Modeling the Evolution of Residual Stresses in Thermally Sprayed YSZ Coating on Stainless Steel Substrate
Abstract
This study is based on Eulerian method to model residual stresses for yttrium-stabilized zirconia coating applied to stainless steel substrate. A commercially available finite element software ABAQUS/Explicit is used to conduct this study. Single and multiple-particle impact analyses were carried out, and the residual stress data have been reported. The analysis is performed for two different values of thermal contact resistance and the through-thickness residual stress profiles obtained within the coating for single particle are tensile, while the substrate has a mixture of tensile and compressive residual stresses. For multiple impact model, the residual stress data have been presented for substrate with and without cooling. The residual stresses within the coating without substrate cooling are mostly tensile while the substrate is compressive. The residual stresses within the coating with substrate cooling are mostly tensile with compressive stresses on the top of the coating, while the substrate consists of compressive stresses. The obtained residual stresses are compared with experimental and analytical data.
Keywords
ABAQUS Eulerian finite element modeling heat transfer residual stress solidification thermal sprayIntroduction
Thermal spray technology comprises a group of coating processes in which finely divided metallic or nonmetallic particles are deposited in molten or semi-molten condition to form a coating. The coating material may be in the form of powder, ceramic rod, wire or molten material. For plasma spraying, the particle is heated up to or above its melting point and is made to impact the substrate at moderate velocity (100-300 m/s) (Ref 1). The invention of thermal spray credit goes to MU Schoop (1911), who received patents along with several collaborators to commercialize the process (Ref 1). The need for coatings has increased over the past few years since it improves functional performance; reduces wear due to abrasion, erosion and corrosion; extends the component life by rebuilding the worn part; and reduces cost by applying expensive coating over cheaper material (Ref 1-7). Understanding of lamella bonding, formation of microstructural features and residual stresses in the finished parts are some of the technological challenges. This paper deals with the evolution of residual stresses of YSZ particle from the point of impact of lamella particle until it has cooled down as the building block of coating microstructure.
To achieve uniform properties in thermally sprayed components, it requires careful control of particle diameter, particle impact velocity and temperature. It is cost-effective to optimize the operating parameters using computational methods rather than experiments due to the high operational costs of the experiment. The first experimental observations of droplet impacting substrate were performed by Worthington Ramsden (1903) (Ref 8). Worthington observed and recorded the splashing and fingering of milk and mercury droplets impacting a smooth substrate. The first known numerical modeling of splashing of liquid drop was performed by Harlow and Shannon (1967) using Marker and Cell technique (MAC) (Ref 9). With the development of computing power, computational methods have been widely used to model thermal spray droplet impact.
Summary of some of the particle and substrate parameters available in the literature for numerical simulation of thermal spray droplet impact
Particle | Substrate | Simulated time period | HT | RS | Method | Notes | References | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Material | Diameter | Velocity (m/s) | Initial temp (K) | Final temp (K) | Material | Initial temp (K) | Final temp (K) | ||||||
YSZ | 30 µm 80 µm | 100-240 | 3250 | … | SS | 423 | … | 0.45 µs | ✗ | ✗ | CEL ABAQUS/Explicit | Flattening degree increases if the solid core is smaller and plastic deformation is larger if the core is bigger. | Ref 58 |
YSZ | 20 µm | 180 | 3400 | 2300 | SS | 1200 | 1600 | 10 µs | ✓ | ✗ | FEPS developed by ICA | Cooling of molten particle is dominated by conduction between particle and substrate. Solid core decreases flattening degree | Ref 59 |
YSZ | 50 µm | 10 | 3400 | 500 | SS | 300 | 600 | 96.7 ms | ✓ | ✗ | ANSYS FLUENT | Entire particle was simulated (not axisymmetric) with details of freezing-induced breakup phenomenon | Ref 60 |
Tin (Sn) | 2.7 mm | 1 | 513 | 505 | SS | 298 | 423 | 17.3 ms | ✓ | ✗ | RIPPLE code 2D fixed grid Eulerian | Compared simulation with experiment. Liquid–solid contact angles are used. Particle–substrate contact resistance | Ref 21 |
2.2 mm | 2.35 | 513 | 513 | SS | 298 | 373 | 5.1 ms | Performed incline impact (458) | |||||
Tin (Sn) | 2.1 mm | 4 | 519 | 420 | SS | 298 | … | 7.5 ms | ✓ | ✗ | SIMPLE QUICK | Surface structure of previous droplet affects the second droplet | Ref 20 |
Ni | 100 µm | 50-300 | … | … | Rigid surface | … | … | 2.4 µs | ✗ | ✗ | LS-Dyna (Lagrangian) | Increase velocity increases flattening degree. Al flattens quicker than Ni | Ref 23 |
Al | 50 µm | 1.6 µs | |||||||||||
Al | 3.92 mm | 3 | 903 | 673 | H13 tool steel | 473 | 653 | 8.5 ms | ✓ | ✗ | RIPPLE code 2D fixed grid Eulerian | Al was in good agreement while Ni wasn’t. Contact resistance modeled through conductivity and roughness | Ref 28 |
Ni | 50 µm | 72 | 1927 | … | SS | 293 | … | 3 µs | |||||
Ni | 60 µm | 73 | 1873 | … | SS | 563 673 | … … | 10 µs | ✓ | ✗ | RIPPLE code 2D fixed grid Eulerian | Performed single, double and multiple-particle impact. Formation of fingers and splashing is caused due to early solidification and to overcome this contact resistance is increased. temp of substrate didn’t have effect on splash | Ref 27 |
Two Ni | 60 µm | 48 | 2323 | … | 467 | … | 10 µs | ||||||
Multiple Ni | 40-80 µm | 40-80 | 1873-2273 | … | 293 | … | 26 µs |
The most advanced finite element simulation for un-melted solid particles impact can be found in Ref 11 for copper particle impacting copper substrate. Due to the limited computational resources, some of the earlier works presented in Ref 3, 18, 23 are limited to 2D axisymmetric simulations which hinders the extent of the study that can be performed on the models, such as the splat morphology of the droplets deposited. With further development of faster processing machines and advancement in simulation software, 3D models were widely published and some of them can be found in Ref 20, 21, 24-26. A sequential droplet impingement analysis was carried out in Ref 20 where formations of detached rings were reported, which were caused due to the momentum gained by the impact of the second droplet. This also led to fragmentation (satellite droplets). While the work presented in Ref 24 looks at the number of fingers caused when a droplet impacts a surface using Rayleigh–Taylor (RT) instability theory, the computational results were in good agreement with experimental results. The study of heat transfer and solidification are crucial elements for the study of splat morphology and some of the works can be found in Ref 21, 26. The work presented by Fard et al. (Ref 26) studied the heat transfer of a tin droplet impacting stainless steel substrate and performed experiments to validate their results. The work presented in Ref 21 extends the work done in Ref 26, by studying the heat transfer of normal and incline impact. Experimental and numerical simulation of single and multiple Nickel particle impacting stainless steel substrate was performed by Fard et al. (Ref 27) while including the effect of heat transfer and solidification for the simulations. Observations of splashing were recorded from the experimental observations for Nickel particles impacting stainless steel substrate for substrate temperature of 563 K while no splashing was observed for substrate temperature of 673 K. However, in numerical simulations increasing the substrate temperature didn’t make much of a difference in splat morphology but increasing the thermal contact resistance drastically changed the morphology. Another notable assumption by Xue et al. was that the thermal contact resistance value need not be provided to the model, it can be varied through substrate roughness and thermal conductivity (Ref 28). Although different modeling techniques and advancement in computational efficiency have significantly improved the splat modeling in thermal spray coatings, the technological challenge of fine-tuning the material parameters such as very high strain rates, work hardening, high cooling rates and temperature-dependent physical parameters require further work. This coupled with challenges in attaining experimental data which is predominantly limited to post-deposition process makes the validation of the numerical models difficult.
Residual stresses are formed during the thermal spraying of coating on a substrate. Residual stresses affect the adhesive strength, cohesive strength, thermal shock resistance, thermal fatigue life, corrosion resistance, wear properties and service life of coatings (Ref 4, 29-35). There are two types of residual stresses—deposition stress (occurring at micro-scale) and post-deposition stress (occurring at macro-scale). Deposition stress is caused due to rapid cooling and solidification of splat, peening action (impact) of droplets on a pre-deposited layer or due to high thermal gradients developed (Ref 36). Post-deposition stress is caused by the cooling of the splats to room temperature and due to the mismatch of coefficient of thermal expansion (CTE) of the coating and substrate. Substrate geometry and surface treatment also influence the evolution of residual stresses (Ref 37-39).
Residual stresses are measured experimentally using various methods. Some of the frequently used methods are x-ray diffraction (XRD), in situ curvature measurements, neutron diffraction and incremental hole-drilling methods. XRD is not able to measure residual stresses in the coating/substrate interface due to the limited penetration of the x-rays (Ref 40). XRD can give inaccurate stress values due to uncertainties in determining elastic parameters (Ref 41, 42). Despite these limitations, XRD has been widely used by many researchers and has been validated with other methods (Ref 43-47). Neutron diffraction utilizes high-energy neutrons which are allowed to penetrate the sample, and the scattering caused by the atoms and nuclei is collected and analyzed (Ref 40). The cost of obtaining sufficient and accurate residual stress data using neutron diffraction is high (Ref 48). In situ curvature measurement is another form of experimental measurement for residual stress. The change in substrate curvature and temperature is used to predict the residual stresses (Ref 49, 50). It is the only experimental technique that can track deposition and post-deposition stresses separately (Ref 40).
The work presented in Ref 51 by Mutter et al. used in situ curvature measurement to predict residual stresses developed due to the impact of YSZ particle on various substrates while employing the XRD and hole-drilling methods to obtain the residual stress depth profiles in stainless steel. The residual stresses were compressive (− 500 MPa) in nature closer to the interface and then had a gradual change to tensile stresses (50 MPa) through the thickness of the SS substrate. Unfortunately, there was no information of residual stress in the YSZ coating. Montay et al. (Ref 52) employed the incremental hole-drilling method to determine the residual stresses developed due to thermal spraying of YSZ on various substrates for different substrate initial temperatures. It was concluded that the change in substrate temperature had little or no influence on the residual stresses for cast iron substrate but had a drastic influence for aluminum and stainless steel substrates. For higher substrate temperatures, the residual stresses in the coating are compressive in nature. For stainless steel substrate at 423 K, the through-thickness residual stress of the coating is tensile closer to the surface (100 MPa) and then follows a very low magnitude of stress (− 10 to + 10 MPa) and then becomes compressive (− 150 MPa) closer to the particle–substrate interface. The residual stress on stainless steel is compressive in nature (− 250 MPa). Matejicek et al. (Ref 47) used XRD method to analyze residual stresses developed due to deposition of various coating material (YSZ, Mo, NiCrAlY and Ni) of different thicknesses on steel and Al substrates. Notably the in-plane residual stress for the YSZ coating has low stress values (average 15 ± 10 MPa) and sometimes close to zero. Possible explanation being that the quenching and thermal mismatch stress having opposite signs and cancel each other out (Ref 53, 54). Another possible explanation is being stress relaxation due to the formation of micro-cracks (Ref 47). Wang and Xiao (Ref 55) employed Cr 3+ fluorescence spectroscopy to determine residual stresses in Al_{2}O_{3}/YSZ coatings. It was found that the macro-compressive residual stresses were high (− 500 to − 300 MPa) for coating thickness less than 20 µm. and theoretical model was presented to validate this behavior. Scardi et al. (Ref 54) studied the effect of deposition temperature on the microstructure of YSZ coating on Al substrate using XRD. It was concluded that the surface of the coating was always in tension (30-40 MPa). Levit et al. (Ref 53) performed residual stress analysis using XRD for YSZ coating on Ni-based alloy for various substrate temperatures. It was found that the stresses changed from tensile (40 MPa) to compressive (− 20 MPa) as the temperature was increased and employed mathematical model to verify the results. It was seen that the residual stresses developed in the YSZ coating and Ni substrate is directly related to the substrate temperature. A problem common to all experimental methods is that they give average stress values which cannot be used to predict the micro-stresses (or localized stresses) that often occur near areas of stress concentration and longer duration is required to optimize spray process experimentally. Hence, numerical simulation (FEM) has been the prime focus to model residual stresses developed in thermal spray coatings (Ref 56).
Summary of researches where different techniques are compared (experimental, numerical and analytical methods) used to evaluate residual stresses in YSZ coatings
Coating | Substrate | AM | FEM | Experimental validation | Process | Notes | References | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Material | Thickness (mm) | Temp (K) | Material | Thickness (mm) | Temp (K) | XRD | MR | CM | ND | |||||
YSZ | 0.2 | … | Steel | 2.5 | ~ 423 | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | APS | RS on the coating plane is 15 ± 10 MPa. The stress values in YSZ specimen are very low in magnitude and sometimes close to zero | Ref 47 |
YSZ | ~0.58 | … | SS Al Cast iron | ~ 0.22 ~ 0.42 ~ 0.42 | 358 423 483 | ✗ | ✓ | ✗ | ✓ | ✗ | ✗ | APS | RS on YSZ coating varies from 100 MPa to − 150 MPa. RS on SS substrate is around − 250 MPa. The RS is tensile on the top of coating and becomes compressive closer to the particle–substrate interface | Ref 52 |
YSZ | 0.5 | 3203 3307 3649 | SS Inconel 718 + BC | 1.5 1.6 + 0.2 | 432 594 683 1033 | ✗ | ✓ | ✓ | ✗ | ✓ | ✗ | APS | RS on the substrate varied from − 500 MPa closer to the surface to about + 50 MPa through the thickness | Ref 51 |
YSZ | 0.3 | … | Al | 6 | 328 383 523 | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | APS | RS on the surface of YSZ coatings were tensile in nature with maximum value of 30-40 MPa | Ref 54 |
YSZ | 0.4 | … | BC Ni-alloy | 0.1 10 | 348 423 573 773 | ✓ | ✗ | ✓ | ✗ | ✗ | ✗ | APS | Coat (40.1-6.7 MPa) Sub (− 3 to 1.3 MPa) Coat (31.2-14 MPa) Sub (− 2 to 0.7 MPa) Coat (13.2-30.2 MPa) Sub (3 to − 0.7 MPa) Coat (− 11.2to − 50.2 MPa) Sub (11.2 to − 7 MPa) | Ref 53 |
This paper builds upon the previous work done by Zhu et al. (Ref 58) for molten YSZ particle impacting a stainless steel substrate. The numerical simulation is performed to validate the model done by Zhu et al. (Ref 58) using coupled Eulerian–Lagrangian method (CEL) in ABAQUS/Explicit. Due to the limited availability of the numerical models in the literature that provides deposition and post-deposition residual stress analysis, heat transfer model is simulated while including the effect of coefficient of thermal expansion (CTE) using pure Eulerian method in ABAQUS/Explicit.
Numerical Method
Validation Model: CEL Method
Details of mesh and elements for validation model (CEL method)
Solver used | ABAQUS/Explicit |
Method | CEL |
Element type—substrate | C3D8R |
Element type—particle | EC3D8R |
No. of elements—particle | 1,279,104 |
No. of elements—substrate | 247,590 |
Comparison of material properties used for the CEL and Eulerian model
CEL model | Eulerian model | |||
---|---|---|---|---|
YSZ | SS | YSZ | SS | |
Young’s modulus | ✗ | ✓ | ✓ | ✓ |
Poisson’s ratio | ✗ | ✓ | ✓ | ✓ |
Density | ✓ | ✓ | ✓ | ✓ |
Latent heat | ✓ | ✓ | ✓ | ✓ |
Thermal conductivity | ✓ | ✓ | ✓ | ✓ |
Specific heat | ✓ | ✓ | ✓ | ✓ |
Johnson–Cook plasticity | ✗ | ✓ | ✓ | ✓ |
Equation of state | ✓ | ✗ | ✗ | ✗ |
Dynamic viscosity | ✓ | ✗ | ✗ | ✗ |
Thermal expansion | ✗ | ✗ | ✓ | ✓ |
Heat Transfer Model: Eulerian Method
- 1.
Surface roughness of the substrate is not considered
- 2.
The particle is assumed to be fully molten
- 3.
Phase transformation is not considered
- 4.
Phase change from liquid to solid is considered
- 5.
The oxidation and impurities in the coating is ignored
- 6.
The intermediate cooling between the layer is ignored
- 7.
Perfect bonding between the coating and substrate is considered
- 8.
Heat transfer between the coating and substrate is only through conduction
- 9.
The formation of macro- and micro-cracks in the coating is ignored
Details of mesh and elements for heat transfer model (Eulerian method)
Solver used | ABAQUS/Explicit |
Method | Eulerian |
Element type—substrate | EC3D8RT |
Element type—particle | EC3D8RT |
No. of elements—particle | 440,570 |
No. of elements—substrate | 402,570 |
Multiple Impact Model Without Substrate Cooling
A multiple impact model has been simulated with a total number of 100 YSZ particles (diameter of 80 µm) impacting SS substrate (circular disk of radius 100 µm and height of 37.5 µm) with an impact velocity of 240 m/s for Case A. In reality, the particles impact in a random manner to form layers but to reduce computational time the particles were modeled to impact in the same location and axisymmetric model has been simulated. The particles have been preheated to a temperature of 3000 K and the substrate was preheated to 423 K. The material properties of the YSZ and SS used in the multiple impact model are the same as describer earlier in "Heat Transfer Model: Eulerian Method" section. The model considers heat transfer using Eulerian thermally coupled brick element (EC3D8RT) and uses dynamic explicit temperature-displacement step for a total time step of 140 µs. The simulation took around 15 days on Lenovo^{®} ThinkCentre workstation with 6 parallel processors.
Multiple Impact Model with Substrate Cooling
A multiple impact model has been simulated with a total number of 100 YSZ particles (diameter of 80 µm) impacting SS substrate (circular disk of radius 100 µm and height of 37.5 µm) with an impact velocity of 100 m/s for Case A. An axisymmetric model has been simulated to reduce computational time and the particles impact in the same location. The particles have been preheated to a temperature of 3000 K, and the top surface of the substrate was preheated to 423 K while the rest of the substrate was heated to 298 K to mimic the cooling effects generated in the experimental setup. The lower temperature of 298 K was given as a boundary condition to the outer surface, and this region maintains the same temperature throughout the simulation to mimic air cooling of substrate during spraying. While, the substrate temperature of 423 K was given as a pre-defined field and the temperature in this region can change during the simulation. A smooth temperature gradient in the substrate would be more realistic but due to the lack of experimental data, a sharp temperature gradient was used in the model. The material properties of the YSZ and SS used in the multiple impact model are same as in "Heat Transfer Model: Eulerian Method" section. The model considers heat transfer using Eulerian thermally coupled brick element (EC3D8RT) and uses dynamic explicit temperature-displacement step for a total time step of 100 µs. The simulation took around 20 days on Lenovo^{®} ThinkCentre workstation with 6 parallel processors.
Computational Parameters
Mie–Gruneisen Equation of State
Linear U _{s}–U _{p} Hugoniot Form
The speed of sound in YSZ is taken as 3000 m/s and the dimensionless parameter s is taken as 2.39 (Ref 67, 68).
Johnson–Cook Plasticity Model
Material properties used in the numerical model for yttrium-stabilized zirconia (YSZ) and stainless steel (SS)
YSZ | SS | ||
---|---|---|---|
Thermal conductivity (solid) | 2.32 | 14.9 | W/mK |
Thermal conductivity (liquid) | 2 | 33 | W/mK |
Latent heat | 706,800 | 272,000 | J/kg |
Solidus temperature | 2799 | 1710 | K |
Liquidus temperature | 2801 | 1774 | K |
Density | 5890 | 7900 | kg/m^{3} |
Specific heat capacity (solid) | 580 | 477 | J/(kg K) |
Specific heat capacity (liquid) | 713 | 627 | J/(kg K) |
Young’s modulus | 241 | 200 | GPa |
Poisson’s ratio | 0.32 | 0.3 | – |
Coefficient of thermal expansion (CTE) | 6.3 × 10^{−6} | 1.54 × 10^{−5} | K^{−1} |
Johnson–Cook fitting parameter (A) | 420 | 310 | MPa |
Johnson–Cook fitting parameter (B) | 521 | 1000 | MPa |
Johnson–Cook fitting parameter (C) | 0.07 | 0.07 | … |
Johnson–Cook fitting parameter (n) | 0.184 | 0.65 | … |
Johnson–Cook fitting parameter (m) | 0.0197 | 1 | … |
Johnson–Cook fitting parameter (ε_{o}) | 0.418 | 0.418 | … |
Melting temperature | 2988 | 1673 | K |
Transition temperature | 298 | 298 | K |
Speed of sound (liquid) | 3000 | … | m/s |
EOS parameter (s) | 2.39 | … | … |
Temperature-Dependent Viscosity
Results and Discussion
Validation Model
Heat Transfer Model
Multiplication factor used for thermal conductivities for YSZ and SS in ABAQUS^{®}
YSZ | SS | |
---|---|---|
Case A | 10 | 10 |
Case B | 1 | 10 |
Droplet Impact, Spreading and Solidification
For Case B (Fig. 5b), it is noticed that it experiences less freezing-induced breakup phenomenon when compared with Case A. This is due to the comparatively slower rate of heat transfer between the splat and the substrate since only the conductivity of YSZ was multiplied with a factor of 10, while the conductivity of SS material was left at the original conductivity values which makes the thermal conductance value lower. At time instant of 0.12 μs, as soon as the droplet impacts the substrate, there are formations of very tiny satellite droplets. This is also due to sudden heat transfer, which causes the momentum of the molten droplet to overcome the solidified layer and reach an unstable condition leading to the formation of these droplets. Comparing the cooling rates of Case A and Case B, it is seen that the splat cools down relatively faster for Case A and most of the splat has obtained a uniform temperature value ranging from 423 to 635 K with the exceptions of some fragments in the outer region that are at a relatively higher temperature. Whereas for Case B, it is seen that the outer region of the splat is still at higher temperature range of 2800 K at the end of time instant of 6 μs. This shows the slower rate of cooling for Case B even though it was run at twice the time step of Case A, showing that the splat requires extra time to completely cool down.
There have been experimental claims that the splat morphology is affected by the substrate temperature and that above a critical temperature known as transition temperature (TT) (Ref 1) the obtained splats are less prone to splashing. The experimental observations by Shinoda and Murakami (Ref 74) of YSZ droplets impacting quartz glass at various substrate temperatures predicted that the transition temperature was between 513 and 673 K. However, the transition temperature varies for each substrate material. The numerical simulation done by Xue et al. (Ref 28) for metallic droplets impacting substrates using variable thermal contact resistance concluded that for a particular thermal contact resistance, increasing the substrate temperature did not reduce the splashing experienced by the splat. There have been experimental reports that increasing the temperature of the substrate increases the thermal contact resistance by the formation of oxide layer which is the main reason due to which droplets experience lesser degree of splashing (Ref 76). Hence, increasing substrate temperature in numerical models does not affect the results as oxide layer formation is ignored and thermal contact resistance is varied.
Evolution of Residual Stress for Single Particle
For time instants of 1.8-3 μs, post-deposition mismatch stresses are dominant over the peening and quenching stresses. Occurring at a macro-scale, post-deposition mismatch stress is primarily caused due to the difference in the properties (CTE, coefficient of thermal expansion) of the coating and substrate material (Ref 40). Post-deposition mismatch stresses are often known to have highest magnitudes and affect the overall residual stresses significantly. For ceramic coatings, the post-deposition mismatch stress is usually overall compressive in nature, which is the outcome of the substrate residual stresses from 0.48 μs onwards. The stresses are compressive due to the lower CTE of the YSZ when compared with SS.
Through-Thickness Residual Stresses For Single Particle
The through-thickness residual stress for Case B is shown in Fig. 8(b). The residual stresses acting within the coating are mostly tensile with a maximum stress of 65 MPa. At time instant of 1.8 μs, the stress acting on the top surface is low tensile stress (10 MPa) and then reaches a maximum peak value of 40 MPa followed by a dip through the thickness (25 MPa). The coating stress profile for the following time instants have a similar behavior with the values being slightly different with the final time instant having the highest magnitude. The residual stress acting in the substrate is tensile at the interface and then becomes compressive which is then followed by a tensile peak. The highest tensile stress in the substrate (445 MPa) occurs at time instants 5.1 and 6 μs while the highest compressive stress (− 305 MPa) occurs at time instants of 1.8 and 2.7 μs. Comparing the behavior of Case A and Case B for coating stress profile, it is seen that they are quite similar in nature with the exception of higher stress values for Case B. Additionally, the compressive stress highest value is lower for Case B (about − 300 MPa) than Case A (− 409 MPa).
Residual Stresses in Thick Coating Without Substrate Cooling
Differences were observed for the YSZ coating for the numerical data and HDM. The numerical data predicted the stresses within the coating to be mostly tensile while the hole-drilling method predicted it to be tensile on the surface and then through thickness compressive. The possible explanation for this residual stress behavior in the substrate is due to the influence of measurement technique on the residual stress profile. HDM is known to affect the residual stress behavior by the formation of micro-cracks in the vicinity of the hole (Ref 4). Recently, neutron diffraction measurement techniques have widely been used due to their non-destructive and high penetration capabilities and a comparative study of neutron diffraction and hole-drilling method was carried out by Ahmed et al. (Ref 4). It was concluded that the hole-drilling method predicts residual stress in the top layer of the coating reasonably well but through the thickness there is a significant difference in these experimental values of the residual stresses. The residual stresses predicted by HDM are macro-stresses. Neutron diffraction (ND) techniques are much more effective in predicting residual stresses and the profile obtained from ND technique can be compared with stress profile from numerical data. However, there is very limited work available on neutron diffraction for YSZ and SS combination.
Residual Stresses in Thick Coating with Substrate Cooling
Comparison with Coefficient of Thermal Expansion Model
Calculated thermal stress (analytical method) for YSZ coating and SS substrate for different coating thickness using Eq 11
No. | Material | Young’s modulus (GPa) | Poisson’s ratio | CTE (K^{−1}) | Thickness (μm) | Temperature change (K) | Calculated thermal stress (MPa) |
---|---|---|---|---|---|---|---|
1 | YSZ | E_{c} = 241 | υ_{c} = 0.32 | α_{c} = 6.3 × 10^{−6} | t_{c} = 2.14 | \(\Delta T = 2827\) | σ_{c} = 8514 |
SS | E_{s} = 200 | υ_{s} = 0.3 | α_{s} = 1.54 × 10^{−5} | t_{s} = 37.5 | σ_{s} = − 485 | ||
2 | YSZ | E_{c} = 241 | υ_{c} = 0.32 | α_{c} = 6.3 × 10^{−6} | t_{c} = 17.3 | \(\Delta T = 2827\) | σ_{c} = 5798 |
SS | E_{s} = 200 | υ_{s} = 0.3 | α_{s} = 1.54 × 10^{−5} | t_{s} = 37.5 | σ_{s} = − 2675 | ||
3 | YSZ | E_{c} = 241 | υ_{c} = 0.32 | α_{c} = 6.3 × 10^{−6} | t_{c} = 61.3 | \(\Delta T = 2827\) | σ_{c} = 3011 |
SS | E_{s} = 200 | υ_{s} = 0.3 | α_{s} = 1.54 × 10^{−5} | t_{s} = 37.5 | σ_{s} = − 4922 |
Conclusion
- 1.
The final splat shape obtained highly depends on the thermal conductance between the particle and substrate. Higher thermal conductance leads to the formation of fingers and leads to splashing.
- 2.
For single particle impact, the thermal conductance used in the model influences the through-thickness residual stresses obtained in the coating and substrate. The nature of the stresses is same, but the magnitude obtained for lower conductance is slightly higher.
- 3.
For multiple impact model without substrate cooling, the residual stress profile in the coating is only tensile which is balanced by compressive stresses in the substrate.
- 4.
For multiple impact model with substrate cooling, the residual stress in the coating is low compressive on the top surface and then becomes tensile while the substrate is mostly compressive.
Notes
References
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