Engineering Diffraction: Update and Future Plans

Transcription

1 Engineering Diffraction: Update and Future Plans Ersan Üstündag S.Y. Lee, S.M. Motahari, G. Tutuncu and H. Ceylan Iowa State University L. Li and I.C. Noyan Columbia University DANSE Annual Review, 31 May 27

2 Engineering Diffraction: Scope Main objective: Predict lifetime and performance Needed: Accurate in-situ constitutive laws: σ = f 1 (ε, t, T, a O2, ) Measurement of service conditions: residual and internal stress Approach: Measure diffraction pattern: d Calculate lattice strain: el d d ε = d = d d Calculate stress: σ = f 2 (ε) A complicated inverse problem: Integration of mechanics, crystallography, materials science, diffraction physics

3 Engineering Diffraction: Typical Experiment Typical engineering studies: Deformation studies Residual stress mapping Texture analysis Phase transformations Challenges: Small strains (~.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 ε el Eng. Diffractometers: SMARTS (LANSCE) = ENGIN X (ISIS) VULCAN (SNS) d d d = d d E = f 3 (h,k,l) Need for a sophisticated forward model of experiment 1 Incident h 1 k 1 l 1-9 Detector Bank Incident Neutron Beam Q Q Scattered h 1 k 1 l 1 Incident h 2 k 2 l 2 +9 Detector Bank Compression axis Scattered h 2 k 2 l 2 3

4 Engineering Diffraction: Vision for DANSE Objectives: Enable new science (and enhance the value of EngND output) Utilize beam time more efficiently Help enlarge user community Approach: Make it easy to use existing tools (e.g., ABAQUS) Introduce new methods for existing tools (e.g., optimization); complex analysis Develop new tools (e.g., experiment design and simulation) Educate users (documentation, Expert System ) Conduct new science along the way (e.g., microstructure simulation) DANSE advantage: modularity, extensive libraries, new tools Impact: Re-definition of diffraction stress analysis Easy transfer to synchrotron XRD, NDE analysis, damage prognosis 4

5 Engineering Diffraction: Plans for DANSE Proposed Flagship Applications 1. Mechanics Modeling I: finite element analysis (FEA): ABAQUS integration Model optimization via input from experiment 2. Mechanics Modeling II: self-consistent modeling (SCM): EPSC, etc. integration Model optimization via input from experiment 3. Data Analysis: Diffraction data analysis (Rietveld and single-peak fitting) Comparison to mechanics modeling 4. Experiment Design and Simulation ( Expert System ): Instrument simulation (McStas) Optimization of parameters Microstructure simulation (PolyViggen) Efforts underway in all of these tasks 5

6 Mechanics Modeling Finite element analysis (FEA) ABAQUS Optimization of material parameters Self-consistent modeling (SCM) EPSC and VPSC code from LANL Incident beam Scattering Vector Detector Ferro-SCM from ISU Optimization of material parameters Grain C Grain A 2 4 Grain B 3 2 6

7 Mechanics Modeling: FEA (Finite Element Analysis) SNS Laptop Linux cluster Archive NeXus σ(p) Rietveld a 1 (P), a 2 (P) ε 1 (a 1 ), ε 2 (a 2 ) E 1, Y 1, E 2, Y 2 ABAQUS ε 1c, ε 2c Compare (fmin) & Optimize (E 1,Y 1 ) σ 1 (ε 1 ), σ 2 (ε 2 ) 7

8 ABAQUS: High Level Use Case Diagram Planned release: Summer 27 8

9 ABAQUS: System Boundary Have.inp (yes, no) Phases Sample Geometry E, v for each phase Plastic law (Power, Voce) Invoke Loading Failure Done Results ABAQUS Power law (yield point, n) Voce law (4 parameters) Sampling volume Strain gauge volume Residual stress (yes, no) Temperature T1, T2 for freezing conditions CTE for each phase Loading history Optimization (yes, no) Phase selection ABAQUS FRONT END (AFE) Invoke Optimizer Cost function Parameters Convergence criteria Max iteration Status New parameters Optimizer Data selection (neutron, macro) Parameters and initial values Algorithm selection Convergence criteria Max iteration number Experimental Data (neutron, macro) Start visualizer Plot data Visualizer Function to plot Specify plotter to use 9

10 ABAQUS: Stimulus and Abstract Classes Not Reusable User Input Control Reusable Set Phase Info Set σ(ε) FEA General Loading History ABAQUS Specific ABAQUS Set Experiment Info Set File Input Set Opt. Data Set Visualization Sampling Volume ABAQUS Input Cost function Geometry Start Simulation Start Opt, Visualization Optimizer Materials Data Other FEA code: OOF (NIST) Opt Parameter 3-D FEM (Dawson) Visualizer ANSYS Plot request Experiment Data 1

11 ABAQUS Example: BMG-W fiber composite Residual stresses Compression loading at SMARTS Experiments on 2% to 8% volume fraction of W Unit cell finite element model Rietveld (GSAS) output for average elastic strain in W in the longitudinal direction BMG W-BMG composite 2% W/BMG 8% W/BMG Reference: B. Clausen et al., Scripta Mater. 49 (23) p

12 ABAQUS + Neural Network Analysis Sensitivity Studies New use of current tools Applied composite stress (MPa) W Lattice Strain (%) Effect of W σ 1 parameter W lattice strain (%) Applied Stress (MPa) Diffraction data Voce Power-law Series1 Series2 Series3 Series4 Series5 W Lattice Strain (%) Series Series2 Important region Series3 -.3 Series4 Series Effect of W θ parameter Applied Stress (MPa) Strong influence by parameters: (σ ) BMG, (σ ) W, (σ 1 ) W and (θ ) W Weak/no influence by parameters: n BMG,(θ 1 ) W and ΔT L. Li et al. Rigorous experiment planning to optimize data collection 12

13 ABAQUS + 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 von Mises Stress (MPa) W Consittutive Laws W (as-received) W (in-situ by manual anal.) W (in-situ by leastsq) W (in-situ by ANN) Total Strain (%) L. Li et al. 13

14 Self-Consistent Modeling: System Boundary EXPERIMENTAL/RUN CONDS. Have input files (yes, no) Experiment temperature Residual stress (yes, no) ΔT for residual stress Loading history EXPERIMENTAL GEOMETRY Sample geometry Scattering vector(s) Detector acceptance angle(s) Invoke loading Failure Done Results Planned release: Fall 27 EPSC VPSC Ferro-SCM MATERIAL PARAMETERS Phases Phase morphology Elastic & piezoelec. tensors Crystal symmetry Plasticity parameters Thermal expansion coefficients Number of slip/twinning modes Slip, twin systems Grain orientations OPTIMIZATION PARAMETERS Optimization (yes, no) Phase selection Data selection (neutron, macro) Parameters and initial values Opt. algorithm selection Convergence criteria Max. iteration number Exp. data (neutron, macro) SCM front end Invoke Optimizer Cost function Parameters Convergence criteria Max. iteration Status New parameters Start Visualizer Plot data Optimizer Visualizer PLOTTING PARAMETERS Plotter selection Function/data to plot 14

15 Data Analysis Peak fitting Rietveld (full-pattern) analysis GSAS, DiffLab Single-peak fitting Integration of mechanics models to peak fitting Strain anisotropy analysis Texture analysis and visualization (MAUD) Real-time data analysis 15

16 Data Analysis: High Level Use Case Diagram Reduction Package Reducer +rawdata +makenexusfile() Mechanical Modeling Package Finite Element Analysis (FEA) Planned release: Summer 28 2 nd Reducer +makegsasfile() +makefullproffile() +makedifflabfile() <<access>> Self-Consistent Modeling (SCM) Optimizer Package Mechanical Model Optimizer Peak Fitting Package O..* Rietveld 1 Single-Peak Fitting Texture Calculator +(): dictionary <<access>> +caculatetexture() MAUD Texture Modeling Package Texture Texture Model Optimizer 16

17 Data Analysis: Mechanical Loading of BaTiO 3 Time-of-flight neutron diffraction data from ISIS Incident Neutron Beam Complete diffraction patterns in one setting Q Q +9 Detector Bank Simultaneous measurement of two strain directions -9 Detector Bank Analysis Methods rsca c strain regular Rietveld c strain single peak 2 Elastic Applied Stress (MPa) M. Motahari et al Lattice Strain Compression axis 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 17

18 Diffraction Strain Analysis: Cubic Materials d d ε = d = d h + k + l a ε = a a a 1 E = S Isotropic 2( S11 S12 S44 / 2) A 11 Anisotropic A = ( hk kl lh) + + ( h + k + l ) l σ 1 2 Grains experience different strains based on their orientation and elastic anisotropy ε d d = + γa d Anisotropic Isotropic Correction needed in strain analysis via Rietveld σ Reuss (equal stress) assumption: ε = σ E 18

19 = Diffraction Strain Analysis: Hexagonal Materials d h + hk + k ( ) a 1 Three refineable parameters (γ i ) E l c equation exact Good fits for Be and Mg (1 l3 ) S11 l3 S33 l3 (1 l3 )(2 S13 S44) E = ε ε = ε γ 1(1 l3 ) γ 2l3 γ 3l3 (1 l isotropic = ε isotropic New science New use of current tools + γ cos φ (1) 2 3 ) (12) E (GPa) E Eq. (12) Eq. (1) E (GPa) Mg E Eq. (12) Eq. (1) φ c Be 35 ρ Phi angle (degrees) Phi angle (degrees) a 19

20 Diffraction Strain Analysis: Tetragonal Materials = 1 2 d 2 2 h + k ( ) + 2 a l c 2 2 New science New use of current tools l = sin φ.sin ρ; l = sin φ.cos ρ; l = cosφ c φ 1 E = ( l + l ) S + l S + l l (2 S + S ) + l (1 l )(2 S + S ) (14) ρ a ε = ε isotropic + γ 1( l1 + l2 ) + γ 2l3 + γ 3l1 l2 + γ 4l3 (1 l3 ) (16) Very good fit for tetragonal E with 3 parameters 1/E Original Formula for BaTiO 3, Eq. (14) 1/E term fit to Eq. (16) G. Tutuncu et al phi rho phi rho 2

21 Integration of Crystallographic and Mechanics Models Macro σ-ε SCM Model data Match in elas. & inelas. regimes? Yes Done VULCAN ε ; I No ε ; I I(Q) Single peak fitting Rietveld Exp. data I(Q) Peak profile params. 1 st cycle in black; 2 nd cycle in red. Both SCM and the peak fitting routines have optimizers inside. Integration of peak fitting with self-consistent model (SCM) Iterative refinement of SCM & Rietveld Rigorous determination of constitutive law New science New use of current tools 21

22 Experiment Design and Simulation Instrument simulation McStas Machine studies (SMARTS, ENGIN X) Optimization of parameters Sample setup and alignment (SScanSS) Parametric studies (e.g., neural network analysis) Microstructure simulation Defining the sample kernel for experiment simulation Full forward simulation of experiment 22

23 Expert System : System Boundary New science Start Mechanics model Experimental Data ε, I, ε PC, σ Peak fitting (pattern simul.) Material data McStas Exp. geometry Expert System Failure Results Done Database Invoke Optimizer Instrum. geometry Cost function Parameters Convergence criteria Max. iteration Optimizer Status New parameters Start Visualizer Plot data Visualizer 23

24 Expert System : Stimulus and Abstract Classes Experiment simulation McStas <use> Instrum. geometry <use> SScanSS Exp. geometry SScanSS Sample kernel Visualizer PolyViggen <use> Material data Mechanics model Grain definitions (no., Euler angles, volume) array 24

25 Microstructure Simulation New science Si single crystal (2 mm thick) ENGIN-X depth scan Data originates from surface layers Detectors Shield 2θ= 9 Incident beam θ= 45 Sampling volume Depth Shield Sample (b) Intensity (a.u.) +.16 mm (edge) mm mm mm mm mm (center) mm mm mm mm mm (edge) Critical question: Transition between a single crystal and polycrystal? d spacing (Angstrom) E. Ustundag et al., Appl. Phys. Lett. (26) 25

26 Engineering Diffraction: Team E. Üstündag, S.Y. Lee, S.M. Motahari, G. Tutuncu (ISU) + undergrads (J. Barthel, J. Jones) X.L. Wang (SNS) - VULCAN I.C. Noyan, L. Li, A. Ying (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 New skills for young scientists Internal training Community involvement Member of EngND Executive Committee 26