Numerical investigation of transient coating build-up ...

Surface & Coatings Technology 326 (2017) 355–365

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Surface & Coatings Technology journal homepage: www.elsevier.com/locate/surfcoat

Numerical investigation of transient coating build-up and heat transfer in cold spray Chaoyue Chen a, Yingchun Xie a,c,⁎, Christophe Verdy a, Renzhong Huang c, Hanlin Liao a, Zhongming Ren b, Sihao Deng a,⁎⁎ a

ICB UMR 6303, CNRS, Univ. Bourgogne Franche-Comté, UTBM, F-90010, Belfort, France Shanghai University & State Key Laboratory of Advanced Special Steel, 149 Yanchang Road, Shanghai 200072, PR China National Engineering Laboratory for Modern Materials Surface Engineering Technology, The Key Lab of Guangdong for Modern Surface Engineering Technology, Guangdong Institute of New Materials, Guangzhou 510651, PR China

b c

a r t i c l e

i n f o

Article history: Received 5 March 2017 Revised 31 May 2017 Accepted in revised form 29 July 2017 Available online 31 July 2017 Keywords: Cold spray Finite element analysis (FEA) Transient coating build-up Thermal analysis Coating thickness

a b s t r a c t Since cold spray is widely considered as an additive manufacturing and damage repair technology, it is crucial to understand the coating build-up process and the temperature evolution. In this work, a 3D numerical model was developed to simulate the transient coating build-up process as well as the heat transfer in cold spray. By coupling the heat transfer with the ALE (Arbitrary Lagrangian–Eulerian) moving mesh and coating thickness model, this 3D model is able to investigate the temperature evolution of a coating which simultaneously grows according to the nozzle trajectory. The nozzle trajectory that represents the heat source and mass flux of particle impact is generated and simulated in the offline programming software RobotStudio™. By assigning the results of coating thickness distribution, the simultaneous build-up of coating computational domain is achieved by ALE moving mesh method. The validation of the FEA (finite element analysis) model was carried out by measuring the coating surface temperature via an infrared imaging camera. The effects of nozzle traverse speed on the coating surface temperature as well as coating thickness in cold spray were also investigated. With the proposed model, it is able to study the actual coating build-up process as well as the heat transfer phenomena, which may provide more insights for the application in additive manufacturing and damage repair. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Cold spray that is also called cold gas dynamic spray (CGDS) or kinetic spray (KS) has drawn more and more attention due to its unique ‘cold’ characteristics [1–3]. In this process, the particles are accelerated to a high velocity (300 m/s–1200 m/s) by a supersonic protective nitrogen, helium gas or air at a relatively low temperature, and deposited onto the substrate. With its feature of low temperature and high impacting velocity, a dense and thick coating with low porosity and less oxidation can be achieved. Recently, cold spray has been widely applied in the domains of additive manufacturing [4–6], damaged component restoration [7,8], protective coating building [9,10]. In order to better control the additive manufacturing by cold spray and improve the sample quality, it is of great importance to study the thermal distribution during the coating build-up process. Numerous studies have been made to understand the heat exchange [11] and ⁎ Correspondence to: Y. Xie, ICB UMR 6303, CNRS, Univ. Bourgogne Franche-Comté, UTBM, F-90010 Belfort, France. ⁎⁎ Corresponding author. E-mail addresses: [email protected] (Y. Xie), [email protected] (S. Deng).

http://dx.doi.org/10.1016/j.surfcoat.2017.07.069 0257-8972/© 2017 Elsevier B.V. All rights reserved.

temperature distribution by different approaches. By methods of thermocouple [12,13] and infrared thermal camera [14], it is able to measure the transient temperature variation during spray process. Meanwhile, numerical simulation is also used to provide more details about temperature distribution in cold spray process. However, the difficulty stays with the transient coating build-up process by the simultaneous nozzle movement. In most of early studies [12,15], coating was partitioned as a part of predefined geometry without accounting the transient and gradual coating deposition process. Obviously, such treatment has significant difference from the actual coating deposition process, where the thickness and topology of coating changes along with nozzle movement. Lately, different kinds of numerical approaches have been developed to investigate such transient coating build-up process. In cold spray, most finite element analyses were made to study the temporal evolution of deformation behavior and associating variables [16–18] (stress, strain and temperature) of single or several particles onto substrate in micro-scale, which is usually achieved by mesh based Eulerian [19] or Lagrangian models [14,20]. By imposing appropriate plasticity and elasticity model, it is able to investigate the deformation behavior of particle and substrate [20,21], the formation mechanism of residual stress and the distribution of temperature and

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C. Chen et al. / Surface & Coatings Technology 326 (2017) 355–365

Nomenclature Cp ρ u x, y T k Q Pr k ξ(θ) v h σ Re

specific heat [J kg−1 K−1] density [kg/m3] velocity vector [m/s] Displacement in x and y direction [m] Temperature [K] Thermal conductivity [W/(m K)] Additional heat source [W/m2] Prandtl number Thermal conductivity [W/(m K)] Coefficient of spray angle Coating thickness value [m] Heat transfer coefficient [W/(m2 K)] Standard deviation of Gaussian distribution [m] Reynolds number

strain [16]. Thus, by increasing the particle quantity, it is able to simulate the coating formation process with such methods, which is usually dedicated to the study of residual stress [16,18] and the formation mechanism of composite coating [21]. However, such methods based on particle deformation is very consumptive in terms of computational resource for full coating deposition, which cannot be extended to large scale modeling. Alternatively, the layer-by-layer method [13,22–25] is used to simulate macro-scale coating formation, which is widely applied to study the thermomechanical phenomena in thermal spray. In this method, the Birth/Death element feature in ANSYS software was used to simulate the coating growth by progressively activating the elements layer by layer with a certain thickness. During this process, the heat flux by impinging heat source and sprayed particles are applied on the surface of the latest activated layer. However, inconsistence between experimental and simulation result [13,24] was reported due to the neglect of the continuous and gradual deposition in real experiments. In order to simulate the temperature evolution with transient coating build-up process, a 3D model based on ALE (Arbitrary Lagrangian– Eulerian) moving mesh method was established by accounting the transient coating build-up as real coating deposition process. By coupling between the heat transfer, moving mesh and coating thickness simulation, the proposed model enables the simulation of the transient temperature distribution as the simultaneous nozzle movement in cold spray. Based on the results of coating thickness model, the transient coating build-up is achieved by assigning the coating thickness

distribution to the mesh deformation value of coating surface, which is namely the coating build-up. This work aims to study the transient temperature evolution in the cold spray process. Experimental validation was also performed by measuring the transient temperature history on the coating surface by imaging infrared camera. Furthermore, the effects of nozzle traverse speed on heat transfer as well as coating thickness are investigated by the proposed model. 2. Numerical model 2.1. Governing equation and boundary conditions As the schematic is shown in Fig. 1, dissimilar to traditional thermal spray process, cold sprayed coating is formed by the deposition of solidstate particle. Particles are carried by heated gas and then deposit onto substrate. According to the finite element analysis (FEA) of particle acceleration and heating in the De Laval nozzle used in cold spray [26], the particle in cold spray before impacting onto substrate is found to be slightly heated. Thus, the heat conduction within the deposited particle can be assumed to be neglected. Furthermore, during the impact within tens of nanoseconds, it is considered that the kinetic energy of a particle is converted to local thermal energy input due to the dissipation of kinetic energy into heat during plastic deformation [27]. It is essential to account the temperature rise due to the plastic deformation of deposited particle. As a result, the heat transfer between the gas-particle mixture out of nozzle and the coating-substrate structure is taken into account in this work via the addition of heat source terms and a third kind of boundary condition. The governing transient heat transfer equation for the coating and the substrate in three dimensional is written as below. ρ Cp

∂T ¼ ∇ ðk∇TÞ þ Q ∂t

ð1Þ

Where ρ is the density Cp is the heat capacity, k is the thermal conductivity, Q is the additional heat source. As for the heat input by the high-temperature gas flow, a third kind of boundary condition was used as the thermal condition at the substrate surface to describe the heat transfer on substrate surface [28], which is given in Eq. (2). −n ð−k∇TÞ ¼ h ðText −TÞ

ð2Þ

Where, n is the normal vector to the surface, h is the heat transfer coefficient and Text is the temperature of the external fluid far from the boundary. The term Text was defined as the temperature of gas prior to the impact onto the substrate, which was obtained by the simulation in ANSYS-Fluent 14.1 based on the powder and working conditions in the experiment. The details of the ANSYS-Fluent model can be referred

Fig. 1. Schematic of the cold spray system.


to the work [29]. Based on the Gaussian distribution of heat flux out of nozzle that was frequently applied in the numerical studies [25,30,31], the heat transfer coefficient between the gas and substrate was set as the Eq. (3). ðx−x0 Þ2 þðy−y0 Þ2 − A 2σ 2 h ¼ h0 pffiffiffiffiffiffi e σ 2π

ð3Þ

Where the h0 is the heat transfer coefficient obtained by the equation of external forced convection [32]. The definition of the heat transfer coefficient by external force convection is given as below. The σ is the standard deviation of the Gaussian distribution, which means that the diameter of the jet impact is 6σ. The (x0, y0) is the coordinate of the jet impact onto the substrate, which is the variable based on time and is defined through the nozzle trajectory. The details about the nozzle trajectory generation will be discussed in the following section. 0

1=2

0:3387Pr1=3 ReL k 5 B2 1=4 if ReL ≤5 10 B L 1 þ ð0:0468= PrÞ2=3 h¼B B @ k 4=5 2 Pr1=3 0:037ReL −871 if ReL N5 105 L

ð4Þ

where Pr = μCp ⁄k and ReL = ρUextL⁄μ, k is the thermal conductivity of the gas. The plate length of L is the length of the substrate. The exterior velocity of Uext is the gas velocity prior to the impact upon substrate, which is calculated by ANSYS-Fluent 14.1 simulation as mentioned above. The heat transfer due to the surrounding air circulation in workspace was considered as the heat loss by cooling effect. Similar to the heat accumulation, the heat transfers by cooling effect is also treated as the third kind of boundary condition in Eq. (2). Beside the heat input by gas flow, according to Li's studies on the impact fusion at particle interfaces [33], part of the temperature rise of a cold sprayed coating is owing to the heat dissipation by the plastic deformation of the particle or substrate under adiabatic conditions, which is transformed from the kinetic energy by the particle impact. The kinetic energy (Ek) of a particle with a diameter of dp and a velocity of vp can be defined as the Eq. (5). Ek ¼

1 mp v2p 2

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Table 1 Material properties. Material

Coating/nickel [34]

Temperature Density (K) (kg/m3)

295 350 400 500 600 Substrate/aluminum – [35]

8900 8880.6 8862 8822.4 8780.5 2700

Thermal conductivity (W/(m K))

Specific heat (J/(kg K))

90.6 85 80.2 72.2 65.5 160

444.3 463.6 482.3 530 593.7 900

result of the transient heat transfer of the coating/substrate than that of the layer-by-layer model [24]. However, these methods lack accuracies to account the transient coating build-up process in a 3D model. Therefore, it is of great importance to propose this coating build-up model in 3D that is based on the transient coating thickness distribution model. In this model, the coating build-up process is achieved by the ALE moving mesh method based on the transient coating thickness distribution. It allows the evolution of computational domain according to the coating formation as the spray nozzle trajectory. Generally, in a finite element method, the partial differential equations (PDE) of physics are usually formulated either in a spatial coordinate system, with coordinate axes fixed in space (a Eulerian formulation), or in a material coordinate system, fixed to the material in its reference configuration and following the material as it deforms (a Lagrangian formulation). One-dimensional example of the and particle motion in Lagrangian and Eulerian methods is given in Fig. 2.

ð5Þ

Where mp is the particle mass. Thus, based on the Gaussian distribution of particle impact onto the substrate, the heat input due to the heat dissipation by the plastic deformation of the particle can be formulated as the Eq. (6). Qp ¼ α

ðx−x0 Þ2 þðy−y0 Þ2 − Ek α A 2σ 2 f ðx; yÞ ¼ mp v2p pffiffiffiffiffiffi e S 2 σ 2π

ð6Þ

where, α is the kinetic energy conversion factor to generate the temperature rise, f(x, y) is the Gaussian distribution function that is defined similar with Eq. (3), and A is the amplitude factor accounting the mass flux of deposited particle that is obtained from experimental data. Under the consideration of perfect bonding between coating and substrate, the heat transfer between them is regarded as thermal conduction. The material properties of the coating and the substrate used in the FEA model are given in Table 1. The numerical model is built in the software COMSOL and solved by coupling between the multiphysics of heat transfer, moving mesh and coating thickness distribution, which will be discussed in the following sections. 2.2. Description of coating build-up model According to related work, a proper coating formation model has dominant effects on the finite element analysis results [24]. It is reported that the stochastic deposition model can provide a more objective

Fig. 2. One-dimensional example of Lagrangian, Eulerian and ALE mesh and particle motion [36].

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However, the main idea of ALE is to introduce a third coordinate. The PDEs are formulated in the mesh coordinate system, and then mapped from the reference domain (mesh coordinate) to the physical domain (material coordinate). The ALE method is therefore an intermediate between the Lagrangian and Eulerian methods [36], and it combines the best features of both. It allows moving boundaries without the need for the mesh movement to follow the material. The ALE method has been widely applied to deal with the numerical problems in fluid dynamics and nonlinear solid mechanics that encounters strong distortions of the computational domain while allowing for a clear delineation of free surfaces and fluid–fluid [37,38], solid–solid [39], or fluid–structure interfaces [40]. As the overall model is shown in Fig. 3(a), mesh deformation of the geometry is achieved based on the control of boundary condition. Because the generation of a new computational domain is not allowed, it is necessary to give a preliminary computational domain of coating. As indicated in the left of Fig. 3(a), the preliminary computational domain is modeled allowing the successive build-up of coating on the substrate surface. The initial coating thickness is controlled at such a small value of 50 μm (approximately the thickness of a single particle layer). Thus, an assumption is made here that the preliminary computational domain of coating has little effect on the heat transfer with the substrate. As the moving mesh method description shown in Fig. 3(b), the mesh displacement value of the coating surface is zero in the directions of x and y, which means no horizontal coating grow-up is allowed and the coating growth on the substrate surface is restricted vertically. A variable that represents the coating thickness distribution on the substrate surface is assigned as the coating growth value in the direction of axisz. The transient distribution of coating thickness is obtained by the results of the coating thickness distribution model, which will be

introduced in the next section. The mesh deformation in the computational domain of substrate is fixed as zero, which means no deformation is assigned to substrate. 2.3. Coating thickness distribution According to the related studies [41–43], the operating parameters in spray process can directly affect the coating quality as well as the coating thickness. However, the previous work on the finite element analysis in the coating formation process seldom takes into account the effects of operating parameters on coating thickness. The computational domain of coating is usually treated as a static as-sprayed one, instead of transient coating formation process. In this study, the coating thickness distribution is simulated according to the coating thickness model proposed in the reference [44]. It takes into account the effects of operating parameters in spray process, such as nozzle traverse speed, spray angle, scanning step between two successive passes of trajectory. The coating thickness model is given as an ODE (ordinary differential equation) in equation below, which is solved prior to the heat transfer problem during the simulation to define the transient coating thickness growth. Z φ ¼ ζðθÞ

0

T

Z

! ðx−μ x Þ2 ðy−μ y Þ2 − þ A 2σ 2 2σ 2 pffiffiffiffiffiffi e dxdy dt σ 2π

ð7Þ

Where ξ(θ) is the coefficient to account the influence of spray angle on coating thickness, A is the amplitude factor accounting the mass flux of deposited particle that is obtained from experimental data, σ is the standard deviation of the Gaussian distribution. The coating profile

Fig. 3. 3D numerical model based on deformed mesh method: (a) overall geometry and detailed description of ALE moving mesh method; (b) meshing.


deposited at the duration of time step dt is considered as a Gaussian distribution, which is widely applied in the simulation of coating thickness [45–47]. The variables in the Gaussian distribution equation are obtained by measurement of coating profile by single nozzle pass in experiment. By assigning the transient coating thickness distribution to the mesh displacement of the coating surface, the coating build-up process can be realized. It allows the simultaneous calculation of thermo-mechanical effects during the coating build-up process.

2.4. Robot kinematics The nozzle trajectory represents the nozzle movement in relative to the substrate during spray process, which is also the movement of heat source and particle source. Manipulated by robot, the nozzle trajectory in real spray process is found to be directly affected by the robot kinematics [48,49]. For example, an undesired robot performance can result in the fluctuation of nozzle traverse speed [42,49], which can cause local over-heating [30], uneven coating thickness, and arise of residual stress. Thus, it is of great significance to include the robot kinematics into the simulation of cold spray process. As is shown in Fig. 4, a round-trip trajectory was generated in this study by an offline programming software RobotStudio™. The predefined TCP (tool center point) speed is 150 mm/s. The trajectory has a full coverage of the substrate surface with an offset of 5 mm at the edge of the substrate, which is used to maintain the stability of TCP speed at the predefined value after each change of movement direction. By using the virtual robot system in RobotStudio™, the position and the speed of TCP that is the representation of the movement of particle impact point were obtained through trajectory simulation. The TCP speed at each point in the trajectory are shown in Fig. 4, with the color indicating its speed value. It can be found that the nozzle speed within the substrate area is well maintained at the value of 150 mm/s. By importing the position and the speed of TCP in the model as a form of interpolation, the nozzle movement was well defined by accounting its speed variation along the trajectory. Thus, the nozzle trajectory by the simulation in RobotStudio™ can be used to account the movement of heat source and mass flux of particle impact in cold spray.

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3. Experimental details In order to validate the finite element model, experimental validation was carried out by measuring the temperature history during the coating deposition process in cold spray. Coatings were fabricated by using a CGT K3000 system (LERMPS, UTBM, France). Compressed air was used as the driving gas with the pressure and the temperature at the inlet of 2.4 MPa and 360 °C, respectively. The standoff distance from the nozzle exit to the substrate surface was set as 30 mm. The round-trip nozzle trajectory as well as the nozzle traverse speed were defined as the description in previous section of nozzle trajectory. Under such conditions, the coating was obtained by repeating the nozzle trajectory 5 times. The gas-atomized pure Ni powder (Praxair Surface Technologies, Inc., U.S.A) with spherical morphology was chosen as the feedstock, while aluminum was chosen as the substrate. The powder morphology by scanning electron microscopy (SEM) as well as its size distribution is shown in Fig. 5. Microstructures of coatings were examined by optical microscope (OM, Nikon, Japan). In order to evaluate the temperature history during the coating build-up process, the surface temperature of coating was measured and simultaneously recorded by a thermal imaging camera (SC5000, FLIR Systems, U.S.A). The temperature variation at the middle point of coating surface was continuously recorded by measurement software, which enables the investigation of temperature evolution on the coating surface. The camera operating at a frequency of 10 Hz and a waveband of 2.5–5.1 μm was fixed on a tripod with a distance of about 1.0 m to the sample. 4. Results and discussion 4.1. Experimental validation Before experimental validation, a numerical validation was made to study the influence of preliminary computational domain of coating on the heat transfer with the substrate. For such purpose, two finite element analyses of the heat transfer process that does not account the transient coating build-up process was made respectively with the computational domain that includes and excludes the preliminary computational domain of coating. The trajectory of the heat source of gas flow

Fig. 4. Round-trip nozzle trajectory on the substrate surface with color indicating the nozzle traverse speed of each target point.

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Fig. 5. (a) SEM morphology and (b) size distribution of Ni particles.

out of nozzle exit was represented by the nozzle trajectory simulated by RobotStudio as given in the Section 2.4. The comparison of temperature history on the center of coating surface in the case with preliminary coating domain and substrate surface in the case without it was shown in Fig. 6. It can be seen that the preliminary coating domain has little effect on the numerical simulation of the temperature evolution and heat transfer between the substrate during cold spray. The average deviation of surface temperature between these two results is 3.47 °C. Thus, it can be confirmed that this preliminary coating domain with thickness of 50 μm that is nearly the size of particle size used in this work has little effect on the heat transfer between the gas flow and the substrate domain. The simulation results of the transient coating build-up process on substrate is shown in Fig. 7, where the contour indicates the temperature magnitude. The predefined nozzle traverse speed in this case is 150 mm/s. It can be found that the coating formation continues gradually from the top-end of substrate to the bottom with the round-trip trajectory of nozzle movement, which presents the heat source and the mass flux of the particle impact. In order to better observe the coating build-up process, a detail image of coating build-up process t = 0.1 s is given in Fig. 8. It can be seen that the computational domain of coating is gradually deformed along with the movement of nozzle, which represents the build-up process of coating. The Gaussian distribution of coating thickness as nozzle movement can also be noticed. At the meantime,

a Gaussian distributed temperature can be found at the end of assprayed coating, which is the heat source by the nozzle impacting onto the coating surface. The scanning step that is the separation between two successive nozzle pass is 2 mm in this simulation. As shown in Fig. 7, the coating deposited by each single nozzle pass can be clear observed. At the same time, with the movement of heat source and the formation of coating, the temperature at coating surface is gradually increasing. After the execution of first pass of trajectory, a thin coating can be observed in Fig. 7(d). As shown in Fig. 9, the temperature history on the central position of coating surface during its build-up obtained by numerical simulation is compared with experimental measurement by imaging infrared camera. Due to the existence of measurement lag by the thermocouple [12], the imaging infrared camera was used to collect the temperature history instead of thermocouple. The temperature evolution from simulation is simultaneously obtained at the center of coating surface as the coating build-up process. A good agreement is found to be obtained between the numerical model and experimental validation. Thus, it can be convinced that the proposed coating build-up model is well validated by the experimental results. The temperature increases rapidly from room temperature as the execution of nozzle trajectory. 5 temperature peaks can be observed in Fig. 9, which indicates that the nozzle is traversing by the central point of coating surface. Coating surface temperature decreases between two successive passes of nozzle trajectory, which is caused by the cooling effects by the ambient temperature. As the continuation of nozzle trajectory, coating surface temperature maintains around 150 °C and no further increment of temperature can be observed after three passes of trajectory. 4.2. Effect of nozzle traverse speed on temperature history

Fig. 6. Validation of the dependence of the preliminary coating domain on the heat transfer simulation without accounting transient coating build-up.

The Fig. 10 shows the temperature variation on the coating surface at different nozzle traverse speeds. It can be observed that a good agreement is obtained between the experimental and numerical results. As shown in Fig. 10, the coating surface temperature gradually increases with the movement of nozzle towards to measurement point, and then it decreases with nozzle moving away and under the cooling effect of room-temperature environment. The coating surface temperature is found to be stabilized around a value after several passes of nozzle trajectory. According to the temperature history at different nozzle traverse speeds, it can be found that maximum temperature on the coating surface decreases accordingly as the increment of the speed and the decrement of process duration. It can be considered as the decrement of heat input by the nozzle with the decrement of process duration. It is also noticed that it takes less time for the coating to reach the maximum temperature and thermal equilibrium state at higher nozzle


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Fig. 7. Transient coating build-up process during the nozzle movement with contour indicating the temperature magnitude.

traverse speed. At the speed of 50 mm/s, the coating surface temperature reaches the maximum value after one pass of the nozzle trajectory. However, it takes 2 or more passes of trajectory for the coating surface

temperature to reach the maximum value. The average temperature at the central coating surface is given in Fig. 11. It can be noticed that the average temperature at the coating surface decreases with the

Fig. 8. Detailed coating thickness build-up process with the nozzle movement at t = 0.1 s and the nozzle traverse speed of 150 mm/s.

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Fig. 9. Comparison of temperature history on the coating surface between numerical simulation and experimental measurement by imaging infrared camera. Fig. 11. Comparison of average temperature on central coating surface between experiment and simulation at different nozzle traverse speeds.

increment of nozzle traverse speed. With the further increment of nozzle speed, the average temperature is also stabilized at the value of 202 °C, which means that at a relatively high nozzle traverse speed, the coating temperature can be independent of the nozzle speed. Fig. 12 shows the coating surface temperature by infrared imaging camera after fivepass deposition as a function of nozzle traverse speed. The coating surface temperature can be found have a roughly upward trend with increasing nozzle traverse speed. 4.3. Effect of nozzle traverse speed on coating thickness Another potential influence of nozzle traverse speed is its effect on the particle deposition process and coating build-up. According to the Fig. 11, a lower nozzle traverse speed can efficiently improve the

temperature increment in the deposited coating and substrate. Thus, it is of great interests to look into the coating thickness variation at different nozzle traverse speeds. The Fig. 13 gives the relative deposition efficiency (DE) at different nozzle traverse speeds based on the coating weight at speed of 50 mm/s. It can be found the deposition efficiency decreases as the nozzle traverse speed gradually increases, which can be attributed to the decrement of substrate/coating temperature as shown in Fig. 11. According to the relative work on bonding mechanism in cold spray, the substrate with higher temperature can largely promote the thermal softening of the substrate material and decrease its elastic modulus, which can make the metal behave like viscous material [14,50]. Thus, the substrate with high temperature is beneficial to the

Fig. 10. Effects of nozzle traverse speed on the temperature variation on the coating surface: (a) 50 mm/s and 100 mm/s; (b) 150 mm/s and 200 mm/s.


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Fig. 12. Infrared images of the coating surface temperature at different nozzle traverse speed: (a) v = 50 mm/s, (b) v = 100 mm/s, (c) v = 150 mm/s, (d) v = 200 mm/s.

metallurgical bonding and mechanical interlocking [51] between particle and substrate, and further promotes the particle deposition [51,52]. By applying the relative deposition efficiency to the coating thickness model given in Eq. (2), the coating build-up process can be simulated by the proposed model that accounts the effects of nozzle traverse speed. Fig. 14 shows the comparison of average coating thickness between experiment and simulation at different nozzle traverse speeds. A satisfactory consistency is obtained between the experimental and numerical results. Meanwhile, a non-linear relationship between the nozzle traverse speed and coating thickness can be seen, which is attributed to the similar trend of relative deposition efficiency at different

Fig. 13. Relative deposition efficiency at different nozzle traverse speeds.

speeds. The average coating thickness decreases gradually with the increment of nozzle transverse speed. Fig. 15 shows the cross-sectional microstructures at different nozzle traverse speed, which shows the obvious trend of coating thickness. 5. Conclusion In this work, a 3D FEA model was developed to simulate the transient coating build-up process and the heat transfer in cold spray. The proposed model enables the study of coating thickness as well as the

Fig. 14. Comparison of average coating thickness between experiment and simulation at different nozzle traverse speeds.

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Fig. 15. Cross-sectional morphology of Ni coating at different nozzle traverse speeds: (a) v = 50 mm/s, (b) v = 100 mm/s, (c) v = 150 mm/s, (d) v = 200 mm/s.

temperature distribution under the influence of robot trajectory and different operating parameters. Meanwhile it also provides the possibilities to investigate the additive manufacturing process of samples with complex geometry by CS. By coupling the heat transfer with the ALE moving mesh and coating thickness modeling, this 3D model is able to investigate the temperature evolution of a coating which is transiently building up according to the nozzle trajectory. By assigning the results of coating thickness modeling, the simultaneous build-up of coating computational domain is achieved by ALE moving mesh method. Thus, it enables the heat transfer modeling of a transient coating build-up process. The validation of the FEA model was carried out by measuring the coating surface temperature via an infrared imaging camera during a cold spray experiment. The satisfactory agreement was found between the FEA modeling result and the experimental measurement. The effects of nozzle traverse speed on the coating surface temperature as well as coating thickness in cold spray were investigated numerically by the proposed FEA model. The coating surface temperature increases gradually with the movement of nozzle towards to measurement point, and then it decreases under moving away of nozzle and the cooling effect of room-temperature environment. According to the temperature history at different nozzle traverse speeds, it can be found that maximum temperature on the coating surface decreases accordingly as the increment of the speed and the decrement of process duration. According to the average coating thickness value at different nozzle traverse speeds, it is found that it decreases gradually with the increment of nozzle transverse speed.

Acknowledgments The authors would like to acknowledge the support by High-level Leading Talent Introduction Program of GDAS (Grants No. 2016GDASRC-0204).

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