Probability at the Micro and Nanoscale Workshop, January 5-7, 2005
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
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
A world of materials to explore
Novel Ti-base nanostructure-dendrite
composite with enhanced plasticity
by Guo He, Jürgen Eckert, Wolfgang
Löser and Ludwig Schultz, 2003
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
GBs in biotite, “Recrystallization
and grain growth in minerals:
recent developments”, JL Urai and
M Jessell, 2001
Kumar et al 2003
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
s
sc
Gc  s cd c 2
Kumar et al 2003
Atomistically sharp GB
dc
d
 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 GPa
Average 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?
Kumar et al 2003
(strength distribution?)
•What constitutes a special boundary?
•What are optimum spatial distributions?
•Example: nanocrystalline copper (lots of GBs)
Deformation Mechanisms in
Nanocrystalline Metals
1. Inter-granular
Triple junction cavitation:
Kumar et al., 2003 (TEM)
Grain Boundary sliding:
Van Swygenhoven et al., 1999-2002 (MD)
Kumar et al.,2003 (TEM)
2. Intra-granular
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)
Deformation Mechanisms  Grain Boundary Behavior
3. Collective behavior Example: grain rotation and realignment
Kumar et al., 2003 (TEM, MD)
Yamakov et al., 2004 (MD)
Schiotz and Jacobsen, 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
Shear and Tensile
Equivalent
atomistic
model
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
GB, localized atom shuffling
Circles are interstitial sites
where shuffling occurs. Note
that no dislocations appear in
crystal lattice outside GB region.
Collective migration of GB atoms
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
GB Sliding
Intragranular Plasticity
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
•Exploration of new nanomaterials
•Microstructure optimization (e.g. grain
size distributions)
Ma et. al, Nature 2002
Nanograins blocking initiation and
propagation of shear bands in nonuniform grain size distributions
GB Mechanical Behavior
F. Sansoz and J.F. Molinari submitted to Acta Materialia (2004)
• 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)
GB Properties at Room Temperature
 0  1.4 ~ 2.1 GP a
V ( 297   0 )
]
kT
 60 ~ 760 MP a
  N v Abvexp[
 297
V  7b3
Tension
d c  1.0nm
Rice and Beltz 1994
Shear Displacement
GB shear strengths
distributed uniformly
between 60 ~760 MPa for
all high angle boundaries
(90%)
Tensile Stress
s 0  12.6 GPa  s 297  2.4GPa
Shear Stress
Shear
Opening Displacement
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
GB Sliding
Amount of GB sliding is correlated
with macroscopic response
Increased Stress Heterogeneity
GB Sliding
Intragranular Plasticity