Slide 1: Mechanical Property Predictions of Additively Manufactured Microstructures via Surrogate Modeling
MECHANICAL PROPERTY PREDICTIONS OF ADDITIVELY MANUFACTURED MICROSTRUCTURES VIA SURROGATE MODELING Robert Saunders U.S. Naval Research Laboratory, Washington, DC 20375 *robert.saunders@nrl.navy.mil; +1 (202) 404-3489 7 October 2020 Distribution A: Approved for public release, distribution is unlimite
Slide 2: Motivation & Needs
Motivation & Needs Powder-based AM produces non-uniform microstructures • Process parameters define the evolution of the microstructure • Significantly different from conventional manufacturing • Columnar grains are widely reported • Grain size and shape variations • Conventional crystal plasticity
Slide 3: Motivation & Needs
Motivation & Needs Develop a data-driven statistical surrogate to capture the mechanical behavior • Utilize synthetic microstructures and image segmentation techniques Determine process-property correlations • Generate data relating synthetic microstructure features to constitutive behavior • Relate
Slide 4: Microstructure Synthesis
Microstructure Synthesis Continuum diffuse interface model for simulating grain evolution • Generative capability between fidelity of statistical methods (Monte Carlo) and cellular automaton • Extended to 3D with aspect ratio controls • Ability to generate realistic single track AM microstructures w
Slide 5: Microstructure Segmentation
Microstructure Segmentation Matrix data is converted into a bitmapped voxel image • Automatically imported into Simpleware ScanIP using Simpleware Scripting interface • Each grain is segmented based on assigned grain labels using a single multi-label mask • Generation of a surface representation of
Slide 6: Finite Element Discretization
Finite Element Discretization Microstructure grain surfaces converted to FE mesh • Curved quadratic tetrahedral elements generated with Simpleware’s +FE Free algorithm • Varied element density based on geometry • Decimation used to reduce size of the mesh • Exported to Abaqus/Standard *inp file • Ab
Slide 7: Mesh and Grain Variations
Mesh and Grain Variations Vary mesh and number of grain simultaneously 300 Grains (Baseline) • Start from a converged baseline • ~300 grains, ~300k nodes, ~250k elements • Simulation time of ~80 hours on DOD HPC system • Vary grains from 30 to 600 • Scale RVE so that mean/median grain size is consta
Slide 8: Mesh and Grain Variations
Mesh and Grain Variations Stress-Strain used to determine RVE equivalence • 30 grain case shows significant differences • All other cases show no statistically significant differences • Max discrepancy of 15 MPa • Simulation time increased exponentially as node/elements increased • Number of grains
Slide 9: Data Driven Surrogate Modeling
Data Driven Surrogate Modeling Typically 1 RVE → 1 stress-strain plot • 10+ hour simulation time is still relatively long • Data driven models need 100’s or 1000’s of points To increase data, each grain produces 1 stress-strain plot • Increase data 100x • Assume boundary and grain interaction effect
Slide 10: Data Driven Surrogate Modeling
Data Driven Surrogate Modeling Recognize that the FE method is displacement driven • Strain and stress are uniform when plotted against the commanded displacement • Strain can be represented by a function of displacement and fixed parameters • Stress depends on the displacement, fixed parameters, as
Slide 11: Data Driven Surrogate Modeling
Data Driven Surrogate Modeling Methodology • Input: Known grain morphology (experiments, phase field, CA, etc.), constitutive model parameters, displacement • Output 1: Predict strain from inputs • Output 2: Predict stress from inputs and predicted strain • Final: Combine outputs to predict stress-s
Slide 12: Functional Gaussian Process Regression
Functional Gaussian Process Regression Gaussian Process Regression • Want to solve the problem of • By assuming the function follows • With mean, µ, and covariance, K • Squared exponential or Gaussian kernel for covariance U.S. Naval Research Laboratory | Distribution A: Approved for public release,
Slide 13: Functional Gaussian Process Regression
Functional Gaussian Process Regression Gaussian Process Regression • Want to solve the problem of • By assuming the function follows • With mean, µ, and covariance, K • Squared exponential or Gaussian kernel for covariance Functional Gaussian Process Regression • Want to solve the problem of • Both
Slide 14: Functional GP – Demonstration
Functional GP – Demonstration Demonstration • Predicted (black) matches true response (blue) • Larger error bounds for input values (red) that have a lot of noise U.S. Naval Research Laboratory | Distribution A: Approved for public release, distribution is unlimited. 14
Slide 15: fGP Network Predictions
fGP Network Predictions Performance MSE MAPE MAE • Network is trained on the 50 RVE data sets Strain 4.388e-5 9.13% 4.203e-3 • 70% used for training, 30% withheld • Performance on withheld data is under 10% error Stress 1756.9 5.68% 21.51 • Mean behavior is almost indistinguishable between CPFE and
Slide 16: fGP Network Predictions
fGP Network Predictions Performance MSE MAPE MAE • Network is trained on the 50 RVE data sets Strain 4.388e-5 9.13% 4.203e-3 • 70% used for training, 30% withheld • Performance on withheld data is under 10% error Stress 1756.9 5.68% 21.51 • Mean behavior is almost indistinguishable between CPFE and
Slide 17: Prediction On New Data
Prediction On New Data New 300 Grain RVEs MSE MAPE MAE • Previous RVEs contain 100 grains Strain 6.41e-5 11.2% 0.0052 • Generate new RVEs in the same manner with 300 grains Stress 7076.6 8.44% 41.2 • Closer to what is normally done in CPFE • Test how the fGP network scales up Performance • Without r
Slide 18: Cellular Automaton Data
Cellular Automaton Data Cellular Automaton Finite Element (CAFE) Model • High fidelity than CDIM • Still less expensive than phase field models • Further modified for computational efficiency with AM microstructures • Solidification time scale is independent of temperature time steps • Predictions u
Slide 19: Cellular Automaton Data
Cellular Automaton Data Performance MSE MAPE MAE • Without retraining, the fGP network does not perform well Strain 2.28e-4 31.2% 0.0105 • Diagnosis: Stress 46622.6 19.5% 135.74 • The features used to train the CDIM model are always aligned with an axis • The CDIM produces microstructures that resem
Slide 20: Summary & Future Work
Summary & Future Work A functional Gaussian Process network has been developed • Use continuum diffuse interface model to generate RVEs • ScanIP to segment and mesh RVEs automatically • Grain size and shape dependent crystal plasticity model to simulate RVE mechanical behavior • Train a network of f
Slide 21: Questions?
Questions? This work was supported by the Office of Naval Research (ONR) through the Naval Research Lab Basic Research Program and the Department of Defense (DoD) High Performance Computing Modernization Program (HPCMP) using the Air Force Research Laboratory (AFRL) Major Shared Resource Center (MSR
Slide 22: Classical Crystal Plasticity
Classical Crystal Plasticity Dislocation nucleation and motion produce plasticity 𝑡 • Shear strength of a slip system α g (r, t) = τ0∞ + න gሶ α (r, t ′ ) dt′ 0 • Strain hardening rule gሶ α (r, t) = hαβ γ γሶ β (β) • Flow rule and cumulative shear flow strain γሶ α = γሶ α τ α , g α t γ= න γሶ α dt α
Slide 23: Size-Dependent Crystal Plasticity
Size-Dependent Crystal Plasticity Higher resistance to dislocation nucleation and motion near the grain boundary • Extending the crystal plasticity framework to capture the resistance to dislocation in the grain boundary mantle • Strength and hardening modulus in the grain boundary region related th
Slide 24: Grain Homogenization
Grain Homogenization • Material point implementation is computationally challenging and requires a precise spatial description • Homogenize the boundary for each grain to achieve an equivalent grain volume average effect 𝛾𝐺𝐵 𝑔𝐺𝐵 (𝑟) 𝑉 γ 𝐺𝐵 𝑟 dV 𝐺𝐵 γ 𝐺𝐵 = 𝑉 gሶ α γ, γሶ α ⟶ gሶ α…
Slide 25: Grain Constitutive Shape Representation
Grain Constitutive Shape Representation Map each grain to a simple equivalent domain for homogenization • Simple spherical representation is sufficient to capture size effects • Ellipsoidal representation is used to capture columnar nature of grains • Fit a general quadric surface to the nodes on th
Slide 26: Grain Size Effect Validation
Grain Size Effect Validation Compare with Hansen et al. experiments • Copper with 125 randomly sized grains • Grains have a specified average diameter • Size effect only • Grains represented as simple spheres • Linear γ 𝐺𝐵 profile • 𝛿𝐺𝐵 = 0.33𝜇𝑚 • Uniaxial loading rate of 350 MPa/s •…