Ductile fracture (of metals) An introduction

Transcription

1 Ductile fracture (of metals) An introduction Jérémy Hure CEA Saclay, Department of Materials for Nuclear Applications Special thanks to : Tom Petit, Pierre-Olivier Barrioz, Arnaud Courcelle (CEA), Kim Nielsen (DTU)

2 Experimental observations Engineering de nition : Fracture associated with a large amount of plastic strain (Tipper, 1949) (Yesterday's) observations after mechanical loading (Tipper, 1949) (Puttick, 1959) 2/29

3 Experimental observations Engineering de nition : Fracture associated with a large amount of plastic strain (Tipper, 1949) (Today's) observations after mechanical loading (Babout et al, 2004) 5µ m (Benzerga, 1999) 3/29

4 Experimental observations Fractographic observations (Plateau et al., 1957) (Courcelle, CEA) Characteristics of ductile fracture surfaces Dimples Broken inclusions (Petit & Morgeneyer, CEA, CDM) 4/29

5 Summary of experimental observations Three di erent phases Nucleation Voids nucleate from particles Decohesion from the matrix Growth Fracture of the particle Enlargement of voids Through di use plastic ow Without interactions between voids Coalescence Enlargement of voids Through localized plastic ow With interactions between voids The material becomes porous The porosity increases The porosity increases (Puttick, 1959) (Cox, 1973) (Puttick, 1959) 5/29

6 From a dense material to a porous material Nucleation criteria (from particles) Energetic approach (Gurland & Plateau, 1963) Brittle particles (or interfaces) : Gri th-like model Fracture!"#$%&'()*)+,-./+0#')()*)+,- Debonding Interfacial strength / Fracture stress Models used in ductile fracture modeling Initial Porosity From particles GDR MePhy - Atelier "Nouveaux dè s en mè canique de la rupture" Novembre /29

7 Behavior of a porous material under mechanical loading Simpli ed case: Periodic arrangement of voids of porosity Simulation box Numerical simulations à la (Koplik & Needleman, 1988) Average stress Porosity evolution 7/29

8 Behavior of a porous material under mechanical loading Void growth to coalescence (Average) Stress: Softening due to the increase of porosity ) Towards an analytical homogenized model 7/29

9 Plastic behavior of porous materials Macroscopic (representative volume element scale) behavior Average stress Local stress Homogenized behavior law in the growth regime Void size / Porosity evolution in the coalescence regime GDR MePhy - Atelier "Nouveaux dè s en mè canique de la rupture" Novembre /29

10 Plastic behavior of porous materials A simpli ed model to describe the material around the voids Rigid (no elasticity) Perfectly plastic (no hardening) Isotropic Constitutive equations Plastic yield criterion Plastic ow = Stress - Hydrostatic pressure Metal plasticity (without voids) is only sensitive to local shear (dislocations motion) Isochoric deformation Rigid perfectly plastic ~ Bingham plastic uid 9/29

11 Plastic behavior of porous materials Macroscopic yield criterion / yield stress Under shear!"#$%&'$()*$&%! Under hydrostatic pressure!)*$&%! GDR MePhy - Atelier "Nouveaux dè s en mè canique de la rupture" Novembre /29

12 Plastic behavior of porous materials Macroscopic yield criterion for porous material (spherical voids) Shear Hydrostatic pressure Stress triaxiality Gurson-Tvergaard-Needleman (GTN) criterion (1977, 1981, 1984) Reduced yield stress as increases Plastic ow? 11/29

13 Plastic behavior of porous materials Plastic ow under hydrostatic pressure Yield criterion Material incompressibility Plastic ow under shear Rice & Tracey law (1969) Void growth Material incompressibility No void growth, but... GDR MePhy - Atelier "Nouveaux dè s en mè canique de la rupture" Novembre /29

14 Plastic behavior of porous materials Macroscopic behavior Softening due to porosity increase Cavities nucleation Cavities growth Other (important) consequence: Localization The homogenized model can be used in numerical simulations: Fracture corresponds to the case Example : Finite element simulation of ductile tearing Other example: Talk of Jean-Philippe Crété 13/29

15 Plastic behavior of porous materials (Felter & Nielsen, 2017) 13/29

16 Some extensions of early models ( ) Strain-hardening Competition between void softening and matrix hardening (Gurson, 1977) Coalescence modeling Phenomenological law for the evolution of porosity in the coalescence regime Homogenization in the coalescence regime New dimensionless parameters: (Tvergaard & Needleman, 1984) (Thomason, 1985) 14/29

17 Some extensions of early models ( ) Void shapes: Spherical to spheroidal to ellipsoidal (Gologanu et al., 1993; Ponte Castaneda & Zaidman, 1994 ;...) Material : Isotropic to orthotropic: von Mises to Hill plasticity (Benzerga & Besson, 2001;...) Talk of Kostas Danas Models for low stress triaxialities (shear dominant loading) (Tvergaard, 2008; Nahshon & Hutchinson, 2008;...) Talk of Léo Morin (Cao et al., 2015) 15/29

18 Recent review articles /29

19 Ductile fracture : Recent works and challenges Some actual research e orts and challenges in ductile fracture modeling not discussed in the previous recent reviews Void nucleation without inclusions Mechanisms? Physical mechanisms through model experiments Physical mechanisms through direct imaging Void growth in highly anisotropic materials Small voids? Size e ects in ductile fracture 17/29

20 Void nucleation without inclusions Classical models involved particles breaking or debonding but : Other mechanisms to nucleate voids / Cracks? Materials with (almost) no inclusion : Pure metals? (Beevers & Honeycombe, 1962) Crack initiation along slip bands / Highly localized plasticity 18/29

21 Voids nucleation without inclusions (Noell et al., 2017) (Barrioz, CEA) Vacancies condensation? Grain boundary cracking? Models to use in these situations? 19/29

22 Physical mechanisms through model experiments Voids drilling (Laser, Focused-Ion Beam,...) through plates (Rhine, 1961) (Weck & Wilkinson, 2008) Precise control of voids geometry Essentially 2D, but can be done in 3D Allows assessing physical mechanisms for void growth and coalescence 20/29

23 Physical mechanisms through model experiments Sometimes, mechanisms are what we believe they are: Sometimes not... (Barrioz, CEA) (Nemcko & Wilkinson, 2016) Models to use in these situations? (Barrioz, CEA) 21/29

24 Physical mechanisms through direct imaging X-ray tomography to look inside the material Allows visualizing voids inside materials (Petit & Morgeneyer, CEA, Centre des Matériaux Mines) Spatial resolution : down to hundreds of nanometers Talk of Sylvain Dancette 22/29

25 Physical mechanisms through direct imaging X-ray tomography to look inside the material (Petit & Morgeneyer, CEA, Centre des Matériaux Mines) Models accounting for heterogeneities? 23/29

26 Void growth in highly anisotropic materials Voids at the crystal scale Small voids in polycrystalline materials Large voids in single crystals What's di erent? Plastic slips along well-de ned directions / planes Strong e ects of crystallographic orientations (Barrioz, CEA) 24/29

27 Void growth in highly anisotropic materials Strong in uence of crystallographic orientations on: Homogenized yield criterion Porosity evolution Void shape (Mbiakop et al., 2015) (Ling et al., 2016) Talk of Kostas Danas 25/29

28 Size effects in ductile fracture Classical ductile fracture models have no lengthscale, but physical lengthscales appear naturally at lower scales Dislocation density "Plasticity lengthscale" Dimensionless parameter = Continuum case (Barrioz, CEA) (Chang et al., 2015) Limited void growth due to dislocation starvation Additional hardening to strain gradient e ect (Ling et al., 2017) Experimental results? 26/29

29 Size effects in ductile fracture Classical ductile fracture models have no lengthscale, but physical lengthscales appear naturally at lower scales Dislocation density "Plasticity lengthscale" Dimensionless parameter = Continuum case (Barrioz, CEA) If no dislocations around: Dislocation nucleation Void growth Very large stress required Experimental results? (Zhao et al., 2009) 27/29

30 Size effects in ductile fracture Classical ductile fracture models have no lengthscale, but physical lengthscales appear naturally at lower scales Surface tension of the void-matrix interface Surface energy Plastic dissipation Hardening / delayed softening for smaller voids 100nm Experimental results? (Morin et al., 2015) 28/29

31 Conclusion Lots of things have been done, but even more to do! 29/29