Die casting is a type of metal casting in which a liquid metal is solidified in a reusable die. In such a complex process, measuring and controlling the process parameters are difficult. Conventional deterministic simulations are insufficient to completely estimate the effect of stochastic variation in the process parameters on product quality. In this research, a framework to simulate the effect of stochastic variation together with verification, validation, and uncertainty quantification (UQ) is proposed. This framework includes high-speed numerical simulations of solidification, microstructure, and mechanical properties prediction models along with experimental inputs for calibration and validation. Both experimental data and stochastic variation in process parameters with numerical modeling are employed, thus enhancing the utility of traditional numerical simulations used in die casting to have a better prediction of product quality. Although the framework is being developed and applied to die casting, it can be generalized to any manufacturing process or other engineering problems as well.

References

References
1.
Plotkowski
,
A.
,
Fezi
,
K.
, and
Krane
,
M.
,
2015
, “
Estimation of Transient Heat Transfer and Fluid Flow for Alloy Solidification in a Rectangular Cavity With an Isothermal Sidewall
,”
J. Fluid Mech.
,
779
, pp.
53
86
.
2.
Spiegel
,
E.
, and
Veronis
,
G.
,
1960
, “
On the Boussinesq Approximation for a Compressible Fluid
,”
Astrophys. J.
,
131
,
442
.
3.
Voller
,
V.
, and
Swaminathan
,
C.
,
1991
, “
Eral Source-based Method for Solidification Phase Change
,”
Numer. Heat Transfer, Part B Fundamentals
,
19
(
2
), pp.
175
189
.
4.
Harlow
,
F. H.
, and
Welch
,
J. E.
,
1965
, “
Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid With Free Surface
,”
Phys. Fluids
,
8
(
12
), pp.
2182
2189
.
5.
Geuzaine
,
C.
, and
Remacle
,
J.-F.
,
2009
, “
GMSH: A 3-D Finite Element Mesh Generator With Built-In Pre And Post-Processing Facilities
,”
Int. J. Numer. Methods Eng.
,
79
(
11
), pp.
1309
1331
.
6.
HYPRE: Scalable Linear Solvers and Multigrid Methods.
7.
Baker
,
A. H.
,
Falgout
,
R. D.
,
Kolev
,
T. V.
, and
Yang
,
U. M.
,
2012
, “
Scaling HYPRE's multigrid solvers to 100,000 cores
,”
High-Performance Scientific Computing
,
Springer
,
Berlin
, pp.
261
279
.
8.
Backer
,
G.
, and
Wang
,
Q.
,
2007
, “
Microporosity Simulation in Aluminum Castings Using an Integrated Pore Growth and Interdendritic Flow Model
,”
Metallurgical Mater. Trans. B
,
38
(
4
), pp.
533
540
.
9.
Hunt
,
D.
,
1979
,
Solidification and Casting of Metals
,
The Metal Society
,
London
.
10.
Okayasu
,
M.
,
Takeuchi
,
S.
,
Yamamoto
,
M.
,
Ohfuji
,
H.
, and
Ochi
,
T.
,
2015
, “
Precise Analysis of Microstructural Effects on Mechanical Properties of Cast adc12 Aluminum Alloy
,”
Metallurgical Mater. Trans. A
,
46
(
4
), pp.
1597
1609
.
11.
Xiu
,
D.
, and
Karniadakis
,
G. E.
,
2002
, “
The Wiener–Askey Polynomial Chaos for Stochastic Differential Equations
,”
SIAM J. Sci. Comput.
,
24
(
2
), pp.
619
644
.
12.
Wiener
,
N.
,
1938
, “
The Homogeneous Chaos
,”
Am. J. Math.
,
60
(
4
), pp.
897
936
.
13.
Matthies
,
H. G.
, and
Keese
,
A.
,
2005
, “
Galerkin Methods for Linear and Nonlinear Elliptic Stochastic Partial Differential Equations
,”
Comput. Methods Appl. Mech. Eng.
,
194
(
12–16
), pp.
1295
1331
.
14.
Roman
,
L. J.
, and
Sarkis
,
M.
,
2006
, “
Stochastic Galerkin Method for Elliptic SPDES: A White Noise Approach
,”
Discrete Continuous Dynamical Syst.-Ser. B
,
6
(
4
), pp.
941
.
15.
Smith
,
R. C.
,
2013
,
Uncertainty Quantification: Theory, Implementation, and Applications
, Vol.
12
,
SIAM
,
Philadelphia
.
16.
Smolyak
,
S.
,
1963
, “
Quadrature and interpolation formulas for tensor products of certain classes of functions
,”
Soviet Math. Dokl.
,
4
, pp.
240
243
.
17.
Ganapathysubramanian
,
B.
, and
Zabaras
,
N.
,
2007
, “
Sparse Grid Collocation Schemes for Stochastic Natural Convection Problems
,”
J. Comput. Phys.
,
225
(
1
), pp.
652
685
.
18.
Heiss
,
F.
, and
Winschel
,
V.
,
2008
, “
Likelihood Approximation by Numerical Integration on Sparse Grids
,”
J. Econom.
,
144
(
1
), pp.
62
80
.
19.
Fusegi
,
T.
,
Hyun
,
J.
,
Kuwahara
,
K.
, and
Farouk
,
B.
,
1991
, “
A Numerical Study of Three-Dimensional Natural Convection in a Differentially Heated Cubical Enclosure
,”
Int. J. Heat Mass Transfer
,
34
(
6
), pp.
1543
1557
.
This content is only available via PDF.
You do not currently have access to this content.