In this study, the classical Gurson—Tvergaard—Needleman (GTN) model has been extended to a non-local form using damage parameter ‘d’ as a degree of freedom in the finite-element (FE) formulation. The evolution of the non-local damage is related to the actual void volume fraction ‘f’ in ductile fracture using a diffusion type equation. The coupled mechanical equilibrium and damage diffusion equations have been discretized using the finite-element (FE) method. In order to demonstrate the mesh-independent nature of the new formulation, a standard fracture mechanics specimen (i.e. 1T compact tension) has been analysed using different mesh sizes near the crack tip and the results have been compared with those of the experiment. The effect of different GTN parameters on the fracture resistance behaviour of this specimen has been studied for the non-local model and these results have also been compared with those of the experiment.
RousselierG., Ductile fracture models and their potential in local approach of fractureNucl. Eng. Des.105 (1987): 97–111.
2.
GursonA. L., Continuum theory of ductile rupture by void nucleation and growth. Part I. Yield criteria and flow rules for porous ductile mediaASME J. Eng. Mater. Technol.99 (1977): 2–15.
3.
NeedlemanA.TvergaardV., An analysis of ductile rupture in notched barsJ. Mech. Phys. Solids32 (1984): 461–490.
4.
TvergaardV.NeedlemanA., Analysis of cup-cone fracture in a round tensile barActa Metall.32 1 (1984): 157–169.
5.
SeidenfussM., Untersuchungen zur Beschreibung des Versagensverhaltens mit Hilfe von Schädigungsmodellen am Beispiel des Werkstoffes 20MnMoNi5-5. PhD Thesis, Fakultät Energietechnik der Universität Stuttgart, Germany, 1992.
6.
RoosE.SeidenfussM.KrämerD.KrolopS.EiseleU.HindenlangU., Application and evaluation of different numerical methods for determining crack resistance curvesNucl. Eng. Des.130 (1991): 297–308.
7.
BrocksW.KlingbeitD.KuneckeG.SunD. Z.Application of the Gurson model to ductile tearing resistanceConstraint effects in fracture: Theory and applications (Eds KirkMBakkerA.) (West Conshohoken: American Society for Testing and Materials1995): 232–252 ASTM STP 1244.
8.
BrocksW.SunD.-Z.HönigA., Verification of the transferability of micromechanical parameters by cell model calculations with visco-plastic materialsInt. J. Plast.11 8 (1995): 971–989.
9.
XiaL.ShihC. F., Ductile crack growth-I: A numerical study using computational cells with microstructurally based length scalesJ. Mech. Phys. Solids43 (1995): 223–259.
10.
RuggieriC.PanontinT. L.DoddsR. H., Numerical modeling of ductile crack growth in 3-D using computational cell elementsInt. J. Fract.82 (1996): 67–95.
11.
EiseleU.SeidenfussM.Pitard-BouetJ.-M., Comparison between fracture mechanics and local approach models for the analysis of shallow cracksJ. Phys. IV6 (1996): 75–89.
12.
BrocksW.SunD.-Z.HönigA., Verification of micromechanical models for ductile fracture by cell model calculationsComput. Mater. Sci.7 1–2 (1996): 235–241.
13.
SteglichD.BrocksW., Micromechanical modelling of the behaviour of ductile materials including particlesComput. Mater. Sci.9 1–2 (1997): 7–17.
14.
SteglichD.SiegmundT.BrocksW., Micromechanical modeling of damage due to particle cracking in reinforced metalsComput. Mater. Sci.16 1–4 (1999): 404–413.
15.
Pitard-BouetJ.-M.SeidenfussM.BethmontM.KussmaulK., Experimental investigations on the ‘shallow crack effect’ on the 10 MnMoNi 5 5 steel and computational analysis in the upper shelf by means of the global and local approachesNucl. Eng. Des.190 (1999): 171–190.
16.
GullerudA. S.GaoX.DoddsR. H.Haj-AliR., Simulation of ductile crack growth using computational cells: Numerical aspectsEng. Fract. Mech.66 (2000): 65–92.
17.
BessonJ.SteglichD.BrocksW., Modeling of crack growth in round bars and plane strain specimensInt. J. Solids Struct.38 46–47 (2001): 8259–8284.
18.
NègreP.SteglichD.BrocksW.KoçakM., Numerical simulation of crack extension in aluminium weldsComput. Mater. Sci.28 3–4 (2003): 723–731.
19.
BessonJ.SteglichD.BrocksW., Modeling of plane strain ductile ruptureInt. J. Plast.19 10 (2003): 1517–1541.
PoussardC.Sainte CatherineC.ForgetP.MariniB., On the identification of critical damage mechanisms parameters to predict the behavior of charpy specimens on the upper shelfJ. ASTM Int.1 (2004): 1–18.
22.
NègreP.SteglichD.BrocksW., Crack extension in aluminium welds: A numerical approach using the Gurson—Tvergaard—Needleman modelEng. Fract. Mech.71 16–17 (2004): 2365–2383.
23.
PavankumarT. V.SamalM. K.ChattopadhyayJ.DuttaB. K.KushwahaH. S.RoosE.SeidenfussM., Transferability of fracture parameters from specimens to component levelInt. J. Press. Vessels Pip.82 5 (2005): 386–399.
24.
SteglichD.PirondiA.BonoraN.BrocksW., Micromechanical modelling of cyclic plasticity incorporating damageInt. J. Solids Struct.42 2 (2005): 337–351.
25.
PirondiA.BonoraN.SteglichD.BrocksW.HellmannD., Simulation of failure under cyclic plastic loading by damage modelsInt. J. Plast.22 11 (2006): 2146–2170.
26.
SeebichH. P., Mikromechanisch basierte schädigungsmodelle zur Beschreibung des Versagensablaufs ferritischer Bauteile. PhD Thesis, Institut für Materialprü-fung Werkstoffkunde und Festigkeitslehre, Universität Stuttgart, Germany, 2007.
27.
SvendsenB., On the thermodynamic of thermoelastic materials with additional scalar degrees of freedomContin. Mech. Thermodyn.4 (1999): 247–262.
28.
ReuschF.SvendsenB.KlingbeilD., A non-local extension of Gurson-based ductile damage modelingComput. Mater. Sci.26 (2003): 219–229.
29.
ReuschF.SvendsenB.KlingbeilD., Local and non-local Gurson-based ductile damage and failure modelling at large deformationEur. J. Mech. A, Solids22 (2003): 779–792.
30.
SamalM. K., Nonlocal damage models for structural integrity analysis. PhD Thesis, Institut für Materialprüfung Werkstoffkunde und Festigkeitslehre, Universität Stuttgart, Germany, 2007.
31.
ChuC. C.NeedlemanA., Void nucleation effects in biaxially streched sheetsTrans. ASME J. Eng. Mater. Technol.102 (1980): 249–256.
32.
AravasN., On the numerical integration of a class of pressure-dependent plasticity modelsInt. J. Numer. Methods Eng.24 (1987): 395–1416.
33.
BatheK. J., Finite element procedures (Englewood Cliffs, New Jersey: Prentice-Hall1995).
34.
KussmaulK.EiseleU.SeidenfussM.On the applicability of local approach models for the determination of the failure behaviour of steels with different toughnessFatigue and fracture mechanics in pressure vessel and piping (Eds Mehtavol. 304 (New York: ASME1995): 17–25.
