Computational model to build digital twin

Residual stresses and distortion

Building a Digital Twin of Additive ManufacturingGerald L. Knapp, Tuhin Mukherjee, James Zuback, Huiliang Wei, T. DebRoy

Department of Materials Science and Engineering, The Pennsylvania State University

What is a digital twin?

A digital twin is a computational model that includes of all major

phenomena relevant to process, allowing the prediction of important

material properties produced by the process.

Validation of D.E.D. model

To validate the model for directed energy deposition, empirical relations

predicted secondary dendritic arm spacing (SDAS) and micro-hardness

from empirical relations for SS 316L.

Applications to microstructural features

Temperature and velocity fields in D.E.D.

The pool geometry in D.E.D. is dependent on numerous physical phenomena (e.g. surface

tension, laser-powder interactions), and process parameters (e.g. laser power, scanning

speed). An empirical relation was used to calculate the pool shape a priori based on these

parameters.

Conclusions

• Though not intended to replace experiments, a digital twin can help inform

design for AM processes and parts.

• Calculation of temperatures both temporally and spatially allows for

computation of microstructure, residual stress, and more.

• Reduced order models are necessary for large-scale simulations that can be

run on a desktop computer on the order of hours, rather than days.

• A mesoscale model alone cannot predict all of the relevant structures needed

to accurately predict mechanical properties. While empirical relations can be

used, further integration with micro- and nanoscale models is desirable.

Acknowledgements

We thank GRC and NSF for travel support to attend this conference. We also

acknowledge the Department of Energy Nuclear Energy University Program [grant

number DE-NE0008280], an American Welding Society research fellowship [grant

number 179466] and Oakridge National Laboratory for supporting this research.

Many thanks to Dr. T.A. Palmer, Dr. A. De and Dr. W. Zhang for sharing their

expertise.

Residual stress is calculated from

the transient temperature fields,

variations in material properties,

and previous stress states in the

build. Visualizing the residual

stresses strains during an AM build

can indicate risk for failure during

manufacturing.

T. DebRoy, W. Zhang, J. Turner, S.S. Babu. Scripta Mater. (2017)

Furthermore, the importance

of fluid flow was investigated.

The fluid convection helps to

lower thermal gradients by

transporting hot fluid near the

beam to the pool’s trailing

edge.

G. Knapp, et al. Acta Mater. (2017)

Heat transfer and fluid flow are necessary to properly calculate temperature

fields. These vary depending on the process used due to different laser-

powder interactions and processing parameters. Having accurate transient

temperatures enables prediction of metallurgical variables.

(a) Computed temperature and velocity fields

(b) Computed thermal cycles during AM

(c) A comparison of the experimental and

computed cooling rates

(d) Computed G/R values for the AM of three

common alloys

Process Overview

Extract

thermal

cyclesCompute

solidification

parametersT. DebRoy, W. Zhang, J. Turner, S.S. Babu. Scripta Mater. (2016)

H. Wei, J. Mazumder, T. DebRoy. Sci.

Rep. (2015)

T. Mukherjee, W. Zhang, T. DebRoy. Comp. Mat. Sci. (2017)

Fig. 1. Schematics of the model used to solve heat transfer and fluid flow equations.

(left) Directed energy deposition (D.E.D.) processes fuse powder as it is deposited

(right) Powder bed processes require special consideration of powder packing

This result agrees well with

previous conclusions on weld

pool fluid dynamics. Fig. 2. Comparison of experiments to computed

results for SS 316L at varying laser powers.

G. Knapp, et al. Acta Mater. (2017)

Fig. 4. Fitting of empirical data for

catchment efficiency to the

normalized parameter Q

3/2

3/2

LTC

vP

QP

s

This reduced-order approach allows for

faster computations times for mesoscale

modeling compared to volume of fluid or

lattice Boltzmann methods.

Fig. 3. Temperature and velocity fields for SS 316L at

2500W and 10mm/s scanning speed. (a,c,d) Orthogonal

sections of a molten pool with velocities shown as

vectors. (b) Top surface of the pool.

G. Knapp, et al. Acta Mater. (2017)

Fig. 6. Stress and strain calculated for a

thin-walled IN 718 build at 300W laser power

and 15 mm/s scanning speed.

𝜀∗ =𝛽∆𝑇

𝐸𝐼

𝑡

𝐹 𝜌𝐻3/2

For back-of-the-envelope

calculations, a non-dimensional

strain parameter number may be

used to compare different materials

(Fig. 7). It requires no additional

calculations past the heat transfer

and fluid flow results.

Fig. 7. (above) Non-dimensional

strain parameter definition

(right) Computed results for SS

316L and 800H Alloy

G. Knapp, et al. Acta Mater. (2017)

Future work

• Integration of microscale models with the calculated thermal cycles could

reduce physical experiments in creating process maps for new materials.

• Introducing simplified, but accurate, models can make modeling of AM a more

useful AM design tool.

• Taking advantage of parallel computing and big data tools will enable larger

scales of modeling, where predicting build failures is even more critical.

Bead shape in D.E.D. is greatly affected

by how much mass is captured in the

pool from the powder stream (a.k.a.

catchment efficiency, ηc). Fig. 4 shows

how the catchment efficiency correlates

with a function of power (P), nozzle travel

speed (V), and the energy required for

melting.

Knowing the catchment efficiency and the contact

angle of the molten liquid, we can estimate the

shape of a single deposit by mass conservation

(Fig. 5). This matched SS 316L and 800H

experiments ±10% over a range of laser powers

and travel speeds.

Fig. 5. Reduced

order model for

a priori

calculation of

single-deposit

geometry

Deposit geometry determines the

direction of heat transfer, which in turn

determines the direction of primary

dendrite growth.

Transient and spatially-varying temperatures allow for investigation of solidification parameters

at different locations in a build. Calculation of cooling rates, thermal gradients, and solid-liquid

interface velocities can inform material and process design to create desirable microstructures

and phase transformations.

Fig. 6. Primary dendrite growth

direction is heavily dependent on the

direction of thermal gradients