Controlling grain boundary damage mechanisms in micro and

nanostructures: a plea for Grain Boundary Engineering

Jean-François Molinari Department of Mechanical Engineering

The Johns Hopkins University

Derek Warner (JHU), Frederic Sansoz (University of Vermount)

NIRT: Uncovering deformation mechanisms in nanocrystalline materials

Probability at the Micro and Nanoscale Workshop, January 5-7, 2005

Outline

• Introduction

• Objectives and approach

• Microcracking in Al2O3 ceramic material

• Gathering data on GBs: nanocrystalline copper example

_ Atomistic modeling of grain boundary sliding

_ A continuum model for nanocrystalline copper

• Conclusions and outlook

Novel Ti-base nanostructure-dendrite composite with enhanced plasticity

by Guo He, Jürgen Eckert, Wolfgang Löser and Ludwig Schultz, 2003

A world of materials to explore

Enhanced material properties “High tensile ductility in a nanostructured metal”, Nature, Vol. 419, 2002, By Wang, Chen, Zhou, Ma

Grain Boundary Engineering• Fact: grain boundaries (GBs) are performance limiting regions in polycrystalline materials

• GB Engineering (Watanabe 1980) attempts to control damage mechanisms at GBs by understanding:

1) character of individual GBs (and “special” GBs)

2) Collective behavior of GBs (connectedness of special GBs matters more than volume fraction)

• Many success stories have been claimed in corrosion resistance, hydrogen/oxygen embrittlement, creep, ductility, and strength properties

•Yet more fundamental understanding is needed, and industry still has to fully embrace the field Kumar et al 2003

GBs in biotite, “Recrystallization and grain growth in minerals: recent developments”, JL Urai and M Jessell, 2001

A challenge and an opportunity for our community

Computational modeling as an exploratory tool

• Focus: damage mechanisms (cracking/sliding) at grain boundaries (GBs)

• Approach: Finite elements, atomistic, and multiscale codes

•Prediction is very difficult, especially about the future -- Niels Bohr

•All models are wrong. Some are useful -- George E. P. Box

•What is simple is wrong, and what is complicated cannot be understood -- Paul Valery

•We should make things as simple as possible, but not simpler -- Albert Einstein

• Many challenges

What are mechanical properties of GBs???

Example of techniques: research finite element code

Cohesive element approach to cracking

• Cohesive zone concept (Dugdale, Barrenblatt)

• Cohesive elements glue two neighboring ordinary elements

Cracks are created within ordinary elements boundaries

• Cracks explicitly described by cohesive elements

Easy to handle branching, fragmentation

• The opening/closing properties of cohesive elements are governed by a cohesive law

• Will be used to model cracking/sliding at sharp grain boundaries

c

c

2cccG Kumar et al 2003

Atomistically sharp GB

use cohesive element

The effect of confinement pressure on GB micro-cracking in Al2O3

• Ceramic materials: high strength (but low ductility)

• Armor ceramics fail under large compressive stress

• Objective: understand the effect of confinement pressure on failure strength and ductility

500 half-a-micron grains (textured microstructure)

Quasi-static compressive loading

Elastic anisotropic grains, frictional contact

Shear and tensile strength of GBs?

Properties of GBs?• Unknown are shear strength and tensile strength of GBs (local property)

• Macroscopic tensile (1.4 GPa) and compressive (4.4 GPa) strengths are known

Average GB tensile strength = 4.2 GPaAverage GB shear strength = 0.6 GPa

Compressive loading No confinement pressure

Macroscopic stress/strain curve Damage evolution

Effect of confinement pressure

Macroscopic stress/strain curves under increasing confinement pressures

Confinement increases failure strength and ductility

Explanation

Total number of failed GBs at failure is constant

But connectedness decreases with increasing confinement pressure

A plea for GB engineering

•Reducing coalescence of micro-cracks is key to ductility

•Confinement pressure helps (demonstrated with averaged GB properties)

•Connectedness of “special GBs” will have an effect as well

•Fundamental research needs (experimental, numerical, theoretical):

•What are properties of individual GBs in relation to GB structure? (strength distribution?)

•What constitutes a special boundary?

•What are optimum spatial distributions?

•Example: nanocrystalline copper (lots of GBs)

Kumar et al 2003

Deformation Mechanisms in Nanocrystalline Metals1. Inter-granular

Grain Boundary sliding: Van Swygenhoven et al., 1999-2002 (MD)Kumar et al.,2003 (TEM)

Triple junction cavitation: Kumar et al., 2003 (TEM)

Partial dislocation sources and twinning at Grain Boundary: Kumar et al., 2003 (TEM) Milligan et al., 2003 (TEM + theory)

Chen et al., 2003 (TEM) Gleiter et al., 2002 (MD)

2. Intra-granular

Deformation Mechanisms Grain Boundary Behavior

3. Collective behavior Example: grain rotation and realignment

Kumar et al., 2003 (TEM, MD) Schiotz and Jacobsen, 2004 (MD)Yamakov et al., 2004 (MD) Shan et al. , 2004 (TEM)

Data gathering (QC Method)• Gain understanding of the mechanical response of a GB at the

nanoscale• Identify structural parameters relevant to nanomechanical response.

Quasicontinuum model Equivalent atomistic modelShear and Tensile behavior of various symmetric/asymmetric, high/low energy, GBs

Mechanical Response under Shear

Distinct constitutive behaviors:“Stick-slip”– Plateau associated to GB sliding or partial dislocations emission. Modulus of rigidity, G, almost constant for each material regardless of GB structure. Critical parameter is presence of E structural unit at GB (not high energy). Maximum and plateau stresses vary.

“Migration-type” - Elastic loading then sudden decrease and re-loading with same modulus of rigidity. (direction of migration always perpendicular to GB plane);

Observed scatter in GB sliding shear strength

Note: Tensile strength 5 to 10 times shear strength

Interface Deformation Mechanisms

Collective migration of GB atoms

GB, localized atom shuffling

Circles are interstitial sites where shuffling occurs. Note that no dislocations appear in crystal lattice outside GB region.

Collective GB atom migration perpendicular to GB plane

GB-Related Partial Dislocation Emission

Stacking fault (SF) emitted because of a point defect (circled) in GB

Back to continuum modeling: nanocrystalline copper

•Intragranular properties: crystal plasticity

(1/d scaling of flow stress)

•Intergranular properties: adhesive cohesive elements

(properties from atomistic)

•Quasi-Static compressive loading

GB sliding versus intragranular plasticity

Equivalent plastic strain in 50nm and 5nm grains samples

GB Sliding

Increased Stress Heterogeneity

Intragranular PlasticityGB Sliding

Conclusion• Have developed numerical approach to study deformation/damage mechanisms at GBs

• Approach was applied to

_ Al2O3 microstructure (cohesive element approach with averaged properties)

_ Nanocrystalline copper (hierarchical approach: atomistic simulations feeding into continuum model)

•Connectedness of special GBs is promising direction for promoting ductility (by preventing micro-cracks coalescence)

•More fundamental work is needed to determine properties of various GBs under a variety of conditions (data acquisition)

•It is crucial to provide simple strength models that depend on only a few parameters (free volume, vacancies density, GB energy) (data simplification)

•Mathematics are needed to study optimum connectedness and development of stress heterogeneity as function of grain size/GB character.

•Future of GBE is interdisciplinary (Materials Science, Mechanics, Chemistry, Applied Mathematics)

Research outlook

Nanograins blocking initiation and propagation of shear bands in non-uniform grain size distributions

•Exploration of new nanomaterials

•Microstructure optimization (e.g. grain size distributions)

Ma et. al, Nature 2002

GB Mechanical Behavior

• Molecular statics calculations on 13 different tilt GBs – Tensile strength is roughly independent of GB orientation (~12 GPa)

– Shear strength is dependent on GB orientation (1.2 ~ 2.1GPa)

F. Sansoz and J.F. Molinari submitted to Acta Materialia (2004)

GB Properties at Room Temperature

MPa 760~60

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exp[

GPa 1.2~4.1

297

0297

0

kT

VAbvNv

37bV

Shear

Tension

4GPa.2GPa 6.12 2970

Opening Displacement

Te

nsi

le S

tre

ss

Shear Displacement

She

ar S

tres

s

.0nm1c

GB shear strengths distributed uniformly between 60 ~760 MPa for all high angle boundaries (90%)

Rice and Beltz 1994

Microstructure and Loading

•200 grains constructed using Voronoi Tessellation

• Lognormal distribution created via Monte Carlo method

•Standard deviation = 0.26 * average grain size

•14,866 elements

•Refined Mesh at GBs

•Quasi-Static loading

•Uniaxial compression

Isolation of Deformation Mechanisms

• 10 nm grain size

• Intragranular plasticity initiated from grain boundary activity

only small amounts of grain rotation were observed

Variation of GB Shear Strength

More GB sliding in calculation with distribution of GB strengths

Amount of GB sliding is correlated with macroscopic response

GB Sliding

Increased Stress Heterogeneity

Intragranular PlasticityGB Sliding