Numerical study of residual stresses formation during the APS process

Transcription

1 Numerical study of residual stresses formation during the APS process J.Li, R. Bolot, H.Liao and C.Coddet, LERMPS-UTBM, Belfort /F The formation of residual stresses during thermal spray processes may affect significantly the coating quality and performances. In this work, a numerical model based on the Finite Element Method is proposed in order to simulate the formation of residual stresses during the atmospheric plasma spray process (APS). A measurement of the deposit thickness profile was previously performed and the corresponding particle flux distribution was then deduced to determine the heat flux transferred by the particles to the substrate. Additionally, a CFD numerical model was used to estimate the contribution of the plasma jet to the substrate heating. These results were used to study the transient heat transfer in the substrate using a finite element approach. The growth of the coating was considered on the basis of a progressive activation of elements in the coating layer. The temperature evolution was obtained by solving the -D transient heat transfer equation and the stress distribution in the substrate/deposit system was then solved. Finally, a qualitative comparison with measurements of the stress state is also proposed. 1 Introduction Residual stresses induced by the thermal spray process are commonly generated. These stresses appear essentially from two sources: 1) when the molten particles impinge onto the substrate, a stress is generated due to the contraction of each individual splat during fast solidification (quenching stress); ) Once the as-sprayed specimen cools down to the ambient temperature, a stress is generated due to the incompatible thermal contraction between the coating and the substrate (thermal stress). Moreover, residual stresses can be induced by the volume change associated to the solid phase transformations and the through-thickness temperature gradient [1]. Residual stresses act strongly on the coating performances, such as adhesion strength or fatigue or thermal cycling lifetime [, 3]. Hence, it is recognized that residual stresses have significant effects in the thermal spray technology, so that considerable works are made in order to understand and predict the residual stress state. Several techniques are reported in the literature. In particular, numerical modeling using the Finite Element Method (FEM) is a widely used approach to determine residual stresses. The numerical model can be adjusted by comparing the simulation results with experimental measurements, and then the validated model may be used to predict the residual stress state. The work presented in this paper concerns a numerical study of residual stresses induced in the plasma sprayed work-piece during the coating elaboration process. The use of a coupled thermo-mechanical model using the Finite Element Method is proposed. Both the coating formation and the as-sprayed component cooling are integrated in the model. Experimental conditions: The study case concerns the elaboration of a single material coating (i.e. ceramic or metallic), upon a thin stainless steel substrate (AISI 316L) with a planar shape. The sample dimensions were 5 x 1 mm for a thickness of 1 mm. Concerning experiments, a SULZER-METCO F4 type gun incorporating a 6 mm diameter nozzle was used and the plasma gas was an argon/hydrogen mixture (35/8 slpm). The electric arc current intensity was 6 A and the torch voltage was 55 V. For these conditions, the thermal efficiency of the plasma torch was about 53%. A straight 5 mm long and 1.8 mm internal diameter powder injector was used. It was placed 5 mm downstream the gun exit and 9 mm from the torch axis. The carrier gas flow rate was adjusted at about 3.5 slpm and the powder mass flow was adapted for the different powders in order to obtain the desired coating thickness of µm. The particles injection direction was parallel to the plasma torch displacement direction. A stand-off distance of 1 mm was considered for all specimens. The plasma torch linear displacement velocity was 5 mm.s -1. The commercial Al O 3 powder (Amperit 74.3) and Mo powder (Amperit 16.9) were used. The powders size distributions were µm and -45+5µm respectively. In order to determine the residual stress state during and after the spray process, an in-situ curvature measurement was performed using video recording. Model formulation The use of a finite element model is proposed to evaluate the residual stress state in the coating/ substrate system. Both the coating and the substrate materials were modeled with the SYSWELD commercial Finite Element software. Two-dimensional 4-nodes quadrilateral elements employing a bilinear interpolation function for temperature and displacements were used to generate the mesh in the coupled thermo-mechanical analysis. In order to decrease the computational time, only the specimen cross-section in the plasma jet moving plan was modeled as a 5 mm long and 1. mm thick rectangular area. Hence, a substrate thickness of 1 mm and a coating thickness of µm were considered for all specimens. Moreover, a plan-strain condition was applied. In order to simulate the coating growth, a multi-layer structure was considered in the coating. It was supposed that the µm thick coating was elaborated by ten passes of the plasma jet. Thus, a µm thick individual layer is deposited during each pass of the spray jet. Each coating layer was modeled individually and the cells were progressively activated along the spray jet displacement. Thus, the growth of each coating layer during the plasma jet displacement is progressive. Concerning the mesh, the use of square

2 shape elements is favorable and ensures a good accuracy in the FE analysis. However, in view of the small thickness of elements in the coating layer ( cells for each layer of µm), the mesh was characterized by a quite large aspect ratio (i.e. the ratio between the cell dimension parallel to the coating surface and that perpendicular) in the coating layer. The use of quadrangular elements with a relatively large aspect ratio was necessary in order to decrease the number of elements and subsequently the required computational time. Additionally, a progressive mesh refinement was used at the coating/substrate interface in order to take the presence of important gradients at the interface into account, as shown in figure 1. Stainless steel substrate (1mm) Fig. 1. Structure mesh. A flat, perfect bonding interface hypothesis was used in the model. The thermal contact resistance was not taken into account and the effects of substrate grit blasting and interface roughness on the stress distribution were neglected. The materials (substrate and coating) were assumed to be isotropic and homogenous. The special microstructure of the coating (porosities, lamellar structure, etc.) was not taken into account in the model, except by considering their effective properties [1]. The materials thermo-mechanical properties used in the simulation were temperature-dependent as listed in table 1. Table 1. 1 layers of the coating (µm) Material thermo-mechanical properties. Properties 316L Al O 3 Mo ρ (Kg.m -3 ) K (W.m -1.K -1 ) ( C) 138( C) 6.3(8 C) 58.9(8 C) C (J.Kg -1.K -1 ) E (Gpa) ( C) 6 * 11 * 1(8 C) ν α (1-6.K -1 ) σ Y (MPa) 17( C) 1 ** 3( C) 5(8 C) 193(8 C) * Estimated values from [1] for all temperatures. 3 Thermal analysis In order to evaluate the transient temperature field, the heat supplies due to the impinging plasma jet and the molten particles solidification were considered as mobile heat sources. Moreover, the coating growth was simulated using a progressive activation of elements in the coating layer. 3.1 Heat flux from the impinging plasma jet The contribution of an impinging plasma jet to the substrate heating was studied in a previous paper [4]. In the present work, the CFD numerical results were fitted using a function that provides a quite good approximation of the computed flux profile. The following function was obtained: φ φ ( r ) = r 1 + R in which φ is the maximum value of the thermal flux at the axis of the impinging jet, R is the characteristic dispersion radius and r (mm) is the distance from the jet axis. The values of these parameters were φ =.56 MW/m and R = mm for the stand-off distance of 1 mm. 3. Heat flux due to the sprayed particles solidification and cooling The heat flux due to the molten particles solidification was determined using a two steps method: 1) compute the enthalpy change of the molten particles during their impact and cooling onto the substrate; ) define the particles mass flux on the substrate by considering experimental measurements. In this study, the in-flight particle temperature was assumed to be that of the melting pointt f, and the considered ambient temperature was C. The value of the enthalpy change was then calculated with the following relationship: = C T f T + L ( ) f h mat in which C is the material specific heat (J.kg -1.K -1 ) and L is the latent heat of fusion (J.kg -1 ). The retained f values of hmat were 81 kj.kg -1 for Al O 3 and 955 kj.kg -1 for Mo. The particles injection direction was parallel to that of the plasma torch displacement. Hence, the coating profile was assumed to be symmetric. Spray patterns profile measurements indicated that a Gaussian distribution may be assumed [4]: in which m * ( r) * * m ( ) = s e xp πσ σ m r per unit area (g.mm -.min -1 ), r (eq.1) is the sprayed material mass flow rate m * s is the effective

3 deposition rate (g.min -1 ), r is the distance from the particle spot center and σ is the Gaussian radius. The effective deposition rate s may be determined by measuring the maximum thickness of the spray pattern h max after n passes of the spray jet and can be evaluated from [4]: * m * ( h n) ρv π σ m s = (eq. ) max in which ρ is the material density and V is the displacement velocity. Experimental results in [4] were used to determine the Gaussian profile radius σ whereas the considered maximum thickness h max was µm per pass as indicated previously. Once these two parameters are obtained, the effective deposition rate may be evaluated from eq. and the heat flux due to the molten particles may be expressed by combining eqs.1 and to obtain: h V r ( ) = max ρ πσ φ r exp h mat πσ n σ in which φ ( r) is the heat flux (MW.mm - ). Finally, the distribution of the thermal flux transferred from the sprayed particles to the substrate can de defined as: r ( ) φ r = φ exp (MW.m - ) σ and a maximum value φ of 8.9 MW.m - was obtained for alumina, whereas the corresponding value was 7.78 MW.m - for molybdenum. The two heat sources (plasma jet + particles) were applied as mobile thermal fluxes by using the user program associated to SYSWELD. The position of the thermal fluxes axis is calculated at each time step and the thermal flux distribution is defined using the above equations. Since the particles injection is oriented in the plan of the plasma torch displacement direction, the particles jet and the plasma jet were found to be staggered with an offset of 5 mm. Figure presents the computed thermal flux distribution of the plasma jet and the particle jet and their relative position. thermal flux (MW.m-) plasma jet offset 5mm reference axis particle jet The transient temperature field can be simulated by considering the progressive growth of the coating along with the plasma jet linear movement. The predefined coating mesh was deactivated before the simulation. Two different heat sources are applied to the current layer; the deactivated coating elements are activated when the heat sources arrive for the layer deposition. The elements activation criterion is a position-dependent function. The relative position between each element and the main heat source (particle jet) reference axis is calculated at the current time step. If an element is located inside the particle jet, this element is activated in the current time step. Considering experimental conditions, the delay between two successive layers was supposed to be.5 second. A cooling convection condition was applied at the substrate back face. Concerning the top face (coating), it is immersed in the plasma gas during the spray step. Therefore the thermal exchange with the ambience can be ignored. Moreover, the plasma jet was considered as optically thin and the radiations from the plasma to the coating were neglected. The estimated convection coefficient was 1 W.m - C -1 and the ambient temperature T was C. This boundary condition consists of a combination of convection and radiation from the specimen to the ambience. Moreover, the convection condition is applied to the as-sprayed layer surface nodes as well as those of the back face during the laps of time between two successive layers deposition, allowing taking into account the thermal exchange between the current top surface and the ambience while the plasma jet moves away. In this case, the convection coefficient applied to the coating surface was identical to that at the substrate back face. Figure 3 presents the computed temperature field after partial activation of the first alumina coating sub-layer. The heat sources displacement velocity was 5 mm.s -1 and the substrate material was stainless steel 316L with an initial temperature of C. The plasma jet and the particles jet are moving linearly from the specimen left edge (initial position) to the right, along the Y axis. X Y Heat source moving direction V distance from the particle spot centre (mm) Fig.. Thermal fluxes distributions and their relative position in the model. 3.3 Temperature field simulations during the coating growth Fig. 3. Transient temperature field after partial activation of the first coating layer alumina coating V = 5 mm.s -1.

4 The given temperature field is that after about.75 second so that the position of the spray jet is about 35 mm along the Y axis. The maximum temperature is about 183 C in the coating material. One may observe a large temperature gradient near the activated layer. Figure 4 presents the substrate/coating interface temperature change during the deposition of all 1 alumina coating layers. One may notice that the temperature reaches a maximum value during a very short period mainly due to the main heat source and decreases due to thermal conduction through the underlying material. After an inter-cycle cooling of.5 second, the system resulting temperature field is employed as the initial condition for the next layer deposition. Considering the present conditions, no thermal steady-state was reached and the coating/substrate system temperature increases regularly during each pass. The absence of forced cooling on the coating during the spray step and the relatively low value of the estimated convection coefficient are the reasons. Thus, the final overall temperature reaches an important value. For the current material (Al O 3 ), the as-sprayed specimen temperature is about 5 C after elaboration of the µm thick coating (1 layers). The corresponding calculations were also conducted for the molybdenum coating. In this case, a similar temperature field is obtained, but the temperature value is lower than for alumina. temperature ( C) interface temperature underlying face temperature time (s) Fig. 4. Temperature evolution during the deposition of 1 alumina layers onto the 316L substrate (results at the substrate/coating interface). 4 Thermo-mechanical analysis 4.1 residual stress field simulations during the coating growth The thermal study results were used to perform the mechanical analysis. In order to stabilize the structure, all nodes at the left edge of the substrate (see figure 3) were fixed in both X and Y directions by eliminating all degrees of freedom for the considered nodes. The structure was assumed to be in a stress-free initial state. Considering the coating growth, the new elements are activated similarly to the thermal analysis. The as-activated elements are assumed to be stress-free and in a null thermal deformation state. The residual stress contour after post-spraying cooling is presented in figure 5 for the Al O 3 coating case. The presented part is the free edge of the specimen. Coating Substrate X Y Fig. 5. X and Y direction residual stresses contour for the Al O 3 /316L system after cooling to ambient temperature. It can be seen that the X direction stress (perpendicular to the coating surface, notedσ xx ) is compressive near the free edge across the specimen thickness, and the maximum value of -19 MPa is found in the substrate. The stresses concentrate at the sample free edge close to the interface. For the Y direction stress (parallel to the coating surface, notedσ ), the coating is in a compressive state and the maximum stress of -38 MPa is found close to the interface. The stress value decreases slightly from the interface to the coating surface. Compressive stresses in the coating are balanced by tensile stresses in the substrate. The maximum tensile stress is observed in the substrate, near the interface, and varies to a slightly compressive stress (-8 MPa) at the substrate back face. One has to note that the present results were obtained with a special consideration to the mechanical behavior of the thermally sprayed ceramic material. It was reported in the literature [1, ] that a very low stress magnitude was found in the Al O 3 coating during the coating deposition process (about 1 MPa). The explanation of this phenomenon is that in view of the brittleness behavior of ceramic materials, microcracks formation dominates the stress relaxation mechanisms during the coating formation. Hence, a yield stress of +1 MPa was assigned to the alumina coating during the spray process. Thus, the stress generated during spraying does not exceed this value which means that microcracks formation starts. However, during the sprayed specimen cooling, the ceramic coating behavior was supposed to be perfectly elastic. The reason is that ceramics do not resist to plastic deformation. yy

5 In order to validate the FE model, the calculated final deformation was compared with experiments. Figure 6 presents the comparison between experimental and numerical results for the alumina case. The same trend of deformation was obtained, meaning that the predicted stress state is certainly reasonable. Fig. 6. Comparison between the measured final deformation and the predicted one. Figure 7 presents the through-thickness Y direction residual stress distribution (parallel to the coating surface) for the Al O 3 coating before and after cooling. It was found that the as-sprayed Al O 3 coating presents a very low stress magnitude before cooling to the ambient temperature. The stress values vary from a slight tensile stress of +4 MPa near the interface to -3 MPa at the coating top surface. In the substrate, the stresses are compressive near the interface. Y direction residual stress (Mpa) Experimental before cooling after cooling Numerical prediction substrate coating distance form the interface (mm) Fig. 7. Through-thickness Y direction residual stress distribution of the Al O 3 /316L system before and after cooling (results at the middle point of the specimen). Since the Al O 3 coating has a much lower thermal extension coefficient (CTE) than the 316L substrate (5.1e-6 vs. 16.5e-6 for 316L), it can be seen that the low tensile stress in the Al O 3 coating is annealed completely by thermal stresses after the specimen post-spraying cooling, so that the coating changes to a compressive state. The stress magnitude in the substrate and the coating is quite high after cooling back to the ambient temperature. The maximum compressive stress in the coating is about -38 MPa and the maximum tensile stress in the substrate is + MPa. Concerning the Mo coating case, the elastic-perfect plastic material behavior was used in both spraying and cooling phases. Figure 8 presents the throughthickness Y direction stress distributions before and after post-spraying cooling. One may notice that high tensile stresses are obtained in the coating after the spray step and before the specimen cooling. This is a result of quenching of the as-sprayed layers. Moreover, one may notice that the stress level varies in the coating depth. The maximum value of 5 MPa is observed at the coating top surface. The tensile stress decreases from the top surface to the coating center. A minimum tensile stress of 18 MPa was found at about 5 µm from the top surface. Then the stress level increases again toward the interface and reaches a new peak value at the substrate/coating interface (about MPa). Y direction residual stress (Mpa) before cooling after cooling substrate coating distance form the interface (mm) Fig. 8. Through-thickness Y direction residual stress distribution of the Mo/316L system before and after cooling. After post-spraying cooling, the stress state in the coating changes to a compressive state and that in the substrate to a tensile one. However, the stress profile in the coating does not change. The origin of this through-thickness stress gradient is not clear at the moment. However, some influencing factors may be given [5]. 1) It was found that the specimen temperature increases during the spray process but the substrate initial temperature was assumed to be C; that is to say, the first layer was deposited with a low substrate temperature ( C) that might lead to a higher tensile stress than that of the following layers which were deposited with a higher temperature; ) the energy input due the latter layer deposition acts on the previous layer temperature distribution and consequently on the stress distribution; 3) The interaction between adjacent layers might act on the stress distribution. When the latter layer arrives onto the previous one, the new layer exerts a tensile

6 quenching stress and produces the compressive stress trend in the as-sprayed one. Additionally, the specimen deformation due to the through-thickness temperature gradient may also influence the stress change in the coating material. Consequently, the observed stress gradient may depend on the combination of these influencing factors. The maximum shear stress ( σ ) concentration was found close to the specimen free edges, particularly at the dissimilar material interface. Through the results presented above, it can be summarized that in the plasma spray process, the residual stress magnitude may be significant. As reported in the literature [3], the stress state and magnitude may affect the failure of the coating. Compressive stresses are often desired for ceramic coatings. However, high compressive tangential stresses ( σ ) in the coating material may cause yy bending of the specimen and may reduce the coating adherence. The concentration of the X direction stress and the shear stress at the free edge may produce a horizontal opening at the interface and the propagation toward the center of the coating may lead to the coating delamination. Hence, acting in order to moderate residual stresses is a good way to reduce the coating failure risk and improve the coating properties. 4. Further results of the residual stress study It was reported in the literature [6] that high cooling rates may cause a high stress magnitude. In the present study, a contrary effect of the cooling rate was detected. Convection coefficients of 1, and 5 W.m -. C -1 were applied to the substrate back face in order to simulate different cooling conditions. It was observed that the cooling condition acts strongly on the stress distribution. More precisely, the stress profile is similar for all cases but an increase in the convection coefficient provides a decrease in the stress magnitude inside the coating. For example, considering a convection coefficient of 5 W.m -. C -1, the stress reduces to at the coating top surface as seen in figure 9. y direction residual stress (Mpa) h=1w/m-.k-1 h=w/m-.k distance from the interface (mm) xy h=5w/m-.k-1 Fig. 9. Through-thickness Y direction residual stress distribution in the Mo/316L system after cooling with different cooling rate during the spraying process. It is clear that a high convection coefficient leads to a lower specimen temperature during spraying due to the strong heat dispersion in the surrounding environment. Thus, the component temperature is lower at the end of the spray step. Hence, the thermal deformation due to the post-spraying cooling is reduced. On the contrary, a low deposition temperature can cause more quenching stresses, but this effect was not obvious in the presented cases. While the convection coefficient changes from 1 to 5 W.m -. C -1, the maximum tensile stress obtained before cooling changes from 56 Mpa to 8 Mpa at the coating top surface. Hence, it can be summarized that the use of forced cooling during spraying may be an efficient means in order to reduce the stress magnitude. 5 Conclusions A D coupled thermo-mechanical finite element model was proposed to simulate the stress formation during the coating elaboration. The coating growth was simulated by the element activation technique. The residual stress field was studied for alumina and molybdenum coatings. The qualitative comparison between the calculated final deformation and the experimental one demonstrates that the predicted stress field is reasonable. The residual stress in the alumina coating is very low before cooling due to the brittleness behavior of ceramics (microcracks formation). A higher tensile stress was found in the molybdenum coating with an inhomogeneous through-thickness distribution. After the component cooling, a compressive stress state was found in both cases. Additionally, the use of different cooling conditions during the spray process was considered, and the numerical results demonstrate that a high cooling rate may lead to a lower stress magnitude in the coating, thus improving its quality. 6 References [1] S. Kuroda and T.W. Clyne, "The quenching stress in thermally sprayed coatings", Thin Solid Films, (1991) [] S. Kuroda, T. Fukushima and S. Kitahara, "Significance of the Quenching Stress in the Cohesion and Adhesion of Thermally Sprayed Coatings", pp of Thermal Spray: International Advances in Coatings Technology, Ed. C.C. Berndt, Pub. ASM Int., Materials Park, OH, USA, 199, 144+ pages. [3] C. Godoy, E.A. Souza, M.M. Lima and J.C.A. Batista, "Correlation between residual stresses and adhesion of plasma sprayed coating: effects of a post-annealing treatment", Thin Solid Films, 4-41 () [4] R.Bolot, J.Li, R. Bonnet, C. Mateus and C. Coddet, "Modeling of the substrate temperature evolution during the APS thermal spray process", pp of Thermal Spray 3: advancing the Science and Applying the Technology, Ed. B.R. Marple and C. Moreau, Pub. ASM Int., Materials Park, OH, USA, 3, 178+ pages. [5] O. Kesler, J, Matejicek, S. Sampath, S. Suresh, T. Gnaeupel- Herold, P.C. Brand and H.J. Prask, "Measurement of residual stress in plasma- sprayed metallic, ceramic and composite coatings", Materials Science and Engineering, A57 (1998) [6] S. Widjaja, A.M. Limarga and T.H. Yip, "Modeling of residual stresses in a plasma-sprayed zirconia/ alumina functionally graded-thermal barrier coating", Thin solid Films, 434 (3) 16-7.