Abstract

While numerical models are often used in industry to evaluate the transport phenomena in solidification processes, the uncertainty in the results propagated from uncertain input parameters is rarely considered. In this work, in order to investigate the effects of input uncertainty on the outputs of high pressure die casting (HPDC) simulations, the Center for Prediction of Reliability, Integrity, and Survivability of Microsystems (PRISM) uncertainty quantification (PUQ) framework was applied. Three uncertainty propagation trials investigate the impact of uncertainty in metal material properties, thermal boundary conditions, and a modeling parameter on outputs of interest, such as fraction liquid at different times in the process cycle and shrinkage porosity volume, in an industrial A380 aluminum alloy HPDC process. This quantification of the output uncertainty establishes the reliability of the simulation results and can inform process design choices, such as the determination of the part ejection time. The results are most sensitive to the uncertainty in the interfacial heat transfer (for both outputs of interest) and the feeding effectivity (FE) (a model parameter controlling porosity formation determination), while the other heat transfer boundary conditions, model parameters, and all the properties play a secondary role in output uncertainty.

References

1.
Krane
,
M. J. M.
,
2010
, “
Modeling of Transport Phenomena During Solidification Processes
,”
ASM Handbook Vol. 22B Metals Process Simulation
,
ASM International
,
Materials Park, OH
, pp.
157
167
.
2.
Verma
,
S.
, and
Dewan
,
A.
,
2014
, “
Solidification Modeling: Evolution, Benchmarks, Trends in Handling Turbulence, and Future Directions
,”
Metall. Mater. Trans. B
,
45
(
4
), pp.
1456
1471
.10.1007/s11663-014-0039-6
3.
Yanke
,
J.
,
Fezi
,
K.
,
Trice
,
R. W.
, and
Krane
,
M. J. M.
,
2015
, “
Simulation of Slag-Skin Formation in Electroslag Remelting Using a Volume-of-Fluid Method
,”
Numer. Heat Transfer, Part A: Appl.
,
67
(
3
), pp.
268
292
.10.1080/10407782.2014.937208
4.
Fezi
,
K.
,
Plotkowski
,
A.
, and
Krane
,
M. J. M.
,
2016
, “
Macrosegregation Modeling During Direct-Chill Casting of Aluminum Alloy 7050
,”
Numer. Heat Transfer, Part A: Appl.
,
70
(
9
), pp.
939
963
.10.1080/10407782.2016.1214508
5.
Kharicha
,
A.
,
Karimi‐Sibaki
,
E.
,
Wu
,
M.
,
Ludwig
,
A.
, and
Bohacek
,
J.
,
2018
, “
Review on Modeling and Simulation of Electroslag Remelting
,”
Steel Res. Int.
,
89
(
1
), p.
1700100
.10.1002/srin.201700100
6.
Thomas
,
B. G.
,
2018
, “
Review on Modeling and Simulation of Continuous Casting
,”
Steel Res. Int.
,
89
(
1
), p.
1700312
.10.1002/srin.201700312
7.
Beckermann
,
C.
,
2002
, “
Modelling of Macrosegregation: Applications and Future Needs
,”
Int. Mater. Rev.
,
47
(
5
), pp.
243
261
.10.1179/095066002225006557
8.
Koric
,
S.
, and
Thomas
,
B. G.
,
2006
, “
Efficient Thermo‐Mechanical Model for Solidification Processes
,”
Int. J. Numer. Methods Eng.
,
66
(
12
), pp.
1955
1989
.10.1002/nme.1614
9.
Zhang
,
S.
,
Yanke
,
J.
,
Johnson
,
D. R.
, and
Krane
,
M. J. M.
,
2014
, “
Modeling Defects in Castings Using a Volume of Fluid Method
,”
Int. J. Numer. Methods Heat Fluid Flow
,
24
(
2
), pp.
468
482
.10.1108/HFF-08-2012-0185
10.
Wu
,
M.
,
Ludwig
,
A.
, and
Kharicha
,
A.
,
2017
, “
A Four Phase Model for the Macrosegregation and Shrinkage Cavity During Solidification of Steel Ingot
,”
Appl. Math. Modell.
,
41
, pp.
102
120
.10.1016/j.apm.2016.08.023
11.
Chernatynskiy
,
A.
,
Phillpot
,
S. R.
, and
LeSar
,
R.
,
2013
, “
Uncertainty Quantification in Multiscale Simulation of Materials: A Prospective
,”
Annu. Rev. Mater. Res.
,
43
(
1
), pp.
157
182
.10.1146/annurev-matsci-071312-121708
12.
Kumar
,
A.
,
Založnik
,
M.
, and
Combeau
,
H.
,
2012
, “
Study of the Influence of Mushy Zone Permeability Laws on Macro-and Meso-Segregations Predictions
,”
Int. J. Therm. Sci.
,
54
, pp.
33
47
.10.1016/j.ijthermalsci.2011.11.014
13.
Koslowski
,
M.
, and
Strachan
,
A.
,
2011
, “
Uncertainty Propagation in a Multiscale Model of Nanocrystalline Plasticity
,”
Reliab. Eng. Syst. Saf.
,
96
(
9
), pp.
1161
1170
.10.1016/j.ress.2010.11.011
14.
Prabhakar
,
M.
,
Murthy
,
J. Y.
,
Qiu
,
B.
, and
Ruan
,
X.
,
2014
, “
Quantifying Uncertainty in Multiscale Heat Conduction Calculations
,”
ASME J. Heat Transfer
,
136
(
11
), p.
111301
.10.1115/1.4027348
15.
Hardin
,
R. A.
,
Choi
,
K. K.
,
Gaul
,
N. J.
, and
Beckermann
,
C.
,
2015
, “
Reliability Based Casting Process Design Optimisation
,”
Int. J. Cast Met. Res.
,
28
(
3
), pp.
181
192
.10.1179/1743133614Y.0000000142
16.
Fezi
,
K.
, and
Krane
,
M. J. M.
,
2015
, “
Uncertainty Quantification in Solidification Modelling
,”
IOP Conf. Ser.: Mater. Sci. Eng.
, 84, p.
012001
.10.1088/1757-899X/84/1/012001
17.
Fezi
,
K.
, and
Krane
,
M. J. M.
,
2017
, “
Uncertainty Quantification in Modelling Equiaxed Alloy Solidification
,”
Int. J. Cast Met. Res.
,
30
(
1
), pp.
34
49
.10.1080/13640461.2016.1213525
18.
Fezi
,
K.
, and
Krane
,
M. J. M.
,
2017
, “
Uncertainty Quantification in Modeling Metal Alloy Solidification
,”
ASME J. Heat Transfer
,
139
(
8
), p.
082301
.10.1115/1.4036280
19.
Plotkowski
,
A.
, and
Krane
,
M. J. M.
,
2017
, “
The Sensitivity of an Electroslag Remelting Model to Uncertain Slag Properties
,”
International Symposium on Liquid Metal Processing and Casting (LMPC 2017)
, Philadelphia, PA, Sept. 10–13, pp.
109
117
.
20.
Fezi
,
K.
, and
Krane
,
M. J. M.
,
2018
, “
Quantification of Input Uncertainty Propagation Through Models of Aluminum Alloy Direct Chill Casting
,”
Metall. Mater. Trans. A
,
49
(
10
), pp.
4759
4770
.10.1007/s11661-018-4827-5
21.
Plotkowski
,
A.
, and
Krane
,
M. J. M.
,
2017
, “
Quantification of Epistemic Uncertainty in Grain Attachment Models for Equiaxed Solidification
,”
Metall. Mater. Trans. B
,
48
(
3
), pp.
1636
1651
.10.1007/s11663-017-0933-9
22.
Magmasoft GmbH,
2012
, “MAGMASOFT v5.2,” MAGMA GmbH, Aachen, Germany.
23.
Brandt
,
R.
, and
Neuer
,
G.
,
2007
, “
Electrical Resistivity and Thermal Conductivity of Pure Aluminum and Aluminum Alloys Up to and Above the Melting Temperature
,”
Int. J. Thermophys.
,
28
(
5
), pp.
1429
1446
.10.1007/s10765-006-0144-0
24.
Overfelt
,
R. A.
,
Bakhtiyarov
,
S. I.
, and
Taylor
,
R. E.
,
2002
, “
Thermophysical Properties of A201, A319, and A356 Aluminium Casting Alloys
,”
High Temperatures-High Pressures
,
34
(
4
), pp.
401
410
.10.1068/htjr052
25.
Rudtsch
,
S.
,
2002
, “
Uncertainty of Heat Capacity Measurements With Differential Scanning Calorimeters
,”
Thermochim. Acta
,
382
(
1–2
), pp.
17
25
.10.1016/S0040-6031(01)00730-4
26.
Morrell
,
R.
, and
Quested
,
P.
,
2004
, “
Evaluation of Piston Dilatometry for Studying the Melting Behaviour of Metals and Alloys
,”
High Temperatures-High Pressures
,
35
(
4
), p.
417
.10.1068/htjr118
27.
Đurđević
,
M. B.
,
Đurić
,
B.
,
Mitrašinović
,
A.
, and
Sokolowski
,
S. I.
,
2003
, “
Modeling of Casting Processes Parameters for the 3xx Series of Aluminum Alloys Using the Silicon Equivalency Algorithm
,”
Metalurgija
,
9
(
2
), pp.
91
106
.
28.
Djurdjevic
,
M. B.
,
Francis
,
R.
,
Sokolowski
,
J. H.
,
Emadi
,
D.
, and
Sahoo
,
M.
,
2004
, “
Comparison of Different Analytical Methods for the Calculation of Latent Heat of Solidification of 3XX Aluminum Alloys
,”
Mater. Sci. Eng.: A
,
386
(
1–2
), pp.
277
283
.10.1016/S0921-5093(04)00935-9
29.
Bergman
,
T. L.
,
Incropera
,
F. P.
,
DeWitt
,
D. P.
, and
Lavine
,
A. S.
,
2011
,
Fundamentals of Heat and Mass Transfer
,
Wiley
,
Hoboken, NJ
.
30.
Winterton
,
R. H.
,
1998
, “
Where Did the Dittus and Boelter Equation Come From?
,”
Int. J. Heat Mass Transfer
,
41
(
4–5
), pp.
809
810
.10.1016/S0017-9310(97)00177-4
31.
Daeseong
,
J.
,
Al-Yahia
,
O. S.
,
Altamimi
,
R. M.
,
Park
,
J.
, and
Chae
,
H.
,
2014
, “
Experimental Investigation of Convective Heat Transfer in a Narrow Rectangular Channel for Upward and Downward Flows
,”
Nucl. Eng. Technol.
,
46
(
2
), pp.
195
206
.10.5516/NET.02.2013.057
32.
Plotkowski
,
A.
, and
Krane
,
M. J. M.
,
2015
, “
The Use of Inverse Heat Conduction Models for Estimation of Transient Surface Heat Flux in Electroslag Remelting
,”
ASME J. Heat Transfer
,
137
(
3
), p.
031301
.10.1115/1.4029038
33.
Dargusch
,
M. S.
,
Hamasaiid
,
A.
,
Dour
,
G.
,
Loulou
,
T.
,
Davidson
,
C. J.
, and
StJohn
,
D. H.
,
2007
, “
The Accurate Determination of Heat Transfer Coefficient and Its Evolution With Time During High Pressure Die Casting of Al‐9% Si‐3% Cu and Mg‐9% Al‐1% Zn Alloys
,”
Adv. Eng. Mater.
,
9
(
11
), pp.
995
999
.10.1002/adem.200700189
34.
Dour
,
G.
,
Dargusch
,
M.
,
Davidson
,
C.
, and
Nef
,
A.
,
2005
, “
Development of a Non-Intrusive Heat Transfer Coefficient Gauge and Its Application to High Pressure Die Casting: Effect of the Process Parameters
,”
J. Mater. Process. Technol.
,
169
(
2
), pp.
223
233
.10.1016/j.jmatprotec.2005.03.026
35.
Hunt
,
M.
,
Haley
,
B.
,
McLennan
,
M.
,
Koslowski
,
M.
,
Murthy
,
J.
, and
Strachan
,
A.
,
2015
, “
PUQ: A Code for Non-Intrusive Uncertainty Propagation in Computer Simulations
,”
Comput. Phys. Commun.
,
194
, pp.
97
107
.10.1016/j.cpc.2015.04.011
36.
Smolyak
,
S. A.
,
1963
, “
Quadrature and Interpolation Formulas for Tensor Products of Certain Classes of Functions
,”
Doklady Akademii Nauk SSSR
,
148
(
5
), pp.
1042
1045
.
37.
Eldred
,
M. S.
,
2009
, “
Recent Advances in Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Analysis and Design
,”
AIAA
Paper No. 2009-2274. 10.2514/6.2009-2274
38.
Campolongo
,
F.
,
Cariboni
,
J.
, and
Saltelli
,
A.
,
2007
, “
An Effective Screening Design for Sensitivity Analysis of Large Models
,”
Environ. Modell. Software
,
22
(
10
), pp.
1509
1518
.10.1016/j.envsoft.2006.10.004
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