Crack-Free Joint in a Ni-Al2O3 FGM System Using Three-Dimensional Modeling
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Materials Transactions, Vol. 50, No. 7 (2009) pp. 1875 to 1880
#2009 The Japan Institute of Metals EXPRESS REGULAR ARTICLE
Crack-Free Joint in a Ni-Al2 O3 FGM System Using Three-Dimensional Modeling
Jong Ha Park1 , Jae Chul Lee2 , Sae Hee Ryu1 , Kyu Bong Jung1 , Han-Bok Song1 ,
Joon Chul Yun1 , Yong Ho Choa1 , Sung Hoon Ahn2; * and Caroline Sunyong Lee1; *
1
Division of Materials and Chemical Engineering, Hanyang University, Kyunggi-do, 426-791, Korea
2
School of Mechanical and Aerospace Engineering and Institute of Advanced Machinery and Design,
Seoul National University, Seoul, 151-742, Korea
With the recent emphasis on the importance of successfully joining materials, researchers have tried to join metals and ceramics with
different coefficients of thermal expansion (CTEs) by using the functionally graded material (FGM) method. This involves inserting interlayers
with composition gradients that range from one material to the other, thereby minimizing the stress caused by differences in CTE values. In this
study, the FGM that included 10 layers of Ni-Al2 O3 with eight inter-layers was studied. Previous studies have focused on controlling the
composition of inter-layers and optimizing the dispersion process to prevent cracks. Thermal stress was reduced by varying the weights of the
inter-layers and increasing the green-body density by using several powder sizes. The powders were well-dispersed during fabrication by using
simultaneous dispersion and dry processes followed by a cold isostatic press (CIP) and pressure-less sintering in an inert atmosphere. As a result,
a crack-free Ni-Al2 O3 FGM joint was obtained. The residual stress in each layer was calculated to predict cracks using ANSYS simulation and
maximum principal stress criterion; experimental values matched simulation results. In addition, an oriented Vickers indentation test was used to
assess the quality of the joint. Crack-paths were not deflected across the interface, indicating good bond strength between interfaces. Sample
density was measured using the Archimedes method; the sintered joint was less dense than its theoretical density but was denser than the results
obtained by using previous methods. [doi:10.2320/matertrans.M2009041]
(Received February 4, 2009; Accepted April 20, 2009; Published June 17, 2009)
Keywords: finite element method (FEM), functionally graded material (FGM), linear mixture rule, maximum principal stress theory, Ni-Al2 O3
joint, thermal residual stress
1. Introduction because the CTE values of the two materials differ greatly
(Ni: 13:1 106 / C, Al2 O3 : 8:0 106 / C).4) Even using
Many recent studies have focused on the importance of the FGM construction, many unexpected problems can arise,
joining two materials while simultaneously maintaining good such as porosity in Ni-rich layers or difficulty in mixing
quality. Efficient joining of two materials such as metal- powders, because of the considerable differences in density
ceramic, metal-polymer, and metal-metal can improve the between Ni and Al2 O3 . In previous studies, researchers
materials’ properties and yield many commercial advantages. joined Ni and Al2 O3 using 10 layers; they developed many
During fabrication, joints between dissimilar materials can improvements to control internal cracking, but were unable
fail due to differences in the materials’ co-efficient of thermal to control large cracking on the sample surface.5)
expansion (CTE) values. In particular, large differences in Moreover, The ANSYS simulation was used to predict
CTE values can result in many problems when metals and crack-free composition of FGM between Si3 N4 and Al2 O3 .6)
ceramics are joined directly. Many researchers have applied In this study, a crack-free joint between Ni and Al2 O3 was
the functionally graded material (FGM) approach to provide obtained by controlling the composition of the inter-layers
a solution to this problem. This involves using interlayers to and optimizing the dispersion process. The ANSYS program
join two different materials, with a gradient in composition confirmed the numerical analysis for calculating thermal
from one material to the other. residual stresses. The resulting sample density was also
This method can be used as long as no undesirable reaction measured and compared with previous samples and theoret-
takes places between the two materials. When used to join ical maximum densities. Finally, joint interfaces were
metals and ceramics, this technique retains the desirable qualitatively characterized using an oriented Vickers inden-
properties of both materials: good toughness, the mechanical tation test.
strength of metal, thermal resistance, and resistance to
oxidation at high temperatures. For this reason, the FGM 2. Experimental Procedures
method is frequently applied to the production of various
items, including turbine blades and high-temperature pipes 2.1 Material fabrication
and gears.1) Ten layers of Ni-Al2 O3 were fabricated to enable efficient
Considerable research has been conducted on joining thermal residual stress distribution of Ni and Al2 O3 : 0, 5, 10,
metals and ceramics, especially Ni-Al2 O3 .2,3) Ni has a high 20, 30, 40, 60, 70, 80, and 100 vol% Ni. In addition, Table 1
melting point for a metal (1455 C), making it particularly lists the various combinations of Ni and Al2 O3 powders,
suitable for joining to ceramics; Al2 O3 is easily sintered and designed to prevent the occurrence of surface cracking
has a high CTE that is particularly suitable for joining with (see Fig. 1).5) As shown in Fig. 1, considerable porosity
metal. However, many difficulties arise during fabrication, appeared in the Ni-rich area between the 60% Ni/40%
Al2 O3 layer and the 80% Ni/20% Al2 O3 layer.5) In this
*Corresponding authors, E-mail: sunyonglee@hanyang.ac.kr, ahnsh@ study, the 80% Ni/20% Al2 O3 layer was replaced with an
snu.ac.kr 85% Ni/15% Al2 O3 layer to reduce thermal stress between1876 J. H. Park et al.
Table 1 Powder size and weight of each functionally graded material (FGM) layer.
Powder Size (mm)
Composition Ni Al2 O3 Weight (g)
3 mm 15 mm 0.16 mm 18 mm
100% Al2 O3 75% 25% 2
5% Ni/95% Al2 O3 O O 4
10% Ni/90% Al2 O3 O O 4
20% Ni/80% Al2 O3 10% 10% O 4
30% Ni/70% Al2 O3 15% 15% 70% 4
40% Ni/60% Al2 O3 20% 20% 60% 6
60% Ni/40% Al2 O3 O 20% 20% 6
70% Ni/30% Al2 O3 O 15% 15% 6
85% Ni/15% Al2 O3 O 10% 10% 6
100% Ni 75% 25% 4
Fig. 1 (a) A surface view and (b) a cross-section of the previous 10-layered functionally graded material (FGM) specimen with cracks.5)
the 70% Ni/30% Al2 O3 layer and 100% Ni. In addition,
four different powder sizes were used to reduce porosity
during sintering and to improve the overall density. The
powders had an average particle size of 3 mm (Sigma-
Aldrich Korea): 15 mm (AOmetal, Seoul, South Korea) for
nickel, and 0.16 mm (Taimicron) and 18 mm (Kojundo
Korea, Seoul, South Korea) for Al2 O3 .
The components of each layer were mixed in solvent
(99.9% ethanol) using an ultrasonicator. The powders were
mixed efficiently with simultaneous use of an evaporator and
sonicator to prevent segregation caused by the density
differences between Ni and Al2 O3 powders (Ni: 8.88 g/cm3 ,
Al2 O3 : 3.9 g/cm3 ). Dry powder was sieved and then stacked
sequentially into a cylindrical mold with one inch in diameter Fig. 2 The heating and cooling profile of Ni-Al2 O3 FGM.
(see Table 1 for the order of stacking). The CIP method was
used to improve green-body density. The green body was
sintered in a tube furnace with Ar atmosphere to prevent density of the fabricated sample was compared with
nickel oxidation. The maximum sintering temperature was theoretical values and the densities of samples produced
1350 C, and the sample was cooled slowly at 2 C/min to during previous studies.
minimize residual stress during cooling. Figure 2 presents
the sintering profile. The holding time at 150 C is needed to 2.2 Calculation of thermal residual stress
burn off stearic acid that was used during stacking into a An ANSYS simulation was conducted to analyze thermal
cylindrical mold. The completed specimen was examined, residual stresses in the fabricated crack-free FGM specimen.
and a sample was cut and polished using a 1-mm grit. As shown in Fig. 4, the cylindrical sample was transformed
Figure 3 shows an external view and cross-section of the to a two-dimensional axisymmetric model based on its
sample, viewed under an optical microscope. The measured sample geometry and coordinate systems. This analysisCrack-Free Joint in a Ni-Al2 O3 FGM System Using Three-Dimensional Modeling 1877
Fig. 3 (a) A surface view and (b) cross section of a crack-free 10-layered functionally graded material (FGM) specimen.
Fig. 4 Sample geometry and coordinate systems.5)
assumed ideal joining and dispersion between the two
materials. In addition, the elastic modulus, CTE, Poisson’s
ratio, and critical strength of each layer were calculated based
on the linear rule of mixtures. The residual stresses were
computed using a finite element method (FEM): the ANSYS Fig. 5 (a) Element condition and boundary condition and (b) PLANE82
geometry configuration.5)
program. A two-dimensional eight-node plane element
(PLANE82) was used; the two-dimensional axisymmetric
model had 102,133 nodes and 33,782 elements by meshing 2.4 Oriented vickers indentation test
with a 0.1-mm element size. Figure 5 shows (a) the element Previous studies have measured Vickers hardness values
state and boundary conditions used for finite element for Ni and Al2 O3 FGM specimens; hardness tends to decrease
analysis, and (b) a schematic diagram of PLANE82. Table 2 in the nickel-rich layers due to porosity.5) In this study, the
lists the material properties and critical failure strength of the oriented Vickers indentation test was used to determine the
FGM based on the linear rule of mixtures, which were used in indent crack path, which enabled qualitative characterization
the finite element analysis. Generally, researchers use of strong interfaces within the FGM joint. Cracks propagat-
maximum tensile stress theory and maximum principle stress ing from indents were formed by the application of 10 kgf
theory to estimate the failure of brittle materials such as pressure near each interface (100% Al2 O3 –5% Ni/95%
ceramics, and maximum deformation energy theory to Al2 O3 layer, 5% Ni/95% Al2 O3 –10% Ni/90% Al2 O3 layer)
estimate the failure of ductile materials such as metals.6) and the crack path deflection was observed.
Because cracks in this FGM tend to occur mainly in the
ceramic element, maximum tensile stress theory was used to 3. Results and Discussion
estimate residual stress.
3.1 Material fabrication
2.3 Failure criteria To eliminate cracks in the FGM specimen, eight inter-
Maximum principal stress theory used in brittle material layers were inserted to reduce the residual stress in each layer
was applied to estimate the failure in this study. and to control the weight of each layer. Particle sizes were
also varied to reduce pores and thereby improve density
1 > yt OR 1 > yc ð1Þ
(Table 1, 3). Figure 3 shows an external view and a cross-
Where 1 are 1st principal stress, and yt and yc are tensile section of the fabricated sample. As shown in Fig. 3, no
and compressive yield strength respectively.6) This formula cracks appeared inside or outside the specimen. By replacing
can be used to predict the onset of crack formation. the 80% Ni/20% Al2 O3 layer with an 85% Ni/15% Al2 O31878 J. H. Park et al.
Table 2 Physical constants for the materials used in numerical analyses.4Þ
Layer Composition Poisson’s ratio Elastic modulus (MPa) CTE (/ C) Critical strength (MPa)
1 Al2 O3 100% 0.220 300000 8.000E-06 300
2 5% Ni + 95% Al2 O3 0.224 295350 8.255E-06 309
3 10% Ni + 90% Al2 O3 0.229 290700 8.510E-06 318
4 20% Ni + 80% Al2 O3 0.238 281400 9.020E-06 336
5 30% Ni + 70% Al2 O3 0.247 272100 9.530E-06 354
6 40% Ni + 60% Al2 O3 0.256 262800 1.004E-05 372
7 60% Ni + 40% Al2 O3 0.274 244200 1.106E-05 408
8 70% Ni + 30% Al2 O3 0.283 234900 1.157E-05 426
9 85% Ni + 15% Al2 O3 0.297 220950 1.234E-05 453
10 Ni 100% 0.310 207000 1.310E-05 480
layer, a 10-layer FGM sample free of surface or internal
Table 3 Theoretical density of the 10-layered functionally graded material
(FGM) specimens, calculated using the linear rule of mixture. cracks was achieved. This also resulted in a density of
5.70 g/cm3 , 91% of the theoretical maximum density. This
Ni ratio Theoretical density Weight Theoretical density ratio
result is superior to previous results of 5.59 g/cm3 .5)
(%) (g/cm3 ) (g) (g/cm3 )
Considering that the optimized density ratio is approximately
100 8.88 4 0.77
80–85% for a pressure-less sintered sample, the porosity in
80 7.88 6 1.03 this sample was reduced efficiently.
70 7.39 6 0.96
60 6.89 6 0.90 3.2 Numerical analysis of FGM specimen
40 5.89 6 0.77 Figure 6(a) shows the distribution of the first principal
stress on the axisymmetric specimen. The maximum value of
30 5.39 4 0.47
principal stress was located on the outer interface between
20 4.90 4 0.43
60%-Ni/40%-alumina and 40%-Ni/60%-alumina layers.
10 4.40 4 0.38 The distribution of first principal stress along the line B-B0
5 4.15 4 0.36 which is on the outer surface of the specimen together with
0 3.90 2 0.17 the strength distribution of the material is shown in Fig. 6(b).
Total density 46 6.24 For this crack-free specimen, it was shown that maximum
principal stress was well below the critical failure strength,
Fig. 6 Comparison of the computed 1st principal sress at the boundary (B-B0 ) with critical failure strength calculated using the numerical
analysis method (maximum principal stress theory).Crack-Free Joint in a Ni-Al2 O3 FGM System Using Three-Dimensional Modeling 1879
Table 4 Numerical values, calculated using the maximum principal stress model.
Residual stress (MPa)
Layer Composition Strength (MPa)
1st principal stress 2nd principal stress 3rd principal stress
1 Al2 O3 100% 300 295.2 232.3 64.3
2 5% Ni + 95% Al2 O3 309 156.4 156.4 6.2
3 10% Ni + 90% Al2 O3 318 138.4 135.7 19.9
4 20% Ni + 80% Al2 O3 336 241.4 70.1 60.3
5 30% Ni + 70% Al2 O3 354 214.8 133.9 65.4
6 40% Ni + 60% Al2 O3 372 193.9 141.3 61.8
7 60% Ni + 40% Al2 O3 408 295.2 128.5 64.3
8 70% Ni + 30% Al2 O3 426 331.3 264.1 31.8
9 85% Ni + 15% Al2 O3 453 193.4 136.1 24.4
10 Ni 100% 480 196.6 149.2 34.4
Fig. 7 Optical micrographs of the joint showing Vickers indents at shallow incident angles in the interface between the 5% Ni/95% Al2 O3
and 100% Al2 O3 layers: (a) 200 X magnification and (b) 500 X magnification. The white dotted lines indicate the position of the
interfaces.
Fig. 8 Optical micrographs of the joint showing Vickers indents at shallow incident angles in the interface between the 5% Ni/95% Al2 O3
and 10% Ni/90% Al2 O3 layers: (a) 200 X magnification and (b) 500 X magnification. The white dotted lines indicate the position of the
interfaces.
justifying its experimental results (Table 4). It means that no and between the 5% Ni/95% Al2 O3 and 10% Ni/90% Al2 O3
failure occurred in the numerical analysis, and the simulation layers. In the brittle material, crack paths formed at each
results matched the experimental results for the crack-free corner of the indent when Vickers pressure was increased to
sample well. more than regular pressure. The indent crack-path ostensibly
traversed the interfaces at all angles of incidence and was
3.3 Oriented vickers indentation test only minimally deflected, implying strong interfaces within
The oriented Vickers indentation test was used to inves- the FGM joint. Figures 7 and 8 show some indentations in the
tigate crack paths observed at the interfaces of the FGM Al2 O3 -rich area of the joint, and the indent cracks shown in
layers, as shown in Figs. 7–8. These figures show the crack both figures are minimally deflected, implying qualitatively
paths between the 100% Al2 O3 and 5% Ni/95% Al2 O3 layers strong interfaces within the FGM joint.1880 J. H. Park et al.
4. Conclusions In future studies, the CTE of each graded layer will be
measured experimentally and three-point bend tests will be
In this study, the FGM method was used to produce crack- conducted to determine mechanical properties of this FGM
free Ni-Al2 O3 joints. The residual stress caused by the joint.
differences in CTE values between Ni and Al2 O3 was
reduced by inserting 10 inter-layers and controlling the Acknowledgements
stacking weight of each layer. Green-body density was
improved by using four different powder sizes, and each layer This work was supported by the Korean government
was well mixed using simultaneous dry and dispersion (MOEHRD, Basic Research Promotion Fund #KRF-2007-
processes. Replacing the 80% Ni/20% Al2 O3 layer with an 311-D00516), the Korea Science and Engineering Foun-
85% Ni/15% Al2 O3 layer prevented the surface cracks that dation (#R0I-2008-000-11015-0), Micro Thermal System
formed in previous research, and finally produced a crack- (ERC) of Seoul National University and Brain Korea 21 at
free FGM joint using the same process. ANSYS simulation Hanyang University, South Korea. The authors would like
was conducted to determine thermal residual stresses in the to thank Professor Deug-Joong Kim at Sungkyunkwan
FGM specimen based on the linear rule of mixtures. The University for his assistance with the Vickers indenter.
results of the numerical analysis indicated that the residual
stresses were below critical failure strength in all layers. REFERENCES
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