Simulation of the effect of creep on stress fields during vacuum plasma spraying onto titanium substrates

Surface and Coatings Technology, 64 (1994) 61-68

61

Simulation of the effect of creep on stress fields during vacuum plasma spraying onto titanium substrates v.c Tsui, S.c. Gill and T.W. Clyne Department oj Materials Science andMetallurgy, University of Cambridge, Pembroke Street, Cambridge, CB2 3QZ (UK) (Received August 25,1993; accepted in final form September 30, 1993)

Abstract Boron carbide has been deposited by vacuum plasma spraying onto thin substrates of Ti-6wt. %AI-4wt.%V alloy. Substrate/deposit curvature histories have been measured by analysis of a series of video images. These results, together with thermal histories, have been compared with predictions obtained from a numerical process model describing the development ofresidual stresses. It is shown that, when using the standard form of the model, a discrepancy arises between predicted and observed curvature histories. This is attributed to the effect of creep in the substrate under the influence of the residual stresses. A modification to the model accounting for the effect of creep allowed good agreement to be obtained between theory and experiment. It is shown that creep effects can be significant with titanium, although they become less significant as the substrate thickness increases. In general, the effect of creep is to lower the stress levels during spraying, although the final residual stresses can actually be higher than would be the case in the absence of creep.

1. Introduction Residual stresses in thermally sprayed coatings are thought to be highly significant in affecting their stability and performance. It is certainly clear, for example, that they can cause spontaneous spallation of the coating during spraying or subsequent cooling. There have been many recent studies aimed at the measurement [1-6J ofresidual stresses and modelling [7-11J of their development during spraying. However, there have been virtually no studies in which reliable correlations have been established between process conditions, measured stress levels and indicators of coating performance. In addition, agreement between measurements made on nominally similar coatings using different methods, or indeed by different workers using the same methods, has in general been poor. There are several reasons for this. Measurement using X-ray diffraction is complicated by the limited penetration depth, particularly since the coating surface is often relatively rough, and by the possibility of high through-thickness gradients of residual stress. Some of the other methods used, such as hole drilling, can also be difficult to interpret. Another common problem concerns thermophysical properties of the coatings, notably the stiffness, which often differ substantially from handbook values and should be measured directly [12, 13]. Finally, modelling of the generation of residual stresses (and particularly their effects on coating stability and adhesion [14J) is still in an evolutionary stage.

0257-8972/94/$7.00 SSDI 0257-8972(93 )02217-Z

In the present paper, the development of an existing numerical model is described. This involves incorporation of the effect of creel? in the substrate during the deposition process. Although such creep may often be negligible, it is shown to have a significant effect with titanium substrates using vacuum plasma spraying. Titanium is known to be very susceptible to creep, and substrate temperatures can become quite high during the vacuum plasma process. The model is briefly described in the following section. It is essentially quite simple, with relatively modest data storage and computation time requirements. Nevertheless, results obtained to date [10, 15-18J are in general very encouraging in terms of agreement between measured and predicted temperature and curvature histories. The present paper describes part of ongoing work aimed at developing the model and associated database so that it is useful in a wide variety of practical situations.

2. Modelling of residual stress development during spraying 2.1. Basic model

A finite differencemodel previously developed by Gill and Clyne [13, 15, 17-19J has been used in the current work. This is based on one-dimensional heat flow through the thickness of the deposit/substrate couple. This heat flow is modelled at a typical point, with

© 1994 - Elsevier Sequoia. AU rights reserved

Y.C. Tsui et al. / Simulation of creep effect on stress during VPS onto Ti

62

specified coordinates relative to the axis of the spray gun. The flux of gas-borne heat and molten droplets is then calculated as a function of time during the spraying operation. Residual stresses arise from (a) the rapid solidification and cooling of droplets immediately after impact (the so-called "quenching stress" [20-22J), (b) differential thermal expansion or contraction as the deposit/substrate couple changes in temperature and (c) transient through-thickness thermal gradients (although the final stress state will only be influenced by these if they give rise to inelastic processes such as plastic flow or creep). The basic assumptions of the model are that lateral heat flow within the plane of the specimen is neglected and that the stress state is always a simple equal biaxial state, so that stresses in the through-thickness direction and edge effects are neglected. Stresses are calculated using the concept of each volume element in the stack having an identifiable "relaxed (i.e. stress-free) width" in the in-plane direction being considered. This is initially determined by the width of the underlying element at the time of deposition (before the quenching stress is generated), but it may subsequently be altered by changes in the temperature of the element or by inelastic processes such as plastic flow, microcracking or creep. Once the relaxed widths of all the elements in a stack are known, the actual widths of all the elements (and hence the stress in each of them) are established by applying force and moment balances. This operation also reveals the curvature of the specimen, which can be directly compared with experimentalmeasurements. This comparison is central to effective model validation and boundary condition specification, particularly if the curvature can be monitored experimentally during the spraying operation.

listed in Table 1. The creep algorithm can easily be applied to the deposit as well, provided that the creep rate data are available, but for the case being considered here this had a negligible effect. Since time increments for stress level prediction in the model are typically only a fraction of a second, and stresses do not in general change very rapidly, it was assumed that a constant stress level applied over the duration of each time increment. It has been confirmed that for the cases of interest no significant changes in the predictions result from taking account of the variations in stress or temperature during each time increment. It may also be noted that, for the runs described here, the stresses in the substrate never reached the flow stress for the temperature concerned, so that pla 'ic flow was never predicted to occur.

Symbol

Description

2.2. Incorporation of the effectof substrate creep Incorporation of the effect of creep is a simple development of the model. The treatment of plastic flow and microcracking has already been described [19 J. These phenomena are simulated by allowing the relaxed width of an element to change in response to its stress state. For plastic flow and microcracking, this change is triggered by a critical stress level being reached, a check being made every time that the stress levels are updated. For creep, on the contrary, the relaxed width is altered at every time interval, the rate of change being calculated from the current stress level and temperature of the element concerned. The creep rate equation used [23, 24] is as follows:

Il

Creep strain rate Dorn's constant 1000 Shear stress Shear modulus See Table 3 Stress exponent 4.3 Burgers' vector 0.289 1.38 x 10- 23 Boltzmann's constant Temperature Diffusivity frequency factor 1.0 Activation energy for diffusion 247 Gas constant 8.314

. (r)n It ub

B=A

(-Q)

kT Do exp RT

(1)

The meanings of these terms and the values used here for simulation of creep in Ti-6wt. % AI-4wt. % V are

3. Experimental procedure

3.1. Substrate preparation and spraying conditions Substrates of Ti-6wt. % AI-4wt. % V in the form of thin (2 mm) strips were prepared by pickling in acid (8% HF and 40% HN0 3 ) for 1 min to remove surface oxide, degreased by rinsing in acetone and clamped at one end in the spraying chamber. Further surface cleaning was carried out in situ by partial transfer of the plasma arc to the specimen immediately prior to spraying. The specimens were then coated with boron carbide, using the spraying conditions given in Table 2. The TABLE 1. The meanings and the values of the terms used for simulation of creep in Ti-6wt. % AI-4wt. % V

A 'l"

II

n b

k T Do

Q R

Units

Value

TABLE 2. Spraying conditions Chamber pressure (mbar) Spraying stand-off distance (mm) Plasma arc current (A) Voltage across electrodes in gun (V) Argon flow rate in plasma (I min -1 ) Hydrogen flow rate in plasma (I min -1) Nozzle internal diameter (mm)

300 270 750 66 50 15

8

MPa GPa nm JK- 1 K m2

S-1

kJ mol- 1 J mol- 1

Y.C. Tsui et al. / Simulation of creep effect on stress during VPS onto Ti

spraying equipment employed was a PT VPS system, with an F4-V gun. A single spraying pattern was used, involving 30 cycles, each consisting of ten passes of the gun, followed by a pause. In order to check the reproducibility, nominally identical deposition runs were carried out on four specimens.

63

modulus of the deposit. These properties were measured on the boron carbide coatings using the laser flash [27J and ultrasonic vibration frequency [28J methods. The data used in modelling of the deposition of B4C on Ti-6wt. %A1-4wt. %V substrates are summarized in Table 3.

3.2. Measurement of temperature and curvature histories Thermal histories during spraying were recorded from thermocouples spot welded to the backs of the strips. Curvature histories were obtained using a video recording technique [16, 25]. This involves recording the image of the end of the strip, followed by automatic image analysis in order to establish the curvature. This allows the rapid assimulation of data from a large number of image frames, carrying detailed information about stress development.

33. Establishment of boundary conditions for model The boundary conditions needed for implementation of the model fall into three main groups. Firstly, the heat transfer between specimen and environment is described in terms of gas-borne fluxes, droplet flux distribution, heat transfer coefficients and emissivities. These have been established, for different spraying conditions, in previous studies. Secondly, the gun motion must be specified for the spraying pattern concerned. In combination with the droplet flux distribution, this defines the thickness of the deposit which is built up. Finally, material property data must be established. These include the quenching stress, which can be regarded as a material property since it appears to depend uniquely on deposit material and substrate temperature [20, 21, 26J(but not on substrate material). Also important are the thermal conductivity and Young's

4. Results and discussion 4.1. Comparison between observed and predicted behaviour The four specimens studied were found to behave in a very similar manner; so results are presented for only one of them. It is fairly straightforward to obtain good agreement between measured and modelled thermal histories for the rear of the specimen, by suitable adjustment of the boundary conditions. The comparison shown in Fig. 1 demonstrates that such agreement was obtained in the present case. For the curvature histories, on the contrary, there are fewer adjustable parameters, since most of the relevant variables are independently measured. The quenching stress is to some degree an adjustable parameter, although a database is now being built up of measured values as a function of average substrate temperature for commonly sprayed materials and large deviations from these values would be difficult to explain. For spraying of boron carbide, little information has been published hitherto. Previous experience with pure ceramics [20, 21J suggests that the quenching stress is expected to be of the order of 10-20 MPa, since extensive microcracking tends to inhibit the attainment of large values. It may be noted, however, that examination of the free surfaces of coatings, such as that shown in Fig. 2, suggested that micro cracking was somewhat

TABLE 3. Thermophysical and mechanical properties of B4C and Ti-tiwt, % AI-4wt. % V used in the numerical process model Property

Value Ti-6wt. % A-4wt. % V

Thermal conductivity (W m" K- 1 ) Specific heat capacity (J kg- 1 K- 1 ) Latent heat of fusion (kJ kg-I) Melting point eC) Droplet temperature (0C) Density (Mg m -3) Room-temperature thermal expansion coefficient (MK -1) Thermal expansion coefficient temperature dependence (MK- 2 ) Young's modulus (GPa) Young's modulus temperature dependence (MPa K- 1 ) Poisson's ratio Elastic limit (MPa) Quenching stress (MPa)

29

10 650

1048 300 2430 2430 2.38

4.42

4.32

8.55

1.12 X 10- 3

o

116 -112.5

106 -56.3 0.31 1030 room temperature to 150 (700°C)

0.19 ::::;300 30

Y.C. Ts ui et al. / Simulation

64

e:

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~

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100

-0.4

o

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0.8

600

0.6

500

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200

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B400

~

0

200

700

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0.

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0.6

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(a)

during VPS Ollto Ti

~

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B400 ~

0 11 stress

700

Q)

E

effect

o

SOD

1000

1500

2000

2500

3000

Time (s)

(b)

kd~~

U1Hf

II. I~

\

-0 .6 1.0

Fig. 1. Thermal histories for the back face of the substrate obtained (a) experimentally and (b) from the nume rical model.

0.8

0.6

§ ......

111 ::J

0.4

0.2

AlA.1\


~

0

::l

o -0.2

.1111

I~

-0.4 -0.6 (c)

o

500

1000

1500

lime

2000

2500

\

3000

(5)

Fig. 3. Cur vature histories for the specimen obtained (a) experimentally, ( b) from the model without creep and (c) from the model with creep incorpo rated.

Fig. 2. Scan ning electron microgr aph showing th e free surface of a boron carbide coating.

less extensive than in many ceramic deposits. A value of 30 MPa was therefore used for the qu enching stress. Curv ature history comparisons a re shown in Fig. 3. Fair agreement with experiment was obtained using the standard form of the model, but the predi cted curvatures were too low and the shape of the experimental curve, with a rather sharp reduction in the rate of curvature incre ase per cycle observed after about 20 cycles, was not consistent with the model predictions. On incorporating the effect of substrate creep in the model (Fig. 3(c)), however, the agreement became good, with a

not iceable plateau in the envelope of the curv atu re values for the later spraying cycles. It should be noted that the thermal and cur vature histories shown in Figs. 1 and 3 contain fine structure associated with individual passes of the gun. In Fig. 4, magnified views are shown of the tempera ture and cur vature changes during a single cycle often gun passes. It is instructive to consider how the various features of the curvature history arise. Before the gun comes close to the specimen, the curva ture is decreasing (i.e. the specimen is becoming less concave towards the gun) as a result of differential therm al contraction (since the expansivity of the deposit is less than that of the substrate). The first thing to happen as the gun approaches is actually an acceleration of this decrease, caused by

Y.c. Tsui et al. / Simulation of creep effect on stress during VPS onto Ti 650

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1Q 0.2

t::

<30.1

o -0.1

00

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900

910

920

930

940

950

960

970

~me~

Fig. 4. Plot showing predictions of (a) temperature and (b) curvature for a cycle of gun passes during spraying.

the high heat flux incident on the front of the specimen, which generates a high through-thickness thermal gradient, expanding the front of the specimen more than the rear. This is quickly followed, however, by a reversal of the trend and a sharp increase in curvature. Two effects contribute to this change. Firstly, as the temperature of the whole specimen rises, the substrate starts to expand more than the deposit, since it has the higher expansivity. Secondly, the flux of droplets incident on the specimen becomes significant. These form new layers, which are subject to the quenching stress; since this stress is always tensile, the specimen curves towards the gun (curvature rises) as it is generated. As the incident droplet flux decreases, this effect falls off, although the subsequent drop in curvature is less marked than the first, since thermal conduction through the specimen has by now led to lower through-thickness thermal gradients. The sequence is repeated during the next pass of the gun, with the net effect of each pass usually being an increment of increased curvature. In the absence of inelastic processes, this increment is solely due to the quenching stress, since both the through-thickness thermal gradients and the overall temperature rises are transient. 4.2. Creep strain distributions It is clear from the data in Fig. 3 that creep is

influencing the curvature histories, and therefore the

65

development of residual stress. An indication of the nature of the creep behaviour can be obtained by plotting the instantaneous creep strain rate at different depths within the substrate. This is done in Fig. 5, for the cycle depicted in Fig. 4 and for a later cycle. Also shown in this figure are the positions of the gun axis relative to the modelling point at different stages. It is clear that the thermal histories (e.g. see Fig. 4(a)) are such that creep tends to become significant only during the latter part of each cycle. In this regime (e.g. from 940 to 950 s in Fig. 5(a)), creep rates peak sharply as the stresses become sufficiently large. In this case, these stresses are tensile towards the back of the substrate and compressive towards the front. The peaks in creep rate approximately coincide with the thermal peaks, reflecting the sensitivity of creep rate to temperature. It may also be noted that the stresses are transiently augmented by the through-thickness thermal gradients which arise from the surge in incident heat flux, although this is a relatively small effect in the case being considered. It may be noted from Fig.5(b) that the creep rates become lower towards the end of the spraying period, even though the temperatures attained are not very different from those of the earlier cycles. This effect is further quantified in Fig. 6, which shows the peak creep rates within each cycle. The decrease for the later cycles is not due to the effect of the creep on the stress levels 5 ........ ~1Il

0

,

.~

'"

I~

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~

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-5

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•

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t t

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Fig. 5. Plots showing predictions or the creep rate variations during a spray cycle at different points within the substrate during (0) the twelfth cycle and (b) the twenty fourth cycle. e, modelling point; X, gun axis; ---, path or gun movement.

66

Y.C. Tsui et al.

I Simulation of creep effect on stress during VPS onto Ti 60 40

....

co 20 a, ~

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10 15 20 Spray cycle number

25

30 (b)

..........-'-'-~~ ..........~..........~~~--'--'-:' 1.0 2.0 3.0 Distance from rear face of substrate (mm)

'-"-~~~

o

Fig. 6. Plot showing predicted changes in peak creep rate in the substrate within a spray cycle, as a function of the cycle number, for quenching stress values of (a) 30 MPa and (b) 0 MPa.

Fig. 7. Predicted distributions of stress within the specimen at four different times during spraying (a) with no creep and (b) with creep included.

in the substrate, since these stabilise after about 10 cycles (see section 4.3 below). Additional information on the origin of the variations in peak creep strain rates is presented in Fig. 6(b), which shows qualitatively similar behaviour when the quenching stress set to zero. This confirms that the rise and subsequent fall in peak creep rate is not dependent on the stress fields caused by the quenching stress, although they affect the magnitude of the changes.

stabilize at levels substantially below those generated in the absence of creep. This leaves the question as to why the creep rates fall off towards the end of the process. The main reason for this is that the deposit increasingly provides thermal insulation for the substrate, so that the maximum temperature experienced by the substrate as the gun passes by is progressively reduced, lowering the peak creep rate. The predicted residual stress distributions which remain after final cooling to room temperature are shown in Fig. 8, with and without creep occurring in the substrate. It is noticeable that the final levels of residual stress are actually greater in the presence of creep. This occurs because the differential thermal contraction taking place during the final cooling, which makes a large contribution to the final stress levels, is offset to a greater degree in the absence of creep by the higher stress levels present at the end of spraying in that case. Finally, it may be noted that somewhat different behaviour is predicted when the substrate is relatively thick, as indeed it would be for many cases of commercial interest. In Fig. 9, plots of residual stress are compared for three different substrate thickness levels. As expected, the residual stresses in the substrate (and the stress levels during spraying) are reduced as its thickness is increased. Also, it can be seen from the increasing linearity of the

4.3. Effects ofcreep on residual stress levels The creep rate variations described above can be understood on examining the changing stress distribution within the specimen during the process. In Fig. 7, this distribution is plotted at four different times (remote from transient heating effects), for the model runs carried out with and without substrate creep. In Fig. 7(a), with no creep, it can be seen that deposition leads to a continuously increasing stress gradient in the substrate. This is because the net tensile force exerted by the deposit increases, bending the substrate over towards the gun so that its front face is compressed. When creep occurs (Fig. 7(b)), however, the stress distributions are substantially modified. Stress levels in the substrate are still low during the early cycles, accounting for the low creep rates. After 10 or so cycles, however, the stresses

Y.c. Tsui er at. / 200

Simulation of creep effect on stress during VPS onto Ti

r-~......~.......--,-.-~....~ ~.....~....~......-,

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.~ -100

-150 -2000 (b)

0.5

1.0

1.5

2.0

2.5

3.0

Distance from rear face of substrate (mm)

Fig. 8. Predicted distributions of residual stress within the specimen after cooling to room temperature (a) with no creep and (b) with creep included.

c;; 0-

:2

100

en en

... Q)

ti

substrate stress distributions as thickness increases that the amount of creep which occurs has become negligible for the thick substrate case shown. It should, however, be noted that the average residual stress level in the coating is not very sensitive to substrate thickness, although the gradient of stress is markedly greater when the substrate is thin.

5. Conclusions The following conclusions may be drawn from this study. (1) Experiments have been carried out in which the temperature and curvature histories of thin titanium substrates have been recorded during thermal spraying with boron carbide coatings. These results have been compared with predictions from a numerical model of the spraying process in which the changing stress distribution within the specimen is described. (2) Agreement between model and experiment was fair for the basic form of the model but could be improved by incorporating the effect of creep in the substrate during spraying. Although significant amounts of creep were predicted by the model to be occurring

a

OJ

;;l

"0

.~ -100

a:

(c)

5.0

10.0

15.0

20.0

25.0

Distance from rear face of substrate {mm)

Fig. 9. Predicted distribution s of residual st ress within the specimen after cooling to room tempera ture, with creep included and substrate thickne sses of (a) 2 mrn, (b) 4 mm and (c) 20 mm.

only at specific points during the spraying process, this had a marked effect on the stress levels. (3) Creep was found to reduce the levels of stress in the substrate during spraying, but the final residual stress levels were predicted to be higher. This occurred because of the reduced degree to which the stresses present at the end of spraying were able to offset the stresses arising during subsequent cooling as a result of differential thermal contraction. (4) The stress levels in the substrate, and hence the creep rates during the process , are reduced as the thickness of the substrate is increased. The average final residual stress level in the coating does not change very

68

Y.c. Tsui et al. I Simulation of creep effect on stress during VPS onto Ti

much as the substrate thickness rises, but the magnitude of the through-thickness stress gradient decreases.

Acknowledgments

This work forms part of an ongoing programme supported by the Science and Engineering Research Council, concerned with residual stresses in sprayed coatings and the scope for their control via functional grading and process control. In addition, financial support for one of us (YCT.) is being provided by the Commonwealth Scholarship Commission in the UK. Various discussions with Dr. S.J. Howard, of Cambridge University, have proved very useful.

References 1 M. K. Hobbs and H. Reiter, Residual stresses in Zr02-8%Y203 plasma-sprayed thermal barrier coatings, Surf Coat. Technol.; 34 (1988) 33-42. 2 H. Zhuang and C. Gu, A study on residual stress of ZrO + MgO plasma sprayed coating, in H. Eschenauer, P. Huber, A. R. NicoIl and S. Sandmeier (eds.), Proc. 1st Plasma-Technik Symp., Lucerne, 1988, Vol. 2, Plasma Technik, Wahlen, 1988 pp. 277-284. 3 R. Kingswell, K. T. Scott and D. T. Gawne, Measurement of residual stress in vacuum plasma sprayed alumina coatings, Proc. l st Int. Conf. on Plasma Surface Engineering, Garmisch Parten kitchen, 1988, Deutsche Gesellschuft fur Metallkunde Informationsgesellschaft, Oberursel 1989, pp. 695-702. 4 U. Selvadurai and W. Reimers, Characterisation of phase composition and residual stress state in plasma sprayed ceramic coatings, in P. Vincenzini (ed.), Proc. 7th World Congo on High Technology Amsterdam, 1990, Ceramics, Montecatini, 1990, Elsevier, pp.319-328. 5 D. Stover, D. A. Jager and H. G. Schutz, Residual stresses in low pressure plasma sprayed chromia coatings, in T. F. Bernecki (ed.), Proc. 4th Nat. Thermal Spray Conf., Pittsburgh, PA, 1991, American Society for Metals, Metals Park, OR, 1991, pp. 215-219. 6 R. Kingswell, K. T. Scott and B. Sorensen, Measurement of residual stress in plasma sprayed ceramic coatings, in S. Blum-Sandmeier, H. Eschnauer, P. Huber and A. R. Nicoll (eds.), Proc. 2nd PlasmaTechnik Symp. Lucerne, (1991), Vol. 3, Hafliger Druck AG, Wettingen, 1991, pp. 377-388. 7 D. S. Rickerby, K. T. Scott and G. Eckold, Analysis of the residual stresses in plasma sprayed coatings, in H. Eschenauer, P. Huber, A. R. Nicoll and S. Sandmeier [eds.), Proc. 1st Plasma-Technik Symp., Lucerne, 1988 Switzerland, Vol. 2, Plasma Technik, Wahlen, 1988, pp.267-276. 8 R. Elsing, O. Knotek and U. Baiting, Calculation of residual thermal stress in plasma-sprayed coatings, Surf. Coat. Technol., 43-44 (1990) 416-425. 9 S. Takeuchi, M. Ito and K. Takeda, Modelling of residual stress in plasma-sprayed coatings: effect of substrate temperature, SIIIf. Coat. Technol., 43-44 (1990) 426-435. 10 S. C, Gill, Residual stresses in plasma sprayed deposits, Ph.D. Thesis, University of Cambridge, 1991. 11 J. D. Lee, H. Y. Ra, K. T. Hong and S. K. Hur, Analysis of

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deposition phenomena and residual stress in plasma spray coatings, Surf. Coat. Technol., 56 (1992) 27-37. R. Elsing, O. Knotek and U. Balting, The influence of physical properties and spraying parameters on the creation of residual thermal stresses during the spraying process, Surf. Coat. Technol.; 41 (1990) 147-156. S. C. Gill and T. W. Clyne, Property data evaluation for the modelling of residual stress development during vacuum plasma spray deposition, in H. Exner (ed.), Proc. 1st Eur. Conf. on Advanced Materials lind Processes, Aachen, 1990, Vol. I, Deutsche Gesellschafr fiir Metallkunde, Darmstadt, 1990, pp. 1221-1230. S. J. Howard, The interfacial toughness of plasma sprayed coatings on titanium alloys, Ph.D. Thesis, University of Cambridge, 1993. S. C. Gill and T. W. Clyne, Residual stress modelling and characterisation of thermally sprayed ceramic coatings, in P. Vincinzini (ed.), Advanced Structural Inorganic Composites, Elsevier, Amsterdam, 1991, pp.339-352. S. Gill and T. W. Clyne, Thermomechanical modelling of the development of residual stress during thermal spraying, in H. Eschenauer, P. Huber, A. R. Nicoll and S. Sandrneier (eds.), Proc. 2nd Plasma-Technik Symp., Lucerne, 1991, Vol. 3, Plasma Technik, Wahlen, 1991, pp. 227-238. S. C. Gill and T. W. Clyne, The effect of substrate temperature and thickness on residual stresses in plasma sprayed deposits during thermal spraying, in T. W. Clyne and P. J. Withers (eds.), Proc. 2nd Eur. Conf. on Advanced Mmerials and Processes, Cambridge, 1992, Vol. 1, Institute of Materials, London, 1992, pp. 289-297. T. W. Clyne and S. C. Gill, Heat flow and thermal contraction during plasma spray deposition, in I. Tanasawa (ed.), Heat Transfer in Mamljacturing and Processing of New Materials, Oji Jilt. Semill., Tomakomai Hokkaido, 1990, Hemisphere, New York, 1990, pp.33-48. S. C. Gill and T. W. Clyne, Modelling of the generation of residual stress during thermal spraying of ceramic coatings, in P. Vincenzini (ed.), Proc. Zth World Congr. on High Technology Ceramics Montecatini, 1990, Elsevier, Amsterdam, 1990, pp. 339-352. S. Kuroda and T. W. Clyne, The quenching stress in thermally sprayed coatings, Thin Solid Films, 200, (1991) 49-66. S. Kuroda and T. W. Clyne, The origin and quantification of the quenching stress associated with splat cooling during spray deposition, in H. Eschenauer, P. Huber, A. R. Nicoll and S. Sandmeier (eds.), Proc. Znd Plasma- Technik Symp., Lucerne, 1991, Vol. 3, Plasma Technik, Wahlen, 1991, pp. 273-284. S. Kuroda, T. Fukushima and S. Kitahara, Significance of the quenching stress in the cohesion and adhesion of thermally sprayed coatings, in C. C. Berndt (ed.), Proe. Int. Thermal Spray Conf. and Exposition, Orlando, FL 1992, American Society for Metals, Metals Park, OH, 1992, pp. 903-909. K. Janghorban and S. Esmaeli, Deformation mechanism map for Ti-6wt%AI alloy, J. Mater. 26 (1991) 3362-3365. P. M. Sargent and M. F. Ashby, Deformation maps for titanium and zirconium, Ser. Metall., 16 (1982) 1415-1422. S. C. Gill and T. W. Clyne, Investigation of residual stress generation during thermal spraying by continuous curvature measurement, Thin Solid Films, submitted for publication. S. Kuroda, T. Kukushima and S. Kitahara, Simultaneous measurement of coating thickness and deposition stress during thermal spraying, Thin Solid Films, 164 (1988) 157-163. W. J. Parker, R. J. Jenkins, C. P. Butler and G. L. Abbott, Flash method of determining thermal diffusivity, heat capacity and thermal conductivity, J. Appl. PIlys., 32 (1961) 1679-1684. K. Heritage, C. Frisby and A. Wolfenden, Impulse excitation technique for dynamic flexural measurements at moderate temperature, Rev. Sci. Illstrt/m., 59 (1988) 973-974.

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