Understanding Cohesive Law Parameters in Ductile Fracture Initiation and Propagation
DOI:
https://doi.org/10.13052/ejcm1779-7179.3012Keywords:
Ductile fracture, XFEM, Cohesive LawAbstract
Continuum Damage Mechanics is successfully employed to describe the behaviour of metallic materials up to the onset of fracture. Nevertheless, on its own, it is not able to accurately trace discrete crack paths. In this contribution, Continuous Damage Mechanics is combined with the XFEM and a Cohesive Law to allow the full simulation of a ductile fracture process. In particular, the Cohesive Law assures an energetically consistent transition from damage to crack for critical damage values lower than one. Moreover, a novel interpretation is given to the parameters of the cohesive law. A fitting method derived directly from the damage model is proposed for these parameters, avoiding additional experimental characterization.
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Jacques Besson. Continuum models of ductile fracture: a review. International Journal of Damage Mechanics, 19(1):3–52, 2010.
Arthur L Gurson. Continuum theory of ductile rupture by void nucleation and growth: Part i?yield criteria and flow rules for porous ductile media. 1977.
Viggo Tvergaard and Alan Needleman. Analysis of the cup-cone fracture in a round tensile bar. Acta metallurgica, 32(1):157–169, 1984.
L. M. Kachanov. Time of the rupture process under creep condition. Izv. Akad. Nauk. SSSR Otd. Tekhn. Nauk., 8:26–31, 1958.
Y. N. Rabotnov. On the equation of state of creep. Proceedings of the Institution of Mechanical Engineers, Conference Proceedings, 178(1):2–117–2–122, 1963.
J. Lemaitre. A continuous damage mechanics model for ductile fracture. J. Eng. Mater. Technol., 107(1):83–89, 1985.
J. Lemaitre. Coupled elasto-plasticity and damage constitutive equations. Compt. Meth. App. Mech. Engng., 51(1-3):31–49, 1985.
J. Lemaitre. A course on damage mechanics. Springer, New York, 1996.
J. Chaboche. Continuum damage mechanics - a tool to describe phenomena before crack initiation. Nuclear Engineering and Design, 64(2):233–247, 1981.
J. Lemaitre and J. L. Chaboche. Mechanics of Solid Materials. Cambridge University Press, Cambridge, 1990.
Cihan Tekoğlu, JW Hutchinson, and Thomas Pardoen. On localization and void coalescence as a precursor to ductile fracture. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 373(2038):20140121, 2015.
Nima Allahverdizadeh, Andrea Gilioli, Andrea Manes, and Marco Giglio. An experimental and numerical study for the damage characterization of a ti–6al–4v titanium alloy. International Journal of Mechanical Sciences, 93:32–47, 2015.
M. Vaz and D. R. J. Owen. Aspects of ductile fracture and adaptive mesh refinement in damaged elasto-plastic materials. Int. J. Num. Meth. Engng., 50(1):29–54, 2001.
J. Mediavilla, R.H.J. Peerlings, and M.G.D. Geers. A robust and consistent remeshing-transfer operator for ductile fracture simulations. Comput. Struct., 84(8-9):604–623, 2006.
J Mediavilla, RHJ Peerlings, and MGD Geers. A robust and consistent remeshing-transfer operator for ductile fracture simulations. Computers & structures, 84(8-9):604–623, 2006.
P. Areias, N. Van Goethem, and E. Pires. A damage model for ductile crack initiation and propagation. Comput.Mech., 47:641–656, 2011.
K. Saanouni. On the numerical prediction of the ductile fracture in metal forming. Engng Fract. Mech., 75(11):3545–3559, 2008.
T. Belytschko, W. K. Liu, and B. Moran. Nonlinear Finite Elements for Continua and Structures. Wiley, Chichester, 2000.
P.O. Bouchard, F. Bay, Y. Chastel, and I. Tovena. Crack propagation modelling using an advanced remeshing technique. Comput. Meth. Appl. Mech. Engrg, 189(3):723–742, 2000.
J-H Song, H. Wang, and T. Belytschko. A comparative study on finite element methods for dynamic fracture. Comput Mech, 42(2):239–250, 2008.
S.R. Beissel, G.R. Johnson, and C.H. Popelar. An element-failure algorithm for dynamic crack propagation in general directions. Engng Fract. Mech., 61(3-4):407–425, 1998.
M. Jirásek and T. Zimmermann. Analysis of rotating crack model. J. Engng. Mech., ASCE, 124:842–851, 1998.
Mariana RR Seabra, Primož Šuštarič, Jose MA Cesar de Sa, and Tomaž Rodič. Damage driven crack initiation and propagation in ductile metals using xfem. Computational mechanics, 52(1):161–179, 2013.
N Vajragupta, V Uthaisangsuk, B Schmaling, S Münstermann, A Hartmaier, and W Bleck. A micromechanical damage simulation of dual phase steels using xfem. Computational Materials Science, 54:271–279, 2012.
J. Mazars and G. Pijaudier-Cabot. From damage to fracture mechanics and conversely: A combined approach. Int. J. Solid Struct., 33(20-22):3327–3342, 1996.
G.I. Barenblatt. The mathematical theory of equilibrium cracks in brittle fracture. volume 7 of Advances in Applied Mechanics, pages 55–129. Elsevier, 1962.
D. S. Dugdale. Yielding of steel sheets containing slits. J. Mech. Physics Solids, 8(2):100–104, 1960.
V. Tvergaard and J.W. Hutchinson. Effect of strain-dependent cohesive zone model on predictions of crack growth resistance. Int. J. Solids Struct., 33(20-22):3297–3308, 1996.
N. Chandra, H. Li, C. Shet, and H. Ghonem. Some issues in the application of cohesive zone models for metal-ceramic interfaces. Int. J. Solids Struct., 39(10):2827–2855, 2002.
H. Li and N. Chandra. Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models. Int. J. Plasticity, 19(6):849–882, 2003.
F. Cazes, M. Coret, A. Combescure, and A. Gravouil. A thermodynamic method for the construction of a cohesive law from a non local damage model. Int. J. Solids Struct., 46:1476–1490, 2009.
F. Cazes, A. Simatos, M. Coret, and A. Combescure. A cohesive zone model which is energetically equivalent to a gradient-enhanced coupled damage-plasticity model. Eur. J. Mech. A/Solids, 29:976–989, 2010.
Huan Li, Lei Li, Jiangkun Fan, and Zhufeng Yue. Verification of a cohesive model-based extended finite element method for ductile crack propagation. Fatigue & Fracture of Engineering Materials & Structures, 44(3):762–775, 2021.
P. Areias, J. Cesar de Sa, and C. Conceição António. A gradient model for finite strain elastoplasticity coupled with damage. Finite Elem. Anal. Des., 39(13):1191–1235, 2003.
B. Moran, M. Ortiz, and F. Shih. Formulation of implicit finite element methods for multiplicative finite deformation plasticity. Int. J. Num. Meth. Engng., 29:438–514, 1990.
J.C. Simo, R.L. Taylor, and K.S. Pister. Variational and projection methods for for volume constraint in finite deformation elasto-plasticity. Compt. Meth. App. Mech. Engng., 51:177–208, 1985.
C. Miehe. A constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric. Int. J. Solid Struct., 35(30):3859–3897, 1998.
R. de Borst and E. Giessen. Material Instabilities in Solids. Wiley, New York, 1998.
A. S. Gullerud, X. Gao, R. H. Dodds Jr, and R. Haj-Ali. Simulation of ductile crack growth using computational cells: numerical aspects. Engng. Fract. Mech., 66(1):65–92, 2000.
K.L. Nielsen and J.W. Hutchinson. Cohesive traction-separation laws for tearing of ductile metal plates. Int. J. Impact Engng, 48(0):15–23, 2012.
C.R. Chen, O. Kolednik, J. Heerens, and F.D. Fischer. Three-dimensional modeling of ductile crack growth: Cohesive zone parameters and crack tip triaxiality. Engng. Fract. Mech., 72(13):2072–2094, 2005.
J. Alfaiate, G. Wells, and .J. Sluys. On the use of embedded discontinuity elements with crack path continuity for mode-I and mixed-mode fracture. Engng, Fract. Mech., 69(6):661–686, 2002.
G. C. Sih. Mechanics of Fracture Initiation and Propagation. Kluwer Academic Publishers, Dordrecht, 1991.
N. Moës and T. Belytschko. Extended finite element method for cohesive crack growth. Engng. Fract. Mech., 69(7):813–833, 2002.