Stochastic simulation as a basis for optimizing microstructural characterization protocols Lori Graham-Brady*, Kirubel Teferra**, Michael Uchic***, Michael Groeber*** *Department of Civil Engineering, Johns Hopkins University **US Naval Research Laboratory (formerly JHU) ***US Air Force Research Laboratory * supported by the US Air Force Research Laboratory through the Center of Excellence on Integrated Materials Modeling
Role le o of U Unc ncertaint nty Q y Quant ntification i n in: n: “The Digital Material Workflow” Uncertainty Quantification Collection+Digital Idealization 1 Processing 1 Digital Structure Real Property/ Model Material Response Collection+Digital Idealization i Processing i Collection+Digital Idealization N Processing N Characterization Mechanical Modeling/Testing Collection+Digital Processing Examples: Idealization Examples: Collection – resolution, data modes, scan rate, averaging, etc. Structure Model – mesh type, smoothing, synthetic surrogate, Processing – forward model, size filtering, averaging, segmentation ‘representative’ volume, etc. method, smoothing, etc. Response Model – constitutive description, empirical v. physics- based, explicit structure v. analytical/statistical, etc.
Role le o of U Unc ncertaint nty Q y Quant ntification i n in: n: “The Digital Material Workflow” Uncertainty Quantification Collection+Digital Idealization 1 Processing 1 Digital Structure Real Property/ Model Material Response Collection+Digital Idealization i Processing i Collection+Digital Idealization N Processing N Characterization Mechanical Modeling/Testing Collection+Digital Processing Examples: Idealization Examples: Collection – resolution, data modes, scan rate, averaging, etc. Structure Model – mesh type, smoothing, synthetic surrogate, Processing – forward model, size filtering, averaging, segmentation ‘representative’ volume, etc. method, smoothing, etc. Response Model – constitutive description, empirical v. physics- based, explicit structure v. analytical/statistical, etc.
Sens nsitivity S y Study i y in S n Structure-P -Property R y Rela lations nshi hip Structures from Virtual Collection Experiments & Meshing & Simulation Comparison of Simulated Reconstruction/Processing DoE Properties/Responses ‘Round-Robin’ Idealization 1 Idealization i Idealization N • Various representation, meshing & simulation techniques lead to range of responses • Quantify confidence bounds on material properties/responses as P(Error) • Generate instantiations of microstructure consistent with statistics of data
Microstructure S Simu mula lation: E n: Elli llipsoidal Gr l Growth T h Tessella llation ( n (Te Teferra & & Gr Graha ham-B m-Brady, C , Comp. M . Mat. S . Sci. 2 . 2015)
Variations ns i in ho n homo mogeni nized s stress-s -strain b n beha havior f for v varyi ying ng s sample le si size ze
Role le o of U Unc ncertaint nty Q y Quant ntification i n in: n: “The Digital Material Workflow” Uncertainty Quantification Collection+Digital Idealization 1 Processing 1 Digital Structure Real Property/ Model Material Response Collection+Digital Idealization i Processing i Collection+Digital Idealization N Processing N Characterization Mechanical Modeling/Testing Collection+Digital Processing Examples: Idealization Examples: Collection – resolution, data modes, scan rate, averaging, etc. Structure Model – mesh type, smoothing, synthetic surrogate, Processing – forward model, size filtering, averaging, segmentation ‘representative’ volume, etc. method, smoothing, etc. Response Model – constitutive description, empirical v. physics- based, explicit structure v. analytical/statistical, etc.
Role le o of U Unc ncertaint nty Q y Quant ntification i n in: n: “The Digital Material Workflow” Uncertainty Quantification Collection+Digital Idealization 1 Processing 1 Digital Structure Real Property/ Model Material Response Collection+Digital Idealization i Processing i Collection+Digital Idealization N Processing N Characterization Mechanical Modeling/Testing Collection+Digital Processing Examples: Idealization Examples: Collection – resolution, data modes, scan rate, averaging, etc. Structure Model – mesh type, smoothing, synthetic surrogate, Processing – forward model, size filtering, averaging, segmentation ‘representative’ volume, etc. method, smoothing, etc. Response Model – constitutive description, empirical v. physics- based, explicit structure v. analytical/statistical, etc.
Error P Propagation i n in F n Feature R Represent ntation ( n (Forward P Proble lem) m) Every Data Point Has: 1) Location Uncertainty 2) ‘Value’ Uncertainty Sources of Location Uncertainty 1) Material Removal/Sample Translation Error - planarity, removal/translation variability, etc. 2) Distortions - optics, sample positioning, drift, etc. Sources of ‘Value’ Uncertainty 1) Physical Interaction with Sample - probe size, surface topology, etc. 2) Software/Hardware Interaction - detector noise, indexing methods, etc. Level of uncertainty affected by choices made (“knobs turned”) during characterization: • dwell time • polishing time • spatial resolution, …
Error P Propagation i n in F n Feature R Represent ntation ( n (Forward P Proble lem) m) Physical experiment True material Collection experiments Reconstructed microstructure, microstructure & reconstruction/processing unknown error Collection+Digital Processing 1 Variability of boundary position Collection+Digital Processing i Collection+Digital Processing N
Error P Propagation i n in F n Feature R Represent ntation ( n (Forward P Proble lem) m) Physical experiment True material Collection experiments Reconstructed microstructure, microstructure & reconstruction/processing unknown error Collection+Digital Processing 1 Variability of boundary position Collection+Digital Processing i Collection+Digital Processing N Ground-truth, or “phantom” Virtual collection experiments Compare digital and “phantom” microstructure & reconstruction/processing microstructure, “known” error Virtual “experiment”
Error P Propagation i n in F n Feature R Represent ntation ( n (Forward P Proble lem) m) Physical experiment True material Collection experiments Reconstructed microstructure, microstructure & reconstruction/processing unknown error Collection+Digital Processing 1 Variability of boundary position Collection+Digital Processing i Collection+Digital Processing N Ground-truth, or “phantom” Virtual collection experiments Compare digital and “phantom” microstructure & reconstruction/processing microstructure, “known” error Virtual “experiment” Valuable uncertainty quantification – enables optimization of data collection parameters!
Cons nstraine ned O Optimi mization P n Proble lem m ~ Minimize: E ( Cost ) such that P ( Error ) < ε Cheapest ~ ( P i ( E ), C i ) ( P i ( E ), C i ) technique within error ~ tolerance ( P i ( E ), C i ) ( P i ( E ), C i ) ~ ( P i ( E ), C i ) ( P i ( E ), C i ) ~ ( P i ( E ), C i ) ( P i ( E ), C i ) Data Cleanup Data Collection Framework to be a communication tool for modeler & experimentalist to exchange requirements/constraints
Optimi mization F n Formu mula lation n • Simple objective function to start (time of data collection): • Similarly simple constraint function (error in mean grain size dist.): y=(t δ , Δ x , Δ z ) , parameters to be optimized CDF T (s) = target CDF known and computed from “ground truth” microstructure D = threshold on error of CDF difference CDF(s,y) = CDF of reconstructed microstructure from EBSD simulation • Minimize cost under the constraint that expected value of CDF of grain size is within tolerance of target CDF • Trick is to calculate CDF(s,y)
Error P Propagation i n in F n Feature R Represent ntation ( n (Forward P Proble lem) m) 70 • Data clean-up required to address 60 unindexed pixels % Zero Solutions 50 • Relationships may be sensitive to 40 30 microscope, software, etc. 20 • Data clean-up tools may alter 10 relationships 0 0 5 10 15 20 Data Collection Time (milliseconds/pixel) Original Data Reprocessed Data (using M. DeGraef dictionary comparison)
Simple le p process mo model l • Scan locations in phantom microstructure according to Δ x and Δ z • Identify probability of unindexed data (per t δ ) • Generate unindexed data • Filter simulated data using Dream3D data cleanup
Smo moothne hness o of c cons nstraint nt f func nction n 10 1.4 constraint (not including errthresh) constraint (not including errthresh) 1.2 8 1 6 0.8 0.6 4 0.4 2 0.2 0 0 0 10 20 30 40 50 60 30 40 50 60 70 80 90 dwell time (dx1=.5 dz=.5) dx1 (tdwell=30 dz=.5) 0.5 constraint (not including errthresh) 0.4 Lack of smoothness suggests 0.3 implicit filtering to be an 0.2 appropriate optimization tool 0.1 0 5 10 15 20 25 dz (tdwell=30 dx1=.5)
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