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Effects of compositional gradient and thickness of coating on the residual stresses within the graded coating
Materials & Design Materials and Design 28 (2007) 1192–1197 www.elsevier.com/locate/matdes
Effects of compositional gradient and thickness of coating on the residual stresses within the graded coating X.C. Zhang a
a,b,*
, B.S. Xu a, H.D. Wang a, Y.X. Wu a, Y. Jiang
a
State Key Laboratory of Metal Matrix Composites, Shanghai Jiaotong University, Shanghai 200030, China b National Key Laboratory for Remanufacturing, Beijing 100072, China Received 22 July 2005; accepted 13 January 2006 Available online 9 March 2006
Abstract The effects of compositional gradient and thickness of coating on the residual stresses within the ZrO2/NiCoCrAlY graded coating were analysed using finite element method. The compositional gradient was characterized by the gradient component. Modeling results showed that the presence of graded properties and compositions within the coating did reduce the stresses discontinuities at the interfaces in the coating. The compositional gradient of coating had an obvious influence on the residual stress magnitude at the coating/substrate interface and the location of stress concentration near the edge of the coating. Also, the magnitudes of residual stresses on the coating surface and at the coating/substrate interface were dependent on the coating thickness. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Graded coating; Compositional gradient; Residual stress; Stress concentration
1. Introduction The modeling and calculation of the residual stresses with the coatings has been, and still are, of great interest [1–3]. During the thermal cycling processes, some high-temperature coatings were prone to premature failure because of thermal residual stresses due to thermal expansion mismatches among the coating layers and the substrate. Hence, with the development of the coating technologies, some advanced graded coatings were fabricated to reduce the thermal expansion mismatches [4–6]. However, there were few studies on the effectiveness of graded property and composition of coating on the reduction of thermal residual stresses and the improvement of properties. Several models have been developed so far in order to estimate induced residual stresses in coatings. However, * Corresponding author. Present address: National Key Laboratory for Remanufacturing, Beijing 100072, China. Tel.: +86 10 66718541; fax: +86 10 66717144. E-mail address: [email protected] (X.C. Zhang).
0261-3069/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2006.01.012
the shear stress and axial stress were commonly not considered and the normal stresses in individual layer were assumed to be uniform along the length thickness in these models. Chiu developed a model to predict the shear and axial stresses within a coating, however, it should be noted that their model was only limited to bilayer system. With increasing the number of coating layers, the number of continuity conditions to be satisfied increased [7]. In such case, obtaining a closed-form solution was highly complicated. The analysis was often left to the computer. The finite element method has been utilized to analyze the residual stresses generated during the cooling process and deposition process of single-layer and multilayer coatings. However, up to present, there were few studies on the effect of compositional gradient of coating within the graded coating. The purpose of this paper was to investigate the effects of compositional gradient and thickness of coating on the residual stresses within the ZrO2/NiCoCrAlY graded coating using finite element method.
X.C. Zhang et al. / Materials and Design 28 (2007) 1192–1197
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2. Model description and materials
Table 1 Material properties used for calculations [4]
Residual stresses within ZrO2/NiCoCrAlY graded coatings are modeled by thermo-mechanical finite element analysis using finite element code ANSYS 6.0. The modeling process consists two steps, i.e., thermal model and mechanical model [1]. The used model represents a shape Ni-alloy substrate of 12 mm in diameter and 5 mm in height with a functionally graded coating deposited on the top surface, as shown in Fig. 1. In this paper, the total number of the coating layers is 11 and the coordinate system is defined such that the interface between the substrate and 1st coating layer is located at z = 0. The analytical model is assumed to be a perfect elastic body without plastic deformation in the whole analysis procedure. An axial symmetric problem is chosen in order to reduce the data processing time. The meshes in the zone near the coating/substrate interface are refined to improve the accuracy of calculation. The constraints were imposed on the axial line and bottom sides of the analyzed models and the heat transfer was only allowed from the top surface of the model. Four-node thermal-structure couple element PLANE13 was used. During the whole thermal analysis, thermal radiation was not considered. All specimens are assumed to be stress free at the temperature of 427 °C (i.e., reference temperature), at which the spraying process is assumed to end [3]. Hence, the final residual stresses are only generated due to the cooling of the whole coating specimens from the reference temperature to home temperature (i.e., 25 °C). Residual stress components resulting from the FEA were obtained in the following directions: (1) radial stress corresponding to stress value along the radial direction, (2) axial stress component that refers to stress profile along the thickness direction, and (3) shear stress component that acts along the tangential direction. The material properties of ZrO2 ceramic component, NiCoCrAlY metallic component, and Ni-alloy substrate as functions of temperature from 25 °C to 800 °C were shown in Table 1 [3]. The ZrO2/NiCrAlY graded coating can be characterized by a changing physical property due to a stepwise change in composition, in morphology, or in microstructure from material NiCoCrAlY to ZrO2. If the first layer and the last layer of the coating are deposited by material NiCoCrAlY and ZrO2, respectively, the volume fraction of material ZrO2 in ith layer, ðV ZrO2 Þi , is described by a power-law, similar to that proposed by Drake et al. [8]
Material
T (°C)
E (GPa)
q (kg/m3)
a (106/K)
t
k (W/m K)
C (J/kg K)
Ni-alloy substrate
25 400 800
200 179 149
8220
14.4 14.4 14.4
0.3
11.5 17.5 23.8
431 524 627
NiCoCrAlY
25 400 800
225 186 147
7320
14 24 47
0.3
4.3 6.4 10.2
501 592 781
ZrO2
25 400 800
53 52 46
6037
7.2 9.4 16
0.25
1.5 1.2 1.2
500 576 637
ðV ZrO2 Þi ¼
i1 n1
m ð1Þ
where i denote the ith coating layer and ranges from 1 to 11, and n = 11 is the number of the coating layers, m is the gradient exponent that controls the shape of non-linear or linear compositional gradient, as shown in Fig. 2. In the case of elastic deformation, the individual material property of ith coating layer at a setting temperature can be modeled by the Vegard’s rule [9]
1.0
Volume fraction of ZrO2
0.9
m=0.1
0.8 0.7
0.5
0.6
0.75 1.0
0.5 0.4
2.0
0.3
5.0 7.5
0.2
10.0
0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(i-1)/(n-1) Fig. 2. Relationship between the volume fraction of material ZrO2 in the graded coating and the ratio of (i 1)/(n 1) with various values of the gradient exponent, m.
M i ¼ M ZrO2 ðV ZrO2 Þi þ M NiCoCrAlY ð1 ðV ZrO2 Þi Þ
ð2Þ
where Mi is the individual material property of ith layer, M ZrO2 and MNiCoCrAlY are the material properties of ZrO2 and NiCoCrAlY in Table 1, respectively.
Fig. 1. Schematic description of the geometry used in the finite element modeling.
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X.C. Zhang et al. / Materials and Design 28 (2007) 1192–1197
3. Results and discussions 3.1. Effect of compositional gradient of coating It is well known that the compositional gradient of coating has an obviously influence on the residual stresses within the coating-based system [10,11]. In this paper, this issue is also investigated and the compositional gradient of a ZrO2/NiCoCrAlY graded coating is characterized by the gradient exponent m in Eq. (1). The thickness of the individual coating layer is 20 lm, hence, the coating thickness is 220 lm. Eight different gradient exponents are chosen. The maximum tensile radial stress and shear stress at the coating/substrate interface near the edge decrease with increasing the magnitude of m, as shown in Fig. 3. This is because with increasing the magnitude of m, the volume fraction of material ZrO2 decreases significantly near the interface. Accordingly, the volume fraction of material
Radial stress on the coating surface (MPa)
25
-25 -50 -75 -100 -125 -150 -175 -200 -225
m increasing 0
1
Fig. 4. Effect of compositional gradient on the radial stress on the coating surface.
50 0
Radial stress (MPa)
150
100
50
0
-100 -150
m=0.1 m=0.5 m=0.75 m=1.0
-250
m increasing 0
1
2
3
-300 -0 .4
4
5
-0 .3
6
-0 .2
-0 .1
0.0
0.1
0.2
Distance from interface (mm)
a
Distance along radius (mm)
a 80
50
70
0
60
Radial stress (MPa)
Shear stress at the interface (MPa)
Coating
Substrate
-50
-200
-50
50 40 30 20
-100 -150
m=2.5 m=5.0 m=7.5 m=10.0
10 -250 0
m increasing 0
1
2
3
4
5
-300 -0 .4
6
b
Coating
Substrate
-50
-200
-10
b
6
5
4
3
2
Distance along radius (mm)
200
Radial stress at the interface (MPa)
0
-0 .3
-0.2
-0.1
0.0
0 .1
0.2
Distance from interface (mm)
Distance along radius (mm)
Fig. 3. Effect of compositional gradient on the residual stresses at the coating/substrate interface: (a) radial stress, and (b) shear stress.
Fig. 5. Effect of compositional gradient on the radial stress within the coating system along the axial line: (a) m = 0.1, 0.5, 0.75, and 1.0 and (b) m = 2.5, 5.0, 7.5, and 10.0.
X.C. Zhang et al. / Materials and Design 28 (2007) 1192–1197
NiCoCrAlY increases in the metallic-rich region near the interface, thereby producing less shrinkage of the coating system and smaller residual stresses during cooling. At the same time, the axial stress at the interface is very small and is not discussed here. The effect of compositional gradient on the radial stress at the coating surface is stronger than it on the shear and axial stresses. Even so, the compressive radial stresses are almost not changed with increasing the magnitude of m, as sown in Fig. 4. This is because at the coating surface, the volume fraction of material ZrO2 is constant. Some models have been proposed to predict the radial stresses along the thickness direction within the graded coating. However, it should be noted that the radial stress is assumed to be unchanged along the radial direction. In this paper, the radial stresses at the axial line along the thickness direction of the coating system with different composition gradients whether discussed, as shown in Fig. 5. It is interesting to find that the maximal compressive radial stress was not on the coating surface or at the coating/substrate interface, but in the coating and becomes less compressive towards the coating surface, where the compo-
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sitional gradient is linear or non-linear. When m becomes extremely small (m = 0.1) and extremely large (m = 10.0), the maximal stresses are relatively low and are located near the interface and coating surface, respectively. In addition, these residual stress in the substrate near the coating/substrate interface decreases with increasing the magnitude of m. For typically duplex ZrO2/NiCoCrAlY system, the stress concentration is located at the edge of the interface between the ceramic layer and the metallic layer [1]. However, for graded coating, the location of stress concentration is changed. When m becomes extremely small (m = 0.1), the stress concentration is located at the edge of the interface between the first layer and the second layer. This is because when m = 0.1, there is a remarkable material mismatch between the first layer and the second layer, as shown in Fig. 6. With increasing the magnitude of m, the location of stress concentration is changed along the thickness direction. When m becomes extremely large (i.e., m = 10.0), the stress concentration is located at the edge of the interface between the last layer and the penultimate layer, as shown in Fig. 7. This is because there is a remarkable
Fig. 6. Typical contour plot of stress distributions in the graded coating with low gradient component (m = 0.1) and the substrate near the edge of interface.
Fig. 7. Typical contour plot of stress distributions in the graded coating with high gradient component (m = 10.0) and the substrate near the edge of interface.
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X.C. Zhang et al. / Materials and Design 28 (2007) 1192–1197
material mismatch between the two layers when m = 10.0. However, when the linear profile is assumed (i.e., m = 1.0), the stress concentration is not visible, as shown in Fig. 8.
3.2. Effect of coating thickness Various coating-based systems with different coating thicknesses are used to investigate the effect of coating
Fig. 8. Typical contour plot of stress distributions in the graded coating with linear profile (m = 1.0) and the substrate near the edge of interface.
70
Shear stress at the interface (MPa)
Radial stress at the interface (MPa)
140 120 100 80 tc = 550 μm
60
440
40
330 220
20
110 0 -20 0
a
1
2
3
4
5
50 40 30
tc increasing
20 10 0 -10
6
0
Distance along radius (mm)
1
2
3
4
5
6
Distance along radius (mm)
b
50
Axial stress at the interface (MPa)
60
tc increasing
0 -50 -100 -150 -200 -250 -300 0
c
1
2
3
4
5
6
Distance along radius (mm)
Fig. 9. Effect of coating thickness on the residual stresses at the coating/substrate interface: (a) radial stress, (b) shear stress, and (c) axial stress.
Radial stress on the coating surface (MPa)
X.C. Zhang et al. / Materials and Design 28 (2007) 1192–1197 25 0 -25 -50 -75 -100 -125
tc increasing
-150 -175 -200 -225
0
1
2
3
4
5
6
1197
the coating/substrate interface near the edge were decreased and the compressive radial stress on the coating surface was increased with increasing the magnitude of m. With increasing the magnitude of m, the location of stress concentration was changed from the edge of interface between the first layer and the second layer to the edge of the interface between the last layer and the penultimate layer. When the coating was extremely thin and the linear profile was assumed, the compressive radial stress was developed at the coating/substrate interface and was changed to tensile with increasing the distance from the center along the radial direction. When the coating was relatively thick, the radial stress at the interface was always tensile and was increased with increasing the coating thickness.
Distance along radius (mm) Fig. 10. Effect of coating thickness on the radial stress on the coating surface.
thickness on the residual stresses within graded coatings. For different systems, it is assumed that the graded layers of the coating have the identical thickness. When the coating is extremely thin, i.e., tc = 110 lm, and the linear profile is assumed, the compressive radial stress is developed at the coating/substrate interface and is changed to tensile with increasing the distance from the center along the radial direction, as shown in Fig. 9a. When the coating thickness is larger than and equal to 220 lm, the radial stress at the interface is always tensile and is increased with increasing the coating thickness. The shear stress is always tensile and is increased with increasing the coating thickness, as shown in Fig. 9b. The maximal tensile radial stress and shear stress are located at the edge of the interface, whether the coating is thin or thick. With increasing the coating thickness, these maximal tensile stresses increase gradually. The axial stress mainly occurs near the edge of the interface and the maximal tensile stress is almost not changed with increasing the coating thickness, as shown in Fig. 9c. The radial stress on the coating surface is usually compressive and changed to zero at the edge, as shown in Fig. 10. With increasing the coating thickness, the compressive stress decreases. Whether the coating is thick or thin, the stress distribution is almost not changed. 4. Conclusions The effects of compositional gradient and thickness of coating on the residual stresses within the ZrO2/NiCoCrAlY graded coating were analysed using finite element method. It was found that the compositional gradient characterized by the gradient component had an obviously influence on the residual stresses within coating. The maximum tensile radial stress and shear stress at
Acknowledgements Financial supports of this work from China Natural Science Foundation (50235030), National Development Scheme of Key Fundamental Research (Nation ‘‘973’’ Project) of China (G1999065009) and ‘‘863’’ Project (2003AA331130) are gratefully acknowledged. References [1] Zhang XC, Xu BS, Wang HD, Wu YX. Effects of oxide thickness, Al2O3 interlayer and interface asperity on residual stresses in thermal barrier coatings. Mater and Des, doi:10.1016/j.matdes.2005.02.008. [2] Zhang XC, Xu BS, Wang HD, Wu YX. Modeling of the residual stresses in plasma-spraying functionally graded ZrO2/NiCoCrAlY coatings using finite element method. Mater and Des 2006;27:308–15. [3] Khor KA, Gu YW. Effects of residual stress on the performance of plasma sprayed functionally graded ZrO2/NiCoCrAlY coatings. Mater Sci Eng 2000;A277:64–76. [4] Kokini K, DeJonge J, Rangaraj S, Beardsley B. Thermal shock of functionally graded thermal barrier coatings with similar thermal resistance. Surf Coat Technol 2002;154:223–31. [5] Takeuchi H, Tsunekawa Y, Okumiya M. Formation of compositionally graded Ni–P deposits containing SiC particles by jet electroplating. Mate T JIM 1997;38:43–8. [6] Hou P, Basu SN, Sarin VK. Structure and high-temperature stability of compositionally graded CVD mullite coatings. Int J Refract Met H 2001;19:467–77. [7] Zhang XC, Xu BS, Wang HD, Wu YX. An analytical model for predicting thermal residual stresses in multilayer coating systems. Thin Sold Films 2005;488:274–82. [8] Drake JT, Williamson RL, Rabin BH. Finite element analysis of thermal residual stresses at graded ceramic-metal interfaces. Part I. Model description and geometrical effects. J Appl Phys 1993;74:1310–20. [9] Adachi S. GaAs, AlAs, and AlxGa1–xAs Material parameters for use in research and device applications. J Appl Phys 1985;58:R1–R29. [10] Zhang XC, Xu BS, Wang HD, Wu YX, Jiang Y. Modeling of thermal residual stresses in multilayer coatings with graded properties and compositions. Thin Sold Films 2006;497:222–31. [11] Shaw LL. Thermal residual stresses in plates and coatings composed of multi-layered and functionally graded materials. Comps Part BEng 1998;29:199–210.
Effects of compositional gradient and thickness of coating on the residual stresses within the graded coating X.C. Zhang a
a,b,*
, B.S. Xu a, H.D. Wang a, Y.X. Wu a, Y. Jiang
a
State Key Laboratory of Metal Matrix Composites, Shanghai Jiaotong University, Shanghai 200030, China b National Key Laboratory for Remanufacturing, Beijing 100072, China Received 22 July 2005; accepted 13 January 2006 Available online 9 March 2006
Abstract The effects of compositional gradient and thickness of coating on the residual stresses within the ZrO2/NiCoCrAlY graded coating were analysed using finite element method. The compositional gradient was characterized by the gradient component. Modeling results showed that the presence of graded properties and compositions within the coating did reduce the stresses discontinuities at the interfaces in the coating. The compositional gradient of coating had an obvious influence on the residual stress magnitude at the coating/substrate interface and the location of stress concentration near the edge of the coating. Also, the magnitudes of residual stresses on the coating surface and at the coating/substrate interface were dependent on the coating thickness. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Graded coating; Compositional gradient; Residual stress; Stress concentration
1. Introduction The modeling and calculation of the residual stresses with the coatings has been, and still are, of great interest [1–3]. During the thermal cycling processes, some high-temperature coatings were prone to premature failure because of thermal residual stresses due to thermal expansion mismatches among the coating layers and the substrate. Hence, with the development of the coating technologies, some advanced graded coatings were fabricated to reduce the thermal expansion mismatches [4–6]. However, there were few studies on the effectiveness of graded property and composition of coating on the reduction of thermal residual stresses and the improvement of properties. Several models have been developed so far in order to estimate induced residual stresses in coatings. However, * Corresponding author. Present address: National Key Laboratory for Remanufacturing, Beijing 100072, China. Tel.: +86 10 66718541; fax: +86 10 66717144. E-mail address: [email protected] (X.C. Zhang).
0261-3069/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2006.01.012
the shear stress and axial stress were commonly not considered and the normal stresses in individual layer were assumed to be uniform along the length thickness in these models. Chiu developed a model to predict the shear and axial stresses within a coating, however, it should be noted that their model was only limited to bilayer system. With increasing the number of coating layers, the number of continuity conditions to be satisfied increased [7]. In such case, obtaining a closed-form solution was highly complicated. The analysis was often left to the computer. The finite element method has been utilized to analyze the residual stresses generated during the cooling process and deposition process of single-layer and multilayer coatings. However, up to present, there were few studies on the effect of compositional gradient of coating within the graded coating. The purpose of this paper was to investigate the effects of compositional gradient and thickness of coating on the residual stresses within the ZrO2/NiCoCrAlY graded coating using finite element method.
X.C. Zhang et al. / Materials and Design 28 (2007) 1192–1197
1193
2. Model description and materials
Table 1 Material properties used for calculations [4]
Residual stresses within ZrO2/NiCoCrAlY graded coatings are modeled by thermo-mechanical finite element analysis using finite element code ANSYS 6.0. The modeling process consists two steps, i.e., thermal model and mechanical model [1]. The used model represents a shape Ni-alloy substrate of 12 mm in diameter and 5 mm in height with a functionally graded coating deposited on the top surface, as shown in Fig. 1. In this paper, the total number of the coating layers is 11 and the coordinate system is defined such that the interface between the substrate and 1st coating layer is located at z = 0. The analytical model is assumed to be a perfect elastic body without plastic deformation in the whole analysis procedure. An axial symmetric problem is chosen in order to reduce the data processing time. The meshes in the zone near the coating/substrate interface are refined to improve the accuracy of calculation. The constraints were imposed on the axial line and bottom sides of the analyzed models and the heat transfer was only allowed from the top surface of the model. Four-node thermal-structure couple element PLANE13 was used. During the whole thermal analysis, thermal radiation was not considered. All specimens are assumed to be stress free at the temperature of 427 °C (i.e., reference temperature), at which the spraying process is assumed to end [3]. Hence, the final residual stresses are only generated due to the cooling of the whole coating specimens from the reference temperature to home temperature (i.e., 25 °C). Residual stress components resulting from the FEA were obtained in the following directions: (1) radial stress corresponding to stress value along the radial direction, (2) axial stress component that refers to stress profile along the thickness direction, and (3) shear stress component that acts along the tangential direction. The material properties of ZrO2 ceramic component, NiCoCrAlY metallic component, and Ni-alloy substrate as functions of temperature from 25 °C to 800 °C were shown in Table 1 [3]. The ZrO2/NiCrAlY graded coating can be characterized by a changing physical property due to a stepwise change in composition, in morphology, or in microstructure from material NiCoCrAlY to ZrO2. If the first layer and the last layer of the coating are deposited by material NiCoCrAlY and ZrO2, respectively, the volume fraction of material ZrO2 in ith layer, ðV ZrO2 Þi , is described by a power-law, similar to that proposed by Drake et al. [8]
Material
T (°C)
E (GPa)
q (kg/m3)
a (106/K)
t
k (W/m K)
C (J/kg K)
Ni-alloy substrate
25 400 800
200 179 149
8220
14.4 14.4 14.4
0.3
11.5 17.5 23.8
431 524 627
NiCoCrAlY
25 400 800
225 186 147
7320
14 24 47
0.3
4.3 6.4 10.2
501 592 781
ZrO2
25 400 800
53 52 46
6037
7.2 9.4 16
0.25
1.5 1.2 1.2
500 576 637
ðV ZrO2 Þi ¼
i1 n1
m ð1Þ
where i denote the ith coating layer and ranges from 1 to 11, and n = 11 is the number of the coating layers, m is the gradient exponent that controls the shape of non-linear or linear compositional gradient, as shown in Fig. 2. In the case of elastic deformation, the individual material property of ith coating layer at a setting temperature can be modeled by the Vegard’s rule [9]
1.0
Volume fraction of ZrO2
0.9
m=0.1
0.8 0.7
0.5
0.6
0.75 1.0
0.5 0.4
2.0
0.3
5.0 7.5
0.2
10.0
0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(i-1)/(n-1) Fig. 2. Relationship between the volume fraction of material ZrO2 in the graded coating and the ratio of (i 1)/(n 1) with various values of the gradient exponent, m.
M i ¼ M ZrO2 ðV ZrO2 Þi þ M NiCoCrAlY ð1 ðV ZrO2 Þi Þ
ð2Þ
where Mi is the individual material property of ith layer, M ZrO2 and MNiCoCrAlY are the material properties of ZrO2 and NiCoCrAlY in Table 1, respectively.
Fig. 1. Schematic description of the geometry used in the finite element modeling.
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X.C. Zhang et al. / Materials and Design 28 (2007) 1192–1197
3. Results and discussions 3.1. Effect of compositional gradient of coating It is well known that the compositional gradient of coating has an obviously influence on the residual stresses within the coating-based system [10,11]. In this paper, this issue is also investigated and the compositional gradient of a ZrO2/NiCoCrAlY graded coating is characterized by the gradient exponent m in Eq. (1). The thickness of the individual coating layer is 20 lm, hence, the coating thickness is 220 lm. Eight different gradient exponents are chosen. The maximum tensile radial stress and shear stress at the coating/substrate interface near the edge decrease with increasing the magnitude of m, as shown in Fig. 3. This is because with increasing the magnitude of m, the volume fraction of material ZrO2 decreases significantly near the interface. Accordingly, the volume fraction of material
Radial stress on the coating surface (MPa)
25
-25 -50 -75 -100 -125 -150 -175 -200 -225
m increasing 0
1
Fig. 4. Effect of compositional gradient on the radial stress on the coating surface.
50 0
Radial stress (MPa)
150
100
50
0
-100 -150
m=0.1 m=0.5 m=0.75 m=1.0
-250
m increasing 0
1
2
3
-300 -0 .4
4
5
-0 .3
6
-0 .2
-0 .1
0.0
0.1
0.2
Distance from interface (mm)
a
Distance along radius (mm)
a 80
50
70
0
60
Radial stress (MPa)
Shear stress at the interface (MPa)
Coating
Substrate
-50
-200
-50
50 40 30 20
-100 -150
m=2.5 m=5.0 m=7.5 m=10.0
10 -250 0
m increasing 0
1
2
3
4
5
-300 -0 .4
6
b
Coating
Substrate
-50
-200
-10
b
6
5
4
3
2
Distance along radius (mm)
200
Radial stress at the interface (MPa)
0
-0 .3
-0.2
-0.1
0.0
0 .1
0.2
Distance from interface (mm)
Distance along radius (mm)
Fig. 3. Effect of compositional gradient on the residual stresses at the coating/substrate interface: (a) radial stress, and (b) shear stress.
Fig. 5. Effect of compositional gradient on the radial stress within the coating system along the axial line: (a) m = 0.1, 0.5, 0.75, and 1.0 and (b) m = 2.5, 5.0, 7.5, and 10.0.
X.C. Zhang et al. / Materials and Design 28 (2007) 1192–1197
NiCoCrAlY increases in the metallic-rich region near the interface, thereby producing less shrinkage of the coating system and smaller residual stresses during cooling. At the same time, the axial stress at the interface is very small and is not discussed here. The effect of compositional gradient on the radial stress at the coating surface is stronger than it on the shear and axial stresses. Even so, the compressive radial stresses are almost not changed with increasing the magnitude of m, as sown in Fig. 4. This is because at the coating surface, the volume fraction of material ZrO2 is constant. Some models have been proposed to predict the radial stresses along the thickness direction within the graded coating. However, it should be noted that the radial stress is assumed to be unchanged along the radial direction. In this paper, the radial stresses at the axial line along the thickness direction of the coating system with different composition gradients whether discussed, as shown in Fig. 5. It is interesting to find that the maximal compressive radial stress was not on the coating surface or at the coating/substrate interface, but in the coating and becomes less compressive towards the coating surface, where the compo-
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sitional gradient is linear or non-linear. When m becomes extremely small (m = 0.1) and extremely large (m = 10.0), the maximal stresses are relatively low and are located near the interface and coating surface, respectively. In addition, these residual stress in the substrate near the coating/substrate interface decreases with increasing the magnitude of m. For typically duplex ZrO2/NiCoCrAlY system, the stress concentration is located at the edge of the interface between the ceramic layer and the metallic layer [1]. However, for graded coating, the location of stress concentration is changed. When m becomes extremely small (m = 0.1), the stress concentration is located at the edge of the interface between the first layer and the second layer. This is because when m = 0.1, there is a remarkable material mismatch between the first layer and the second layer, as shown in Fig. 6. With increasing the magnitude of m, the location of stress concentration is changed along the thickness direction. When m becomes extremely large (i.e., m = 10.0), the stress concentration is located at the edge of the interface between the last layer and the penultimate layer, as shown in Fig. 7. This is because there is a remarkable
Fig. 6. Typical contour plot of stress distributions in the graded coating with low gradient component (m = 0.1) and the substrate near the edge of interface.
Fig. 7. Typical contour plot of stress distributions in the graded coating with high gradient component (m = 10.0) and the substrate near the edge of interface.
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material mismatch between the two layers when m = 10.0. However, when the linear profile is assumed (i.e., m = 1.0), the stress concentration is not visible, as shown in Fig. 8.
3.2. Effect of coating thickness Various coating-based systems with different coating thicknesses are used to investigate the effect of coating
Fig. 8. Typical contour plot of stress distributions in the graded coating with linear profile (m = 1.0) and the substrate near the edge of interface.
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Fig. 9. Effect of coating thickness on the residual stresses at the coating/substrate interface: (a) radial stress, (b) shear stress, and (c) axial stress.
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the coating/substrate interface near the edge were decreased and the compressive radial stress on the coating surface was increased with increasing the magnitude of m. With increasing the magnitude of m, the location of stress concentration was changed from the edge of interface between the first layer and the second layer to the edge of the interface between the last layer and the penultimate layer. When the coating was extremely thin and the linear profile was assumed, the compressive radial stress was developed at the coating/substrate interface and was changed to tensile with increasing the distance from the center along the radial direction. When the coating was relatively thick, the radial stress at the interface was always tensile and was increased with increasing the coating thickness.
Distance along radius (mm) Fig. 10. Effect of coating thickness on the radial stress on the coating surface.
thickness on the residual stresses within graded coatings. For different systems, it is assumed that the graded layers of the coating have the identical thickness. When the coating is extremely thin, i.e., tc = 110 lm, and the linear profile is assumed, the compressive radial stress is developed at the coating/substrate interface and is changed to tensile with increasing the distance from the center along the radial direction, as shown in Fig. 9a. When the coating thickness is larger than and equal to 220 lm, the radial stress at the interface is always tensile and is increased with increasing the coating thickness. The shear stress is always tensile and is increased with increasing the coating thickness, as shown in Fig. 9b. The maximal tensile radial stress and shear stress are located at the edge of the interface, whether the coating is thin or thick. With increasing the coating thickness, these maximal tensile stresses increase gradually. The axial stress mainly occurs near the edge of the interface and the maximal tensile stress is almost not changed with increasing the coating thickness, as shown in Fig. 9c. The radial stress on the coating surface is usually compressive and changed to zero at the edge, as shown in Fig. 10. With increasing the coating thickness, the compressive stress decreases. Whether the coating is thick or thin, the stress distribution is almost not changed. 4. Conclusions The effects of compositional gradient and thickness of coating on the residual stresses within the ZrO2/NiCoCrAlY graded coating were analysed using finite element method. It was found that the compositional gradient characterized by the gradient component had an obviously influence on the residual stresses within coating. The maximum tensile radial stress and shear stress at
Acknowledgements Financial supports of this work from China Natural Science Foundation (50235030), National Development Scheme of Key Fundamental Research (Nation ‘‘973’’ Project) of China (G1999065009) and ‘‘863’’ Project (2003AA331130) are gratefully acknowledged. References [1] Zhang XC, Xu BS, Wang HD, Wu YX. Effects of oxide thickness, Al2O3 interlayer and interface asperity on residual stresses in thermal barrier coatings. Mater and Des, doi:10.1016/j.matdes.2005.02.008. [2] Zhang XC, Xu BS, Wang HD, Wu YX. Modeling of the residual stresses in plasma-spraying functionally graded ZrO2/NiCoCrAlY coatings using finite element method. Mater and Des 2006;27:308–15. [3] Khor KA, Gu YW. Effects of residual stress on the performance of plasma sprayed functionally graded ZrO2/NiCoCrAlY coatings. Mater Sci Eng 2000;A277:64–76. [4] Kokini K, DeJonge J, Rangaraj S, Beardsley B. Thermal shock of functionally graded thermal barrier coatings with similar thermal resistance. Surf Coat Technol 2002;154:223–31. [5] Takeuchi H, Tsunekawa Y, Okumiya M. Formation of compositionally graded Ni–P deposits containing SiC particles by jet electroplating. Mate T JIM 1997;38:43–8. [6] Hou P, Basu SN, Sarin VK. Structure and high-temperature stability of compositionally graded CVD mullite coatings. Int J Refract Met H 2001;19:467–77. [7] Zhang XC, Xu BS, Wang HD, Wu YX. An analytical model for predicting thermal residual stresses in multilayer coating systems. Thin Sold Films 2005;488:274–82. [8] Drake JT, Williamson RL, Rabin BH. Finite element analysis of thermal residual stresses at graded ceramic-metal interfaces. Part I. Model description and geometrical effects. J Appl Phys 1993;74:1310–20. [9] Adachi S. GaAs, AlAs, and AlxGa1–xAs Material parameters for use in research and device applications. J Appl Phys 1985;58:R1–R29. [10] Zhang XC, Xu BS, Wang HD, Wu YX, Jiang Y. Modeling of thermal residual stresses in multilayer coatings with graded properties and compositions. Thin Sold Films 2006;497:222–31. [11] Shaw LL. Thermal residual stresses in plates and coatings composed of multi-layered and functionally graded materials. Comps Part BEng 1998;29:199–210.