Analysis of stresses in aluminum±silicon alloys

Computational Materials Science 21 (2001) 149±158
www.elsevier.com/locate/commatsci
Analysis of stresses in aluminum±silicon alloys
Anil Saigal a,*, Edwin R. Fuller Jr. b
b
a
Department of Mechanical Engineering, Tufts University, Medford, MA 02155, USA
Ceramics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
Received 2 September 1998; accepted 10 August 2000
Abstract
Two-phase aluminum±silicon-based alloys are widely used for premium quality castings for aerospace and automotive applications. While it is clear that silicon improves ¯uidity in the molten state, providing excellent castability to
the alloy, and increases the tensile strength of the alloy, much needs to be done to improve the understanding of the
structure±property relationships in castings. This paper deals with the application of a microstructural ®nite element
method and the OOF program to study the eect of size and shape of silicon particles on the stresses in the silicon
particles and the aluminum matrix. The highest stress in the matrix increases with increasing particle size for a given
volume fraction of silicon particles. Therefore, the yield strength of a microstructure containing coarse particles would
be lower than one containing ®ne particles. Once the silicon particles with large aspect ratios crack or the microstructure
containing large silicon particles yield, the eective stiness of the aluminum matrix decreases which signi®cantly increases the average stress in the silicon particles and the highest stresses in both the silicon particles and the aluminum
matrix. This indicates that once the matrix yields, the potential for particle cracking increases dramatically. Ó 2001
Elsevier Science B.V. All rights reserved.
1. Introduction
Hypoeutectic aluminum alloys containing silicon as an alloying element are used extensively for
producing premium quality castings for aerospace
and automotive industries for use as structural
components primarily because of their excellent
casting characteristics. The re®nement and modi®cation of silicon particles, the size, distribution
and shape of which in the resulting eutectic microstructure are decided mainly by the cooling
process variables, such as cooling rate, pouring
*
Corresponding author. Tel.: +1-617-627-2549; fax: +1-617627-3058.
E-mail address: [email protected] (A. Saigal).
temperature, etc., are found to signi®cantly eect
the bulk mechanical properties of the aluminum
alloys [1]. In general, it is found experimentally
that the as-cast mechanical properties of aluminum
alloys are a strong function of the microstructural
features of the eutectic structure. The sharp edges
of the coarse acicular silicon phase that occur in
the microstructure promote crack initiation and
propagation, which result in poor mechanical
properties [2]. The mechanical properties improve
as one reduces the size and aspect ratio of silicon
particles by increasing the cooling rate and/or re®ning and modifying the grain structure.
Gundlach et al. [3] found that the thermal fatigue life decreased with a decrease in the degree of
silicon modi®cation. Two unmodi®ed 319 alloys
displayed the lowest thermal fatigue resistance,
0927-0256/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
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A. Saigal, E.R. Fuller Jr. / Computational Materials Science 21 (2001) 149±158
while two of the most highly modi®ed alloys had
the greatest thermal fatigue life. Mandal et al. [4]
has clearly demonstrated that re®nement of silicon
particles is extremely important with respect to
tensile strength. Voigt and Bye [5] concluded that
crack initiation or propagation is preceded by
fracture of the b-silicon particles at relatively low
values of strain, and the size and shape of b-silicon
particles control the resistance to microcrack initiation and propagation. Besides experimental
studies [6], there have been signi®cant developments in the computational micromechanics and
damage mechanics techniques for ®nite element
based simulations of stress distributions and mechanical behavior of alloys [7±9] and fracture
processes [10]. In the use of experimental techniques, however sophisticated, it is impossible to
independently vary the various microstructural
parameters and thus isolate their eects. Brockenbrough et al. [11] captured the digital image of
a microstructural ®eld of an Al±Si alloy and performed the ®nite element analysis. They approximated the shape of each silicon particle by an
equivalent circle. This research attempts to independently quantify the eect of size and shape of
silicon particles on the stresses in the silicon particles and the aluminum matrix using ®nite element
analysis.
2. Finite element analysis
Two-dimensional ®nite element simulations
were performed using the program OOF; an object
oriented ®nite element program developed at the
Center for Computational and Theoretical Materials Science (CTCMS) at NIST, on a Silicon
Graphics workstation. 1 OOF is a public domain
program that is available for free downloading via
the Internet at http://www.ctcms.nist.gov/langer/
oof [12].
1
Disclaimer: Certain trade names and company products are
mentioned in the text in order to specify adequately the
equipment used. In no case does such identi®cation imply
recommendation or endorsement by the National Institute of
Standards and Technology, nor does it imply that the products
are necessarily the best available for the purpose.
The program OOF is a combination of two
programs. The ®rst program, PPM2OOF, is designed to read an image ®le such as a micrograph.
The individual pixels that constitute the micrograph may be collected into groups and their
material properties assigned. For example, the elements corresponding to a speci®c grain in the
micrograph may be grouped together as a single
unit. Material properties such as Young's modulus, Poison's ratio, the single-crystal thermal expansion coecients, the orientation via Euler
angles, and the stress-state (plane stress or plane
strain) are then speci®ed. PPM2OOF is now used
to create the ®nite element model/mesh that OOF
then reads.
OOF performs elastic ®nite element calculations on the ®les created by PPM2OOF. Boundary
conditions, changes in temperature and thermal
loading, and distortions to the ®nite element mesh
are applied using the OOF interface. The user can
also reassign the properties to any group of elements, modify the element groups and ®nally
equilibrate the microstructure model to determine
the stress-state in each element and the residual
stress distribution. For example, Fig. 1 shows
randomly generated microstructures containing
equiaxed particles having a size of 1, 2, 4, and 8
pixels in radius. In each case, the microstructure
contains approximately 11 vol.% silicon particles.
The region is 128 128 pixels and consists of
16,641 nodes, 32,768 triangular elements, and
33,282 degrees of freedom. The properties of aluminum and silicon used in the analyses are:
EAl 70 GPa and ESilicon 114 GPa. All microstructures are subjected to a uniaxial mechanical
load of 294 MPa. The average stresses were obtained by independently loading the microstructures in the x- and y-directions (the edges were
unconstrained in the transverse direction) and
calculating the average stresses in the particles and
the matrix along the loading direction.
3. Results
Table 1 shows that as the particle size is increased from 1 to 8 (including the eect of nonuniformly distributed spatial arrangement), the
A. Saigal, E.R. Fuller Jr. / Computational Materials Science 21 (2001) 149±158
151
Fig. 1. Microstructures containing silicon particles of size (a) 1, (b) 2, (c) 4 and (d) 8.
Table 1
Eect of particle size on stresses in Si particles and Al matrix
Size
Average stress in
Si particles (MPa)
Average stress in
Al matrix (MPa)
Highest stress in
Al matrix (MPa)
Stress range in
Al matrix (MPa)
1
2
4
8
355
341
333
333
286
288
289
289
360
379
383
384
166
198
213
213
152
A. Saigal, E.R. Fuller Jr. / Computational Materials Science 21 (2001) 149±158
Fig. 2. SYY stresses in (a) aluminum matrix and (b) silicon particles for the microstructure with size 2 silicon particles.
A. Saigal, E.R. Fuller Jr. / Computational Materials Science 21 (2001) 149±158
153
Fig. 3. Microstructures containing silicon particles of aspect ratio (a) 1.125, (b) 2, (c) 8 and (d) 18.
Table 2
Eect of aspect ratio on stresses in Si particles and Al matrix
Aspect ratio
Average stress in Si
particles (MPa)
Highest stress in Si
particles (MPa)
Stress range in Si
particles (MPa)
Average stress in Al
matrix (MPa)
1
1.125
2
8
18
333
334
351
403
417
450
459
462
504
505
160
174
181
195
202
290
289
287
280
279
154
A. Saigal, E.R. Fuller Jr. / Computational Materials Science 21 (2001) 149±158
Fig. 4. Dierent microstructures containing silicon particles with aspect ratio of 2.
average stresses in the silicon particle decreases.
However, the average stresses, the largest stress
and the stress range (the dierence between the
highest and lowest normal stress along the loading
direction) in the aluminum matrix increases with
increasing particle size. As the highest stress in the
matrix increases with increasing particle size, one
would expect that the yield strength/tensile
strength of the microstructure containing coarse
particles would be lower than the ones containing
®ne particles. This is in agreement with the experimental work by Mandal et al. [4] on alumi-
num±silicon alloys containing 17±27% Si, in which
they found that
Tensile strength MPa
252:8
3:73 particle size lm:
1
In addition, the microstructures containing coarse
particles have a lower interface area per unit volume, which reduces the strengthening due to dislocation density. The stresses in the silicon
particles or the aluminum matrix do not seem to
change signi®cantly as the particle size is increased
A. Saigal, E.R. Fuller Jr. / Computational Materials Science 21 (2001) 149±158
155
Fig. 5. SYY stresses in (a) aluminum matrix and (b) silicon particles for the microstructure with aspect ratio 2 silicon particles.
156
A. Saigal, E.R. Fuller Jr. / Computational Materials Science 21 (2001) 149±158
Fig. 6. SYY stresses in (a) aluminum matrix and (b) silicon particles for the microstructure with aspect ratio 8 silicon particles.
A. Saigal, E.R. Fuller Jr. / Computational Materials Science 21 (2001) 149±158
157
Table 3
Eect of eective stiness of aluminum matrix on stresses in Si particles and Al matrix
Eective stiness Al matrix
(GPa)
Average stress in Si particles
(MPa)
Highest stress in Si particles
(MPa)
Highest stress in Al matrix
(MPa)
70
63
56
49
337
347
357
369
447
513
567
631
391
412
434
460
from 4 to 8. Fig. 2 shows the SYY stresses in
the aluminum matrix and the silicon particles for
the microstructure with particle size 2 loaded in
the y-direction (the stress range is from minimum
to maximum in GPa).
In order to study the eect of shape of silicon
particles on the stress in the silicon particles and the
aluminum matrix, Fig. 3 shows the typical randomly generated textured microstructures containing silicon particles (volume of each particle is a
constant) with aspect ratios of 1.125, 2, 8 and 18.
The average stresses in the texture direction were
obtained by loading four dierent microstructures
for each aspect ratio: two textured in the x-direction and loaded in the x-direction (see, e.g., Fig.
4(a) and (b)) and two textured in the y-direction
and loaded in the y-direction (see, e.g., Fig. 4(c)
and (d)). Fig. 4 shows the microstructures analyzed
containing silicon particles with aspect ratio of 2.
Table 2 shows that as the aspect ratio of silicon
particles increases, the average stresses, maximum
stress and stress range in the silicon particles increases and the average stress in the aluminum
matrix decreases. The maximum stress in the aluminum matrix was found to be independent of the
aspect ratio of silicon particles. As the average and
maximum stresses in the silicon particles are signi®cantly higher at higher aspect ratios than the
stresses at lower aspect ratios or any particle size, it
is expected that the high aspect ratio silicon particles are most prone to cracking. Figs. 5 and 6 show
the stress distribution in the particles and matrix
having silicon particles with aspect ratios of 2 and
8, respectively. In each case, the microstructures in
Fig. 3(b) and (c) were loaded in the y-direction.
Once the aluminum matrix in the microstructure yields as a result of cracking of silicon particles with large aspect ratios or the presence of large
silicon particles, the `eective' stiness of the alu-
minum matrix decreases. Table 3 shows the average and highest stresses in the silicon particles and
the average stresses in the aluminum matrix, for
the microstructure loaded in the x-direction containing silicon particles of size 4, as the eective
stiness of aluminum matrix is varied from 70 to
49 GPa. The average stresses in the silicon particles and the highest stresses in both the silicon
particles and the aluminum matrix increase rapidly
as the eective stiness of the aluminum matrix
decreases. This indicates that once the matrix
yields, the potential for particle cracking increases
dramatically. This agrees with the experimental
observation that there is gradual fracture and
debonding of silicon particles, which initiates at
stresses slightly above the yield stress and that the
extent of this damage increases with increasing
applied strain/stress [13±15] (see Fig. 7). Further,
Fig. 7. Fraction of broken silicon particles as a function of
strain during early stages of deformation [15].
158
A. Saigal, E.R. Fuller Jr. / Computational Materials Science 21 (2001) 149±158
larger and elongated silicon particles fracture and
debond preferentially [16].
4. Conclusions
The size and aspect ratio of silicon particles in
aluminum alloys have a signi®cant eect on bulk
mechanical properties. As the highest stress in
matrix increases with increasing particle size, one
would expect that the yield strength of the microstructure containing coarse particles would be
lower than the ones containing ®ne particles. Silicon particles with large aspect ratios are most
prone to cracking. Once the silicon particles with
large aspect ratios crack or the microstructure
containing large silicon particles yields, the eective stiness of the aluminum matrix decreases
which signi®cantly increases the average stress in
the silicon particles and the highest stresses in both
the silicon particles and the aluminum matrix. This
indicates that once the matrix yields, the potential
for particle cracking increases dramatically.
Acknowledgements
One of the authors (AS) would like to thank
The Center for Theoretical and Computational
Materials Science at NIST for providing the ®nancial support for this research.
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