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Calculation of residual thermal stress in plasma-sprayed coatings
416
Surface and Coatings Technology, 43/44 (1990) 41&-425
CALCULATION OF RESIDUAL THERMAL STRESS IN PLASMA-SPRAYED COATINGS* R. ELSING, 0. KNOTEK and U. BALTING Institut für Werkstoffkunde, Technical University, Templegraben 55, D-5100 Aachen (F.R.G.)
Abstract Residual internal stresses are induced in thermally-sprayed coating composite materials during deposition, owing to the different thermophysical properties of the substrate and coating materials and to the different spraying parameters. These residual stresses have a substantial effect on working properties, and therefore need to be taken into account in any optimization of the coating. Due to the wide variety of material and process parameters determining residual thermal stresses, systematic experimental testing is extremely effort, time and cost intensive. It is therefore necessary to determine residual stresses by means of mathematical techniques which, following experimental validation of the model, enable the influence of individual parameters on the residual thermal stress state of coating composite materials to be studied and the behaviour of the composite under practical conditions to be predicted. This paper presents a model of this kind. Calculated results for aluminium oxide and zirconium oxide on various substrates (process: plasma spraying) are compared with measured results, showing good agreement.
1. Introduction Residual thermal stresses are induced in thermally-sprayed coating materials during deposition. Hot particles, as far as possible in the molten state, impinge on relatively cold substrates or on an existing partial coating, where they solidify, releasing their melting heat, and continue to cool. As a result, the layer on which the particles impinge is heated. This process is repeated throughout deposition of the coating, until the last particle has impinged on the surface and the desired coating thickness has been achieved. The process of coating deposition is thus associated with widely oscillating temperature loads both on the growing film and on the substrate, temperature fluctuations in the lower layers of the coating decreasing as the coating thickness increases. Temperature levels and the temperature curve are de*Winner of a 1990 ICMC/ICTF Bunshah Award for Outstanding Paper. 0257.8972/90/$3.50
~Elsevier Sequoia/Printed in The Netherlands
417
pendent on the various thermophysical parameters of the coating and substrate materials, the melting heat of the particles and the temperature loading caused by the hot plasma flowing onto the growing film and thus on the process parameters. We have previously investigated and represented these interrelationships in detail, using mathematical models [1, 2]. Constant or oscillating temperature loads lead to the formation of internal stresses in materials consisting of different phases, i.e. especially in composites or coating composites. In accordance with the fundamental equation for the calculation of changes in length as a function of temperature, these stresses are similarly dependent on different moduli of elasticity, different thermal expansion coefficients and temperature, and hence on all the other parameters of the materials constituting the composite and on the process parameters. During the use of the coating system, internal stresses in a coating composite material act as pre-stresses on which the mechanical or thermal operational loads are superimposed. Depending on their orientation and strength, they may lengthen or shorten service lives or, in extreme cases, result in immediate spalling of the coating. Their great importance makes the precise knowledge of residual thermal stresses a topic of interest for both coating manufacturers and users. In the past, residual thermal stresses have repeatedly been the subject of scientific investigation. Experimental determination of residual stresses in coating composite systems is based on strain measurements, which are generally destructive and which produce results applicable only to a single special case. Interpretation of conflicting results is also frequently difficult, since measurements provide no information on the way in which residual stresses originate in a particular case and on the resulting level and behaviour over a cross-section of the composite system. Mathematical calculations which take into account the process by which the composite material originates are of assistance in this respect. A model for relatively thick coatings is given in ref. 3; residual stress states in thinner coatings can be characterized according to a model devised by us [4], which has been considerably sophisticated in the present investigation to achieve a closer description of the real process. Phase transformations in films are of importance chiefly in terms of thermal operational loads, not in terms of film deposition. The cooling rates of the molten particles are so high that the high temperature modification generally stabilizes and any further modifications at lower temperatures are suppressed. These are therefore not allowed for in the present model.
2. Description of the model The calculation of thermal stresses is based on temperature curves during deposition of the coating and on subsequent temperature equalization processes. These are described in a coating structure model and are shown
418
Temperature T
‘:L~~ ~ting
(7
~ra~
Fig. 1. Incremental growth of films: temperature curves of coating composite materials over cross-section and time.
diagrammatically in Fig. 1 over the period of coating deposition. It will be evident that the film in the model grows in incremental elements, yielding different temperature curves in the composite material over time. The method of calculation has been described in detail elsewhere [1, 2]. The fundamental concept of the temperature curve determination model is based on the sub-division of the coating deposition process into time elements (approximately 10_c s), the calculation of the existing coating thickness for each time element and the determination of the temperature curve for the entire composite from the amounts of heat introduced (via the hot gas plasma and the particles) and dissipated for each time element. The thermal constraints of the model are convective heat loss at the substrate and coating surfaces, ideal contact between the substrate and the coating and negligible radiation losses [1, 2j. On the basis of calculated results, the thermal internal strain state of the coating composite material is then described in a two-stage calculation model. (i) The total lateral expansion of the coated workpiece, which is assumed to be plate-shaped, together with changes due to thermal influences, are first calculated by numerical integration of the equation I~~
=x~~E~A~/l0~ ~
—®~~)
where i is an index (s for substrate, c for coating), x, x, i are the path coordinates along the substrate surface, velocity and acceleration during thermal expansion and contraction, E, is the Young’s modulus of the coating and substrate material, A, is the cross-sectional area of the individual element, is the temperature-dependent coefficient of thermal expansion, m, is the mass of the individual element, e, is the instantaneous temperature of each individual element, l~,is the length of the element in the unstressed ~,
419
state and ®~, is the maximum temperature’of the supporting layer on which the particle impinges during the cooling process of the uppermost lamella. This equation essentially represents a special form of the basic newtonian mechanics equation, applied to the individual substrate and coating elements. The forces, and thus the stresses, in each of these elements consist of the deformation-dependent influences resulting from the incorporation of the element in the composite minus the temperature-dependent strain of the element itself. The sum of these forces on the left-hand side of the equation is not equal to zero, because the relatively large acceleration forces which may occur due to rapid contraction during solidification of the particles and the rapid heating of the particles immediately below them, also due to thermal expansions, cannot be neglected. Incorporation of an impinging particle in the coating composite occurs at the moment when the supporting layer has just attained its maximum temperature. The total lateral expansion of the coating composite can hence be calculated from the instantaneous thermal expansion and the size of the substrate prior to deposition. The temperature curve model referred to above assigns the temperatures to various times during deposition of the coating and to the local coordinates, enabling these values to be integrated directly in the equation. (ii) The above equation is used during the period in which the thermally-sprayed coating is being deposited. Following termination of the spraying process, during the ensuing cooling phase and at later times when operational loading occurs at raised temperatures, the equation 10i {1 + ;(®~)(O, ®Oi)} ii = is used for each element of the coating and substrate. 1, is the length which an element would possess at the temperature 0 if it could adjust freely, i.e. unconstrained by the surrounding elements. Within the composite, however, the elements interact with and obstruct one another, and these influences are calculated, taking into account the bending moments and using formulae similar to those for bimetallic strips. Table 1 shows the material data used in the temperature curve and strain model. —
3. Results and discussion Internal strains in plasma-sprayed coatings deposited on austenitic and ferritic steel using the parameters given below were measured by the familiar ring-core method [5], modified to include the use of diamond drill bits [6]. The resiliences were determined by measuring the resulting surface internal strains in several directions with the aid of specially developed strain gauges. The deeper the milling depth, the lower the measurable deformations. This behaviour, typical of the process, was taken into account by defining a damping function, which can be determined either mathematically or experi-
420
x
C.) ~I
—I
~-c~ -—
C’:,
x
.~
:;i
-:;~
C:,
0 C
C-)
C. C
—— x 0
— —j
C0-’.~
._~
—
C’C.
c’i
CC ~
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a a
a
~
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~
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—
~
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I
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~
~
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—
.~
—-~.
a ~
<
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>~
,~L L
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I
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a~ E ~
~
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a
I —
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.0
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421
t
1.50
0.75
-
o /00
___
I
100
0
100 pm 200 0 100
0.25
coating
substrate
I
0
coating
I
100 pm 200
substrate
Fig. 2. Measured internal strain curves (Al
203 on ferrite).
Fig. 3. Measured internal strain curves (Al203 on austenite).
mentally on a specimen with known, depth-constant internal strain state. The method is valid given that the strain at right angles to the surface is zero. This constraint is satisfied exactly only at the surface, but also applies with sufficient accuracy over the entire cross-section of thin coatings. Figures 2 and 3 show the results for Al2 03 on ferrite and austenite. Calculation on the temperature curves and the inferred strains was based on the following spraying parameters, which were also used to plasma spray the specimen coatings: substrate thickness, 7.8 mm; gas temperature at the substrate, 2700 °C; gas velocity at the substrate, 200m s’; torch feed rate, 5 cm s’; nozzle diameter, 8mm. Apart from thermophysical parameters, the substrate thickness, the temperature of the plasma flowing onto the substrate or the growing film, the gas velocity, the torch feed rate and the nozzle diameter, which determines the size of the spot, were included in the temperature curve calculation. The velocity of the particles at the moment of impact was not taken into account. The melting points of Al2 03 and Zr02 were taken 2 as K1 the particle temperain the spot and tures. Heat transmission coefficients of 1000W m lOW m2 K~’at the reverse side of the substrate were used. At the given torch rate, films of 100 jim (A1 203) and 40 jim (Zr02) were deposited in a single pass.
422
H ~
~ +
—
~
~
+
%,
-~i~-~-
.—.
1
Aj te~I
+
.1
•
I
Ii,
I
I,
I •
.-
I
•
.
S
S
•
Fig. 4. Calculated internal strain curves: Al:,O~,on ferrite and austenite.
The results of the strain calculations from the temperature curves are presented in Figs. 4 and 5. A comparison between the measured and calculated results shows that the measured values for internal strains are lower than the calculated equivalents. This is partly attributable to the assumptions or simplifications in the model, but the method of measurement also contains some typical sources of error, as, incidentally, do all other methods for measuring internal strains in sprayed coatings. The measured absolute value of the internal strain is, for example, dependent on the lateral convexity produced by drilling, the calibration function chosen to determine the depth curve, the drilling feed rate and the size of the hole drilled and hence the size of the influencing zone. Conversely, there is good agreement between the qualitative curves of the measured and calculated internal strains and between the differences produced by deposition on ferritic and austenitic substrate materials. The measured and calculated internal strains at the coating surface are twice as high on austenite as on ferrite, whereas the calculated and measured differences in internal strains in the various substrates are much less pronounced. The results from the internal strain curves may be summarized as follows.
423
COATING3
SUBSTRATE
ZrO,/Ferrlte
S
I
~
i~ t
ZrOO
5)
3
+ 1:
—
2
~\
S~..
•~ ~I
I
-50
I
0
•
o
yflIjle ofralrcompressIve 011010
room - fenlpnraiul end of spraying orclcess 1 sec. offer end of sprvying process
L...~ 50 I
I
I
I
S
•
I
50
100 S
200
pm S
S
S
Fig. 5. Calculated internal strain curves: Zr0 2 on ferrite and austenite.
(i) In the four coating—substrate combinations considered, tensile loads occurred in the coating and compressive loads in the substrate. The transition from tension to compression occurs in the vicinity of, but not always exactly at, the interface. (ii) The loads are time dependent and therefore dynamic. The strongest loading of the coatings occurs between the end of the spraying process and complete cooling. This phenomenon may be attributed to inadequate temperature equalization in the coating composite during this phase, reinforced by the poor thermal conductivity of the coating and/or substrate. Only during the course of the spraying process and thereafter can the introduced heat gradually penetrate the substrate zones further from the interface, causing thermal expansions which have to be taken up by the entire composite system and hence also by the coating. (iii) The loads on the coatings after cooling to room temperature are, in part, far lower than those encountered during cooling. Currently, however, it is possible to measure only the loads after complete cooling, which yield hardly any information on the actual loading of the coatings. (iv) As may be expected from the poor thermal conductivity of the austenite and the resulting higher temperature gradients during production,
424
TABLE 2 Moduli of elasticity for ZrO:, Material
Young’s modulus (GPa) Lackey et al. [7/
Zr0
2 Zr02 Y:,0., Zr02-8Y20,, ZrO:,—2OMgO ZrO:,—24Mg0
48 (B) --
205 (B) 97 207 (B) ---
Hobbs [8/
~-
34.5 (S) 3.4—6.9 (5) 46.2 (5) 4.7 (5)
Hancock [9] 170 (5) 32-40 (S)
-
B, bulk, sintered; S. as sprayed.
the coatings on austenitic substrate materials exhibit the largest internal strains. (v) The differences between the thermal expansion coefficients of Zr02 and the two steels investigated are less than in the case of Al2 03. Nonetheless, the strains are larger. This may be attributed partly to the changed temperature curves and partly to the much lower modulus of elasticity of the compact material, which also explains the higher internal stress state generally assigned to the Al2 03 as opposed to the Zr02 coatings. (vi) The internal stresses can be inferred from the calculated internal strains via the moduli of elasticity, using the values for the sprayed state of the relevant material. In the equation given above, this is unnecessary, since the lateral extent of the individual elements may be assumed to be so small that the material in these zones can be regarded as ideal and not affected by pores, loosely adhering particles, etc. In real coatings, however, these two phenomena occur, substantially reducing the modulus of elasticity as compared with that of the compact material, as exemplified in the case of zirconium oxide in Table 2 [7—9]. The internal strain state therefore appears to provide a much better basis for evaluating pre-stressing of a coating. The interrelationships noted above and illustrated in the figures remain valid irrespective of the absolute value of the modulus of elasticity (as sprayed), and the curves presented reflect the internal stress curves if the modulus of elasticity fluctuates by the same mean value at all points within a coating.
4. Conclusions The determination of thermally-induced residual internal stresses in coating composite materials is of great significance for their behaviour under load. The internal stresses depend on the thermophysical data of the substrate and coating materials and on the spraying parameters. Experimental and mathematical methods are available for determining internal strains. A
425
mathematical method is described and the internal strain curves obtained by this method are compared with experimental values. The various curves for different material combinations can be demonstrated both mathematically and experimentally. In principle, it is extremely simple to calculate internal stresses from internal strains. However, precise determination of the required mechanical parameters for the sprayed state is problematical, and it is suggested that loading of the coatings should be characterized via the internal strain state.
Acknowledgment The authors wish to express their thanks to Dr. P. Pantucek of the Fraunhofer-Institut für Betriebsfestigkeit (LBF) in Darmstadt for performance of the internal strain measurements.
References 1 0. Knotek, R. Elsing and U. Balting, Surf. Coat. Technol., 36(1988) 99. 2 H. Elsing, 0. Knotek and U. Baiting, Proc. mt. Thermal Spraying Con!. 1989, London, June 1989. 3 D. S. Rickerby, G. Eckold, U. T. Scott and I. M. Buckly-Jobbs, Thin Solid Films, 154 (1987) 125. 4 H. Eising, 0. Knotek and U. Baiting, Surf. Coat. Technol., 41 (1990) 147. 5 M. T. Fiaman, Experimental Techniques, January (1982) 26. 6 P. Pantucek, VDI-Berchte, No. 679, Verein Deutscher Ingenieure Verlag, Düsseldorf, 1988. 7 W. J. Lackey, D. P. Stinton, G. A. Cerny, L. L. Fehrenbacher and A. C. Schifauser, Ceramic Coatings for Heat Engine Materials—Status and Future Needs, Proc. mt. Symp. on Ceramic Components for Heat Engines, October 1 7—21, 1983, Hakine, Japan. 8 M. Hobbs, Surf. J., 16(4) (1985) 155. 9 P. Hancock, Degradation Processes for Ceramic Coatings, E-MRS Con!. on Advanced Materials Research and Development for Transport, Strasbourg, November 1985.
Surface and Coatings Technology, 43/44 (1990) 41&-425
CALCULATION OF RESIDUAL THERMAL STRESS IN PLASMA-SPRAYED COATINGS* R. ELSING, 0. KNOTEK and U. BALTING Institut für Werkstoffkunde, Technical University, Templegraben 55, D-5100 Aachen (F.R.G.)
Abstract Residual internal stresses are induced in thermally-sprayed coating composite materials during deposition, owing to the different thermophysical properties of the substrate and coating materials and to the different spraying parameters. These residual stresses have a substantial effect on working properties, and therefore need to be taken into account in any optimization of the coating. Due to the wide variety of material and process parameters determining residual thermal stresses, systematic experimental testing is extremely effort, time and cost intensive. It is therefore necessary to determine residual stresses by means of mathematical techniques which, following experimental validation of the model, enable the influence of individual parameters on the residual thermal stress state of coating composite materials to be studied and the behaviour of the composite under practical conditions to be predicted. This paper presents a model of this kind. Calculated results for aluminium oxide and zirconium oxide on various substrates (process: plasma spraying) are compared with measured results, showing good agreement.
1. Introduction Residual thermal stresses are induced in thermally-sprayed coating materials during deposition. Hot particles, as far as possible in the molten state, impinge on relatively cold substrates or on an existing partial coating, where they solidify, releasing their melting heat, and continue to cool. As a result, the layer on which the particles impinge is heated. This process is repeated throughout deposition of the coating, until the last particle has impinged on the surface and the desired coating thickness has been achieved. The process of coating deposition is thus associated with widely oscillating temperature loads both on the growing film and on the substrate, temperature fluctuations in the lower layers of the coating decreasing as the coating thickness increases. Temperature levels and the temperature curve are de*Winner of a 1990 ICMC/ICTF Bunshah Award for Outstanding Paper. 0257.8972/90/$3.50
~Elsevier Sequoia/Printed in The Netherlands
417
pendent on the various thermophysical parameters of the coating and substrate materials, the melting heat of the particles and the temperature loading caused by the hot plasma flowing onto the growing film and thus on the process parameters. We have previously investigated and represented these interrelationships in detail, using mathematical models [1, 2]. Constant or oscillating temperature loads lead to the formation of internal stresses in materials consisting of different phases, i.e. especially in composites or coating composites. In accordance with the fundamental equation for the calculation of changes in length as a function of temperature, these stresses are similarly dependent on different moduli of elasticity, different thermal expansion coefficients and temperature, and hence on all the other parameters of the materials constituting the composite and on the process parameters. During the use of the coating system, internal stresses in a coating composite material act as pre-stresses on which the mechanical or thermal operational loads are superimposed. Depending on their orientation and strength, they may lengthen or shorten service lives or, in extreme cases, result in immediate spalling of the coating. Their great importance makes the precise knowledge of residual thermal stresses a topic of interest for both coating manufacturers and users. In the past, residual thermal stresses have repeatedly been the subject of scientific investigation. Experimental determination of residual stresses in coating composite systems is based on strain measurements, which are generally destructive and which produce results applicable only to a single special case. Interpretation of conflicting results is also frequently difficult, since measurements provide no information on the way in which residual stresses originate in a particular case and on the resulting level and behaviour over a cross-section of the composite system. Mathematical calculations which take into account the process by which the composite material originates are of assistance in this respect. A model for relatively thick coatings is given in ref. 3; residual stress states in thinner coatings can be characterized according to a model devised by us [4], which has been considerably sophisticated in the present investigation to achieve a closer description of the real process. Phase transformations in films are of importance chiefly in terms of thermal operational loads, not in terms of film deposition. The cooling rates of the molten particles are so high that the high temperature modification generally stabilizes and any further modifications at lower temperatures are suppressed. These are therefore not allowed for in the present model.
2. Description of the model The calculation of thermal stresses is based on temperature curves during deposition of the coating and on subsequent temperature equalization processes. These are described in a coating structure model and are shown
418
Temperature T
‘:L~~ ~ting
(7
~ra~
Fig. 1. Incremental growth of films: temperature curves of coating composite materials over cross-section and time.
diagrammatically in Fig. 1 over the period of coating deposition. It will be evident that the film in the model grows in incremental elements, yielding different temperature curves in the composite material over time. The method of calculation has been described in detail elsewhere [1, 2]. The fundamental concept of the temperature curve determination model is based on the sub-division of the coating deposition process into time elements (approximately 10_c s), the calculation of the existing coating thickness for each time element and the determination of the temperature curve for the entire composite from the amounts of heat introduced (via the hot gas plasma and the particles) and dissipated for each time element. The thermal constraints of the model are convective heat loss at the substrate and coating surfaces, ideal contact between the substrate and the coating and negligible radiation losses [1, 2j. On the basis of calculated results, the thermal internal strain state of the coating composite material is then described in a two-stage calculation model. (i) The total lateral expansion of the coated workpiece, which is assumed to be plate-shaped, together with changes due to thermal influences, are first calculated by numerical integration of the equation I~~
=x~~E~A~/l0~ ~
—®~~)
where i is an index (s for substrate, c for coating), x, x, i are the path coordinates along the substrate surface, velocity and acceleration during thermal expansion and contraction, E, is the Young’s modulus of the coating and substrate material, A, is the cross-sectional area of the individual element, is the temperature-dependent coefficient of thermal expansion, m, is the mass of the individual element, e, is the instantaneous temperature of each individual element, l~,is the length of the element in the unstressed ~,
419
state and ®~, is the maximum temperature’of the supporting layer on which the particle impinges during the cooling process of the uppermost lamella. This equation essentially represents a special form of the basic newtonian mechanics equation, applied to the individual substrate and coating elements. The forces, and thus the stresses, in each of these elements consist of the deformation-dependent influences resulting from the incorporation of the element in the composite minus the temperature-dependent strain of the element itself. The sum of these forces on the left-hand side of the equation is not equal to zero, because the relatively large acceleration forces which may occur due to rapid contraction during solidification of the particles and the rapid heating of the particles immediately below them, also due to thermal expansions, cannot be neglected. Incorporation of an impinging particle in the coating composite occurs at the moment when the supporting layer has just attained its maximum temperature. The total lateral expansion of the coating composite can hence be calculated from the instantaneous thermal expansion and the size of the substrate prior to deposition. The temperature curve model referred to above assigns the temperatures to various times during deposition of the coating and to the local coordinates, enabling these values to be integrated directly in the equation. (ii) The above equation is used during the period in which the thermally-sprayed coating is being deposited. Following termination of the spraying process, during the ensuing cooling phase and at later times when operational loading occurs at raised temperatures, the equation 10i {1 + ;(®~)(O, ®Oi)} ii = is used for each element of the coating and substrate. 1, is the length which an element would possess at the temperature 0 if it could adjust freely, i.e. unconstrained by the surrounding elements. Within the composite, however, the elements interact with and obstruct one another, and these influences are calculated, taking into account the bending moments and using formulae similar to those for bimetallic strips. Table 1 shows the material data used in the temperature curve and strain model. —
3. Results and discussion Internal strains in plasma-sprayed coatings deposited on austenitic and ferritic steel using the parameters given below were measured by the familiar ring-core method [5], modified to include the use of diamond drill bits [6]. The resiliences were determined by measuring the resulting surface internal strains in several directions with the aid of specially developed strain gauges. The deeper the milling depth, the lower the measurable deformations. This behaviour, typical of the process, was taken into account by defining a damping function, which can be determined either mathematically or experi-
420
x
C.) ~I
—I
~-c~ -—
C’:,
x
.~
:;i
-:;~
C:,
0 C
C-)
C. C
—— x 0
— —j
C0-’.~
._~
—
C’C.
c’i
CC ~
©
C/i
a a
a
~
©
~
I
—
~
©
I
C
~
~
CC C’.’.
a a0
0
—
.~
—-~.
a ~
<
•~
>~
,~L L
E~ .‘Z
I
OX >~_~
•~
a~ E ~
~
E—o
a
I —
C C ~lC/
.0
C-)
421
t
1.50
0.75
-
o /00
___
I
100
0
100 pm 200 0 100
0.25
coating
substrate
I
0
coating
I
100 pm 200
substrate
Fig. 2. Measured internal strain curves (Al
203 on ferrite).
Fig. 3. Measured internal strain curves (Al203 on austenite).
mentally on a specimen with known, depth-constant internal strain state. The method is valid given that the strain at right angles to the surface is zero. This constraint is satisfied exactly only at the surface, but also applies with sufficient accuracy over the entire cross-section of thin coatings. Figures 2 and 3 show the results for Al2 03 on ferrite and austenite. Calculation on the temperature curves and the inferred strains was based on the following spraying parameters, which were also used to plasma spray the specimen coatings: substrate thickness, 7.8 mm; gas temperature at the substrate, 2700 °C; gas velocity at the substrate, 200m s’; torch feed rate, 5 cm s’; nozzle diameter, 8mm. Apart from thermophysical parameters, the substrate thickness, the temperature of the plasma flowing onto the substrate or the growing film, the gas velocity, the torch feed rate and the nozzle diameter, which determines the size of the spot, were included in the temperature curve calculation. The velocity of the particles at the moment of impact was not taken into account. The melting points of Al2 03 and Zr02 were taken 2 as K1 the particle temperain the spot and tures. Heat transmission coefficients of 1000W m lOW m2 K~’at the reverse side of the substrate were used. At the given torch rate, films of 100 jim (A1 203) and 40 jim (Zr02) were deposited in a single pass.
422
H ~
~ +
—
~
~
+
%,
-~i~-~-
.—.
1
Aj te~I
+
.1
•
I
Ii,
I
I,
I •
.-
I
•
.
S
S
•
Fig. 4. Calculated internal strain curves: Al:,O~,on ferrite and austenite.
The results of the strain calculations from the temperature curves are presented in Figs. 4 and 5. A comparison between the measured and calculated results shows that the measured values for internal strains are lower than the calculated equivalents. This is partly attributable to the assumptions or simplifications in the model, but the method of measurement also contains some typical sources of error, as, incidentally, do all other methods for measuring internal strains in sprayed coatings. The measured absolute value of the internal strain is, for example, dependent on the lateral convexity produced by drilling, the calibration function chosen to determine the depth curve, the drilling feed rate and the size of the hole drilled and hence the size of the influencing zone. Conversely, there is good agreement between the qualitative curves of the measured and calculated internal strains and between the differences produced by deposition on ferritic and austenitic substrate materials. The measured and calculated internal strains at the coating surface are twice as high on austenite as on ferrite, whereas the calculated and measured differences in internal strains in the various substrates are much less pronounced. The results from the internal strain curves may be summarized as follows.
423
COATING3
SUBSTRATE
ZrO,/Ferrlte
S
I
~
i~ t
ZrOO
5)
3
+ 1:
—
2
~\
S~..
•~ ~I
I
-50
I
0
•
o
yflIjle ofralrcompressIve 011010
room - fenlpnraiul end of spraying orclcess 1 sec. offer end of sprvying process
L...~ 50 I
I
I
I
S
•
I
50
100 S
200
pm S
S
S
Fig. 5. Calculated internal strain curves: Zr0 2 on ferrite and austenite.
(i) In the four coating—substrate combinations considered, tensile loads occurred in the coating and compressive loads in the substrate. The transition from tension to compression occurs in the vicinity of, but not always exactly at, the interface. (ii) The loads are time dependent and therefore dynamic. The strongest loading of the coatings occurs between the end of the spraying process and complete cooling. This phenomenon may be attributed to inadequate temperature equalization in the coating composite during this phase, reinforced by the poor thermal conductivity of the coating and/or substrate. Only during the course of the spraying process and thereafter can the introduced heat gradually penetrate the substrate zones further from the interface, causing thermal expansions which have to be taken up by the entire composite system and hence also by the coating. (iii) The loads on the coatings after cooling to room temperature are, in part, far lower than those encountered during cooling. Currently, however, it is possible to measure only the loads after complete cooling, which yield hardly any information on the actual loading of the coatings. (iv) As may be expected from the poor thermal conductivity of the austenite and the resulting higher temperature gradients during production,
424
TABLE 2 Moduli of elasticity for ZrO:, Material
Young’s modulus (GPa) Lackey et al. [7/
Zr0
2 Zr02 Y:,0., Zr02-8Y20,, ZrO:,—2OMgO ZrO:,—24Mg0
48 (B) --
205 (B) 97 207 (B) ---
Hobbs [8/
~-
34.5 (S) 3.4—6.9 (5) 46.2 (5) 4.7 (5)
Hancock [9] 170 (5) 32-40 (S)
-
B, bulk, sintered; S. as sprayed.
the coatings on austenitic substrate materials exhibit the largest internal strains. (v) The differences between the thermal expansion coefficients of Zr02 and the two steels investigated are less than in the case of Al2 03. Nonetheless, the strains are larger. This may be attributed partly to the changed temperature curves and partly to the much lower modulus of elasticity of the compact material, which also explains the higher internal stress state generally assigned to the Al2 03 as opposed to the Zr02 coatings. (vi) The internal stresses can be inferred from the calculated internal strains via the moduli of elasticity, using the values for the sprayed state of the relevant material. In the equation given above, this is unnecessary, since the lateral extent of the individual elements may be assumed to be so small that the material in these zones can be regarded as ideal and not affected by pores, loosely adhering particles, etc. In real coatings, however, these two phenomena occur, substantially reducing the modulus of elasticity as compared with that of the compact material, as exemplified in the case of zirconium oxide in Table 2 [7—9]. The internal strain state therefore appears to provide a much better basis for evaluating pre-stressing of a coating. The interrelationships noted above and illustrated in the figures remain valid irrespective of the absolute value of the modulus of elasticity (as sprayed), and the curves presented reflect the internal stress curves if the modulus of elasticity fluctuates by the same mean value at all points within a coating.
4. Conclusions The determination of thermally-induced residual internal stresses in coating composite materials is of great significance for their behaviour under load. The internal stresses depend on the thermophysical data of the substrate and coating materials and on the spraying parameters. Experimental and mathematical methods are available for determining internal strains. A
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mathematical method is described and the internal strain curves obtained by this method are compared with experimental values. The various curves for different material combinations can be demonstrated both mathematically and experimentally. In principle, it is extremely simple to calculate internal stresses from internal strains. However, precise determination of the required mechanical parameters for the sprayed state is problematical, and it is suggested that loading of the coatings should be characterized via the internal strain state.
Acknowledgment The authors wish to express their thanks to Dr. P. Pantucek of the Fraunhofer-Institut für Betriebsfestigkeit (LBF) in Darmstadt for performance of the internal strain measurements.
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