Experimental study and numerical simulation of the indentation test of a coating prepared by thermal spraying before and after annealing treatment

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1 ème Congrès Français de Mécanique Bordeaux, 6 au 0 août 0 Experimental study and numerical simulation of the indentation test of a coating prepared by thermal spraying before and after annealing treatment Y. FIZI, Y. MEBDOUA, S. DJERAF and R. LAKHDARI Centre de Développement des Technologies Avancées, 0 Août 96 Baba Hassen 60 ALGER Résumé : Cette étude présente l'essai de l indentation instrumentée d'un revêtement déposé par projection thermique. Ce test est effectué sur des dépôts d acier inoxydable avec et sans recuit. La courbe charge-déplacement mesurée expérimentalement est comparée avec celle obtenue à partir de la simulation par éléments finis du processus de l indentation à l'aide du logiciel ABAQUS. Les résultats numériques de ce test, avant et après recuit, sont comparés aux résultats expérimentaux, un bon accord est surtout observé dans le cas des dépôts n ayant pas subis de traitement thermique. Abstract This study presents the instrumented indentation test of an arc sprayed stainless steel coating. Annealed and not annealed specimens were tested. The experimental load-displacement curves are compared to the numerical results obtained from finite element simulation of the indentation process using ABAQUS software. The simulation results of annealed and not annealed specimens are compared to the experimental ones, a good agreement is observed in the case of coating without annealing treatment. Keywords: Thermal spray, indentation, coating, simulation, mechanical behavior, annealing. Introduction The arc spraying process is a well-established technology due to its low operating and experiment costs, high deposit rate and its applicability to treat large structures. Arc sprayed coatings can be used to protect components parts of machines against corrosion and wear. This latter relies on mechanical properties of these coatings especially hardness and yield modulus []. The thermal sprayed stainless steel coating is a good candidate for corrosion protection as a cathodic-stainless steel coating, and increasing wear resistance in slight conditions such as shaft pumps and textile rolls []. The high temperature of the arc melts the wire tips and compressed air is generally used to atomize the molten tips and propel the droplets towards the substrate. The coating service performances are closely linked to the coating mechanical state which depends on the coating microstructure, mechanical properties and internal residual stresses developed during the spray process. The stacking of the deposited splats induces a lamellar structure with high rate of porosity and oxide content yielding coatings with different properties compared to the bulk material with different methods of properties evaluation. Numerous works were aimed to measure thermal spray coating properties by instrumented indentation [-6]. This method provides significant information on mechanical properties of thermal sprayed coatings. In this method, a hard tip of known geometry is applied perpendicular to the surface of the tested material, the depth of the penetration h is continuously followed taking into account the applied load. A characteristic curve penetration-strength is obtained for both loading and unloading penetrator, as shown in figure (). This is different from conventional indentation which cannot take into account, a possible relaxation of the material and measures only the plastic deformation from residual indentation imprints. The analysis of the curve force-penetration issued by instrumented indentation makes use analytical models such as that of Oliver and Pharr [7], which allows the determination of the hardness and elastic modulus of the

2 ème Congrès Français de Mécanique Bordeaux, 6 au 0 août 0 material and identify their elasto-plastic behavior. The recording of the normal load F z according to the displacement of the indenter point h allows the calculation of the stiffness S and the projected contact area A p. The stiffness S is the slope of the discharge curve at the top (Fig.). It is given by the following equation [8-0]: S df dh z () h h max Where F zmax is the maximum load of indentation, h is the displacement of the tip of the indenter, A p is the projected contact area, S (df Z / dh) is the contact stiffness, FIG. Load-displacement curve [8] Hardness H and elastic modulus E are in fact derived from the analysis of the load-displacement curves (F z -h) (Fig. ) with reference to the following equations [9]: H F A z max () p For a Vickers indenter, the relationship between the projected area A p of the indentation and the distance h c (the contact depth) is given by[9]: Thus: A p,0 h () c dfz, S h h h max c E () r dh The displacement h c is found from the intersection of the linear unloading curve with the displacement axis (Figure ).The quantity E r combines the modulus of the indenter E i and the that of the specimen E, it is given by []: r E E E i () i where ν, is the Poisson's ratio of the indented material, and E r their elastic modulus. E i and ν i are respectively the elastic modulus and Poisson's ratio of the tip of the indenter. This method provides E and H from the load displacement curve. However, several effects could take place leading to deviations in the measured mechanical properties. One possibility to solve these problems is to consider equations () as a linear relationship between F zmax and A p where the hardness is the slope. Similarly, equation () represents a linear relationship between S and A p / where the slope is proportional to the reduced

ème Congrès Français de Mécanique Bordeaux, 6 au 0 août 0 modulus, E r. These relationships will provide an approach to estimate E and H from several tests carried out at different loads [,].

Some researchers have studied the process after the removal of the indenter load, using the numerical approach of the finite element method [,6].

So far, the verification of the finite element method could be an effective tool to simulate hardness measurements.

and finite element modeling using ABQUS software. Behavior modeling is performed in order to optimize the studied material plastic law.

3 ème Congrès Français de Mécanique Bordeaux, 6 au 0 août 0 modulus, E r. These relationships will provide an approach to estimate E and H from several tests carried out at different loads [,]. Recently, various numerical techniques have been developed that can be used in problems of indentation. Some researchers have studied the process after the removal of the indenter load, using the numerical approach of the finite element method [,6]. An early example of comparison between finite element analysis and experimental results were proposed by Bathyscaphe Nix [7] in which they simulated a submicron indentation test. So far, the verification of the finite element method could be an effective tool to simulate hardness measurements. The focus of this article is the application of a method to identify the mechanical properties (elastic and inelastic) of an arc-sprayed coating with the help of instrumented indentation technique and finite element modeling using ABQUS software. Behavior modeling is performed in order to optimize the studied material plastic law. Materials and experimental techniques In this study, a twin wire arc spray facility (ARCSPRAY Metallization Company) was employed to spray stainless steel material (AISI 0) on grit blasted and cleaned steel substrate (C). The thickness of coating was measured by profile projector (MP0) with a magnification of 0X in different positions in the sample. The calculated value is the average of ten measurements, it is about 77,μm. The instrumented indentation test is carried out using a durometer brand Zwick / Roell, equipped with a Vickers diamond tip of pyramidal shape with four faces. The applied load is N with a holding time of s and loading rate indentation of 0. mm / min. The set of experiment indentation was performed in the coating zone of the polished cross section of the sample (Fig. ). Test leads the load-displacement curve. Coating d=6. µm d=9. µm a) d c) d) b) d FIG. a) Schematic of a Vickers or diamond pyramid hardness indenter, b) face of the cross section of the sample, c) coating zone in front of the cross section, d) processing image. The numerical simulations (D axisymmetric) were performed using the ABAQUS software. Due to the axisymmetric character of pyramid- shaped indentation process, the problem was analyzed in a two dimensional axisymmetric. The specimen was meshed with a total of 76 axisymmetric elements; its density is very important around the indenter and decreases progressively away from the indenter. This allows our discretization to increase the accuracy and reduce the calculation time, while the indenter was considered as infinitely rigid, it is set at an angle of 68 o and a reference point considered along the loading point. The contact between the indenter and the material is assumed to be perfect and without friction. Materials modeled are supposed isotropic and the behavior is elasto-plastic type, and assuming that the Poisson's ratio of stainless steel (0) deposit is 0.. An optimization processes allowed to determine a bi-linear plastic law in good agreement with the experimental data. The simulation results are compared to the experimental ones measured by instrumented indentation of the coating before and after annealing. Results and Discussions

Load (N) ème Congrès Français de Mécanique Bordeaux, 6 au 0 août 0 Figure (a) presents simulated and experimental load-displacement curves of the coating before annealing treatment, whereas figure

This discrepancy can be attributed to the approximations made in the test simulation such as perfect indenter, isotropic material, and neglected friction at the contact.

4 Load (N) ème Congrès Français de Mécanique Bordeaux, 6 au 0 août 0 Figure (a) presents simulated and experimental load-displacement curves of the coating before annealing treatment, whereas figure (b) shows the numerical stress distribution for loading and unloading phases in the coating. A difference between simulated curve and experimental one is observed during loading phase. This discrepancy can be attributed to the approximations made in the test simulation such as perfect indenter, isotropic material, and neglected friction at the contact. During the unloading phase, the experimental and simulated curves coincide. Elastic behavior of indented material was explored from the results of finite element simulations. The figure -b shows the stress distribution of penetration of the indenter (microns) into the indented material, at the end of phase loading and unloading. There is a strong stress concentration at the edge of the indenter and we also observe a permanent deformation after the unloading phase of the indenter. 6 a) b) experiment simulation Loading Unloading Displacement FIG. a) Comparison of simulated and measured load-displacement curves of stainless steel coating, b) Numerical stress distribution for the loading and unloading phases. Mechanical properties (Young's modulus and hardness) deduced from the experiment curves, referring to equations () and () are given in Table.The material hardness and Young's modulus covered is 8, Hv 0, and,7 GPa, respectively. Table. Mechanical properties measured from the experimental load-displacement curve, stainless steel coating without annealing treatment. Mechanical properties Experimental results h min 8,07 h max 8,8 F max (N),0 E r 6,0 E,7 Hv 0, 8, Figure shows the experimental and simulated indentation curves (force - displacement) of annealed stainless steel coating at 80 C for 0 min followed by cooling in air. A difference between the simulated and experimental curve is observed. The maximum load applied in the test of the indentation (N) is not reached in the simulated curve; this is due to the introduced mechanical properties into the software ABAQUS to simulate the plastic behavior of 0 stainless steel coating. This offset can be adjusted by varying this value until the superposition of the curve simulated with the experimental curve. It is also observed that the distribution of the residual stress after unloading is more pronounced as compared to that observed on the sample before annealing; figure (.b) shows a permanent deformation after the discharge phase of the indenter. Figure and Table, show a decrease in the coating hardness from, Hv 0, to 7,6 Hv 0,, for annealed specimen at 80 C for 0 min followed by cooling in air. This decrease is due to relaxation of residual stresses allowing a recrystallization and coalescence of the grains. The coating which has not undergone annealing treatment has a hard structure with small grains due to a rapid cooling of the droplets. This results in compressive residual stresses in the coating, inducing an increase in hardness and a decrease in toughness. For annealed coating, the decrease in coating hardness could be compromised with their improved toughness and

Load (N) Load (N) ème Congrès Français de Mécanique Bordeaux, 6 au 0 août 0 decrease of porosity rate. The Young's modulus, increases from,7 GPa before treatment to 9, 97 GPa after annealing [,].

a) Comparison of load-displacement curve calculated and measured after heat treatment, b) Numerical stress distribution for the loading and unloading phases. Table.

5 Load (N) Load (N) ème Congrès Français de Mécanique Bordeaux, 6 au 0 août 0 decrease of porosity rate. The Young's modulus, increases from,7 GPa before treatment to 9, 97 GPa after annealing [,]. a) Experiment Simulation b) Loading Unloading Displacement FIG. a) Comparison of load-displacement curve calculated and measured after heat treatment, b) Numerical stress distribution for the loading and unloading phases. Table. Mechanical properties of the experimental load-displacement curve with and without annealing treatment. Mechanical properties without annealing treatment h min 8,07 h max 8,8 F max (N),0 E r 6,0 E,7 Hv 0, 8, ±0 after annealing treatment 0,6,8,0 90,0 9,97 7,6±7 Before annealing treatment After annealing treatment Displacement FIG. Comparison of load-displacement curve measured before and after annealing In our calculations a qualitative consistency between the calculated and measured load-displacement curves is observed, quantitatively, there is a difference with regarding the unloading phase for the second test. This can be explained by the fact that our optimization is based on a maximum load of N. The determination of the material behavior, yield point and the coordinates (σ i = - ; ɛ i = - ) are optimized for the first test and the results show a good agreement. After sample annealing, the material mechanical properties change and the optimization of plastic properties becomes more difficult. It is necessary to use an optimization method such as the inverse

6 ème Congrès Français de Mécanique Bordeaux, 6 au 0 août 0 analysis method [9-0] which allows more accurate optimization in order to determine the parameters involved in the constitutive law. Table reports the difference between calculated and measured result. Table. Difference between calculated and measured results Test Before annealing treatment After annealing treatment Difference ( ) Loading 7.98 Unloading 0.7 Loading. Unloading.0 Conclusion The use of instrumented indentation device was used to determine the mechanical properties of the arc sprayed 0 stainless steel coating, namely, hardness and Young's modulus. The comparison between the numerical curve and the experimental one shows a good agreement before annealing treatment, due to the fact that the slope of unloading the experimental curve is in good agreement with that of the calculated curve using ABAQUS software. Annealing treatment of 0 stainless steel coating at 80 C for 0 min followed by cooling in air, leads to a decrease in hardness and this could be compromised with their improved toughness and decrease in the rate porosity. References [] R. J. K. Wood and Manish Roy, Tribology of Thermal-Sprayed Coatings Surface Engineering for Enhanced Performance against Wear 0, pp - [] Spraying, A.W.S.C.O.T. and A.W.S.T.A. Committee, Thermal Spraying: Practice, Theory, and Application98: American Welding Society. [] Dina Goldbaum and al, Mechanical behavior of Ti cold spray coatings determined by a multi-scale indentation method,materials Science and Engineering A 0 (0) 6 [] W.G. Mao and al Evaluation of microhardness, fracture toughness and residual stress in a thermal barrier coating system: A modified Vickers indentation technique [] Salmon M. Kalkhoran and al Estimation of plastic anisotropy in Ni % Al coatings via spherical indentation, Acta Materialia 60 (0) [6] A. Rico, J and al Mechanical properties of thermal barrier coatings after isothermal oxidation. Depth sensing indentation analysis Surface & Coatings Technology 0 (009) 07 [7] OliverW.C., PharrG.M., J. Mater. Res. 7, n 6, 6,99. [8] Fischer-Cripps, Nanoindentation, third edition, Springer Science+Business Media, p. 6-7, 0. [9] Anthony C., Cripps F., Nanoindentation, third edition, Springer Science+Business Media, p. -7, 0. [0] Dao et al. ActaMaterialia, 9 (9), , 00. [] GiannakopoulosA.E., Suresh S.,Scripta Mater, 0(0), 9-98, 999. [] Pelletier H., Tribology International, 9, 9-606, 006. [] J. Rodríguez, A. Rico, E. Otero, W.M. Rainforth, Acta Mater.0, 0, 009 [] A. Rico, M.A. Garrido, J. Rodríguez, Bol. Soc. Esp. Ceram. V. 7. 0, 008 [] SunY., BellT., ZhangS., Finite Element Analysis of the Critical Ratio of CoatingThickness to Indentation Depth for Coating PropertyMeasurement by Nanoindentation, Thin Solid Films, Vol. 8, 98-0, 99. [6] KnappJ.A., FollstaedtD.M., MyersS. M., Barbour J.Cand FriedmannT.A., Finite-Element Modeling of Nanindentation, J. Applied Physics, Vol. 8, 60-7, 999. [7] BhattacharyaA.K., NixW.D., Int. J. Solids Struct., Vol., 88, 988. [8] DavisJ. R., A.I.T.S. S.T.,Handbook of Thermal Spray Technology, ASM International,00. [9] W.Tillmann, et al, Journal of thermal spray technology, July 8, 00. [0] J. Jiang, P. Nylén, Object-oriented finte element analysis to simulate microindentation of thermal sprayed Max-phase Coatings. International conference on computer modeling and simulation,

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