.
[24] Chen J., Fox D., 2012, Numerical investigation into multi-delamination failure of composite t-piece specimens under mixed-mode loading using a modified cohesive zone model, Composite Structures 94(6): 2010-2016.
[25] Tvergaard V., Needleman A., 1984, Analysis of the cup-cone fracture in a round tensile bar, Acta Metallurgica 32: 157-169.
[26] Needleman A., Tvergaard V., 1984, An analysis of ductile rupture in notched bars, Journal of the Mechanics and Physics of Solids 32: 461-490.
[27] Li H., Chandra N., 2003, Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models, International Journal of Plasticity 19: 849-882.
[28] Tvergaard V., 2001, Crack growth predictions by cohesive zone model for ductile fracture, Journal of the Mechanics and Physics of Solids 49: 2191-2207.
[29] Geubelle P.H., Baylor J., 1998, Impact-induced delamination of laminated composites: a 2D simulation, Composites 29: 589-602.
[30] Fernandes R.M.R.P., Chousal J.A.G., De Moura M.F.S.F., Xavier J., 2013, Determination of the cohesive laws of composite bonded joints under mode-II loading, Composites Part B: Engineering 52: 269-274.
[31] Dourado N., Pereira F.A.M., De Moura M.F.S.F., Morais J.J.L., Dias M.I.R., 2013, Bone fracture characterization using the end notched flexure tests, Materials Science and Engineerin C 33(1): 405-410.
[32] Zou Z., Reid S.R., Li S., 2003, A continuum damage model for delamination in laminated composites, Journal of the Mechanics and Physics of Solids 51(2): 333-356.
[33] Xu X. P., Needleman A., 1993, Void nucleation by inclusion debonding in a crystal matrix, Modeing and Simulation in Materials Science and Engineering 1: 111-132.
[34] Hsu C. L., Lo J., Yu J., Lee X. G., Tan P., 2003, Residual strength analysis using CTOA criteria for fuselage structures containing multiple site damage, Engineering Fracture Mechanics 70: 525-545.
[35] James M.A., Newman Jr. J.C., 2003, The effect of crack tunneling on crack growth: experiments and CTOA analysis, Engineering Fracture Mechanics 70: 457-468.
[36] Anandarajah A., 2010, Computational Methods in Elasticity and Plasticity: Solids and Porous Media, Springer Science International.