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Simulation of thermal stress in magnetron sputtered thin coating by finite element analysis
Journal of Materials Processing Technology 168 (2005) 36–41
Simulation of thermal stress in magnetron sputtered thin coating by finite element analysis Julfikar Haidera,∗ , Mahfujur Rahmana , Brian Corcoranb , M.S.J. Hashmia,b b
a NCPST and MPRC, Dublin City University, Dublin-9, Ireland School of Mechanical and Manufacturing Engineering, Dublin City University, Dublin-9, Ireland
Received 25 August 2004; accepted 22 September 2004
Abstract Stresses due to thermal mismatch develop in thin coatings deposited by physical vapour deposition (PVD) processes when cooled down to room temperature from deposition temperature. Despite having lower processing temperature, thermal stress can be significant when a large difference in physical and thermal properties of the bonded materials exists. A 2D finite element (FE) model for coating substrate system (TiN on stainless steel) has been investigated to simulate thermal mismatch stress. Several parametric effects i.e., deposition temperature, substrate thickness, coating thickness, Young’s modulus, and thermal expansion coefficient were studied to get the description of the thermal stress states. The effect of interlayer material on thermal stress has also been studied. FEA results in terms of radial, shear and axial stress were compared with the analytical results and good agreement was found. © 2004 Elsevier B.V. All rights reserved. Keywords: Thermal stress; FEM; Thin coating; TiN; PVD
1. Introduction Residual stress is very common in coating deposition techniques such as plasma spraying, physical vapour deposition and chemical vapour deposition. The stress state in coating is very complicated and could vary within the thickness of the coating. Higher stress gradient between the coating and substrate is observed in case of thin coating system. Residual stress can strongly influence coating quality and performance of a coated system since it is directly related to other coating properties such as hardness, adhesion, fatigue strength, etc. [1]. They can give rise to deformation of coated workpieces by several stress relaxing mechanisms such as adhesive failure (delamination at the interface) or cohesive failure (spalling or micro-cracking within the coating) of the coating or subsurface fracture (substrate failure) [2,3]. In most of the cases the first two mechanisms are very likely to occur because thin coatings on metal surface usually have poor adhesion. Near the edges, a complex stress state will be present, ∗
Corresponding author. Tel.: +353 1 7007674; fax: +353 1 7005345. E-mail address: [email protected] (J. Haider).
0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.09.093
but away from the edges, this appears to be a simple stress state where the stresses normal to the substrate and the shear stresses are zero [4–6]. Residual stress in thin PVD coatings is a stress under no external loading and is the sum of growth stress and thermal stress. Thermal mismatch stress results from the physical and thermal property mismatch between the coating and the substrate when cooled to the room temperature from the deposition temperature. The various physical parameters of both the coating and the substrate on which thermal stress depends can be listed as coefficient of thermal expansion (CTE), Young’s modulus, Poisson’s ratio, thickness, thermal conductivity, temperature histories during deposition and cooling and stress relaxation mechanisms. In general, thermal stresses develop at the interface between coating and substrate [7]. From the literature, it is evident that major component of the residual stress in PVD deposited coatings comes from growth stress. Usually the thermal stresses are neglected for approximation. But sometimes the thermal stress would also be significant (as high as 20–25% of the total stress) [8] if the deposition temperature or the mismatch of elastic properties and CTE of coating and substrate materials are
J. Haider et al. / Journal of Materials Processing Technology 168 (2005) 36–41
high. Therefore, the residual stresses in the sputtered coating cannot be regarded as entirely due to growth. Stress management has been an essential aspect of coating manufacturing and stress estimation has increasingly become a matter of great importance for the soundness of the coating. Generally, analytical equations have been developed to describe the biaxial thermal stress states in coating substrate system for linear–elastic or simple elastic–plastic materials [9]. Recently, for a more general 2D or 3D problem numerical methods such as finite element analysis (FEA) has been accepted as an attractive tool to simulate thermal stress in coating substrate systems [2,10–14]. Sometimes the results are verified against the experimental results if thermally induced stresses are the major contributor in total stress. Most of these studies are done for thick coating deposited mainly by thermal spraying. Thermal stress simulation using FEA in thin coating is often performed in wafer processing technology [15] to test the wafer reliability. There are very few studies of thermal stress modelling in thin hard coating for mechanical applications [16–18]. The objective of this study is to study the distribution of thermal stress developed in thin TiN coating on stainless steel substrate due to cooling from deposition to room temperature by FEA.
2. Thermal stress equation in thin coating Combining the analytical model [9] of thermal stress in progressively deposited coating for simple planar geometry with the well-known Stoney’s [19] equation, the following equation for thermal stress in thin coating can be derived as T Eef Tdr (αs − αf ) dT σf = (1) 1 + 4(Eef /Ees )(h/H) where Eef [=Ef /(1 − νf )], Ees [=Es /(1 − νs )], νs , νf , h, H, Td , Tr , αs , and αf are effective Young’s modulus of the coating, effective Young’s modulus of the substrate, Poisson ratio of the substrate, Poisson ratio of the coating, coating thickness, substrate thickness, deposition temperature, room temperature, thermal expansion coefficients of the substrate and the coating, respectively. The whole coating substrate system is considered as a composite beam, where the coating is very thin compared to the substrate. Then biaxial stress (σ x = σ z = σ and σ y = 0) state can be assumed.
3. Finite element considerations 3.1. Material properties The physical and thermal material properties of the coating (TiN), interlayer (Ti) and the substrate (stainless steel) are shown in Table 1 [8,20–23]. The coating properties are not consistent in the literature due to differences in coating quality and thickness.
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Table 1 Physical and thermal properties of coating, interlayer and substrate materials Property
Young’s modulus (GPa) Poisson’s ratio Thermal expansion coefficient (× 10−6 ◦ C−1 )
Materials Ti
TiN
Stainless steel
140 0.41 10.48
600 0.25 9.4
200 0.3 13
3.2. Model formulation For the modelling of residual thermal stress generated after TiN coating deposition by sputtering method, a simple cylindrical shaped stainless steel sample (30 mm diameter and 0.05 mm thick) with coating on top of the sample (typical thickness 5 m) was considered. Although quite thin, this substrate thickness was large in comparison to the coating thickness. These dimensions were chosen to keep the model reasonably sized [24] and to allow the coating substrate system bending after the development of thermal stress. For 2D analysis an axisymmetric plane parallel to the global XY plane was considered as shown in Fig. 1. Several assumptions were made for simplicity of calculations [17,18]. It was assumed that the coating and substrate materials are isotropic and linear thermoelastic; perfect bonding between coating and substrate; plain biaxial stress; and uniform temperature was established in the body both at the processing temperature and at the temperature after cooling. 3.3. Analysis details Numerical simulation of residual thermal stresses generated after the deposition of the coating was simulated using ANSYS finite element analysis code [25]. TiN coating on stainless steel substrate was modelled using four-node structural and quadratic element PLANE 42, with axisymmetric option. Mapped meshing with quadrilateral-shaped elements was used to mesh the model. Element size across the plane was minimized in a graded fashion near the coating–substrate interface (Fig. 2), as this area was very prone to high stress concentration [7,24]. Fine mesh was also introduced near the edge across the thickness of the coating and substrate. The mesh was refined until results showed only small change [22,24]. The left side of the model was used as the axis of the axisymmetric model. The bottom left corner of the axisymmetric model was pinned to restrict any movement. All other edges were free so that bending was permitted to take place during cooling. Thermal loading was applied by setting the reference temperature as the deposition temperature (500 ◦ C) and uniform temperature as room temperature (25 ◦ C). Numerical verification of the model was done by putting different property and dimension values of coating and substrate in the general equation of thin coating (Eq. (1)). As αs > αf coating substrate system takes convex shape due to the
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J. Haider et al. / Journal of Materials Processing Technology 168 (2005) 36–41
Fig. 1. Schematic diagram of axisymmetric 2D solid model.
developed thermal stress after cooling from deposition temperature. Opposite phenomenon occurs during heating from room temperature to deposition temperature. Both events were verified by FEA.
4. Results and discussions 4.1. Parametric studies In order to examine the effects of the parameters on thermal stress (maximum von Mises stress in the coating) five sets of analyses were performed by holding four of other parameters constant. The constant values used for different parameters were as follows: deposition temperature (500 ◦ C), substrate thickness (0.5 mm), coating thickness (5 m), coefficient of thermal expansion (9.4 × 10−6 ◦ C−1 ), and elastic modulus (600 GPa). Typically, deposition temperature in sputtering technique varies between 100 and 500 ◦ C depending on operating parameters. From Fig. 3, it is seen that the thermal stress varies linearly with the deposition temperature. This proportionality has been reflected in the graph both for analytical and finite element analysis.
The Young’s modulus of the coating deposited by PVD techniques depends on the processing parameters (deposition pressure, deposition current, N2 percentage in the coating, etc.). Usually understoichiometric TiN has lower Young’s modulus values whereas overstoichiometric TiN coating has higher Young’s modulus [20]. The reported values of Young’s modulus of TiN coating in the literature vary within the range of 250–600 GPa mainly due to the porosity induced in the coating. From Fig. 4, it is seen that thermal stress increases with coatings Young’s modulus agreeing with the analytical equation (Eq. (1)). This plot gives an indication of the error introduced in the thermal stress calculation with different young’s modulus of the coating. As the porosity increases in the coating the Young’s modulus and thermal conductivity values decrease and also Poisson’s ratio decreases [6,26]. This result gives an indirect relation between the coating porosity and thermal stress. Thermal stress decreases with the increase of the coating thickness [2] as seen in Fig. 5. The reason for this is bending-induced stress relaxation at high coating thickness and consistent with the analytical solution in literature [27]. The stress in the coating and substrate is reduced in proportion to the bending strain when the coating–substrate system is bent. This bending effect is negligible for very thin films, due to their very low stiffness; it is significant
Fig. 2. Physical boundary conditions applied in the model.
J. Haider et al. / Journal of Materials Processing Technology 168 (2005) 36–41
Fig. 3. Variation of analytical and FEA thermal stress with deposition temperature.
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Fig. 6. Variation of analytical and FEA thermal stress with substrate thickness.
to the higher substrate thickness and consequently higher residual stress develops in the coating. Similar correlation for thermal stress with Poisson’s ratio and CTE has been found according to Eq. (1). 4.2. Stress distribution through thickness
Fig. 4. Variation of analytical and FEA thermal stress with different Young’s modulus of coating.
as the film thickness increases. When coating thickness is increased larger bending curvature in the coating–substrate system occurs. This causes considerable bending-induced stress relaxation [2] and consequently lower stress in the coating. Thermal stress increases with the substrate thickness as shown in Fig. 6. With lower substrate thickness the stress in the coating is relaxed by the deformation of the substrate while for higher substrate thickness bending is prevented due
Fig. 5. Variation of analytical and FEA thermal stress with coating thickness.
The coating failure mechanisms are mainly controlled by the magnitude and the distribution of radial stress (σ x ), tangential stress (σ z ), axial stress (σ y ) and shear stress (σ xz ) at or near the radial free edge of the specimen or near the specimen’s axis of symmetry (y-axis). Fig. 7 shows the distribution of radial stress (σ x ) through the thickness of the coating and substrate at different position from the edge of the coating substrate system. Through the thickness of the substrate from bottom to top surface stress gradient and stress reversals (compressive to tensile) were observed and reached maximum value near the interface between the coating and
Fig. 7. Radial stress (σ x ) distribution through the thickness of coating and substrate at different position from the edge to the center.
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J. Haider et al. / Journal of Materials Processing Technology 168 (2005) 36–41
Fig. 9. Shear stress (σ xz ) distribution through the thickness of coating and substrate at the edge without and with interlayer. Fig. 8. Shear stress (σ xz ), distribution through the thickness of coating and substrate at different position from the edge to the center.
substrate. Compressive radial stress exists through the thickness of the coating from bottom to top surface with slight stress gradient but no stress reversal was observed. Radial stress distribution through the thickness of the coating and substrate at different distances away from the edge showed that minimum radial stress value in the coating appeared at the edge while stress values increased away from the edge. At around a distance of 5h (where h is coating thickness) stresses reached the maximum value. Since the substrate-to-coating thickness ratio was very large, the compressive radial stress in the coating was much larger than the tensile stress in the substrate [24]. Similar stress distribution was found for tangential stress (σ z ) component, which confirmed the biaxial stress state in the coating. The shear stress values were far less than the other stress components except near the edge as shown in Fig. 8. The maximum tensile shear stress appeared at the interface near the edge of the coating and decreased to very small compressive stress at the top surface of the coating. But away from the edge no stress reversal in the coating was observed and the tensile stress at the top surface of the coating reached to very small value due to the free surface phenomenon. While at the edge of the substrate, the maximum tensile stress at the interface decreased to very small value at the bottom surface. Stress reversal from tensile at the interface to compressive towards the bottom surface was also observed. Away from the edge the shear stress values at the interface decreased. But the general trend for shear stress distribution in the coating and substrate remained same. The shear stress is equivalent to the adhesion strength of the coating [5]. As the maximum shear stress is at the interface between the coating and substrate, the spallation of the coating is expected to occur from this position if the shear stress is greater than the bonding strength between the coating and substrate [28]. As expected there was very small shear stresses along the axisymmetric line.
4.3. Effect of interlayer It is generally acknowledged that Ti interlayer between TiN coating and steel is used to enhance the adhesion of the coating to substrates and to reduce the thermal mismatch between them, as well as prolong the service life of the coating [16,29]. Chemically, diffused mixing of elements forming a broad interface and strong epitaxial relation between the TiN and Ti layers is attributed for better adhesion with Ti interlayer. Mechanically, the titanium interlayer acts as a soft flexible layer, reducing the shear stresses at the coating–substrate contact and stopping the propagation of cracks in the intersurface area. The shear stress distribution through the thickness of the coating and substrate at the edge of the coating substrate model with and without interlayer is shown in Fig. 9. A significant reduction of shear stress at the interface is evident with introducing Ti interlayer. Smooth transition of thermal properties from TiN to stainless steel and accommodation of shear stress by the deformation of soft Ti layer would be recognised as the possible reasons for the reduction of shear stress. The increase of Ti interlayer thickness could reduce the shear stress levels but not very significant reduction was observed. The reduction of other stress components e.g., radial or tangential and axial stress was also observed by introducing the Ti interlayer.
5. Conclusion A method for analysing thermal stress developed in thin TiN sputtered coating on stainless steel substrate has been performed using finite element simulation package ANSYS and validated by appropriate analytical calculations. The wide ranging parametric studies show how thermal stress varies with the various material properties and dimensions. To obtain minimum peak stress, coating thickness and thermal expansion coefficient should be increased whilst the elastic modulus should be reduced as much as practicable. The
J. Haider et al. / Journal of Materials Processing Technology 168 (2005) 36–41
highest radial stress values found at the interface between the coating and substrate, which indicates that the interface between the coating and substrate is the critical location from the failure point of view. Along the interface higher shear stresses were found at the edge because of stress concentration. This will cause the start of the spallation of the coating from the edge. Results also showed that insertion of Ti interlayer between the TiN coating and substrate can significantly reduce the stress components especially the shear stress. The interlayer thickness has little effect on stress reduction. Finally, FEM analysis provides detailed information about all stress components and proves very useful in providing better understanding of thermal stress developed during cooling down of the thin coating substrate system.
Acknowledgement The funding from Material Processing Research Center (MPRC) and National Center for Plasma Science and Technology (NCPST) to carry out this research is greatly acknowledged.
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Simulation of thermal stress in magnetron sputtered thin coating by finite element analysis Julfikar Haidera,∗ , Mahfujur Rahmana , Brian Corcoranb , M.S.J. Hashmia,b b
a NCPST and MPRC, Dublin City University, Dublin-9, Ireland School of Mechanical and Manufacturing Engineering, Dublin City University, Dublin-9, Ireland
Received 25 August 2004; accepted 22 September 2004
Abstract Stresses due to thermal mismatch develop in thin coatings deposited by physical vapour deposition (PVD) processes when cooled down to room temperature from deposition temperature. Despite having lower processing temperature, thermal stress can be significant when a large difference in physical and thermal properties of the bonded materials exists. A 2D finite element (FE) model for coating substrate system (TiN on stainless steel) has been investigated to simulate thermal mismatch stress. Several parametric effects i.e., deposition temperature, substrate thickness, coating thickness, Young’s modulus, and thermal expansion coefficient were studied to get the description of the thermal stress states. The effect of interlayer material on thermal stress has also been studied. FEA results in terms of radial, shear and axial stress were compared with the analytical results and good agreement was found. © 2004 Elsevier B.V. All rights reserved. Keywords: Thermal stress; FEM; Thin coating; TiN; PVD
1. Introduction Residual stress is very common in coating deposition techniques such as plasma spraying, physical vapour deposition and chemical vapour deposition. The stress state in coating is very complicated and could vary within the thickness of the coating. Higher stress gradient between the coating and substrate is observed in case of thin coating system. Residual stress can strongly influence coating quality and performance of a coated system since it is directly related to other coating properties such as hardness, adhesion, fatigue strength, etc. [1]. They can give rise to deformation of coated workpieces by several stress relaxing mechanisms such as adhesive failure (delamination at the interface) or cohesive failure (spalling or micro-cracking within the coating) of the coating or subsurface fracture (substrate failure) [2,3]. In most of the cases the first two mechanisms are very likely to occur because thin coatings on metal surface usually have poor adhesion. Near the edges, a complex stress state will be present, ∗
Corresponding author. Tel.: +353 1 7007674; fax: +353 1 7005345. E-mail address: [email protected] (J. Haider).
0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.09.093
but away from the edges, this appears to be a simple stress state where the stresses normal to the substrate and the shear stresses are zero [4–6]. Residual stress in thin PVD coatings is a stress under no external loading and is the sum of growth stress and thermal stress. Thermal mismatch stress results from the physical and thermal property mismatch between the coating and the substrate when cooled to the room temperature from the deposition temperature. The various physical parameters of both the coating and the substrate on which thermal stress depends can be listed as coefficient of thermal expansion (CTE), Young’s modulus, Poisson’s ratio, thickness, thermal conductivity, temperature histories during deposition and cooling and stress relaxation mechanisms. In general, thermal stresses develop at the interface between coating and substrate [7]. From the literature, it is evident that major component of the residual stress in PVD deposited coatings comes from growth stress. Usually the thermal stresses are neglected for approximation. But sometimes the thermal stress would also be significant (as high as 20–25% of the total stress) [8] if the deposition temperature or the mismatch of elastic properties and CTE of coating and substrate materials are
J. Haider et al. / Journal of Materials Processing Technology 168 (2005) 36–41
high. Therefore, the residual stresses in the sputtered coating cannot be regarded as entirely due to growth. Stress management has been an essential aspect of coating manufacturing and stress estimation has increasingly become a matter of great importance for the soundness of the coating. Generally, analytical equations have been developed to describe the biaxial thermal stress states in coating substrate system for linear–elastic or simple elastic–plastic materials [9]. Recently, for a more general 2D or 3D problem numerical methods such as finite element analysis (FEA) has been accepted as an attractive tool to simulate thermal stress in coating substrate systems [2,10–14]. Sometimes the results are verified against the experimental results if thermally induced stresses are the major contributor in total stress. Most of these studies are done for thick coating deposited mainly by thermal spraying. Thermal stress simulation using FEA in thin coating is often performed in wafer processing technology [15] to test the wafer reliability. There are very few studies of thermal stress modelling in thin hard coating for mechanical applications [16–18]. The objective of this study is to study the distribution of thermal stress developed in thin TiN coating on stainless steel substrate due to cooling from deposition to room temperature by FEA.
2. Thermal stress equation in thin coating Combining the analytical model [9] of thermal stress in progressively deposited coating for simple planar geometry with the well-known Stoney’s [19] equation, the following equation for thermal stress in thin coating can be derived as T Eef Tdr (αs − αf ) dT σf = (1) 1 + 4(Eef /Ees )(h/H) where Eef [=Ef /(1 − νf )], Ees [=Es /(1 − νs )], νs , νf , h, H, Td , Tr , αs , and αf are effective Young’s modulus of the coating, effective Young’s modulus of the substrate, Poisson ratio of the substrate, Poisson ratio of the coating, coating thickness, substrate thickness, deposition temperature, room temperature, thermal expansion coefficients of the substrate and the coating, respectively. The whole coating substrate system is considered as a composite beam, where the coating is very thin compared to the substrate. Then biaxial stress (σ x = σ z = σ and σ y = 0) state can be assumed.
3. Finite element considerations 3.1. Material properties The physical and thermal material properties of the coating (TiN), interlayer (Ti) and the substrate (stainless steel) are shown in Table 1 [8,20–23]. The coating properties are not consistent in the literature due to differences in coating quality and thickness.
37
Table 1 Physical and thermal properties of coating, interlayer and substrate materials Property
Young’s modulus (GPa) Poisson’s ratio Thermal expansion coefficient (× 10−6 ◦ C−1 )
Materials Ti
TiN
Stainless steel
140 0.41 10.48
600 0.25 9.4
200 0.3 13
3.2. Model formulation For the modelling of residual thermal stress generated after TiN coating deposition by sputtering method, a simple cylindrical shaped stainless steel sample (30 mm diameter and 0.05 mm thick) with coating on top of the sample (typical thickness 5 m) was considered. Although quite thin, this substrate thickness was large in comparison to the coating thickness. These dimensions were chosen to keep the model reasonably sized [24] and to allow the coating substrate system bending after the development of thermal stress. For 2D analysis an axisymmetric plane parallel to the global XY plane was considered as shown in Fig. 1. Several assumptions were made for simplicity of calculations [17,18]. It was assumed that the coating and substrate materials are isotropic and linear thermoelastic; perfect bonding between coating and substrate; plain biaxial stress; and uniform temperature was established in the body both at the processing temperature and at the temperature after cooling. 3.3. Analysis details Numerical simulation of residual thermal stresses generated after the deposition of the coating was simulated using ANSYS finite element analysis code [25]. TiN coating on stainless steel substrate was modelled using four-node structural and quadratic element PLANE 42, with axisymmetric option. Mapped meshing with quadrilateral-shaped elements was used to mesh the model. Element size across the plane was minimized in a graded fashion near the coating–substrate interface (Fig. 2), as this area was very prone to high stress concentration [7,24]. Fine mesh was also introduced near the edge across the thickness of the coating and substrate. The mesh was refined until results showed only small change [22,24]. The left side of the model was used as the axis of the axisymmetric model. The bottom left corner of the axisymmetric model was pinned to restrict any movement. All other edges were free so that bending was permitted to take place during cooling. Thermal loading was applied by setting the reference temperature as the deposition temperature (500 ◦ C) and uniform temperature as room temperature (25 ◦ C). Numerical verification of the model was done by putting different property and dimension values of coating and substrate in the general equation of thin coating (Eq. (1)). As αs > αf coating substrate system takes convex shape due to the
38
J. Haider et al. / Journal of Materials Processing Technology 168 (2005) 36–41
Fig. 1. Schematic diagram of axisymmetric 2D solid model.
developed thermal stress after cooling from deposition temperature. Opposite phenomenon occurs during heating from room temperature to deposition temperature. Both events were verified by FEA.
4. Results and discussions 4.1. Parametric studies In order to examine the effects of the parameters on thermal stress (maximum von Mises stress in the coating) five sets of analyses were performed by holding four of other parameters constant. The constant values used for different parameters were as follows: deposition temperature (500 ◦ C), substrate thickness (0.5 mm), coating thickness (5 m), coefficient of thermal expansion (9.4 × 10−6 ◦ C−1 ), and elastic modulus (600 GPa). Typically, deposition temperature in sputtering technique varies between 100 and 500 ◦ C depending on operating parameters. From Fig. 3, it is seen that the thermal stress varies linearly with the deposition temperature. This proportionality has been reflected in the graph both for analytical and finite element analysis.
The Young’s modulus of the coating deposited by PVD techniques depends on the processing parameters (deposition pressure, deposition current, N2 percentage in the coating, etc.). Usually understoichiometric TiN has lower Young’s modulus values whereas overstoichiometric TiN coating has higher Young’s modulus [20]. The reported values of Young’s modulus of TiN coating in the literature vary within the range of 250–600 GPa mainly due to the porosity induced in the coating. From Fig. 4, it is seen that thermal stress increases with coatings Young’s modulus agreeing with the analytical equation (Eq. (1)). This plot gives an indication of the error introduced in the thermal stress calculation with different young’s modulus of the coating. As the porosity increases in the coating the Young’s modulus and thermal conductivity values decrease and also Poisson’s ratio decreases [6,26]. This result gives an indirect relation between the coating porosity and thermal stress. Thermal stress decreases with the increase of the coating thickness [2] as seen in Fig. 5. The reason for this is bending-induced stress relaxation at high coating thickness and consistent with the analytical solution in literature [27]. The stress in the coating and substrate is reduced in proportion to the bending strain when the coating–substrate system is bent. This bending effect is negligible for very thin films, due to their very low stiffness; it is significant
Fig. 2. Physical boundary conditions applied in the model.
J. Haider et al. / Journal of Materials Processing Technology 168 (2005) 36–41
Fig. 3. Variation of analytical and FEA thermal stress with deposition temperature.
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Fig. 6. Variation of analytical and FEA thermal stress with substrate thickness.
to the higher substrate thickness and consequently higher residual stress develops in the coating. Similar correlation for thermal stress with Poisson’s ratio and CTE has been found according to Eq. (1). 4.2. Stress distribution through thickness
Fig. 4. Variation of analytical and FEA thermal stress with different Young’s modulus of coating.
as the film thickness increases. When coating thickness is increased larger bending curvature in the coating–substrate system occurs. This causes considerable bending-induced stress relaxation [2] and consequently lower stress in the coating. Thermal stress increases with the substrate thickness as shown in Fig. 6. With lower substrate thickness the stress in the coating is relaxed by the deformation of the substrate while for higher substrate thickness bending is prevented due
Fig. 5. Variation of analytical and FEA thermal stress with coating thickness.
The coating failure mechanisms are mainly controlled by the magnitude and the distribution of radial stress (σ x ), tangential stress (σ z ), axial stress (σ y ) and shear stress (σ xz ) at or near the radial free edge of the specimen or near the specimen’s axis of symmetry (y-axis). Fig. 7 shows the distribution of radial stress (σ x ) through the thickness of the coating and substrate at different position from the edge of the coating substrate system. Through the thickness of the substrate from bottom to top surface stress gradient and stress reversals (compressive to tensile) were observed and reached maximum value near the interface between the coating and
Fig. 7. Radial stress (σ x ) distribution through the thickness of coating and substrate at different position from the edge to the center.
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Fig. 9. Shear stress (σ xz ) distribution through the thickness of coating and substrate at the edge without and with interlayer. Fig. 8. Shear stress (σ xz ), distribution through the thickness of coating and substrate at different position from the edge to the center.
substrate. Compressive radial stress exists through the thickness of the coating from bottom to top surface with slight stress gradient but no stress reversal was observed. Radial stress distribution through the thickness of the coating and substrate at different distances away from the edge showed that minimum radial stress value in the coating appeared at the edge while stress values increased away from the edge. At around a distance of 5h (where h is coating thickness) stresses reached the maximum value. Since the substrate-to-coating thickness ratio was very large, the compressive radial stress in the coating was much larger than the tensile stress in the substrate [24]. Similar stress distribution was found for tangential stress (σ z ) component, which confirmed the biaxial stress state in the coating. The shear stress values were far less than the other stress components except near the edge as shown in Fig. 8. The maximum tensile shear stress appeared at the interface near the edge of the coating and decreased to very small compressive stress at the top surface of the coating. But away from the edge no stress reversal in the coating was observed and the tensile stress at the top surface of the coating reached to very small value due to the free surface phenomenon. While at the edge of the substrate, the maximum tensile stress at the interface decreased to very small value at the bottom surface. Stress reversal from tensile at the interface to compressive towards the bottom surface was also observed. Away from the edge the shear stress values at the interface decreased. But the general trend for shear stress distribution in the coating and substrate remained same. The shear stress is equivalent to the adhesion strength of the coating [5]. As the maximum shear stress is at the interface between the coating and substrate, the spallation of the coating is expected to occur from this position if the shear stress is greater than the bonding strength between the coating and substrate [28]. As expected there was very small shear stresses along the axisymmetric line.
4.3. Effect of interlayer It is generally acknowledged that Ti interlayer between TiN coating and steel is used to enhance the adhesion of the coating to substrates and to reduce the thermal mismatch between them, as well as prolong the service life of the coating [16,29]. Chemically, diffused mixing of elements forming a broad interface and strong epitaxial relation between the TiN and Ti layers is attributed for better adhesion with Ti interlayer. Mechanically, the titanium interlayer acts as a soft flexible layer, reducing the shear stresses at the coating–substrate contact and stopping the propagation of cracks in the intersurface area. The shear stress distribution through the thickness of the coating and substrate at the edge of the coating substrate model with and without interlayer is shown in Fig. 9. A significant reduction of shear stress at the interface is evident with introducing Ti interlayer. Smooth transition of thermal properties from TiN to stainless steel and accommodation of shear stress by the deformation of soft Ti layer would be recognised as the possible reasons for the reduction of shear stress. The increase of Ti interlayer thickness could reduce the shear stress levels but not very significant reduction was observed. The reduction of other stress components e.g., radial or tangential and axial stress was also observed by introducing the Ti interlayer.
5. Conclusion A method for analysing thermal stress developed in thin TiN sputtered coating on stainless steel substrate has been performed using finite element simulation package ANSYS and validated by appropriate analytical calculations. The wide ranging parametric studies show how thermal stress varies with the various material properties and dimensions. To obtain minimum peak stress, coating thickness and thermal expansion coefficient should be increased whilst the elastic modulus should be reduced as much as practicable. The
J. Haider et al. / Journal of Materials Processing Technology 168 (2005) 36–41
highest radial stress values found at the interface between the coating and substrate, which indicates that the interface between the coating and substrate is the critical location from the failure point of view. Along the interface higher shear stresses were found at the edge because of stress concentration. This will cause the start of the spallation of the coating from the edge. Results also showed that insertion of Ti interlayer between the TiN coating and substrate can significantly reduce the stress components especially the shear stress. The interlayer thickness has little effect on stress reduction. Finally, FEM analysis provides detailed information about all stress components and proves very useful in providing better understanding of thermal stress developed during cooling down of the thin coating substrate system.
Acknowledgement The funding from Material Processing Research Center (MPRC) and National Center for Plasma Science and Technology (NCPST) to carry out this research is greatly acknowledged.
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