From polycrystals to multicrystals origin of the mechanical behavior modification
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ICACM Paris France. From polycrystals to multicrystals : origin of the mechanical behavior modification. 2-4 June 2010. C. Keller, L. Duchêne, M. Afteni, E. Hug, A-M Habraken. “ smaller is stronger “. Ni micropillars, Ø=1 µm (Dimiduk 2005). ?.

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From polycrystals to multicrystals : origin of the mechanical behavior modification

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From polycrystals to multicrystals origin of the mechanical behavior modification

ICACM

Paris

France

From polycrystals to multicrystals: origin of the mechanical behavior modification

2-4 June 2010

C. Keller, L. Duchêne, M. Afteni, E. Hug, A-M Habraken


From polycrystals to multicrystals origin of the mechanical behavior modification

“ smaller is stronger “

Ni micropillars, Ø=1 µm (Dimiduk 2005)

?

Role played by dislocation sources on surface

Introduction

Dimension reduction

Classical mechanical behavior

Polycrystal or large single crystal


From polycrystals to multicrystals origin of the mechanical behavior modification

Introduction

Meso scale -> microsystems scale

0.5 mm

Geiger et al. CRIP 2001

Vollertsen et al. JMPT 2004

  • Characteristics of small parts:

  • dimensions lower than 500 µm

  • metallic alloy with complex microstructure (second phase, precipitates…)


From polycrystals to multicrystals origin of the mechanical behavior modification

  • Forming process:

  • Know-how for bulk parts cannot be used;

  • turn/cast necessary;

  • low production rates/high costs.

  • Reliability:

  • reduced reliability;

  • unexpected fracture;

  • can lead to security problem.

Introduction

Forming processes and industrial use may be problematic

Geiger et al. CRIP 2001

Airbag sensor: inflate start without accident

Small axis 18 step process

Problem linked to our weak knowledge of the mechanical properties


From polycrystals to multicrystals origin of the mechanical behavior modification

Introduction

Experimental/Numerical study of miniaturization Mechanical behavior of nickel

Why nickel?

  • well known mechanical properties

  • simple microstructure

  • used in Micro-Electro-Mechanical systems (MEMS)

Application to

microforming

Fundamentals

aspects

Multi-scale analysis


From polycrystals to multicrystals origin of the mechanical behavior modification

t

Experimental study

Tensile tests for Ni sheets

PhD thesis C. Keller, Supervisor E. Hug, CRISMAT Lab, Caen/France

Thickness between 10 µm and 3.2 mm and constant grain size 100 µm

Strong mechanical behavior modification due to the decrease of t/d ratio


From polycrystals to multicrystals origin of the mechanical behavior modification

Experimental study

Tensile tests for Ni sheets

PhD thesis C. Keller, Supervisor E. Hug, CRISMAT Lab, Caen/France

Three kinds of behavior depending on grain size and thickness

Keller et al., Int. J. Plasticity. Submitted


From polycrystals to multicrystals origin of the mechanical behavior modification

Experimental study

Tensile tests for Ni sheets

PhD thesis C. Keller, Supervisor E. Hug, CRISMAT Lab, Caen/France

Statistical TEM analysis of dislocation cells  stress gradient

t/d=2,5;ε=0,1

core, Φ=1,25 µm

50 µm below surface: Φ=1,58 µm

Keller et al., Mechanics of Materials, 2010


From polycrystals to multicrystals origin of the mechanical behavior modification

Experimental study

Synthesis

Surface effects enhanced by a decrease ofpolycrystalline character

What are the characteristics of the surface effects (deep of stress gradient…)?

What is the role played by dislocations (escape through free surfaces…) ?

How to model the mechanical behavior of thin samples (prediction of the behavior) ?

multiscale modeling with strain gradient crystal plasticity is needed


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

Strain gradient crystal plasticity model

  • “Non-local crystal plasticity model with intrinsic SSD and GND effects”,

  • Evers, L.P.,Brekelmans, W.A.M., Geers, M.G.D.: J Mech. Phys. Solids 52(2004)

  • Modified L. Duchêne + C. Keller

    Features of the model:

  • Based on dislocation glide on slip systems

  • Accounts for dislocation densities

  • Distinction between SSD (statistically stored dislocations), GND (geometrically necessary dislocations)

  • Visco-plastic slip law including a back-stress accounting for internal stresses due to GND


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

Strain gradient crystal plasticity model

Classic equations for crystalline plasticity

slip rate on slip system α

slip resistance for slip system α

SSD density rate of slip system α

mean free path of dislocation on slip system α


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

Strain gradient crystal plasticity model

Specific equations for GND and backstress

GND density rate of slip system α, f depends

on the screw or edge dislocation character

Formulation of the backstress involved by GND. g function depends on the screw or edge character of the dislocations

Size effects reproduced by the model, 36 parameters to indentify


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

Strain gradient crystal plasticity model

F.E. implementation

Starting equations of the strong form:

  • Equilibrium

  • GND densities evolution laws

     3D coupled element with 20 nodes and 8 IP

     Nodal DOF:

    - Displacements (3)

    - GND densities (18)


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

Identification for nickel

Most of parameter values are obtained from literature

  • Nickel crystallograpical characteristics (µ, b, elastic tensor…)  handbook;

  • Dislocation interaction matrix  work of B. Devincre with DDD;

Other parameters identified by simulations of single crystal tensile curves

Three different orientations

Orientation A [001] (X.Feaugas)

Orientation B [111] (A.W.Thompson,1976)

Orientation C S-G (P.Haasen,1956 )


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

Identification for nickel

Thompson 1976

Haasen 1956

Feaugas 2009

  • Identification acceptable but not perfect. Many reasons:

  • Experimental orientations given +/- 2°  strong influence on simulations

  • Old experimental tests

  • Difference of environment for single glide orientations(test realized in air, simulations correspond to vacuum)


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

Application to single crystals

Preliminary surface effect study Tensile test simulation for different thickness single crystals

Single glide orientation

Stage II delayed if thickness decreases  surface effects

Effects similar to those observed experimentally by Mughrabi (Phys. Stat. Sol. 1971) and Fourie (Phil. Mag. 1967) on Cu single crystals


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

Application to single crystals

Dislocations can emerge through free surfaces

SSD distribution into the median cross section

profile along the slip direction

Core region

Keller et al., J. Mech. Phys. Sol. To be published

Single glide orientation, stage I

thickness decrease  reduction of core regions

Softening effect of free surfaces

deep of gradient depends on dislocation mean free path


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

Application to single crystals

Effect of surface hard layer

001 orientation

Free surfaces

Slip directions

profile along the vertical slip direction

Hard layer

dislocations are blocked in case of hard layer

Slip directions

Strengthening effect of free surfaces


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

Application to polycrystals

12 elements / grain, 300 µm edge grain, grain orientations  EBSD

Effect of t/d ratio correctly reproduced by the model


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

Application to polycrystals

12 elements / grain, 300 µm edge grain, grain orientations  EBSD

profile along the line

Keller et al., Metal Forming 2010

t/d=2, median cross section

Strong stress gradients, surface grain affected on 2/3 grain size


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

New strategy of modeling for metal forming

2/3 surface grains affected

composite modeling for metal forming: 2 elastoplastic constitutive laws

Surface constitutive law applied for distance ≈ 2/3 equivalent grain size below free surface


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

New strategy of modeling for metal forming

Application to tensile tests

  • surface constitutive law identified from experimental tensile tests of thin samples (t/d<1)

  • core constitutive law identified from experimental tensile testsofbulk samples (t/d=27)

Simulations with elastoplastic laws

Keller et al., Numiform 2010


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

Application to micro deep drawing

F.E. modeling strategies

  • Modeling with 2 constitutive laws (composite model)

  • Analytical Mixture modeling:

  • Classical bulk modeling (1 constitutive law )


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

Application to micro deep drawing

Application to micro deep drawing, t=250 µm, punch radius: 2.5 mm

“surface effect” approach

mixture approach

Stress distribution modified

Keller et al., Numiform 2010


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

New strategy of modeling for metal forming

Application to micro deep drawing

Prediction of damage, Cockroft-latham criterion

“surface effect” approach

mixture approach

Damage distribution and maximal value modified


From polycrystals to multicrystals origin of the mechanical behavior modification

Numerical modeling

New strategy of modeling for metal forming

Application to dome test

Thickness: 0.1; 0.2; 0.3 and 0.4 mm, punch radius: 4.8 mm

Keller et al., Metal forming 2010

Force prediction depends on strategy, need experimental validation


From polycrystals to multicrystals origin of the mechanical behavior modification

Conclusions

  • Miniaturization effects governed for meso-scale by free surfaces

  • Strong stress gradients appear and must be taken into account

  • Composite approach of modeling is pertinent and better reproduce stress and damage distribution

Perspectives

  • Surface effects must be investigated for multi-axial loading (decrease of dislocation mean free path)

  • Experimental validation of composite approach: dome test (Singapour/SIMTECH) and deep drawing (Galati/Romania)


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