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Introduction to Computational Materials Science Simulating Plasticity at the Mesoscale

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Introduction to Computational Materials Science Simulating Plasticity at the Mesoscale Introduction to Computational Materials Science Simulating plasticity at the mesoscale Richard LeSar ICMR Summer School, UCSB August 2013 Materials Science and Engineering IOWA STATE UNIVERSITY OF SCIENCE AND TECHNOLOGY 1 ICMR Summer School on Materials in 3 D: Modeling and Imaging at Multiple Length Scales modelingLocation: ESB 1001 talks at the Summer School Week 1 – Aug 19 – 23 Date 9:00 am – 10:30am 11:00am – 12:30pm 2:00pm – 3:30 pm 3:30 pm – 5:00pm Mon Aug 19th Marc De Graef Poster Session Peter Voorhees Emmanuelle Marquis (1001 ESB Patio) Tues Aug 20th Matt Miller Stuart Wright MiKe JacKson McLean Echlin Wed Aug 21st Poster Session MiKe Mills Satoshi Hata Richard LeSar (1001 ESB Patio) Thurs Aug 22nd Dave Rowenhorst Joann Kuchera-Morin Samantha Daly Dan Gianola Matt Wright Fri Aug 23rd Yunzhi Wang Marc DeGraef Open Demo Session Free Time Week 2 – Aug 26 – 30 Date 9:00 am – 10:30am 11:00am – 12:30pm 2:00pm – 3:30 pm 3:30 pm – 5:00pm Mon Aug 26th Poster Session Simon Philpot Matt Begley Michelle Johannes (1001 ESB Patio) Tues Aug 27th Simon Philpot TBA MiKe Uchic Frederic Gibou Wed Aug 28th TBA Michelle Johannes Anton Van der Ven Baron Peters Thurs Aug 29th TBA Jianwei (John) Miao Jianwei (John) Miao Anton Van der Ven Fri Aug 30th James Rondinelli James Rondinelli Barbecue at Goleta Beach Notes: Group Photoshoot (ESB 2001 stairs) on Monday, August 19th. Dinner at El Paseo Restaurant on Thursday, August 22nd. DFT/atomistics multiscale mesoscale 2 Definitions: modeling and simulation A model is an idealization of real behavior, i.e., an approximate description based on empirical and/or physical reasoning. A simulation is a study of the dynamical response of a modeled system found by subjecting models to inputs and constraints that simulate real events. A simulation does not mimic reality, rather it mimics a model of reality. 3 modeling and simulation The accuracy of a simulation depends on many factors, some involving the simulation method itself (accuracy in solving sets of equations, for example). Often, however, the biggest errors in a simulation, as least with respect to how well it describes a real system, are the inadequacies of the models upon which the simulation is based. Thus, one cannot separate simulations from the underlying models. 4 How do we create models? Useful article by Mike Ashby (Materials Science and Technology 8, 102 (1992)) Discusses a systematic procedure that one can follow to produce models. Many models would have been improved if this process had been followed. Think before you compute! 5 MR43CH07-Chernatynskiy ARI 1 June 2013 12:33 1. INTRODUCTION Uncertainty quantification (UQ) and related areas, such as risk analysis and decision making, have a Uncertainty: the long and successful history of development and applications in diverse areas such as climate change maximum estimated (1, 2), structural engineering (3), and medicine (4, 5). UQ has not, however, been fully recognized amount by which the as a central question for materials simulation. The goal of this article is to provide an overview of value of a quantity, the techniques developed for UQ, with a focus on approaches introduced for the description of obtained from experiment, theory, epistemic uncertainty (or lack of knowledge; see definition and more detailed discussion below) simulation, or other and applications, although there are few applications of these approaches in the simulations of means, is expected to materials properties. A key challenge for understanding and predicting the properties of materials differ from the true is the broad range of length scales and timescales that govern materials behavior. These scales value range from the angstrom and subpicoseconds of atomic processes to the meters and years of Simulation: fracture and fatigue phenomena in many materials in engineered applications. Between these numerical analysis of extremes lies a complex set of behaviors that depend on the type of materials as well as on their the equations describing the model specific engineering application. We show a simple example of this range of behaviors in Table 1, behavior; often highlighting the various scales that govern the mechanical behavior of materials, especially metals. performed with the aid A different choice of materials type or property would lead to a figure that would likely be similar of a computer in form, although very different in detail. Model: an The complexity illustrated in Table 1 has long hindered the development of new materials for idealization of the specific applications, with an obvious negative impact on technological and economic develop- phenomenon, i.e., an ment. Over the past few years, it has become increasingly clear that a new approach to accelerated approximate description based on materials development is needed, in which information and data from both experiment and sim- empirical and/or ulation are synthesized across timescales and/or length scales; this approach is sometimes termed physical reasoning that integrated computational materials science and engineering (ICMSE) (6). An even more exciting captures its essential prospect is to go beyond ICMSE to concurrent engineering, in which the computational design of features the material becomes an integral part of the overall design process of the engineered application, optimizing the overall design to take full advantage of the materials characteristics in ways not currently possible (7, 8). Modeling and simulation are central to ICMSE and concurrent design. Theoretical models are abstract, mathematical representations of actual, real-life structures and processes. Constructing ascales model starts of with deformation a choice of which phenomena should be included (and thus, by implication, Table 1 Length scales and timescales used to describe the mechanics of materials, as adapted from Reference 9a by University of Florida - Smathers Library on 07/08/13. For personal use only. Annu. Rev. Mater. Res. 2013.43:157-182. Downloaded from www.annualreviews.org Unit Length scale Timescale Mechanics Complex structure 10 3 m 10 6 s Structural mechanics Simple structure 10 1 m 10 3 s Fracture mechanics Component 10–1 m 10 0 s Continuum mechanics Grain microstructure 10–3 m 10–3 s Crystal plasticity Dislocation microstructure 10–5 m 10–6 s Micromechanics Single dislocation 10–7 m 10–9 s Dislocation dynamics Atomic 10–9 m 10–12 s Molecular dynamics Electron orbitals 10–11 m 10–15 s Quantum mechanics aIn the first column, we indicate an important unit structure at each scale; in the second and third columns, the approximate length scales and timescales; and in the fourth column, the approach used to understand and represent the material’s mechanical webehavior typically at those scales. have methods and models for individual scales of behavior - the coupling across scales is referred to as multiscale 158 Chernatynskiy Phillpot LeSar based on Ashby,· Physical· modelling of materials problems. Mater. Sci. Tech. 8, 102–111 (1992). 6 experiments 7 strain hardening in single fcc crystals Mughrabi, Phil. Mag. 23, 869 (1971) 1 µm Szekely, Groma, Lendvai, Mat. Sci. 1 µm Engin. A 324, 179 (2002) despite 80 years of dislocations, (slope ~ μ) we have no good theories for this 1 µm fundamental single crystal under single slip structure- µ is the shear modulus property relation 1/2 \ Taylor law: ρ ∝ τ Mughrabi, Phil. Mag. 23, 869 (1971) 8 pure Ni at small scales 1000 strong size effects, stochastic variation, intermittent flow, stresses 100 −0.62 sufficient to activate most σ KD Bulk NI slip systems. 10 0.1 1 10 100 Engineering stress at 1% strain Engineering stress Dimiduk, Uchic, and coworkers (many papers, Specimen Diameter (D) in microns including Science 2004). 9 Diffrac'on Contrast STEM Tilt Series 0.6 µm Thick Mo fiber J. Kwon (OSU) EFRC Center for Defect Physics (DOE-BES) courtesy of Mike Mills 10 Plasticity 11 edge dislocations the Burgers vector b is a measure of the displacement of 1934 the lattice ⊥ (Taylor, Polanyi, Orowan) distortion of lattice leads to b x→ strain field and, thus, a stress ←a→ ˆ b ⊥ ξ → → → → movement of an slip plane ⊥ ⊥ ⊥ ⊥ edge dislocation note the deformation that ← ← ← ← arises from the movement of the dislocation ⊥ ⊥ ⊤ ⊤ annihilation 12 screw dislocations b ˆ b || ξ 1939 (Burgers) b the Burgers vector is constant for mixed dislocations a dislocation loop E F F E E E E F S B C F ⊥ ⊤ F A D F S E E E E b || ˆ ˆ ξ F b ⊥ ξ F 13 stress plastic strain d D xi h stress b b N macroscopic displacement: D x = ∑ i d i=1 plastic strain: D D b N N x b x h ε p = = ∑ i = θ h dh i=1 dh ε = bρ x p ε = θ ρ = dislocation density = m/m3 = 1/m2 p −1 ⎛ D⎞ D θ = tan ⎜ ⎟ ≈ Hull and Bacon, Introduction to Dislocations (2001) ⎝ h ⎠ h 14 plasticity σ total strain: ε = ε e + ε p kl kl kl σapp stress/strain: e p σ = c ε = c ε − ε not to scale ij ijkl kl ijkl ( kl kl ) for an applied stress of σ: εp εe ε elastic strain from: σ = c ε e ij ijkl kl b N plastic strain from: x goal of simulations: ε p = ∑ i dh i=1 calculate plastic strain 15 dislocation generation and motion dislocations primarily move on slip (glide) planes: bowing from pinned sites dislocations “grow” Frank-Read source serves to generate new dislocations bowing around obstacles basis for first dislocation simulation by Foreman and Makin (1967) 16 dislocation processes that move edges off their slip plane out of plane motion (activated processes): [101] (111) plane cross slip: (111) plane screw dislocation can move off b slip plane S stress and temperature activated ⊥ ⊥ climb: a diffusive process 17 Simulations 18 MR43CH07-Chernatynskiy ARI 1 June 2013 12:33 1.
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