Jean-Fran ç ois Molinari Department of Mechanical Engineering The Johns Hopkins University

1. Jean-François MolinariDepartment of Mechanical EngineeringThe Johns Hopkins University Derek Warner (JHU), Frederic Sansoz (University of Vermount) 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 NIRT: Uncovering deformation mechanisms in nanocrystalline materials

2. 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

3. 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

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

5. 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

6. 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???

7. Example of techniques: research finite element code

8. 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 s c d d c Cohesive element approach to cracking Kumar et al 2003 Atomistically sharp GB  use cohesive element

9. 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 The effect of confinement pressure on GB micro-cracking in Al2O3 • 500 half-a-micron grains (textured microstructure) • Quasi-static compressive loading • Elastic anisotropic grains, frictional contact • Shear and tensile strength of GBs?

10. Unknown are shear strength and tensile strength of GBs (local property) Macroscopic tensile (1.4 GPa) and compressive (4.4 GPa) strengths are known Properties of GBs? • Average GB tensile strength = 4.2 GPa Average GB shear strength = 0.6 GPa

11. Compressive loading No confinement pressure Macroscopic stress/strain curve Damage evolution

12. Effect of confinement pressure Macroscopic stress/strain curves under increasing confinement pressures Confinement increases failure strength and ductility

13. Explanation But connectedness decreases with increasing confinement pressure Total number of failed GBs at failure is constant

14. 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

15. 1.Inter-granular Deformation Mechanisms in Nanocrystalline Metals 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) Schiotz and Jacobsen, 2004 (MD) Yamakov et al., 2004 (MD) Shan et al. , 2004 (TEM)

16. Gain understanding of the mechanical response of a GB at the nanoscale Identify structural parameters relevant to nanomechanical response. Data gathering (QC Method) Shear and Tensile behavior of various symmetric/asymmetric, high/low energy, GBs Quasicontinuum model Equivalent atomistic model

17. 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);

18. Observed scatter in GB sliding shear strength Note: Tensile strength 5 to 10 times shear strength

19. 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

20. GB-Related Partial Dislocation Emission Stacking fault (SF) emitted because of a point defect (circled) in GB

21. 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

22. GB Sliding Increased Stress Heterogeneity GB Sliding Intragranular Plasticity GB sliding versus intragranular plasticity Equivalent plastic strain in 50nm and 5nm grains samples

23. 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)

24. Exploration of new nanomaterials • Microstructure optimization (e.g. grain size distributions) Research outlook Ma et. al, Nature 2002 Nanograins blocking initiation and propagation of shear bands in non-uniform grain size distributions

25. 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)

26. Shear Stress Shear Displacement Tensile Stress Opening Displacement GB Properties at Room Temperature Shear Tension GB shear strengths distributed uniformly between 60 ~760 MPa for all high angle boundaries (90%) Rice and Beltz 1994

27. 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

28. Isolation of Deformation Mechanisms • 10 nm grain size • Intragranular plasticity initiated from grain boundary activity only small amounts of grain rotation were observed

29. GB Sliding Increased Stress Heterogeneity GB Sliding Intragranular Plasticity Variation of GB Shear Strength More GB sliding in calculation with distribution of GB strengths Amount of GB sliding is correlated with macroscopic response