Modeling size effects on void growth and coalescence in single crystals

(1)

HAL Id: cea-02438716

https://hal-cea.archives-ouvertes.fr/cea-02438716

Submitted on 28 Feb 2020

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Modeling size effects on void growth and coalescence in

single crystals

C. Ling, S. Forest, J. Besson, B. Tanguy, F. Latourte

To cite this version:

C. Ling, S. Forest, J. Besson, B. Tanguy, F. Latourte. Modeling size effects on void growth and coalescence in single crystals. ICTAM 2016 - 24th International Congress of Theoretical and Applied Mechanics, Aug 2016, Montreal, Canada. �cea-02438716�

(2)

Modeling Size Effects on

Void Growth and Coalescence in

Single Crystals

05/07/2016

ICTAM 2016 | 2016/08/23 | Palais des congrès, Montréal, Canada| PAGE 1

C. LING

1,2

_{, S. FOREST}

2

_{, J. BESSON}

2

_,

B. TANGUY

1

_{, F. LATOURTE}

3

1

_{CEA, Université de Paris-Saclay, DEN, Laboratoire de Comportement}

Mécanique des Matériaux Irradiés,91191 Gif-sur-Yvette cedex, France

2

_{MINES ParisTech, PSL Research University, Centre des matériaux,}

CNRS UMR 7633

,

BP 87, 91003 Evry cedex, France

3

_{EDF R&D, MMC, Site des Renardières, 77818 Moret-sur-Loing}

(3)

BACKGROUND AND MOTIVATION

| PAGE 2

Clear bands

Black dots

Frank loops

[Edwards et al. (2003b), Pokor et al. (2004c) and Nogaret (2007)]

Micro-sized precipitate

[Little (1986), Garner et al. (2005)]

Nano-size voids

[Zinkle et Was (2013)]

Fracture surface in the Fe-18Cr-10Ni-TI stainless steel irradiated in

BOR-60

[Neustroev and Garner (2009)]

(4)

OUTLINE

Gradient enhanced single crystal plasticity

Localization analysis

Size dependent void growth

Conclusion

(5)

GRADIENT ENHANCED SINGLE CRYSTAL PLASTICITY

Assumption:

Stress state of a material point depends on plastic strain gradient.

| PAGE 4

Internal forces power

Principle of virtual power

_→

Equilibrium equations and boundary conditions

Positive dissipation density

_→

Yield function and flow rule

Free energy potential

with

*Références : [Forest, 2009], [Aslan et al., 2011], [Wulfinghoff et Böhlke, 2012], [Forest, 2016]

[Germain, 1973]

(6)

GRADIENT ENHANCED SINGLE CRYSTAL PLASTICITY

05/07/2016

Yield functions for the slip system :

Multiplicative decomposition of the deformation gradient:

Plastic strain rate:

Plastic slip rate:

with

(7)

SIMPLE SHEAR ON A DEFECTED PLATE

| PAGE 6

= 10

= 9.9

Point O fixed

Periodic boundary condition

Plane strain

imposed

Localization band. Its width ?

Linear softening

with

< 0

(8)

EFFECTS OF PARAMETER

• Band width varies with .

?

(9)

COMPARISON:

NUMERICAL AND ANALYTICAL RESULTS

| PAGE 8

One periodic solution is

sinusoidal with wave length:

with

= −10

MPa

= 10

MPa and

= 5

N

(10)

SIZE DEPENDENT VOID GROWTH

Plane strain

1% initial void volume fraction

Biaxial tension:

= 5 × 10 MPa

and

= 5 N

3 values for : 0.1mm, 1mm, 10mm

Hardening law based on the evolution

of dislocation density

= !

⁄

!

= 0.625

12 0 s su u c D D u

b

a

τ

= +

τ

µ

∑

ρ

1

s s s D s c D D

g

b

L

ρ

=





−

ρ





γ





&

Multiplication

Annihilation

1 12 ₂ s su u D u

L

κ

b

ρ

−





=

_

_



∑



with

(11)

SIZE DEPENDENT VOID GROWTH

(12)