2. AM can now enable
…control of the overall geometry of a part, which could
be made up of a truss network, where each truss has an
optimized thickness and could have an individually
controllable microstructure or material.
• But we can’t efficiently:
• Design structures this complex in CAD
• Predict what our machines will do when we print
a new geometry we haven’t printed before
• Predict the differences between printing the
same part in two different locations/orientations
• Predict how different process parameters affect
accuracy, microstructure and part performance
Courtesy David Rosen, Georgia Tech
3. Typical Process Variation
Effects
• 2 mm wall made from
Inconel 625
– XZ section showing
effects of scan pattern
variation on
microstructure
• Identical geometries in
the same build give
different distortions
4. (left) Prior beta interfaces ~100 μm
wide show the hatch spacing
(right) Prior beta interfaces not visible
in the bottom layers: microstructure
changes orientation each layer.
(3DSIM predicted values for angular
distortion is ~12-19º, which are in the
observed range.)
• Horizontal Tensile Specimens in
the top (last to be processed) layers
• Horizontal Tensile Specimens
in the bottom (lowest) layers
4
200 X
Microstructural Variations
due to Orientation in Ti6/4
1000 X
200X Bottom, θleast =12°
200X Intermediate layers
θmax =19°
5. 5
200X Bottom
Horizontal samples
200X Bottom
Vertical samples
• Identical process parameters
for identical parts
in an identical layer,
in the same build,
for the same material, but
in different orientations and locations,
result in
different microstructures and properties
• Less residual stress in Vertical samples
columnar grains
• High residual stress in Horizontal samples
martensitic streaks
Microstructural Variations
due to Orientation in Ti6/4
6. The “Support” Problem in
Metal Laser Sintering
• Supports today are
placed based upon
geometric relationships
and user experience
– Extra supports increases
post-processing costs
– Supports can ruin key
features
– Under-supporting regions
causes blade crashes
7. The Current Situation
• We Need An Accurate 3D “Print Preview”
– Based upon Real Process Parameters & Scan Vectors
– To Give us Accurate Geometry Prediction
• Including Distortion and Where we Need Supports
– Internal Microstructure Predictions
– Properties & Performance Predictions
• But what we have today is…
– A CAD file and a “Preview” of 2D slices of a build
– A lot of experimental data to tell us what “might” or
“probably” will happen under different situations
8. What’s Wrong with
Existing Simulation Tools?
• Manufacturing simulations of the past were
developed with the idea that we can take a long
time to get the right answer because we’ll make a
lot of the same thing over and over…
– Most are based upon 20-30 year-old formulations
• They are not optimized for multi-physics, multi-
scale modeling or compatible with GPUs.
• They don’t have a unified computational
infrastructure that enables you to solve all parts of
the problem in one package.
9. • Process simulations that are faster than an AM machine
builds a part
– Predict residual stress and distortion so we know how to place
supports and how to pre-distort our CAD model
• Material simulations which can predict crystal level
details and the resulting mechanical properties
• Lightning fast solutions on GPU-based platforms
• We simulate only what we need to get a practical
answer as FAST as possible
Our Modeling Vision
10. Our Overall Approach
• Most Modeling Tools Link
Process Structure Properties
• We’ve developed two Separate Solvers:
– Process Solver gives – Process Structure
• Thermal history, distortion, residual stress, crystal structure…
– Material Solver gives – Structure Properties
• Based upon the crystal structure, what are the properties
12. Benefits of our Dynamic
Meshing Strategy
• Demonstrated to be 66x faster than
ANSYS for solving AM problems
• ANSYS assembles matrices and calculates
nodal connectivity (stiffness matrix) every
time-step
• Our “intelligent assembly” of matrices
solves an identical problem with no
recalculation of nodal connectivity
• Fine-scale mesh developed for a
particular energy source and/or machine
with no hanging nodes or improperly
skewed meshes
13. Our Core 3DSIM Code
• Formulated for moving
energy source problems
• Multi-scale mesh fits
any size geometry
– Nano-manufacturing to
meters of manufacturing
• Fits whatever energy
source size you choose
– Applicable to ‘n’ scales
of refinement
14. Top Surface Domain in the x direction
TopSurfaceDomainintheydirection
Thermal contours at arbitary time steps during 1st layer of Laser scanning
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 10
-3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
x 10
-3
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Unstable thermal contours at turns
Stable thermal
contours
Scan
Strategy
Simulation Results: Example
Thermal History
15. Effect of Powder Packing
Density on Melt Pool Geometry
(10%, 20%, 30%, 40%, 50%, 60%)
18. How difficult is the
Problem We Want to Model?
• Finite Element Modeling of a commercial full-scale build:
– 200mmx200mmx200mm powder bed size
– 10 microseconds time steps to capture melting
– 20 micron layer thickness
– 10 micron resolution small-scale mesh (2 elements/layer)
• 108 elements per layer, 1012 elements per build if fine meshed everywhere
– 50 hours of actual laser scan time
• 1010 total time steps
19. Time and Efficiency Comparisons
(assuming a 16 teraflops machine)
• BASED UPON OUR CALCULATIONS, WE PROJECT:
• Fine Gridding (using ANSYS or similar method) = 5.7 10 years
• ANSYS (with multi-scale) = 8.9 10 years (89 billion years)
• 3DSIM (with multi-scale) = 1.3 10 years (1.3 billion years)
– It will be much faster in C++, but not fast enough..
• This is why modeling experts only simulate simplified versions of the
problem
• We decided to keep trying to find faster ways to do the entire
problem…
21. Eigensolver
• Strategy
– Compute 3-4 layers using 3DSIM Multi-Scale FEA
– Use the Eigensolver when more than 3-4 layers away from the melt pool
• Advantages
– Time to get the SAME ANSWER is orders of magnitude less
• Disadvantages
– Mode computations are hard to derive for new problems, it is only
applicable to physics problems for which we’ve derived eigenmodal
solutions
• Our Eigensolver is tested and works well for thermal and decoupled
stress/strain problems, but we are still testing our approach for the Material
(crystal plasticity) Eigensolver
22. Comparing Thermal
Eigensolver Answers to FEA
0 1000 2000 3000 4000 5000
0
0.2
0.4
0.6
0.8
1
Linearthermalfieldsolution
(normalized)
# of nodal points
Modal Reconstruction
Finite Element Solution
Solution match for each node when comparing 3DSIM FEA against the
3DSIM Eigensolver for a point heat source
23. Banded Vectorization
Number Sorting
Eliminate Meaningless Computation
7 additively
manufactured
layers
Top surface Boundary condition Optimal tolerance FLOPS
point force 1000 7.00%
center line parallel to X axis 2511.8864 4.00%
Line along one of the diagonal 2511.8864 5.00%
Area force 63.09 40.00%
24. Periodic and Higher
Order Boundary
Conditions (PHOBC)
• We have derived and are testing an eigenmodal
approach to:
– Identify Symmetry & 1st to 4th Order Periodicity in
Boundary Conditions BEFORE calculating FEA for a
New Layer
• Calculation is Based upon Prior Layer Histories and the
Scanning Parameters that will be used for upcoming layer
• If periodicity occurs AND a prior answer is
known… then … feed forward the correct answer
into appropriate portions of the layer
– Calculate any unknown answers using FEA
25. Time and Efficiency Comparisons
(assuming 16 teraflops machine)
• Fine Gridding (using ANSYS or similar method) = 5.7 10 years
• ANSYS (with multi-scale) = 8.9 10 years (89 billion years)
• 3DSIM (with multi-scale) = 1.3 10 years (1.3 billion years)
• 3DSIM(…+Z direction Eigenmodes after 4 layers) = 208 years
• 3DSIM(…+Banded vectorization) = 22.1 years
• 3DSIM(…+PHOBC) = 22.1 10 years~0.2 hours
Typical Desktop Computer will do 3DSIM (…+PHOBC)=166 days
That’s why we buy $20k-$30k GPU computers…
US Fastest GPU Computer (TITAN)
3DSIM (…+Z Direction Eigenmodes)=54 days
3DSIM (…+Banded vectorization)=6 days
3DSIM (…+PHOBC)=720 µs
26. What are we working on
Currently?
• Converting all our Matlab and Fortran code into
C++ and C# code to run on a CUDA GPU
• Running sensitivity analyses on each module as it
is developed
• Validating each module against
– Analytical solutions
– Other software tools
– Our software prior to turning on each new module
– Experiments
27. Our Products
• Full-blown “Everything 3DSIM Offers” Products:
– Simulating problem sets for others as consultancy
– Cloud-based solutions on a per-use basis
– Licenses for combined hardware/software platforms
• Specialty Software Tools:
– Distortion prediction and compensation tool
– Optimum support structure tool
– Future machine control software
– …and more…
28. • An accurate “3D Print Preview” is becoming a reality
• We have developed a modeling infrastructure with never-
before-seen modeling efficiencies
– Combines “upgraded” FEA with Eigensolvers to solve for every
point in space within a machine for every time step to achieve
highly accurate solutions
• 3DSIM tools will:
– Provide guidance to machine users on how to best optimize their
existing machines and build layouts
– Enable rapid materials insertion, optimization & qualification
– Provide a prediction of part performance before building a part
– Make possible the design and manufacture of better AM machines
Conclusions &
Significance
31. 3DSIM Software has Been Developed
and/or is Being Validated Via the
Following Projects
Involving Both 3DSIM and the University of Louisville
• Development of Distortion Prediction and Compensation Methods for Metal Powder-
Bed AM – America Makes, 2014-2015
• Predicting Residual Stress in Metallic Additive Manufacturing – STFC EU consortium,
2014-2015
• Further Development of 3DSIM Models – DARPA (anticipated) 2014-2015
• Modeling of DMLS Ti6/4 Residual Stress & Supports -- AFRL/MLPC, 2012-2015
Based Research at the University of Louisville
• Modeling of DMLS In625 -- NIST, 2013-2015
• Rapid Qualification of DMLS/EBM Ti6/4 -- America Makes, 2013-2015
• Modeling of DMLS Ti6/4 Arbitrary Powders –AFRL/MLPC, 2013
• Modeling of Friction Stir AM -- NSF, 2012-2015
• Modeling & Closed Loop Control of UC -- ONR, 2011-2014
• Multi-Material UC – ONR, 2007-2011
33. Arbitrary Powders in Metal
Laser Sintering
• Takes simple powder tests as inputs
– Powder density, morphology & chemistry
• Uses empirical relationships to convert powder
tests into important processing variables
– Powder bed absorptivity, thermal conductivity, etc.
• Runs our simulation algorithms near previously
determined “good” operating parameters for a
well-known powder type to find equivalent
“good” parameters for the new powder
36. Approach for Polymers
• Find and derive algorithms for the Material &
Process Solvers
– Mathematical relationships which correlate thermal
history to % crystallinity, spherulite morphology, chain
entanglement, molecular weight, % porosity, etc.
– Correlate microstructural features to mechanical
properties mathematically and via experiments
37. Our Estimation Method
• Total # of time steps=50 hours=
∗
1.8 10
• Total Number of Layers ( )= 10
• Time step/layer
Total # of time steps
1.8 10
• Total number of thermal degrees of freedom in a
layer( )= 4 10
38. Theoretical Computational
complexity (in flops)
• Uses Forward substitution for complexity (This is the
expensive term backward is one order less.)
• # of flops= ∑ =
• Since N>>>1, N~N+1
• # of flops=
• Flop Speed per second=F
• Total time=
