Full text of DOI:10.1557/JMR.2002.0165

Evaluation of weak interface effect on the residual stresses in
layered SiC/TiC composites by the finite element method and
x-ray diffraction
Shuyi Qin, Dongliang Jiang, and Jingxian Zhang
The State Key Laboratory of High Performance Ceramics and Superfine Microstructure,
Shanghai Institute of Ceramics, Chinese Academy of Sciences, 1295 Ding Xi Road,
Shanghai 200050, People’s Republic of China
Jining Qin
State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University,
1954 Hua Shan Road, Shanghai 200030, People’s Republic of China
(Received 14 May 2001; accepted 18 February 2002)
A symmetrically layered SiC/TiC ceramic with a gradual structure was designed by the
finite element method (FEM). After sintering, proper thermal residual stress was
introduced into the ceramic due to the coefficients of thermal expansion mismatch
between the different layers. After different SiC + C interlayers were inserted into the
layers to weaken the interface, the effect of the composition of the SiC + C interlayers
between the layers on the residual stress was evaluated. It was found that the weak
SiC + C interlayer had little relaxation effect on the residual stress distribution. These
ceramics were then fabricated by aqueous tape casting, stacking, and hot-press
sintering. An x-ray stress analyzer was used to test the surface stress conditions
of the sintered materials. The tested surface stress of the layered SiC/TiC ceramic
without interlayer was very close to the FEM calculation. However, there were
differences between the tested and calculated results of the layered SiC/TiC
ceramics with interlayers; the reason for this was analyzed.
I. INTRODUCTION
believe that thermal residual stress in a symmetrically
layered ceramic should be designed to vary gradually from
surface compressive stress to inner tensile stress. There-
fore, such a structure should have gradual compositions
from the surface to the center. In such a case, the finite
element method (FEM) is proper for designing the struc-
ture because FEM is a powerful tool for calculating re-
In the past decade, layered ceramics have been studied
extensively because they can show dramatically im-
proved strength, fracture toughness, and damage and fa-
tigue resistance compared with monolithic ceramics.
Layered ceramics can be divided into two categories.
One is surface-compression-strengthened layered ceram-
1–6
13,14
sidual stress distribution in composites.
Furthermore,
ics with strong interface bonding, such as the ZrO /
FEM is also suitable for evaluating the effect of imper-
fect interlaminar interface on the mechanical properties
2
7,8
Al O system. The other is laminated ceramics with
2
3
15,16
weak interface bonding, such as SiC/C and Si N /BN
of laminated composites.
In a ceramic with com-
3
4
9–11
systems.
The former is strengthened or toughened by
bined surface-compression-strengthening and weak-
interface-toughening mechanisms, it is important to
calculate the relaxation effect of the weak interface on
the surface compressive stress accurately so the effect
of the weak interface on the mechanical properties of the
ceramic can be understood.
In the present study, FEM was used to calculate the
thermal residual stress distribution required for optimiz-
ing the structure of a layered SiC/TiC composite and the
relaxation effect of the introduction of some SiC + C
weak interlayers with different compositions into the lay-
ers on the surface stress of the finally designed SiC/TiC
composite. After these ceramics were fabricated, their
the introduction of surface compressive stress due to co-
efficient of thermal expansion (CTE) mismatch between
different layers. The latter is toughened by crack propa-
gation along the weak interface between layers. If
both the above strengthening and toughening mecha-
nisms could synergetically work together, such a ceramic
body could possibly show even better properties. How-
ever, few studies have been done along this approach.
It is evident that when a pure bending load is applied
to a structure with a rectangular cross section, the stress
condition varies linearly from maximum tension on the
12
surface to zero stress on the central plane. Thus, we
1118
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S. Qin et al.: Evaluation of weak interface effect on the residual stresses in layered SiC/TiC composites
surface stress conditions were tested with an x-ray stress
analyzer. The calculated and tested surface stresses were
compared.
proper surface compressive stress and inner tensile
stress. The ␴xx distribution of the model is shown in
Fig. 4. On the central line of the structure (from point A
to B in Fig. 4), the stress varies gradually from compres-
sive to tensile, as shown in Fig. 5.
II. LAYERED STRUCTURE DESIGN AND
FEM CALCULATIONS
To introduce different weak interfacial bonding,
four different SiC + C interlayers composed of 50 wt%
SiC + 50 wt% C; 40 wt% SiC + 60 wt% C; 30 wt% SiC +
A SiC/TiC composite was selected for the present
work because few studies have been done on this type
of layered material. The physical and elastic properties of
SiC and TiC are listed in Table I. The properties of dif-
ferent SiC + TiC composites can be calculated according
70 wt% C; and 20 wt% SiC + 80 wt% C were inserted
into the interfaces between the different layers shown in
Fig. 3. This procedure is modeled in Fig. 6. Because the
thickness of the interlayers was much smaller than that of
10,11,19
17
the layers,
the interlayer was treated as though it
to the rule of mixtures.
had zero thickness for FEM calculations. The interlayer
was different from the layers in elastic property. Table II
lists the elastic modulus of the SiC + C interlayers cal-
A 2-dimensional initial model for FEM calculation is
shown in Fig. 1. The surface layer of the model is SiC,
and the inner layer is TiC; the TiC layer is twice as thick
as the SiC layer. In view of the symmetry, one-quarter of
the model was used for calculation. The right and upper
surfaces are free surfaces. All corners were pinned to
prevent rigid body translations. The model was assumed
to cool from 1850 to 20 °C, with a uniform temperature
field. A generalized plane-stress condition was assumed,
in which the strain along the Z direction was assumed con-
stant. FEM software (MARC 7.1, MARC Analysis Re-
search Corp., Palo Alto, CA) was used for calculation.
Figure 2 shows the thermal residual stress in the
X direction, the ␴xx distribution, for one-quarter of
Fig. 1. After the ceramic was cooled from the assumed
sintering temperature, a large compressive residual stress
was introduced to the surface SiC layer, but the tensile
stress in the inner TiC layer was 1350 MPa, far higher
than the fracture strength of TiC material.
17
culated from the rule of mixtures. Different interlayers
can be regarded as elastic springs with different elastic
moduli connecting original same nodes in the FEM
meshes (Fig. 6, step 3). After re-lamination, the model
FIG. 1. Initial SiC/TiC model composite for FEM calculation.
To decrease the inner tensile stress, the thickness of
the inner layer should be increased or the CTE mismatch
between the surface and the inner layer decreased. To
form a gradually varying stress from the surface to the
inner layer, SiC + TiC layers of different compositions
should be inserted between the selected surface and the
inner layer. The sintered properties of the SiC/TiC com-
posite also should be considered. Jiang et al. have re-
ported that the mechanical properties of a SiC/TiC
composite decrease when the TiC content exceeds
18
20 wt%.
FIG. 2. ␴xx distribution of one-quarter of the initial SiC/TiC model.
After several steps, a final symmetrical SiC/S10T
structure was chosen for the present study, as shown in
Fig. 3. The thickness ratio of SiC:S2T:S4T:S6T:S8T:S10T
is 1:1:1:1:1:10. The structure modeled in Fig. 3 has the
TABLE I. Physical and mechanical properties of SiC and TiC.
Elastic modulus Coefficient of thermal Density Poisson’s
−
6
3
(GPa)
expansion (10 /K)
(g/cm )
ratio
FIG. 3. Model of the finally chosen layered SiC/S10T structure
SiC
TiC
430
430
4.8
7.4
3.17
4.94
0.14
0.19
(where S2T is SiC + 2 wt% TiC, S4T is SiC + 4 wt% TiC, and so
forth).
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S. Qin et al.: Evaluation of weak interface effect on the residual stresses in layered SiC/TiC composites
was geometrically continuous but mechanically discon-
People’s Republic of China) used as sintering aids. The
total volume fraction of the ceramic powders in the slurry
was approximately 50%. A 10% solution of tetrameth-
ylammonium hydroxide was used as the dispersant. The
mixture was ball-milled for 24 h. Solutions of 10% poly-
vinyl alcohol (PVA) and glycerol then were added to
the slurry as binder and plasticizer, respectively. After the
slurry was ball-milled again for 24 h, it was degassed,
using a vacuum pump, then tape cast on a fixed glass
plate with a moving blade at a constant speed of 5 mm/s.
After natural drying, the green sheet was approxi-
mately 220 ␮m thick. The dried green sheet was cut into
rectangles with dimensions of 40 mm × 50 mm. One face
of different sheets was coated with SiC + C slurry. The
SiC + C slurries contained 50, 60, 70, and 80 wt% graph-
ite (9-␮m nominal size, Shanghai Carbon Factory,
Shanghai, People’s Republic of China). Methylcellulose
tinuous from one layer to the adjacent layer. Then the
original thermal residual stress was relaxed by the elastic
springs. The original and relaxed thermal residual stress
distributions from point A to B in Fig. 4 are shown in
Fig. 7. It can be seen that the introduction of the weak
interlayer had little relaxation effect on the residual stress
distribution, and the effect is particularly small in the
inner S10T layer.
III. MATERIALS AND EXPERIMENTS
Various amounts of SiC powder (0.6-␮m nominal
size, Norton AS Corp., Arendel, Norway) and TiC pow-
der (3-␮m nominal size, Zhuzhou Hard Alloy Factory,
Zhuzhou, People’s Republic of China) were mixed in
deionized water with 4.8 wt% alumina (0.48-␮m nomi-
nal size, Shanghai Wusong Chemical Factory, Shanghai,
People’s Republic of China) and 3.6 wt% yttria (4-␮m
nominal size, Shanghai Yuelong Chemical Factory, Shanghai,
(MC) was used as the dispersant for graphite powder in
the SiC + C slurries. The thickness of the coated SiC + C
interlayer was approximately 30 ␮m after natural drying.
Then the sheets were stacked according to the sequence
in Fig. 3 to form five green ceramics, one without an
interlayer and the others with 50 wt% C, 60 wt% C,
70 wt% C, and 80 wt% C interlayers. The stacked sheets
were put into a graphite die for pyrolysis of the organic
components at 700 °C and then hot-press sintered in ar-
gon atmosphere at 1850 °C under 35 MPa for 30 min.
The sintered materials were approximately 4 mm thick.
The ceramics then were cut into nominal 3 × 4 ×
40 mm (width × thickness × length) specimens. The sur-
faces of all of the specimens were ground carefully on a
glass plate, using 32-␮m and then 0.6-␮m SiC powder.
This process must ensure that the thickness of the surface
SiC layer was the same as that of the SiC + TiC layers
(except S10T). One side face of the ceramics was pol-
ished and observed by optical microscopy.
The stress conditions for the center of the surfaces of
the layered SiC/S10T composites and a layered pure SiC
fabricated by the same processes, which was selected as
the standard sample, were tested with an x-ray stress
analyzer (Model X-350A, Handan X-ray Institute,
Handan, People’s Republic of China). The x-ray diffrac-
tion method for measuring strains and stresses in crys-
FIG. 4. ␴xx distribution of one-quarter of the model in Fig. 3.
21
talline solids has been well established. In past years,
many studies on measurements of residual stress and
strain in ceramic matrix composites by x-ray diffraction
22–25
were done.
The method essentially uses the crystal
lattice as an absolute strain gauge.
When an external load is applied to a crystal the lattice
distorts and d changes. By comparing the measured
d value in a distorted crystal with the strain free inter-
planar spacing d , the elastic strain (⑀) can be determined
0
d − d0
⌬͑2␪͒
,
⑀
=
= cot␪0
FIG. 5. ␴xx distribution from point A to point B in Fig. 4.
d0
2
1
120
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S. Qin et al.: Evaluation of weak interface effect on the residual stresses in layered SiC/TiC composites
FIG. 6. Procedure of inserting the SiC + C interlayer into the interfaces between the layers.
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S. Qin et al.: Evaluation of weak interface effect on the residual stresses in layered SiC/TiC composites
TABLE II. Elastic modulus of the SiC + C interlayers.
Elastic modulus
8(g), and 8(i) is TiC particles. It can be seen that the
thickness of the SiC + C interlayer increases with
increasing graphite content because graphite is very
difficult to sinter at this sintering temperature. The inter-
layers are thin, straight, and uniform. Their thickness is
Materials
(GPa)
SiC
430
182
143
106
72
SiC + 50 wt%C
SiC + 60 wt%C
SiC + 70 wt%C
SiC + 80 wt%C
1
2
about 10–16 ␮m, which is ⁄20 – ⁄25 of the SiC + TiC lay-
ers (except S10T).
Figure 9 shows the comparison between the stresses at
the center of the surface calculated by FEM and tested by
x-ray diffraction. In the SiC/S10T ceramic without inter-
layer, the calculated surface stress, −126 MPa, is very
close to the tested, −129 MPa. However, with increasing
graphite content in the interlayers, the decreasing rate in
the tested surface stress is faster than that in the calcu-
lated surface stress.
2
0
C
10
In the calculation of elastic modulus of the interlayer
according to the rule of mixtures, the interlayer was as-
sumed to be completely dense after sintering. However,
graphite is very difficult to sinter at this temperature, so
that the interlayers are porous [Figs. 8(c), 8(e), 8(g), and
8(i)]. So the elastic moduli of the interlayers used for
FEM calculation are higher than that in sintered materi-
als. Thus, the real relaxation effect of the interlayers on
the surface stress is larger than that for the calculated
results.
FIG. 7. Relaxation effects of the SiC + C interlayers on the ␴xx dis-
tribution from point A to B in Fig. 4.
V. CONCLUSIONS
where 2␪ is the angle between the incident and diffracted
beams, and ␭ is the incident wavelength. From the elastic
strain, the corresponding stress can be calculated with the
aid of elastic constants appropriate for the hkl plane used.
A symmetrically layered SiC/S10T ceramic with
proper gradual thermal residual stress was designed by
FEM. It was found that, when different SiC + C inter-
layers containing 50 wt% C, 60 wt% C, 70 wt% C, and
80 wt% C were introduced into the layers to weaken the
interface, the interlayer had little relaxation effect on
the residual stress distribution of the designed SiC/S10T
ceramic by means of FEM calculation. These ceramics
were then fabricated by aqueous tape casting, stacking,
and hot-press sintering in argon atmosphere at 1850 °C
under 35 MPa for 30 min. After sintering, the interfaces
between the different layers in the layered SiC/S10T
ceramic without interlayer disappeared completely. The
interlayers were thin, straight, and uniform. Their thick-
In this work, Cr K radiation was used as the x-ray
␣
source. The penetration depth of the x-ray was less than
10 ␮m. The (222) plane of SiC was selected as the dif-
fraction crystal face. Biaxial stress on the surface of the
specimens was assumed, and the stress along the length
direction of the specimens was tested. The widely rec-
2
ognized sin ␺ method was used, and measurements were
made at two ␺ values of 0° and 45°, corresponding to
2
sin ␺ values of 0 and 0.5. First, the surface stress of the
layered pure SiC ceramic was tested as a standard stress.
Then the surface stresses of the five layered SiC/S10T
ceramics were tested. The tested stress of each layered
SiC/S10T ceramic minus the standard stress was re-
garded as the surface thermal residual stress of the lay-
ered SiC/S10T ceramic.
1
2
ness was about ⁄20– ⁄25 of the SiC + TiC layers (except
S10T). The surface stress conditions of the ceramics
were tested by x-ray stress analysis. The tested surface
stress of the layered SiC/S10T ceramic without interlayer
was very close to FEM calculation. However, the real
relaxation effect of the SiC + C interlayer on the surface
compressive stress was much larger than the theoretical
results. The reason is that the interlayer was assumed to
be completely dense in the FEM model, but the real
interlayer in the sintered materials was porous, so the
selected elastic modulus of the interlayer for FEM cal-
culation was higher than the real elastic modulus.
IV. RESULTS AND DISCUSSION
Figure 8 shows the optical microstructures of the side
faces of the five ceramics. After sintering, the interfaces
between the different SiC + TiC layers in the layered
SiC/S10T ceramic without interlayer disappeared com-
pletely [Fig. 8(a)]. The light phase in Figs. 8(c), 8(e),
1
122
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S. Qin et al.: Evaluation of weak interface effect on the residual stresses in layered SiC/TiC composites
FIG. 8. Optical microstructures of the five SiC/S10T layered ceramics (a) without interlayer; (b) 50 wt% C interlayer; (c) high magnification of
(b); (d) 60 wt% C interlayer; (e) high magnification of (d); (f) 70 wt% C interlayer; (g) high magnification of (f); (h) 80 wt% C interlayer; (i) high
magnification of (h).
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S. Qin et al.: Evaluation of weak interface effect on the residual stresses in layered SiC/TiC composites
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ACKNOWLEDGMENTS
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This work was financially supported by The State Key
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Wang Kuan Cheng Post-Doc Science Foundation of
the Chinese Academy of Sciences. The authors also are
grateful for the support of State Key Laboratory of Metal
Matrix Composites and the assistance with x-ray stress
analysis by Dr. Chuanhai Jiang of the Department of
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