Material parameter characterization for the Gurson model · GTN characterization Approaches...

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Material parameter characterization for the Gurson model Carlos Felipe Guzm´ an MS 2 F Sector Department ArGEnCo University of Li` ege, Belgium [email protected] October 17, 2013

Transcript of Material parameter characterization for the Gurson model · GTN characterization Approaches...

Page 1: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Material parameter characterizationfor the Gurson model

Carlos Felipe Guzman

MS2F SectorDepartment ArGEnCo

University of Liege, [email protected]

October 17, 2013

Page 2: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Contents

1 Introduction

2 GTN characterization

3 Characterization methodologies

4 References

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Page 3: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

The Gurson [1977] model

Fp(σ, f, σY ) =σ2eq

σY 2− 1 + 2f cosh

(3

2

σmσY

)− f2︸ ︷︷ ︸

Damage

= 0

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Page 4: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

The Gurson [1977] model

Fp(σ, f , σY ) =σ2eq

σY 2− 1 + 2 f cosh

(3

2

σmσY

)− f 2︸ ︷︷ ︸

Damage

= 0

f = (1− f) trεp

1 new material parameter: f0

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Page 5: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

GTN extension

The Gurson-Tvergaard-Needleman (GTN) extension:

Nucleation [Chu and Needleman, 1980].

(Corrected) void growth.

Coalescence [Tvergaard and Needleman, 1984].

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Page 6: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

GTN extensionTvergaard [1982]

Fp(σ, f, σ) =σ2eq

σ2 − 1 + 2q1f cosh

(−3

2q2σmσ

)− q3f2 = 0

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Page 7: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

GTN extensionTvergaard [1982]

Fp(σ, f, σ) =σ2eq

σ2 − 1 + 2 q1 f cosh

(−3 q2 σm

)− q3 f

2 = 0

2 new material parameters: q1, q2 (q3 = q12)

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Page 8: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

NucleationChu and Needleman [1980]

f = fg + fn + fs

fn = AεPeq︸︷︷︸Strain

+B (σeq + cσM )︸ ︷︷ ︸Stress

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Page 9: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

NucleationChu and Needleman [1980]

f = fg + fn + fs

fn = AεPeq︸︷︷︸Strain

+B (σeq + cσM )︸ ︷︷ ︸Stress

A(εeq) =1√2π

fNSN

exp

[−1

2

(εeq − εNSN

)2]

B(σ) = 0

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Page 10: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

NucleationChu and Needleman [1980]

f = fg + fn + fs

fn = AεPeq︸︷︷︸Strain

+B (σeq + cσM )︸ ︷︷ ︸Stress

A(εeq) =1√2π

fNSN

exp

[−1

2

(εeq − εNSN

)2]

B(σ) = 0

3 new parameters: fN , εN , SN

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Page 11: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

CoalescenceTvergaard and Needleman [1984]

f∗ =

f if f < fcr

fcr +fu − fcrfF − fcr

(f − fcr) if f > fcr

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Page 12: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

CoalescenceTvergaard and Needleman [1984]

f∗ =

f if f < fcr

fcr +fu − fcrfF − fcr

(f − fcr) if f > fcr

2 new parameters: fcr, fF

(fu =

1

q1

)

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Page 13: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Shear extensionXue [2008]; Nahshon and Hutchinson [2008]

f = fg + fn + fs

fs = kωfω(s)sεP

σeq

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Page 14: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Shear extensionXue [2008]; Nahshon and Hutchinson [2008]

f = fg + fn + fs

fs = kω fω(s)sεP

σeq

1 new parameter: kω

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Page 15: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Resuming. . .

9 material parameters:

f0

q1, q2

Nucleation: fN , εN , SN

Coalescence: fcr, fF

Shear: kω

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Page 16: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

GTN characterization

Approaches

Microscopic measurements.

Macroscopic measurements.

Hybrid experimental-numerical.

Criteria

Parameter scale.

Nature of the parameter (stress state based, fitting, etc.).

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Page 17: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

GTN characterization

Approaches

Microscopic measurements.

Macroscopic measurements.

Hybrid experimental-numerical.

Criteria

Parameter scale.

Nature of the parameter (stress state based, fitting, etc.).

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Page 18: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Microscopic approach

Image analysis, 3D tomography, in-situ neutron diffraction,. . .

Use whenever it is possible.

We can identify 4(5) parameters:

f0, fN , fcr, fF , (SN )

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Page 19: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Microscopic approach

Image analysis, 3D tomography, in-situ neutron diffraction,. . .

Use whenever it is possible.

We can identify 4(5) parameters:

f0, fN , fcr, fF , (SN )

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Page 20: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Tensile test DC01 steel

fF measurement:

f = 0.4− 0.5%

f = 0.04− 0.07%

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Page 21: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Tensile test DC01 steel

Other variables: void spacing, size, distribution SN , etc.

Qualitative measurements:

Ductile

Fragile

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Page 22: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Ductile vs. fragileBarsoum and Faleskog [2007]

Cavity controlled (Dimples)T = 1.10

Shear controlledT = 0.47

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Page 23: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Macroscopic approach

Different notch radius for different triaxiality.

DIC measurements.

Measurements

Load-displacement curve.

Displacement at the onset of fracture and at fracture.

(Sheet) thickness.

DIC: crack appearance.

DIC: strain path to fracture.

We can identify 1(3) parameters:

εN (q1, q2)

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Page 24: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Onset of fractureDunand and Mohr [2010]

Location of the onset offracture:

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Page 25: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Cup-to-cone fractureBenzerga and Leblond [2010]

Macro-micro approach:

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Page 26: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Hybrid numerical-experimental

Finite element simulations coupled with experiments.

Inverse modeling

Deterministic (OPTIM)

Stochastic (AI Lagamine)

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Page 27: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Simple methodologyLi et al. [2011]

Al-alloy 6061 T6

GTN model (without shear).

1 f0 =0.02 from image analysis.

2 q1 =1.25 and q2 =1.0 fixed.

3 εN =0.3, SN =0.01, fN =0.02 fixed.

4 fc =0.045 and fF =0.0475 obtained through iterations.

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Page 28: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Numerical methodologyXue et al. [2010]

DH36 steel

Gurson+coalescence+shear

No microscopic measurements are available.

1 n from a single tensile test.

2 f0 and D (element size) from the load-displacement crackedspecimen.

3 No information about fF =0.25, fcr =0.15.

4 kω from a shear-off test.

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Page 29: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Numerical methodologyXue et al. [2010]

DH36 steel

Gurson+coalescence+shear

No microscopic measurements are available.

1 n from a single tensile test.

2 f0 and D (element size) from the load-displacement crackedspecimen.

3 No information about fF =0.25, fcr =0.15.

4 kω from a shear-off test.

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Page 30: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Hybrid methodologyDunand and Mohr [2010, 2011]

TRIP780 steel sheets.

GTN+shear.

Multiaxial tests and error assesment.

stress and strain from hybrid experimental-numerical.

No inverse modeling.

1 f0 =6× 10=5 from image analysis.

2 Nucleation parameters fitted from tensile specimen.

3 q1 and q2 from a punch test.

4 Coalescence parameters from the punch test.

5 kω from butterfly test (shear).

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Page 31: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Hybrid methodologyDunand and Mohr [2010, 2011]

TRIP780 steel sheets.

GTN+shear.

Multiaxial tests and error assesment.

stress and strain from hybrid experimental-numerical.

No inverse modeling.

1 f0 =6× 10=5 from image analysis.

2 Nucleation parameters fitted from tensile specimen.

3 q1 and q2 from a punch test.

4 Coalescence parameters from the punch test.

5 kω from butterfly test (shear).

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Page 32: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

Hybrid methodologyDunand and Mohr [2010, 2011]

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Page 33: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

To keep in mind. . .

Bad plasticity modeling ⇒ bad damage modeling (coupled criteria)

Fracture is very sensible to loading paths: diverse test are needed.

The sensibility of the load-displacement curve to the parametersshould be evaluated.

Post-necking behaviour seems to be important.

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Page 34: Material parameter characterization for the Gurson model · GTN characterization Approaches Microscopic measurements. Macroscopic measurements. Hybrid experimental-numerical. Criteria

References

Barsoum, I., Faleskog, J., Mar. 2007. Rupture mechanisms in combined tension andshear-Experiments. International Journal of Solids and Structures 44 (6), 1768–1786.

Benzerga, A. A., Leblond, J.-B., 2010. Ductile Fracture by Void Growth to Coalescence. In: Aref,H., van der Giessen, E. (Eds.), Advances in Applied Mechanics. Vol. 44 of Advances in AppliedMechanics. Elsevier, pp. 169–305.

Chu, C. C., Needleman, A., 1980. Void Nucleation Effects in Biaxially Stretched Sheets. Journal ofEngineering Materials and Technology 102 (3), 249.

Dunand, M., Mohr, D., May 2010. Hybrid experimental-numerical analysis of basic ductile fractureexperiments for sheet metals. International Journal of Solids and Structures 47 (9), 1130–1143.

Dunand, M., Mohr, D., Jul. 2011. On the predictive capabilities of the shear modified Gurson andthe modified Mohr-Coulomb fracture models over a wide range of stress triaxialities and Lodeangles. Journal of the Mechanics and Physics of Solids 59 (7), 1374–1394.

Gurson, A. L., 1977. Continuum theory of ductile rupture by void nucleation and growth: PartI-Yield criteria and flow rules for porous ductile media. Journal of Engineering Materials andTechnology 99 (1), 2–15.

Li, H., Fu, M., Lu, J., Yang, H., Feb. 2011. Ductile fracture: Experiments and computations.International Journal of Plasticity 27 (2), 147–180.

Nahshon, K., Hutchinson, J., Jan. 2008. Modification of the Gurson Model for shear failure.European Journal of Mechanics - A/Solids 27 (1), 1–17.

Tvergaard, V., 1982. On localization in ductile materials containing spherical voids. InternationalJournal of Fracture 18 (4), 237–252.

Tvergaard, V., Needleman, A., Jan. 1984. Analysis of the cup-cone fracture in a round tensile bar.Acta Metallurgica 32 (1), 157–169.

Xue, L., Jul. 2008. Constitutive modeling of void shearing effect in ductile fracture of porousmaterials. Engineering Fracture Mechanics 75 (11), 3343–3366.

Xue, Z., Pontin, M., Zok, F., Hutchinson, J., Feb. 2010. Calibration procedures for acomputational model of ductile fracture. Engineering Fracture Mechanics 77 (3), 492–509. 24