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DANSE: Engineering Diffraction

DANSE: Engineering Diffraction. Ersan Üstündag Iowa State University. Engineering Diffraction: Scope. Main objective : Predict lifetime and performance Needed: Accurate in-situ constitutive laws:  = f() Measurement of service conditions: residual and internal stress. Incident

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DANSE: Engineering Diffraction

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  1. DANSE:Engineering Diffraction Ersan Üstündag Iowa State University

  2. Engineering Diffraction: Scope • Main objective: Predict lifetime and performance • Needed: • Accurate in-situ constitutive laws:  = f() • Measurement of service conditions: residual and internal stress

  3. Incident h1k1l1 Scattered h1k1l1 Incident h2k2l2 Scattered h2k2l2 Engineering Diffraction: Typical Experiment Eng. Diffractometers: SMARTS (LANSCE) ENGIN X (ISIS) VULCAN (SNS) Typical engineering studies: • Deformation studies • Residual stress mapping • Texture analysis • Phase transformations Challenges: • Small strains (~0.1%) • Quick and accurate setup • Efficient experiment design and execution • Realistic pattern simulation • Real time data analysis • Realistic error propagation • Comparison to mechanics models • Microstructure simulation Bragg’s law:  = 2dsin

  4. Engineering Diffraction: Vision for DANSE • Objectives: • Enable new science (& enhance the value of EngND output) • Utilize beam time more efficiently • Help enlarge user community • Approach: • Experiment planning and setup: (Task 7.1) • Experiment design • Optimum sample handling (SScanSS) • Error analysis • Mechanics modeling (FEA, SCM): (Task 7.2) • Multiscale (continuum to mesoscale) • Constitutive laws:  = f() • Experiment simulation: (Task 7.3) • Instrument simulation (pyre-mcstas) • Microstructure simulation (forward / inverse analysis) • Impact: • Re-definition of diffraction stress analysis • Easy transfer to synchrotron XRD

  5. Use Case: Engineering Diffraction <include> Reduce NeXus file User <include> ABAQUS () <include> I(TOF) pyre-mcstas

  6. Activity Diagram: FEA (Finite Element Analysis) Laptop SNS Linux cluster (P) NeXus Archive E1, Y1, E2, Y2 Rietveld ABAQUS a1(P), a2(P) 1c, 2c 1(a1), 2(a2) Compare (fmin) & Optimize (E1,Y1…) 1(1), 2(2)

  7. BMG W-BMG composite Example: BMG-W fiber composite • Residual stresses • Compression loading at SMARTS • Experiments on 20% to 80% volume fraction of W • Unit cell finite element model • GSAS output for average elastic strain in W in the longitudinal direction 20% W/BMG 80% W/BMG Reference: B. Clausen et al., Scripta Mater. 49 (2003) p. 123

  8. Voce Power-law Activity Diagram: FEA (Finite Element Analysis) (P) <include> E1, Y1, E2, Y2 <include> ABAQUS experimental data 1c, 2c 1(a1), 2(a2) Compare & Optimize <include> <include> leastsq fmin 1(1), 2(2) Easy utilization of various software components

  9. σ σ θ0 θ1 n=1 n=4 σo σo n=∞ εo ε εo ε Constitutive Laws for W Voce Power-law σ1

  10. Constitutive Laws for W • Voce plasticity more suitable • Unrealistic power-law coefficient (~47) • Unequal weighting of data

  11. Optimization Results: FEA • Also studied: • Stability of algorithms • Effects of initial values -> neural network algorithms

  12. Optimization Results: FEA

  13. Use Case: Engineering Diffraction <include> Reduce NeXus file User <include> EPSC () <include> I(TOF) pyre-mcstas • Self-consistent modeling (SCM) • Estimate of lattice strain (hkl dependent) • Study of deformation mechanisms

  14. Optimization Process Optimizer SCM Code Flow Pre Process Main Process Post Process Set parameters Input Files EPSC Run Output Files Set data Plot appEpsc.py setParameters.py inputGenerate.py runEpsc.py collectData.py plotEngine.py parameters.py materialsInput.py readExpOutput.py textureInput.py readModelOutput.py diffractionInput.py getDataModule.py processInput.py interpolateFunction.py

  15. Optimizer PlotController + interrupt() + plot() Optimization Process OptController + select(): boolean + set() : float Data DataControl ParameterControl + s, e total + s, e hkl + select(): boolean + weigh(): array + select(): boolean + set() : float + collect(): array Post Process Pre Process ExpData EpscOutput EpscInput + smooth(): float + interpolate(): float + collect(): file EpscBlackBox - P: Parameters Main Process - main(): epsc1 ~11.out

  16. Mechanical Loading of BaTiO3 • Time-of-flight neutron diffraction data from ISIS • Complete diffraction patterns in one setting • Simultaneous measurement of two strain directions • Different data analysis approaches: • Single peak fitting: natural candidate; but some peaks vanish as the corresponding domain is depleted • Rietveld: crystallographic model fit to all peaks; but results are ambiguous • Constrained Rietveld: multi-peak fitting, but accounting for strain anisotropy (rsca); most promising M. Motahari et al. 2006

  17. Strain Anisotropy Analysis • Desirable to perform multi-peak fitting (e.g. via Rietveld analysis) to improve counting statistics. • Question: How to account for strain anisotropy (hkl-dependent) due to elastic constants and inelastic deformation (e.g., domain switching)? • Current approach for cubic crystals (in GSAS): •  is called ‘rsca’ and is a refined parameter for some peak profiles. • Works reasonably well in the elastic regime, but not beyond. • Need to develop a rigorous approach to allow multi-peak fitting with peak weighting and peak shift dictated by mechanics modeling.

  18. Activation process to transport input vector into the network Wij X1 1 1 Qjk X2 2 O1 1 T1 2 X3 3 Op p Tp m Xn n k j Error i Backpropagation of error to update weights and biases Neural Network Analysis Schematic Representation Output Vector Target Vector Input Vector H. Ceylan et al.

  19. σ σ θ0 θ1 n=1 n=4 σo σo n=∞ εo ε εo ε Constitutive Laws for W and BMG Voce Power-law σ1 W BMG Input parameters: (σ0)BMG, nBMG, (σ0)W, (σ1)W, (θ0)W, (θ1)Wand T

  20. Neural Network Analysis Approach • 1200 runs of ABAQUS with random input parameters • Training of ANN algorithms with 1100 datasets • Use of 100 datasets as test case • Use of experimental data for inverse analysis: • Prediction of ‘optimum’ values of input parameters • Successful training of ANN • Strong influence for this parameter L. Li et al.

  21. Neural Network Analysis Sensitivity Studies • Strong influence by parameters: (σ0)BMG, (σ0)W, (σ1)W and (θ0)W • Weak/no influence by parameters: nBMG,(θ1)W and T L. Li et al.

  22. Neural Network Analysis Result • Use of experimental data for inverse analysis • Prediction of ‘optimum’ values of all 7 input parameters • Previous analyses optimized only 3 parameters L. Li et al.

  23. (a) Engineering Diffraction: Microstructure • Si single crystals (0.7 and 20 mm thick) • SMARTS data • Double peaks due to dynamical diffraction

  24. (b) Engineering Diffraction: Microstructure • Si single crystal (20 mm thick) • ENGIN-X depth scan • Data originates from surface layers Critical question: Transition between a single crystal and polycrystal? E. Ustundag et al., Appl. Phys. Lett. (2006), in print

  25. Engineering Diffraction: Team • E. Üstündag‡, S. Y. Lee, S. M. Motahari (ISU) • X. L. Wang‡(SNS) - VULCAN • C. Noyan‡, L. Li(Columbia) – microstructure • M. Daymond‡(Queens U., ISIS) – ENGIN X, SCM • L. Edwards‡ and J. James (Open U., U.K.) - SScanSS • C. Aydiner, B. Clausen‡, D. Brown, M. Bourke(LANSCE) - SMARTS • J. Richardson‡ (IPNS) • P. Dawson (Cornell) – 3-D FEA • H. Ceylan (ISU) - optimization ‡ Member of EngND Executive Committee

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