Experimental Measurement of Coefficient of Thermal Expansion for Graded Layers in Ni-Al 2 O 3 FGM Joints for Accurate Residual Stress Analysis

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1 Materials Transactions, Vol. 5, No. 6 (29) pp to 1557 #29 The Japan Institute of Metals EXPRESS REGULAR ARTICLE Experimental Measurement of Coefficient of Thermal Expansion for Graded Layers in Ni-Al 2 O 3 FGM Joints for Accurate Residual Stress Analysis Sae-hee Ryu 1, Jong-ha Park 1, Caroline Sunyong Lee 1; *, Jae-chul Lee 2, Sung-hoon Ahn 2;3 and Sung-tag Oh 4 1 Division of Material and Chemical Engineering, Hanyang University, Gyeonggi-do, Korea 2 School of Mechanical and Aerospace Engineering, Seoul National University, Seoul, Korea 3 Institute of Advanced Machinery and Design, Seoul National University, Seoul, Korea 4 Department of Materials Science and Engineering, Seoul National University of Technology, Seoul, Korea Functionally graded materials have composition gradients from one end to the other as the result of a gradual transition of the properties of different materials. The residual stress caused by the difference of coefficient of thermal expansion can be minimized using functionally graded material. Therefore, the gradient of the coefficient of thermal expansion should vary according to the compositional gradient. In this study, the coefficient of thermal expansion of each compositional layer of Ni-Al 2 O 3 functionally graded material was measured using a dilatometer. These measurements provided the material properties required to calculate the residual stress, using three-dimensional modeling for accurately predicting crack positions, since it is difficult to measure residual stress experimentally. The measurement results showed the gradual increase of the coefficient of thermal expansion from Al 2 O 3 -rich composition to Ni-rich composition. Finally, the results of calculating residual stresses using the measured coefficient of thermal expansion showed that the crack positions were predicted more accurately than those using the coefficient of thermal expansion calculated by the linear rule of. This was because the measured values include the effect of porosity of the composite, whereas the linear rule of cannot account for the porosity of each layer. [doi:1.232/matertrans.m2928] (Received January 26, 29; Accepted March 31, 29; Published May 2, 29) Keywords: functionally graded material, coefficient of thermal expansion, finite element method, thermal residual stress 1. Introduction Functionally graded material (FGM) provides a gradient in thermal properties between two dissimilar materials whose coefficients of thermal expansion (CTE) are significantly different, and reduces the residual stresses due to sharp differences in the thermal properties. The residual stress is an important factor in the design of crack-free FGM joints, but it is difficult to measure experimentally. Numerical analysis techniques such as the finite element method (FEM) are used to estimate the residual stress instead of measuring it directly. The thermal residual stresses are calculated using the CTE of materials, assuming that the stresses are generated during cooling. The accuracy of the CTE values directly influences the calculation of residual stresses. In particular, since thermal expansion is really due to the asymmetric curvature of the potential energy trough, along with the increased atomic vibrational amplitudes that accompany an increase in temperature, it reflects the natural change of thermal properties with temperature. 1) Generally, the CTEs of graded layers using the values cited in published literature are used to calculate the residual stresses of FGM using the rule of. 2) However, unexpected pores within graded layers due to differential shrinkage of each material can result in inaccurate calculations. 3) In this study, the CTE of each graded layer in Ni-Al 2 O 3 FGM was measured, and compared with the calculated CTE using the linear rule of. The residual stresses in Ni- Al 2 O 3 FGM were then calculated using these CTE values to predict the position of cracks. *Corresponding author, sunyonglee@hanyang.ac.kr Table 1 Compositions of samples for CTE measurement of nine-layer Ni- Al 2 O 3 FGM. Layer number Composition 1 1%Ni 2 85%Ni/15%Al 2 O 3 3 7%Ni/3%Al 2 O 3 4 6%Ni/4%Al 2 O 3 5 5%Ni/5%Al 2 O 3 6 3%Ni/7%Al 2 O 3 7 2%Ni/8%Al 2 O 3 8 1%Ni/9%Al 2 O 3 9 1%Al 2 O 3 2. Experimental Procedure 2.1 Material fabrication The various compositions of FGM considered in this study are given in Table 1. Ni and Al 2 O 3 powders were dispersed ultrasonically in ethanol for each composition so that uneven dispersion due to density differences could be reduced by quick evaporation of the ethanol during the ultrasonic dispersion. 4) The mixed powders were grounded and sieved. Nine specimens for CTE measurement were fabricated in molds with 1 mm diameter. Nine layers of Ni-Al 2 O 3 FGM were stacked in a mold with 24.5 mm diameter, and the green bodies were cold pressed isostatically. Specimens were then sintered in an argon atmosphere in a tube furnace as shown in Fig. 1. The holding time at 15 C is needed to burn off stearic acid that was used during stacking into a cylindrical mold. The maximum sintered temperature was 135 C with a cooling rate of 2 C/min to minimize residual stress during

2 1554 S. Ryu et al. 14 3hr 12 1 Temperature( C) C/min 2 C/min Fig min Time(min) FGM sample sintering conditions for CTE measurement. Fig. 2 An axisymmetric finite element, showing stresses associated with axisymmetric loading. cooling. The sintered FGM was cut with a diamond wheel, and then the polished cross section was examined to detect the presence of any cracks. 2.2 CTE measurement The CTEs of the nine cylindrical specimens were measured using a push-rod dilatometer. Each CTE was determined from the change in the specimen length at room temperature and 1 C at a heating rate of 1 C/min. The CTE was calculated from ¼ 1 L 2 L 1 ¼ 1 L ð1þ L T 2 T 1 L T where L is the initial specimen length, L 1 and L 2 represent the initial and final lengths as the temperature changes from T 1 to T 2, and L and T are the change in length and temperature, respectively. The CTE of each composition was determined by averaging the measured CTEs over the various temperature changes. The measurements were performed in an argon atmosphere to prevent any nickel oxidation. 3. Calculation of thermal residual stress The residual stresses of the FGM were computed using the finite element method (FEM); ANSYS. The residual stress of each layer was calculated individually. The thermal strain, " T, of each isotropic layer was determined from f" T g¼ftg ð2þ where is the CTE of the material and T is the temperature change. The thermal stress, T, was calculated from the thermal strain, f T g¼½dšf" T g ð3þ where ½DŠ is the stress-strain matrix derived from Poisson s ratio () of the materials and the one-dimensional elastic modulus (E). 5) If the trivial relations r ¼ and z ¼ are omitted, the most general axisymmetric form of eq. (3) for the coordinates shown in Fig. 2 is as follows: 8 9 6) >< >: r z zr >= ¼ >; ð1 ÞE ð1 þ Þð1 2Þ Fig. 3 (a) Element condition and boundary condition and (b) PLANE82 geometry configuration T >< T >= 1 T >: >; ð1 Þ This analysis assumes ideal joining and dispersion between the two materials. In addition, the elastic modulus, CTE, and Poisson s ratio of each layer are calculated based on the linear rule of as follows: E c ¼ V 1 E 1 þ V 2 E 2 ð5þ c ¼ V 1 1 þ V 2 2 ð6þ c ¼ V 1 1 þ V 2 2 ð7þ where E c, c, and c represent the elastic modulus, coefficient of thermal expansion, and Poisson s ratio of the, respectively; V 1 and V 2 are the volume fractions of phases 1 and 2; and V 1 þ V 2 ¼ 1. 7) For finite element analysis, a two-dimensional eight-node plane element (PLANE82) was used in the ANSYS. The twodimensional axisymmetric model had 54,641 nodes and 18,34 elements, and was meshed using.1 mm elements. Figure 3 shows (a) the elements and boundary conditions used for the finite element analysis, and (b) a schematic diagram of PLANE82. 8) Table 2 lists the material properties of the FGM layers based on the properties obtained from the ð4þ

3 Experimental Measurement of Coefficient of Thermal Expansion for Graded Layers in Ni-Al 2 O 3 FGM Joints 1555 Table 2 Physical constants for calculating residual stresses. Layer Contents Thickness [mm] Elastic modulus [MPa] Poisson s ratio Measured CTE [1 6 / C] Measured CTE values [1 6 / C] 1 1%Ni %Ni/15%Al 2 O %Ni/3%Al 2 O %Ni/4%Al 2 O %Ni/5%Al 2 O %Ni/7%Al 2 O %Ni/8%Al 2 O %Ni/9%Al 2 O %Al 2 O Literature values ( Fig. 4 Comparison of CTE calculated by the linear rule of using measured values of pure materials and measured directly by the dilatometer. Fig. 5 Microstructure of 6% Ni/4% Al 2 O 3. Pores are indicated by white circles, where the white area is Ni and the black area is Al 2 O 3. literature, the measured CTE values, and the values calculated from eqs. (5) (7) that were used in the finite element analysis. Generally, researchers use the maximum tensile stress and maximum principle stress theories to estimate the failure of brittle materials such as ceramics, and the maximum deformation energy theory (von-mises stress theory) to estimate the failure of ductile materials such as metals. 7 1) Therefore the paper used the maximum tensile stress for Al 2 O 3 and the von-mises stress for Ni to estimate their failures. 4. Results and Discussion Figure 4 compares the measured CTE with values from the linear rule of. The measured results showed a gradual increase in the CTE as the Ni content increased, as expected. However, as the samples moved from an Al 2 O 3 - rich composition to a Ni-rich composition, the measured values deviated more from the measured values combined with the linear rule of. These differences between the measured and calculated CTE values could be caused by unexpected porosity in the sintered body. Figure 5 shows the microstructure of the fabricated 6% Ni/4% Al 2 O 3 layer. The microstructure includes much Fig. 6 Residual stresses of Ni-Al 2 O 3 FGM obtained using the linear rule of. The peaks of stress occur at 1% Al 2 O 3 (Layer 9), 6% Ni/ 4% Al 2 O 3 (layer 4), and 8% Ni/15% Al 2 O 3 (Layer 2). small pores marked by white circles, and these pores can cause large deviations from the calculated CTE values. Figure 6 shows the calculated tensile and von-mises stresses obtained using the linear rule of. The failure of FGM sample can be predicted from the peaks of stress in this plot. The figure indicates that the peak stress points are at 1% Al 2 O 3, 6% Ni/4% Al 2 O 3, and 85% Ni/ 15% Al 2 O 3, and suggests that cracks will form at those positions in the FGM.

4 1556 S. Ryu et al. Fig. 7 Residual stresses of Ni-Al 2 O 3 FGM obtained using measured CTE values. The peaks of stress occur at the 1% Al 2 O 3 (Layer 9), 5% Ni/ 5% Al 2 O 3 (Layer 5), and 8% Ni/15% Al 2 O 3 (Layer 2). Figure 7 shows the calculated tensile and von-mises stresses obtained using the measured CTE values. According to the figure, the stress peaks are located at 1% Al 2 O 3, 5% Ni/5% Al 2 O 3, and 85% Ni/15% Al 2 O 3. These three stress peaks correspond to the expected failure positions. Figures 8 and 9 show micrographs of the FGM fabricated using the compositions given in Table 1. Figure 8 shows the surface of the sample, where cracks located between 1% Ni and 85% Ni/15% Al 2 O 3, and cracks at 5% Ni/5% Al 2 O 3 were observed. The cross-section of this sample, shown in Fig. 9, has an additional crack in the 1% Al 2 O 3 layer. The crack positions of the fabricated sample matched the points of peak stress shown in Fig. 7 using the measured CTE values. The maximum stress points calculated using the linear rule of did not accurately predict the crack in Layer 5 (5% Ni/5% Al 2 O 3 ). Therefore, the calculation of residual stress using the linear rule of was unable to predict crack positions accurately in the porous composite, unlike the calculation using measured CTE values. The calculations using the measured CTE values were more accurate because they included the porous effects of the composite. Thus, the porosity of the composite must be reflected in the property of FGM fabricated by pressureless sintering to improve the accuracy of stress calculations. 5. Conclusions The CTE for graded layers in a Ni-Al 2 O 3 FGM were measured to calculate residual stresses. These values were compared to those obtained using the linear rule of. The results showed that the estimated residual stresses obtained using the measured CTE values were more accurate for predicting the crack positions in a fabricated FGM sample than those obtained using the linear rule of. This Fig. 8 Exterior of fabricated Ni-Al 2 O 3 FGM. The micrographs show the magnified cracks at 1% Ni and 85% Ni/15% Al 2 O 3. Fig. 9 Cross section of fabricated Ni-Al 2 O 3 FGM. The micrograph shows the magnified crack at 1% Al 2 O 3.

5 Experimental Measurement of Coefficient of Thermal Expansion for Graded Layers in Ni-Al 2 O 3 FGM Joints 1557 was because the measured CTE values already include the porosity of the composite, whereas the linear rule of cannot account for the porosity of each layer. Therefore, the measured coefficient of thermal expansion must be used in order to predict the crack positions of porous FGMs accurately, otherwise a new mixture rule is required to reflect the porosity of each layer. Acknowledgment This work was supported by the Korean government (MOEHRD, Basic Research Promotion Fund #KRF D516), the Korea Science and Engineering Foundation (#RI ) and Engineering Research Center, ERC (Micro Thermal System Research Center) of Seoul National University. The authors would like to thank Professor Jae-sung Lee at Hanyang University for assistance with the cold isostatic press. The authors would also like to thank Professor Yong-ho Choa and Han-Bok Song at Hanyang University for support with the tube furnace. REFERENCES 1) W. D. Callister, Jr.: Materials Science and Engineering: An Introduction, (John Wiley and Sons, Inc., 23) pp ) S. H. Ryu, J. H. Park, C. S. Lee, J. S. Lee, J. C. Lee, S. H. Ahn, D. K. Kim, J. H. Chae and D. H. Riu: Korean J. Mater. Res. 18 (28) ) L. M. Pines and A. H. Bruck: Acta Mater. 54 (26) ) J. H. Park, S. H. Ryu, C. S. Y. Lee, Y. H. Choa, J. C. Lee and S. H. Ahn: Proc. Multi-functional materials and structures, Hong Kong, China, July 27 31, (28). 5) D. L. Logan: A Firsr Course in the Finite Element Method: Third Edition, (BROOKS/COLE; 22) pp ) R. D. Cook, D. S. Malkus, M. E. Plesha and R. J. Witt: Concepts and Applications of Finite Element Analysis: Fourth Edition, (John Wiley and Sons, Inc., 22) pp ) J. C. Lee, J. H. Park, S. H. Ryu, H. J. Hong, D. H. Riu, S. H. Ahn and C. S. Y. Lee: Mater. Trans. 49 (28) ) ANSYS. Release 11. Documentation for ANSYS. 9) N. E. Dowling: Mechanical Behavior of Materials 2nd edition, (Prentice-Hall International, Inc., London, 1999) pp ) J. G. Choi and S. B. Lee: Analysis material science, (Cheong Moon Gak Publishers, Seoul, 2) pp