Abstract
The goal of this contribution is to formally present an incremental damage model conceived to predict failure of ductile materials in forming and crash applications. Denoted henceforth by the acronym Generalized Incremental Stress State Dependent Damage Model (GISSMO), the present model’s framework is based on an incremental damage accumulation which is dependent on a failure curve which, in turn, is a function of the current stress state. The damage variable is of scalar nature and inherently takes into account the effects of non-proportional loadings. Furthermore, GISSMO includes the evolution of an instability measure based on a critical strain. When this variable reaches unity, the coupling between the stress tensor and the damage variable is considered. This allows capturing the effects in post-critical regime macroscopically, from strain localization to final element erosion and crack formation. Since spurious mesh dependence is a concern when simulating material behavior up to fracture, a regularization strategy is proposed to compensate for the effects of mesh dependence in a global fashion. The aforementioned aspects of GISSMO are presented and discussed in detail in the present contribution as well as the calibration of the model based on experimental data of a dual-phase steel. It is shown that GISSMO is able to reproduce the fracture behavior of the calibrated material for several load paths.
Similar content being viewed by others
References
Andrade FXC (2011) Non-local modelling of ductile damage: formulation and numerical issues. Ph.D. thesis, University of Porto
Andrade F, Feucht M, Haufe A (2014) On the prediction of material failure in LS-DYNA: a comparison between GISSMO and DIEM. In: Proceedings of the 13th international LS-DYNA users conference. Detroit
Andrieux F, Sun D-Z, Feucht M (2013) Effect of stress state on the failure behavior of a dual phase steel. In: Proceedings of 19th international symposium on plasticity and its current applications
Bai Y (2008) Effect of loading history on necking and fracture. Ph.D. thesis, Department of Ocean Engineering, Massachusetts Institute Technology
Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46:81–98
Bao Y, Wierzbicki T (2004) A comparative study on various ductile crack formation criteria. J Eng Mater Technol 126:24–314
Barsoum I, Faleskog J (2007) Rupture mechanisms in combined tension and shear: experiments. Int J Solids Struct 44:1768–1786
Basaran M (2011) Stress state dependent damage modeling with a focus on the Lode angle influence. 2011. Ph.D. thesis, RWTH Aachen
Belytschko T, Liu WK, Doghri I (2000) Nonlinear finite elements for continua and structures. Wiley, New York
Bressan JD, Williams JA (1983) The use of a shear instability criterion to predict local necking in sheet metal deformation. Int J Mech Sci 25:155–168
Bridgman PW (1952) Studies in large flow and fracture. McGraw-Hill, New York
Cervera M, Chiumenti M, Agelet de Saracibar C (2004) Softening, localization and stabilization: capture of discontinuous solutions in J2 plasticity. Int J Numer Anal Methods Geomech 28:373–393
Cervera M, Chiumenti M (2009) Size effect and localization in J2 plasticity. Int J Solids Struct 46:3301–3312
Cesar de Sa JMA, Areias PMA, Zheng C (2006) Damage modelling in metal forming problems using an implicit non-local gradient model. Comput Methods Appl Mech Eng 195:6646–6660
De Borst R, Mühlhaus H (1992) Gradient-dependent plasticity: formulation and algorithmic aspects. Int J Numer Methods Eng 35:521–539
De Souza Neto EA, Peric D, Owen DRJ (2008) Computational methods for plasticity: theory and applications. Wiley, New York
Dunand M, Mohr D (2011) On the predictive capabilities of the shear modified Gurson and the modified Mohr-Coulomb fracture models over a wide range of stress triaxialities and Lode angles. J Mech Phys Solids 59:1374–1394
Effelsberg J, Haufe A, Feucht M, Neukamm F, DuBois P (2012) On the parameter identification for the GISSMO damage model. In: Proceedings of the 12th international LS-DYNA users conference. Detroit
Feucht F (1999) Ein gradientenabhängiges Gursonmodell zur Beschreibung duktiler Schädigung mit Entfestigung. Ph.D. thesis, Technische Universität Darmstadt (in German)
Feucht M, Haufe A (2013) Crashsimulationen und der Einfluss der Umformgeschichte auf das Strukturverhalten. In: Proceedings of forming technology forum. Munich
Feucht M, Neukamm F, Haufe A (2011) A phenomenological damage model to predict material failure in crashworthiness applications. In: Recent developments and innovative applications in computational mechanics, Festschrift for Professor Wriggers 60th Birthday, Eds: Müller-Hoppe, Löhnert, Reese, ISBN 978-3-642-17484-1
Feucht M, Sun D-Z, Erhart T, Frank T (2006) Recent development and applications of the Gurson model. In: Proceedings of the 5th German LS-DYNA forum. Ulm
Geers MGD, Ubachs RLJM, Engelen RAB (2003) Strongly non-local gradient-enhanced finite strain elastoplasticity. Int J Numer Methods Eng 56:2039–2068
Ghahremaninezhad A, Ravi-Chandar K (2013) Crack nucleation from a notch in a ductile material under shear dominant loading. Int J Fract 184(1):253–266
Ghahremaninezhad A, Ravi-Chandar K (2013) Ductile failure behavior of polycrystalline Al 6061-T6 under shear dominant loading. Int J Fract 180:23–39
Gologanu M, Leblond JB, Devaux J (1993) Approximate models for ductile metals containing non-spherical voids: case of axisymmetric prolate ellipsoidal cavities. J Mech Phys Solids 41:1723–1754
Graf AF, Hosford WF (1993) Calculations of forming limit diagrams for changing strain paths. Metall Mater Trans A 24:2497–2501
Graf AF, Hosford WF (1994) The influence of strain-path changes on forming limit diagrams of Al6111-T4. Int J Mech Sci 36:897–910
Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth: part I—yield criteria and flow rules for porous ductile media. J Eng Mater Technol 99(1):2–15
Haufe A, Andrade F, Feucht M, Neukamm F, DuBois P (2014) The forming-to-crash simulation process chain: new challenges and efficient modeling techniques. In: Proceedings of the international conference “new developments in sheet metal forming”. Fellbach
Haufe A, Feucht M (2009) The challenge to predict material failure in crashworthiness applications: simulation of producibility to serviceability. In: Festschrift zum 60. Geburtstag von Professor Klaus Thoma, Hrsg. S. Hiermaier, EMI, Freiburg
Hill R (1952) On discontinuous plastic states with special reference to localized necking in thin sheets. J Mech Phys Solids 1:19–30
Jirásek M (1998) Nonlocal models for damage and fracture: comparison of approaches. Int J Solids Struct 35:4133–4145
Jirásek M (2007) Nonlocal damage mechanics. Rev Eur de Génie Civ 11:993–1021
Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 21:31–48
Kleemola HJ, Pelkkinkangas MT (1977) Effect of predeformation and strain path on the forming limits of steel, copper and brass. Sheet Met Ind 63:559–591
Laukonis JV, Ghosh AK (1978) Effects of strain path changes on the formability of sheet metals. Metall Trans 9A:1849–1856
Lemaitre J (1985) A continuous damage mechanics model for ductile fracture. J Eng Mater Technol 107:83–89
Lemaitre J (1996) A course on damage mechanics. Springer, Berlin, Heidelberg, New York
LTSC (2015a) LS-DYNA theory manual. Livermore
LTSC (2015b) LS-DYNA keyword user’s manual volume II: material models. Livermore
Mackenzie AC, Hancock JW, Brown DK (1977) On the influence of state of stress on ductile failure initiation in high strength steels. Eng Fract Mech 9:167–188
Madou K, Leblond J-B (2012) A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voids–I: limit-analysis of some representative cell. J Mech Phys Solids 60(5):1020–1036
Malcher L, Andrade Pires FM, Cesar de Sa JMA (2014) An extended GTN model for ductile fracture under high and low stress triaxiality. Int J Plast 54:193–228
Marciniak Z, Kuczynski K (1967) Limit strains in processes of stretch forming sheet metal. J Mech Sci 9:609–620
McClintock FA (1968) A criterion for ductile fracture by the growth of holes. J Appl Mech 35(2):363–371
Müschenborn W, Sonne H (1975) Influence of the strain path on the forming limits of sheet metal. Arch für das Eisenhüttenwesen 46(9):597–602
Nahshon K, Hutchinson JW (2008) Modification of the Gurson model for shear failure. Eur J Mech A Solids 27:1–17
Neukamm F, Feucht M, Haufe A (2009) Considering damage history in crashworthiness simulations. In: Proceedings of the 7th European LS-DYNA users conference. Salzburg
Neukamm F, Feucht M, Haufe A, Roll K (2008) On closing the constitutive gap between forming and crash simulation. In: Proceedings of the 10th international LS-DYNA users conference. Detroit
Pardoen T, Hutchinson JW (2000) An extended model for void growth and coalescence. J Mech Phys Solids 48:2467–2512
Pijaudier-Cabot G, Bazant ZP, Tabbara M (1988) Comparison of various models for strain softening. Eng Comput 5:141–150
Pijaudier-Cabot G, Bazant ZP (1987) Nonlocal damage theory. J Eng Mech 113(10):1512–1533
Rice JR, Tracey DM (1969) On the ductile enlargement of voids in triaxial stress fields. J Mech Phys Solids 17:201–217
Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New York
Stoughton TB (2000) A general forming limit criterion for sheet metal forming. Int J Mech Sci 42:1–27
Stoughton TB (2001) Stress-based forming limits in sheet metal forming. J Eng Mater Technol 123:417–422
Stoughton TB, Zhu X (2004) Review of theoretical models of the strain-based FLD and their relevance to the stress-based FLD. Int J Plast 20:1463–1486
Sun D-Z, Ockewitz A (2013) Testing and modeling of deformation and damage behavior of thick-walled aluminum profiles for crash simulation. In: Proceedings of international congress on light materials: science and technology LightMAT 2013. Deutsche Gesellschaft für Materialkunde e.V., Frankfurt a.M
Sun D-Z, Ockewitz A, Falkinger G, Andrieux F (2013) Characterization and modeling of the deformation and damage behavior of thick-walled aluminum profiles. In: Proceedings of 8th world conference aluminium two thousand. Interall Srl, Modena
Swift HW (1952) Plastic instability under plane stress. J Mech Phys Solids 1:1–18
Tasan CC (2010) Micro-mechanical characterization of ductile damage in sheet metal. Ph.D. thesis, Eindhoven University of Technology
Tvergaard V (1981) Influence of voids on shear band instabilities under plane strain conditions. Int J Fract 157:55–69
Tvergaard V, Needleman A (1984) Analysis of cup-cone fracture in a round tensile bar. Acta Metall 32:157–169
Volk W, Suh J (2014) Prediction of formability for non-linear deformation history using generalized forming limit concept. In: Proceedings of NUMISHEET 2014, p 556–561
Volk W, Weiss H, Jocham D, Suh J (2013) Phenomenological and numerical description of localized necking using generalized forming limit concept. In: Proceedings of IDDRG 2013, p 16–21
Walters CL (2014) Framework for adjusting for both stress triaxiality and mesh size effect for failure of metals in shell structures. Int J Crashworth 19(1):1–12
Weck A (2007) The role of coalescence on ductile fracture. Ph.D. thesis, McMaster University, Hamilton
Wierzbicki T, Xue L (2005) On the effect of the third invariant of the stress deviator on ductile fracture. Technical report, Impact and Crashworthiness Laboratory, Massachusetts Institute of Technology, Cambridge
Xue L (2007) Ductile fracture modeling: theory, experimental investigation and numerical verification. Ph.D. thesis, Massachusetts Institute Technology, Cambridge
Zeng D, Chappuis L, Xia ZC, Zhu X (2008) A path independent forming limit criterion for sheet metal forming simulations. SAE Technical Paper Series 2008-01-1445
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Andrade, F.X.C., Feucht, M., Haufe, A. et al. An incremental stress state dependent damage model for ductile failure prediction. Int J Fract 200, 127–150 (2016). https://doi.org/10.1007/s10704-016-0081-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-016-0081-2