PREDICTION OF MECHANICAL PROPERTIES OF THERMALLY SPRAYED COATINGS USING FINITE ELEMENT METHOD POUŽITÍ METODY KONE ČNÝCH PRVKŮ PRO PŘEDPOVĚĎ MECHANICKÝCH VLASTNOSTÍ ŽÁROV Ě NANÁŠENÝCH VRSTEV Mušálek R.1,2, Kovářík O.1, Matějíček, J.2

1Katedra materiálů, Fakulta jaderná a fyzikálně inženýrská, České vysoké učení technické v Praze, Česká republika Tel.: (+420) 224 358 525, radek.musalek@fjfi.cvut.cz, ondrej.kovarik@fjfi.cvut.cz 2Ústav fyziky plazmatu AV ČR, Praha, Česká republika, Tel.: (+420) 266 053 307, jmatejic@ipp.cas.cz Abstract

Feasibility of finite elemenent method (FEM) for prediction of mechanical properties of thermally sprayed

coatings was studied. First, finite element models of microstructures with idealized pores were designed. The influence of pores presence on mechanical response of the structure was evaluated. Secondly, mathematical model based on real tungsten coating microstructure was created using OOF2 software and submitted for further FEM analysis using ABAQUS CAE. Values of Young’s moduli in in-plane and out-of plane directions were estimated. The predictions are compared to the experimental data.

Keywords: thermal spray, finite element method (FEM), OOF2.

INTRODUCTION

During thermal spraying process, particle feedstock is melted and accelerated in the flame (generated e. g. by plasma torch). After impact on the substrate, molten or semimolten particles form so called splats. Resulting structure is highly anisotropic and consists of splats, pores, cracks and resolidified or unmolten particles. High temperatures in the plasma jet enable melting of materials such as ceramics or refractories. Using this technique, corrosion or wear protective surface layers or thermal barrier coating (TBCs) can be formed on the substrate.

Existence of pores and cracks in the microstructure can be both beneficial and detrimental. For example, plasma sprayed ceramics can be more deformable thanks to the sliding of the splats than bulk material. Also, appropriately oriented pores can enhance TBC properties, such as thermal conductivity and thermal shock resistance. On the other hand pores and cracks affect the stiffness of the coating and can decrease value of the Young’s modulus or can lead to premature failure of the coating. Therefore the role of pores and cracks should be carefully studied.

Several analytical [e.g. 1,2,3] and numerical [e.g. 3,4] models were proposed to predict influence of the pores on the coating properties. Significant benefit of the finite element method is that not only overall porosity but also the actual shape and orientation of the pores can be considered. FEM method was already used on thermally sprayed coatings for prediction of thermal properties [5,6]. In this study, 2D FEM model was designed to predict mechanical response of the coating to mechanical loading.

Since thermally sprayed coatings are believed to be transversely isotropic, elastic moduli for models with rectangular and realistic pores estimated in both spraying direction (“out-of-plane” E22) and in one transverse direction (“in-plane” E11) were evaluated.

EXPERIMENTAL PROCEDURE

In the first step, feasibility of the FEM prediction was studied on idealized round pores to verify their influence on the effective property of the microstructure. Several models with different overall porosity were created in Abaqus CAE version 6.6-1. Each model consisted of 20 circular pores with the same radii randomly distributed in the matrix with Young’s modulus E = 1 GPa and Poisson’s ratio µ = 0.28. The overall porosity of each microstructure was set by the change of pore radii. Thanks to the choice of matrix modulus, resulting effective modulus can be comprehended as relative modulus characteristic for the given porosity. The microstructure was then virtually loaded by prescribed boundary conditions (see fig 1.). Along the left edge of the model, displacement in the loading direction was prescribed u1 = 0. At the left bottom corner displacement in the perpendicular direction u2 = 0 was prescribed. Along the right edge displacement in the loading direction u1 corresponding to the overall strain ε11 = 1 % was prescribed. This strain level approximates a typical loading of the thermally sprayed material during 4 point bending test [7].

Approximately 60000 2D plane stress elements CPS4R were used in the idealized models. All models were elastic and considering static equilibrium. Response of the microstructure to the loading was characterized by the reaction forces RF1i in the nodes along the edge with prescribed displacement. Then the effective modulus can be then easily calculated using the formula:

S

RFE i

i

11

1

11 ε

∑= ,

where S is the cross-section of the model (unity thickness is considered in 2D model). Since round pores are symmetric, the elastic moduli in the transverse direction were not evaluated for the models with round pores (see fig. 2).

Fig. 1 – Loading schema used in models. Area dimensions 256x256 pixels relative units.

In the next step, models with rectangular pores were created. For the models with rectangular pores, the

number of pores varied so that overall porosity varied from 0 to 4 %. Two sets of pore dimensions (width:height = 40:1 and 10:1) were considered (see fig. 3). For given number of pores porosity was the same to study effect of pores dimensions on the effective modulus of the microstructure.

As the last step, models based on realistic microstructure were created. Thermally sprayed tungsten coating was chosen for the analysis. The coating was deposited at CREPE, Univeristé de Sherbooke, Quebec, Canada during experimental program described in [8]. Inductively coupled plasma torch Tekna PL-50 operated at 370 kHz installed in a vacuum chamber with automatic pressure regulator was used. The spraying was performed under the following process conditions: plate power P = 80 kW, carrier gas flow rate, qc = 6.3 slpm (standard litres per minute) of He and chamber pressure p = 300 torr. Ar-H2 plasma was used with a central Ar flow rate of 30 slpm, sheath Ar at 90 slpm, and sheath H2 at 15 slpm. The feed rate for the W powder was set at 40 g/min, to provide sufficient throughput to represent potential industrial applications. The coating was deposited on water cooled 304L stainless steel substrate of dimensions 220 mm x 25.4 mm x 17 mm. Mean substrate temperature was 429 oC as measured by Raytek Thermalert TX pyrometer. Details of specimen deposition are given in [8].

Coating microstructure was observed optically on both longitudinal cross-section of the coating. The specimens were electrolytically polished (20 V for 10 s) in a 1.25 % KOH solution. The micromorphology of the coating was observed using JEOL JSM-5510 (JEOL, Osaka, Japan) scanning electron microscope operated in backscattered electron mode (see fig. 5).

"In-plane elastic modulus" of the deposit was measured using four-point bending apparatus on Instron 1362 electro-mechanical testing machine. The apparatus and force/displacement data processing are described elsewhere [7]. The rate of displacement was 0.0063 mm/sec, and maximum loads varied between 100 and 480 N.

In the obtained microstructure, 5 minor areas (640 x 640 pixels ~ 213,3 x 213,3 µm) were considered to study

the possible variability of the FEM method. Images were binarized using ImageJ software [9]. Resulting pores were expanded by 2 pixels so that the pore boundaries were detectable during the mesh generation and to compensate the disregard of thin pores during binarization of the input image. The mesh of finite elements was generated on binarized images using software OOF2 version 2.0.3 [10] with automeshing procedure (Min. size = 5 pixels, Max. size = 20 pixels, Homogenity = 0.9). The generated mesh was exported to Abaqus CAE software for further analysis. This process resulted in meshes with linear triangle and rectangle elements (CPS3 and CPS4 type). Elements representing splat material were prescribed Young’s modulus E = 400 GPa and Poisson’s ratio µ = 0.28. Elements representing pores were removed from the mesh. The subsequent steps of the FEM analysis are illustrated in fig. 6. For more details on OOF procedures, see [6,10,11,12].

Further procedure was the same as for the model with idealized round pores to estimate “in-plane modulus” E11. By rotating the boundary conditions by 90 degrees counterclockwise, elastic response in transverse direction and “out-of-plane modulus” E22 were evaluated.

a) model of randomly placed round pores b) von Mises stress field Fig. 2 – a) Example of idealized microstructure with random circular pores. b) von Mises stress field influenced by pores. Loading mode according to the arrows.

a) in-plane loading b) out-of-plane loading Fig. 3 – Example of stress component in horizontal (S11) and vertical (S22) direction in the vicinity of the pores for idealized structures with rectangular pores and overall porosity 2.5 %. Two sets of pores (width:height 10:1 and 40:1 respectively) are shown. Loading according to the arrows. Note, that the model is elastic with anisotropic material (Young’s modulus set to 1 GPa).

4400::11

1100::11

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10Porosity [%]

ER

[1]

Symmetric circular pores

Rectangular pores 40:1 - in-plane

Rectangular pores 40:1 - out-of-plane

Rectangular pores 10:1 - in-plane

Rectangular pores 10:1 - out-of-plane

10:1

40:1

Fig. 4 – Simulated relative modulus against porosity for round pores and for rectangular pores with different ratios of width:height (10:1 and 40:1).

Fig. 5 – Cross-section of tungsten coating specimen. Highlighted areas (213,3 x 213,3 µm) considered for FEM analysis. Differences in contrast are given by the fact, that this image was merged from 6 images.

a) Real microstructure

b) ImageJ - binarization

c) ImageJ – morfolog. operations

d) OOF2 - meshing e) ABAQUS - solving

f) ABAQUS – postprocessing

Fig. 6 - Steps of the FEM analysis for area 1 from fig. 3.

11 22 33 44 55

Table 1 – Parameters and results of the FEM analysis for the realistic microstructure.

ImageJ – Image analysis OOF2 – Automesh ABAQUS – Model

Area Original porosity [%]

Porosity after pores expansion [%]

Number of elements [1]

E11 [GPa] (in-plane)

E22 [GPa] (out-of-plane)

E11/E22

1 5.66 15.29 17339 166.3 5.5 30.4 2 3.10 11.38 15712 253.5 40.9 6.2 3 4.10 12.06 14940 226.7 16.3 13.9 4 5.42 13.12 13926 221.9 0.0 -

5 5.98 13.06 13304 170.0 11.2 15.1

Average 4.85 12.98 15044 207.7 14.8 16.4

Note: Areas numbering according to fig. 3.

CONCLUSIONS

For the case of idealized microstructures, examples of the resulting stress fields near the pores are shown in fig. 2 and 3. As expected, peak of stress level is higher when the microstructure is loaded perpendicularly to the main pore axis compared to the parallel loading (circa 4 times for case of 40:1 width:height ratio).

Resulting values of simulated relative modulus for models with idealized pores are plotted in fig. 4. It is obvious from the plot that the models meet expectations – with increasing porosity level, relative modulus decreases. This effect is pronounced for the rectangular pores oriented perpendicularly to the loading direction and significantly rises with increasing width:height ratio.

Simulated elastic moduli in both considered directions for model of real tungsten microstructure are given in table 1. Significant scatter in the results was observed, but the average value of in-plane elastic modulus E11 is comparable to the experimental value obtained from the 4 point bending test (E4P = 179 GPa) and from measurement of change in sample curvature during cooling after the coating deposition (Ecurvature = 185 GPa). The presented method also provides an estimate of the elastic moduli in the transversal direction E22 = 14.8 GPa. So far, no experimental data are available for comparison.

It has been observed that the simulated values of elastic moduli are quite sensitive to the choice of representative volume element (RVE) of the material [13]. For example prediction of E22 = 0 GPa for area 3 is due to the extensive horizontal pore dividing the considered area into 2 unconnected parts and thus reducing stiffness of the system in the spraying direction to zero. It seems to be reasonable for the dimensions of the RVE for thermally sprayed coatings to be at least 10 times bigger than the typical length of the pore. Also, a representative number of the splat junctions should be incorporated in the structure model.

The FEM method can give us also some idea about the strain field in the microstructure as well as predict locations, where the stress is concentrated. We can expect that in reality the first cracks initiation or plastic deformation will occur at such locations.

In the simulation, only significant pores or cracks are taken into account. No mutual sliding of the pores, friction between the interfaces nor the crack evolution is considered. On the other hand, this approach considers not only overall porosity level or average orientation of the pores, but it reflects real pores morphology (i. e. dimensions, shape, orientation, mutual position, etc.).

Although relatively simple plane stress 2D model is considered here, creation of 3D model is also feasible [14]. However, the creation of the representative 3D microstructure (e. g. by subsequent cross-sectioning process) is in case of the thermally sprayed materials time-consuming and still some strict restrictive assumptions on microstructure must be made (e. g. pores are represented by polygons, small pores and cracks are apt to be neglected etc.).

The applied method is relatively easy to use and is not limited to the thermally sprayed coatings but can be helpful in case of different cases of multiphase structures, composites or porous media. Another benefit is, that once the mesh is generated, thermal properties of the structure can be also estimated [5].

Even though the agreement of predicted and experimental value of Young’s modulus is significant in this particular presented case, it should be stated, that the aim of the method is not to provide exact predictions of the material properties, but to help to design and compare the structures with most desirable properties for considered application.

REFERENCES [1] I. Sevostianov, M. Kachanov, Materials Science and Engineering A297 (2000) 235-243. [2] F. Kroupa, Journal of Thermal Spray Technology 16(1) (2007) 84-95. [3] S. Zhan, International. Journal of Solids and Structures 36 (1999) 3735-3753. [3] Y. Huang et al., International. Journal of Solids and Structures 33 (1996) 1575-1586. [4] L. Shen, International. Journal of Solids and Structures 41 (2004) 7471-7492. [5] Y. Tan et al., Proceedings of the 2006 Int. Thermal Spray Conference, Seattle, USA, 2006. [6] Z. Wang, Acta Materialia 51 (2003) 5319-5334. [7] V. Harok, K. Neufuss, Journal of Thermal Spray Technology 10(1) (2001) 126-132. [8] O. Kovářík et al., Proceedings of the 2006 Int. Thermal Spray Conference, Beijing, China, 2007. [9] http://rsbweb.nih.gov/ij/ [10] http://www.ctcms.nist.gov/oof/oof2/ [11] S. Langer, Computing in Science and Engineering May/June (2001). [12] N. Chawla et al., Materials Characterization 49 (2003) 395– 407. [13] Z.-Y. Ren, Mechanics of Materials 36 (2004) 1217–1229. [14] P. Ctibor, Materials Characterization 56 (2006) 297–304.

ACKNOWLEDGEMENT This work was supported by the internal grant project (IGS) of Czech Technical University in Prague. Partial

financial support from Czech Ministry of Education, Youth and Sports through grant no. ME901 as well as fruitful discussions with Dr. Yang Tan from the Center for Thermal Spray Research at Stony Brook University, NY, USA are also gratefully acknowledged.