jean-fran ç ois molinari department of mechanical engineering the johns hopkins university
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Jean-Fran ç ois Molinari Department of Mechanical Engineering The Johns Hopkins University Derek Warner (JHU), Frederic Sansoz (University of Vermount). Probability at the Micro and Nanoscale Workshop, January 5-7, 2005. - PowerPoint PPT PresentationTRANSCRIPT
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
])(
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