Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials Design and ... Finite element analysis of residual stress in plasma-sprayed ceramic coatings ...... 18 Perry, A. J., Sue, J. A. and Martin, P. J. Practical measure-.
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Finite element analysis of residual stress in plasma-sprayed ceramic coatings T Valente, C Bartuli, M Sebastiani and F Casadei Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials Design and Applications 2004 218: 321 DOI: 10.1177/146442070421800406 The online version of this article can be found at: http://pil.sagepub.com/content/218/4/321
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Finite element analysis of residual stress in plasma-sprayed ceramic coatings T Valente1, C Bartuli1 , M Sebastiani1 and F Casadei2 1 Department of Chemical and Materials Engineering, University of Rome ‘La Sapienza’, Rome, Italy 2 Centro Sviluppo Materiali Spa, Rome, Italy
Abstract: A numerical study was carried out by finite element analysis (FEA) for the calculation of absolute values and through-thickness variation of residual stress originating in thermal spray coatings. The investigated deposit was an air plasma sprayed alumina coating sprayed on a carbon steel substrate previously coated with Ni20Al bond coat. Results show compressive residual in-plane stresses with linear through-thickness variation and tensile normal and shear stresses having a peak at the coating – substrate interface. The influence of deposition temperature on residual stress was also investigated. The experimental validation of the FEA model was carried out using a high-speed hole drilling technique, suitably adapted for the analysis of a multimaterial structure through FEA calculation of the required calibration coefficients. A very good agreement between simulated and measured stresses was obtained, inspite of the adopted simplification hypothesis. Keywords:
1
residual stress, plasma spray, ceramic coating, finite element, hole drilling
INTRODUCTION
Residual stresses originating within thermal sprayed coatings in different stages of their production process can strongly affect their mechanical properties and therefore play a key role in their functionality and in the lifetime of coated components. Thus, it is important to understand the evolution of the stresses during the coating process and to investigate the influence of processing parameters on their absolute value and spatial distribution. In particular, residual stresses are known to depend firstly on the deposition temperature and secondly on particle temperature and velocity, on deposition rate and, most importantly, on coating thickness [1 – 3]. They also have a fundamental influence on coating structure and substrate – coating adhesion, thus strongly affecting deposit performance in working conditions. Different experimental techniques are available nowadays for their direct measurement or indirect evaluation [4– 10], such as X-ray or neutron diffraction methods, curvature measurements, high-speed hole drilling techniques and metallurgical and layer removal methods. However, numerical modelling tools [11, 12] offering reliable The MS was received on 6 February 2004 and was accepted after revision for publication on 15 June 2004. Corresponding author: Department of Chemical and Materials Engineering, University of Rome ‘La Sapienza’, Via Eudossiana 18, 00184 Rome, Italy.
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predictions of the mechanical properties of a selected substrate – coating system on the basis of the operating conditions of the manufacturing process are of even greater importance, assisting processing parameter optimization procedures, saving time and reducing the economic impact of the trial and error approach. Residual stress evaluation for plasma-sprayed coatings by finite element analysis (FEA) is a complex problem owing to the relevant number of processing parameters involved which can result in non-independent sources of stress contributing to the final state. Such stresses are generally classified as ‘quenching stresses’ and ‘DTC stresses’, originating from differential thermal contractions. Quenching stresses [13 –15] arise from impact, spreading and solidification of each molten particle (at temperature Tm) on the substrate surface. They are always tensile and can be, in principle, approximately estimated by the following equation Tðm
s0 ¼ E0
ac (T) dT
(1)
Ts
where Tm is the coating melting temperature, Ts is the substrate temperature and ac is the coating thermal expansion coefficient. Several sources of error, however, can affect equation (1), usually giving results that do not match experimental data Proc. Instn Mech. Engrs Vol. 218 Part L: J. Materials: Design and Applications
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with good accuracy [13]; among the most important, two need to be mentioned: 1. Young’s modulus of sprayed materials is very different from the elastic modulus of the corresponding bulk materials (with values of the Ec/Eb ratio as low as 1/ 10), mainly as a consequence of coating porosity and lamellar microstructure. 2. Stress relaxation phenomena [13] (creep and yielding for metals, microcracking for ceramics) can be responsible for a remarkable decrease in the final value of quenching stress. In the case of metallic materials, equation (1) can thus be modified as follows
sq ¼
Ec
bð Tm
ar (T) dT
(2)
Ts
where Ec is the actual elastic modulus of the coating, as determined by experimental measurements, and b is a temperature reduction coefficient (approximately equal to about 0.6) adopted to take into account stress relaxation phenomena such as yielding or creep. On the other hand, for ceramic-based coatings, a very marked reduction in quenching stress has also been observed [1, 16, 17], produced as a consequence of extensive microcracking of individual lamellae after droplet impact. As an example, a residual tensile stress of about 10 MPa can be experimentally evaluated by in situ curvature measurements for plasma-sprayed alumina [13], while quenching stresses of the order of GPa would be obtained simply by applying equation (1). This aspect simplifies the numerical evaluation of the total stress generated within ceramic coatings, and the contribution of quenching stresses can be taken into account simply by superimposing a uniform tensile stress, typically in the range 10 –15 MPa, to the thermally induced stress fields [13]. This last source of stress results from misfit strains generated by differential thermal contractions (DTCs) [15, 18] caused by thermal expansion coefficient (CTE) mismatch between coating and substrate; in particular, DTC stresses are induced during the final cooling stage from processing temperature, Ts, to room temperature, Tr. The equation correlating these misfit strains to the thermal properties of the substrate and coating is as follows T ðs D1 ¼ ½ac (T) as (T) dT
where nc is Poisson’s ratio of the coating. Equation (4) shows that, for ac , as compressive thermal stresses arise in the coating owing to final cooling after spraying. Moreover, the CTE is a function of temperature, so that thermal stresses can also arise within individual layers if through-thickness thermal gradients are originated. This is generally the case when the heat flux generated by the plasma torch is repeatedly transferred to the substrate and to the deposited layers during coating build-up. Although complex interactions between coexisting residual stresses of various sources can be generally expected, a sufficiently reliable prediction model can be developed for qualitative stress estimation and preliminary process optimization by adopting realistic simplification hypotheses. The following assumptions are proposed: 1. The coating thickness is negligible compared with the substrate thickness. 2. Spraying is carried out in constant substrate temperature conditions (Ts ). 3. The sprayed deposit is instantly quenched to Ts. 4. The substrate – deposit couple remains isothermal as it cools down to room temperature. 5. The mechanical behaviour of the coating material is linear elastic in the cooling range. 6. Interface bonding between the deposit and the substrate is perfect. On the basis of the above simplifications, the final residual stress state can be expressed as the sum of quenching stresses, sq and DTC stresses, sth
sr ¼ sq þ sth
(5)
The aim of the present study is to evaluate, by using finite element analysis (FEA) [11, 14, 19, 20], average values and spatial distributions of DTC stresses in thermal sprayed ceramic coatings. Experimental validation of the model was carried out using a suitable implementation of the incremental hole drilling method [21], adapted to the analysis of plasma-sprayed deposits by developing a further FEA model for the calculation of calibration coefficients [22 – 24]. Both FEA simulation and experimental measurements were carried out for commercialy pure alumina coatings deposited by air plasma spraying (APS) onto AISI 4037 carbon steel substrates previously coated with a Ni20Al bonding layer.
(3) 2
Tr
where as is the coefficient of thermal expansion of the substrate. Starting from equation (3), residual stress can be evaluated, in the case of linear elastic material behaviour, simply by applying the well-known Hooke’s law T ðs Er sth ¼ ½ac (T) as (T) dT 1 nc
(4)
Tr
FINITE ELEMENT MODELLING
The developed model was implemented using ANSYSw 7.0 software. The complexity of the analytical process made it expedient to carry out the modelling procedure in two consecutive steps: 1. In the first analytical step the aim was to simulate the thermal history of the coating during spraying, in order to calculate the effective deposition temperature of each layer.
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FINITE ELEMENT ANALYSIS OF RESIDUAL STRESS IN PLASMA-SPRAYED CERAMIC COATINGS
2. In the second step a structural analysis was performed to estimate the residual stresses by applying the boundary thermal conditions obtained from the previous step, and by further implementing the final cooling phase. 2.1
The thermal flux, q_ , transferred to the substrate (or to the coating/substrate system) can be expressed as a function of the heat exchange coefficient, h (obtained for calculated Reynolds numbers in the range 1500 – 40 500) by the following equation
Thermal history
In a thermal spray process a source of thermal and kinetic energy is used to melt and accelerate the starting powders towards a solid substrate where successive layers are deposited. In the case of the APS deposition technique, a high energy density plasma is generated electrically within the spraying torch. The heat flux generated by each pass of the torch was estimated by a numerical analysis procedure based on a proprietary one-dimensional Fortran code. Among other features, the analysis requires the calculation of the heat exchange coefficient between the plasma jet and the substrate, starting from the plasma processing parameters. To this end, the Holger approach [25] was adopted, based on the equation Nu ¼
D 1 1:1(D=r) hD Pr 0:42 F(Re) ¼ r 1 þ 0:1((H=D) 6)(D=r) K
q_ ¼ h(Tg Ts ) ¼ K
@T @x
where D ¼ nozzle diameter H ¼ torch–substrate distance cpg mg Pr ¼ (Prandtl number) kg cpg ¼ specific heat of the plasma gas
(7)
where Ts is the temperature of the substrate or the substrate/ coating system and x is the distance from the substrate. As an example, in the case of air plasma spray with a nozzle diameter of 6 mm, for a power input of 40 kW, a plasma gas mixture flowrate of 50 standard liters per minute (slpm) Ar þ 12 slpm H2 and a spraying distance of 115 mm, a heat flux of 283 kW/m2 (Fig. 1) with a spot area of 25 25 mm2 was estimated. The total heat flux released by the substrate, q_ out , in the ordinary temperature range for a spraying process can be considered as the sum of a convection and a radiation term q_ out ¼ k1 (T T0 ) þ k2 (T 4 T04 )
ð6Þ
323
(8)
For the simulation of the mass flow, the simultaneous deposition of a whole layer of material was assumed at each torch pass. Mass flow and heat fluxes were then fitted into a twodimensional finite element model (Fig. 2), built with plane thermal elements (of the type ‘plane 55’). The adopted algorithm involved non-static analyses: the movement of the torch was simulated by the movement of the previously evaluated heat flux, and coating built-up was simulated with the controlled activation (birth) of preselected elements.
mg ¼ viscosity of the plasma gas kg ¼ thermal conductivity of the plasma gas rg jvg vp jdp Re ¼ (Reynolds number) mg
rg ¼ density of the plasma gas vg ¼ velocity of the plasma gas dp ¼ average diameter of the particles in the plasma jet Vp ¼ velocity of the particles in the plasma jet r ¼ 2:5D K ¼ thermal conductivity of the substrate h ¼ heat exchange coefficient The function F(Re) is defined as: F(Re) ¼ 1:36Re0:574
if 2000 , Re , 30 000
F(Re) ¼ 0:54Re0:667
if 30 000 , Re , 120 000
F(Re) ¼ 0:151Re0:775
if 120 000 , Re , 400 000
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Fig. 1 Calculated heat flux on a 50 50 4 mm substrate as a function of spraying distance for a nozzle diameter of 6 mm, a power input of 40 kW and a plasma gas mixture flowrate of 50 slpm Ar þ 12 slpm H2 Proc. Instn Mech. Engrs Vol. 218 Part L: J. Materials: Design and Applications
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Fig. 3 Three-dimensional finite element model: disc Fig. 2
Geometrical model for the simulation of thermal history
The thickness of each layer was kept constant and calculated by dividing the coating final thickness by the number of torch passes. Thermal properties of sintered a-Al2O3, available in the literature [26] and given in Table 1, were used for the simulation of the coating thermal behaviour. This assumption does not introduce significant errors [13] in the case of alumina coatings. The variation in the generic property P with temperature was expressed in the model according to a polynomial function P(T) ¼ C0 þ C1 T þ C2 T 2 þ C3 T 3 þ C4 T 4
(9)
where the coefficients Ci were estimated from the literature values with regression models (least-squares method). A different approach was used for the selection of the value of Young’s modulus, for which the difference between the coating and the bulk (sintered) material cannot be neglected. Four-point bending tests of as-sprayed coatings were performed at room temperature, and they gave an average E value of 55 GPa with a standard deviation of 5 MPa, as calculated on the basis of the beam theory. Ten 3 4 50 mm specimens (AISI4037 substrates coated with Ni20Al/Al2O3, total coating thickness 0.5 mm) were tested according to ASTM C1161-02c standard by means of a MTS Bionix universal testing machine with a load cell of 25 kN. A totally different value of 410 GPa characterizes sintered a-Al2O3 [26]. Table 1
2.2
Residual stress
The selected shape for structural analysis was a threedimensional plane disc (Fig. 3) built with eight-node solid finite elements (‘solid 45’). In consideration of the axial symmetry of the geometrical system, a two-dimensional model (‘plane 42’) was also tested, with a remarkable reduction in the solution time. By implementing the general algorithm illustrated in Fig. 4 for the three- and two-dimensional model, results characterized by the same accuracy were obtained: the two-dimensional model was therefore used for all simulations with consistent simplification of the calculation procedure. The spraying process was simulated using the ANSYSw EKILL/EALIVE function in order to set the birth or death of elements and to build up the coating layer by layer. For each layer, the calculated deposition temperature was imposed as a boundary condition and was also assumed as a reference temperature for the calculation of residual stress according to equation (4). In terms of constitutive relationship models, a bilinear hardening and a pure elastic behaviour were assumed for carbon steel and alumina-sprayed coating respectively. 3 3.1
EXPERIMENTAL PROCEDURES Coating deposition
Coatings simulated in FEA models were fabricated by air plasma spraying starting from alumina powders (Metco 105NS, 2325 mesh þ 15 mm), using the standard spraying parameters reported in Table 2. An average thickness of 320 mm was obtained with 46 torch passes. Metallic bond
Thermo-mechanical properties for sintered alumina at various temperatures (from [26])
Property
20 8C
500 8C
1000 8C
1200 8C
1400 8C
1500 8C
Poisson’s ratio Specific heat (J/kg K) Thermal conductivity (W/m K) Thermal expansion coefficient (1026 K21)
0.231(+0.001) 755(+15) 33(+2) 4.6(+0.2)
0.237 1165 11.4 7.1
0.244 1255 7.22 8.1
0.247 1285 6.67 8.3
0.250 1315 6.34 8.5
0.252 1330 6.23 8.6
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Fig. 5 Microstructure of an air plasma sprayed Al2O3 coating (cross-section, optical microscope, 200)
Fig. 4
Algorithm adopted for the simulation of residual stresses
coats with an average thickness of 180 mm were obtained from Ni20Al powders (Metco 404NS, 2170 þ 270 mesh). X-ray diffraction patterns of as-sprayed coatings revealed a dual-phase microstructure composed of a-Al2O3 and g-Al2O3. A coating cross-section is shown in Fig. 5. 3.2
Residual stresses of as-sprayed coatings were experimentally evaluated using the hole drilling technique on the basis of an incremental method [21, 27]. The procedure consists of the removal of stressed material by drilling a small blind hole in the top surface of the coating, and of the measurement of the strain relaxation occurring in the adjacent material by means of a proper set of strain gauges. By means of suitable stress –strain relationships, residual stresses can be evaluated provided that correct values for calibration coefficients [22, 28] are adopted. The most Table 2 Spraying parameters for the alumina coating APS spraying parameters for Al2O3
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j¼i X
A ij Pj ¼ pi ,
1 4 j 4 i 4 nc
B ij Qj ¼ qi ,
1 4 j 4 i 4 nc
j¼1 j¼i X j¼1 j¼i X
B ij Tj ¼ ti ,
1 4 j 4 i 4 nc
(10)
j¼1
Residual stress measurement
Substrate Spraying distance Gas plasma (slpm) Plasma current Plasma voltage Number of torch passes Cooling gas Coating thickness
widely used method for calculating residual stresses from measured relaxed strains is the ‘integral method’ [22]: stress values are obtained from the strain relaxation measured at various depths with a rosette strain gauge on the basis of the following set of equations
AISI 4037 steel 115 mm 50Ar, 12H2 560 A 73 V 46 Ar, 4.5 bar 320 mm
where
s(1) j þ s(3) j s(1) j s(3) j , Qj ¼ , 2 2 T j ¼ t(13) j 1(1)i þ 1(3)i 1(1)i 1(3)i , qj ¼ , pi ¼ 2 2 1(3)i þ 1(1)i 21(2)i ti ¼ 2
Pj ¼
(11)
(12)
represent stress and strain components in the direction of the three strain gauges (Fig. 6) in accordance with the nc steps in to which the calculation is divided. The terms Pj and pi represent the hydrostatic component of residual stresses and the corresponding volumetric strain relaxation. Similarly, the other variables (Qj, Tj, qi, ti) represent the shear stresses and the shear strain components. The problem can only be solved if the two matrices of calibration constants Aij and Bij appearing in equation (10) (the first relating to the hydrostatic stress component, the second to the deviatoric one) are known. Since this is not the case for blind holes, for which closed analytical Proc. Instn Mech. Engrs Vol. 218 Part L: J. Materials: Design and Applications
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Fig. 6
T VALENTE, C BARTULI, M SEBASTIANI AND F CASADEI
Rosette strain gauge for hole drilling measurements
solutions are not available, calibration constants were calculated by FEA. The adopted procedure to evaluate the general term Aij requires the application of a uniform pressure at the jth step for a hole i steps deep (Fig. 7), and the calculation of the corresponding deformation on the gauge area [29]. Furthermore, the number and distribution of selected steps has to be selected with the maximum care: it has been demonstrated [30] that this number should not be higher than 10. A step distribution that makes it possible to minimize experimental errors is achieved if the following conditions are met Ann ¼ cos t,
1 4 n 4 nc
Bnn ¼ cos t,
1 4 n 4 nc
Fig. 7 FEM model for the calculation of calibration coefficient A32
thermal conductivity of the ceramic coatings, a stop time of 100 s between each drilling step was adopted. 4
RESULTS AND DISCUSSION
4.1
Results of thermal analyses
The substrate temperature was monitored during spraying by three thermocouples placed on the back of the substrate,
(13)
These conditions are substantially subjected by adopting an increasing distribution of calculation steps. In general, the total number of calculation steps, nc, is different from the number of experimental steps, ne. The experimental number is commonly greater, which allows for a better interpolation of strain data. In this case a continuous strain–depth (1–h) curve is available for the optimization of the calculation step process. For better precision of the developed model, the eccentricity of the actual drilled hole was also taken into account using appropriate geometric relations [31] describing the real strain distribution created around the hole. Experimental measurements were carried out using a high-velocity drilling machine (Restan, 350 000 r/min), which allows for minimization of the stresses induced by drilling and accurate measurement of the hole size and eccentricity. To avoid induced thermal strains during the drilling process, possibly generated owing to the low
Fig. 8 Measured substrate temperature during spraying
Fig. 9 Simulation of the variation in substrate temperature during spraying
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Fig. 10
Simulation of the deformed shape of a coating element after spraying and cooling at room temperature
as reported in Fig. 8. A very good agreement is observed between the measured and the numerically predicted temperature values (Fig. 9) with maximum differences of 2 K over the whole temperature profile. The developed thermal model can thus be considered, for the investigated case, as an appropriate simulation model. The substrate temperature was maintained at a maximum value of 415 K by appropriate gas front cooling, with the aim of reducing the amount of residual stress after final cooling to room temperature. 4.2
Results of structural analysis
The first qualitative results in terms of stress evaluation can be obtained by the analysis of the deformed shape of the coating element, as illustrated in Fig. 10: the curvature of the coated specimen indicates the presence of compressive stresses on the top of the coating and tensile stresses on the back of the substrate. This is in agreement with equation (4) since the thermal expansion coefficient of alumina is lower than that of the carbon steel substrate. The results of the simulation of through-thickness variation of in-plane stress are reported in Fig. 11. The graph refers to a middle section of the system and indicates a compressive in-plane stress linearly varying through the coating thickness. At the two interfaces (coating/bond coat and bond coat/substrate) the model predicts discontinuities leading to tensile stresses in the bond coat and in the substrate. Looking at the free edge of the coated substrate (Fig. 12), the model predicts a peak in the axial stress as well as in the shear stress, in accordance with the interface. This result is consistent with problems observed in practice that lead to coating detachment and delamination in this area, thus confirming the strong influence, predicted by the model, of residual stresses on coating adhesion [32]. L00604 # IMechE 2004
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Coating thickness is a fundamental parameter for controlling the occurrence of the above-mentioned problem: according to the model, the value of compressive in-plane stresses decreases with coating thickness. With the same model, the effect of variation in the deposition temperature on residual stress can also be evaluated. Simulated in-plane maximum stresses corresponding to spraying temperatures varying from 150 to 400 8C are reported in Fig. 13. It appears that an eccessively high deposition temperature, while responsible for improved coating cohesion and reduced coating porosity, can lead to residual stresses able to promote coating failure. Appropriate upper limits in the
Fig. 11 Simulation of through-thickness variation of residual in-plane stress Proc. Instn Mech. Engrs Vol. 218 Part L: J. Materials: Design and Applications
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Fig. 13 Simulation of maximum in-plane stress as a function of deposition temperature
temperature (415 K), selected with the aim of evaluating whether the numerical model and the hole drilling measuring technique could also give satisfactory and consistent results in the case of low-stress coatings endowed with improved mechanical properties and prolonged lifetime. The comparison between predicted and measured values of residual stress is graphically illustrated in Fig. 15 as a function of coating thickness. Numerical and experimental values are both compressive and of the same order of magnitude. Nevertheless, Fig. 15a, representing the simulated values of the DTC stress as directly compared with the measured total stress, indicates a slight overestimation of FEA results (in the range from 255 to 265 MPa as opposed to the measured range from 230 to 250 MPa). Taking into Fig. 12
Simulation of axial stresses: (a) contour plot at the edge of the plate; (b) through-thickness variation
deposition temperature, selected as a function of the mechanical resistance of the coating material, should therefore be respected in the optimization of processing parameters. For the purpose of model validation, experimental measurement of the residual stress in plasma-sprayed ceramic coatings was carried out by the hole drilling method. Results obtained with seven calculation steps and for a hole eccentricity lower than 50 mm are reported in Fig. 14. Very low stresses were measured in the direction perpendicular to the torch scanning direction (smax, almost null as an average), whereas an average stress of about 244 MPa was calculated from the measurements of the smin component of the stress, parallel to the torch direction. The measured smin stress is then the quantity that should be compared with the result of in-plane stress calculation obtained from FEA analysis. The low absolute value of the residual stresses in the ceramic coating is to be ascribed to the low deposition
Fig. 14 Main residual stresses calculated from strain gauge smin measurements for different depths: perpendicular and smax parallel to the torch scanning direction
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validated. The model makes it possible to predict the thermal history of the coating during the spraying process, and the through-thickness variation of in-plane normal and shear stresses. An agreement between the predicted and experimental results in the coating was observed. Numerical simulation at a low residual stress level in the case of brittle ceramic coatings should be corrected to consider effects of tensile quenching stress, in order to reproduce the experimental data with the best accuracy. When residual stresses, expected or predicted, exceed 100 MPa, quenching stresses can be neglected since their influence on the final stress state is lower than about 10 per cent of the total. The developed model predicts stress concentrations at the free edge of the specimen as well as stress increase with deposition temperature. The high-speed hole drilling method implemented with FEA calibration of the required coefficients was adopted for the validation of the model with an Al2O3 coating sprayed with standard plasma parameters in air. This method has thus been shown to offer an expert tool for measuring residual stresses and stress profiles over the drilling depth.
REFERENCES
Fig. 15
Comparison between predicted and measured residual stresses, excluding (a) and including (b) the contribution of quenching stresses
account the presence of tensile quenching stresses of about 10 –15 MPa, results of numerical calculation appear to be in very good agreement with measured values, as illustrated in Fig. 15b.
5
CONCLUSIONS
A finite element model to simulate residual stresses for air plasma sprayed ceramic coatings was developed and L00604 # IMechE 2004
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Proc. Instn Mech. Engrs Vol. 218 Part L: J. Materials: Design and Applications
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L00604 # IMechE 2004
