Slide 1

Controlling grain boundary damage mechanisms in micro and nanostructures: a plea for Grain Boundary Engineering Jean-Franois 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 Slide 2 Outline Introduction Objectives and approach Microcracking in Al 2 O 3 ceramic material Gathering data on GBs: nanocrystalline copper example _ Atomistic modeling of grain boundary sliding _A continuum model for nanocrystalline copper Conclusions and outlook Slide 3 Novel Ti-base nanostructure-dendrite composite with enhanced plasticity by Guo He, Jrgen Eckert, Wolfgang Lser and Ludwig Schultz, 2003 A world of materials to explore Slide 4 Enhanced material properties High tensile ductility in a nanostructured metal, Nature, Vol. 419, 2002, By Wang, Chen, Zhou, Ma Slide 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 Kumar et al 2003 GBs in biotite, Recrystallization and grain growth in minerals: recent developments, JL Urai and M Jessell, 2001 Slide 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??? Slide 7 Example of techniques: research finite element code Slide 8 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 Kumar et al 2003 Atomistically sharp GB use cohesive element Slide 9 The effect of confinement pressure on GB micro-cracking in Al 2 O 3 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? Slide 10 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 Slide 11 Compressive loading No confinement pressure Macroscopic stress/strain curveDamage evolution Slide 12 Effect of confinement pressure Macroscopic stress/strain curves under increasing confinement pressures Confinement increases failure strength and ductility Slide 13 Explanation Total number of failed GBs at failure is constant But connectedness decreases with increasing confinement pressure Slide 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 Slide 15 Deformation Mechanisms in Nanocrystalline Metals 1.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) Slide 16 Data gathering (QC Method) Gain understanding of the mechanical response of a GB at the nanoscale Identify structural parameters relevant to nanomechanical response. Quasicontinuum modelEquivalent atomistic model Shear and Tensile behavior of various symmetric/asymmetric, high/low energy, GBs Slide 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); Slide 18 Observed scatter in GB sliding shear strength Note: Tensile strength 5 to 10 times shear strength Slide 19 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 Slide 20 GB-Related Partial Dislocation Emission Stacking fault (SF) emitted because of a point defect (circled) in GB Slide 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 Slide 22 GB sliding versus intragranular plasticity Equivalent plastic strain in 50nm and 5nm grains samples GB Sliding Increased Stress Heterogeneity Intragranular PlasticityGB Sliding Slide 23 Conclusion Have developed numerical approach to study deformation/damage mechanisms at GBs Approach was applied to _ Al 2 O 3 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) Slide 24 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 Slide 25 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) Slide 26 GB Properties at Room Temperature Shear Tension Opening Displacement Tensile Stress Shear Displacement Shear Stress GB shear strengths distributed uniformly between 60 ~760 MPa for all high angle boundaries (90%) Rice and Beltz 1994 Slide 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 Slide 28 Isolation of Deformation Mechanisms 10 nm grain size Intragranular plasticity initiated from grain boundary activity only small amounts of grain rotation were observed Slide 29 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