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Surface & Coatings Technology

Residual stresses and elastic modulus of thermal barrier coatings

graded in porosity

A. Portinhaa, V. Teixeiraa,*, J. Carneiroa, M.G. Beghib, C.E. Bottanib, N. Francoc, R. Vassend,

D. Stoeverd, A.D. Sequeirac

aGRF-Functional Coatings Group, Physics Department, University of Minho, Campus de Azurem, 4800 Guimaraes, PortugalbDepartment of Nuclear Engineering, Polytechnic of Milan, Via Ponzio 34/3, I-20133 Milan, Italy

cNuclear and Technological Institute, Estrada Nacional 10, 2686-953 Sacavem, PortugaldInstitute for Materials and Processes in Energy Systems 1, Forscchungszentrum Julich GmbH, D-52425 Julich, Germany

Available online 11 September 2004

Abstract

Zirconia (ZrO2) stabilized with 8 wt.% Y2O3 is the most common material to be applied in thermal barrier coatings (TBC) owing to its

excellent properties: low thermal conductivity; high toughness and thermal expansion coefficient similar to iron. Nevertheless, in order to

increase the coatings lifetime, improvements in their thermomechanical behavior are still needed. With that purpose, we propose in this paper

a graded ceramic coating. These TBC have been produced by depositing a conventional NiCoCrAlY bond coat on a Inconel 738 LC substrate

followed by an atmospheric plasma sprayed top coat of ZrO2–8wt.%Y2O3 with a porosity gradient along the cross section.

The aim of the present contribution is to study residual stresses and elastic properties of the coating as a function of the porosity gradient.

For the characterization of the TBCs residual stresses, we have used Raman and X-ray diffraction (XRD) in different thermal conditions: as-

sprayed, after thermal shock at 1000 8C, and annealing at 1100 8C in air during 100 h. The top coatings show compressive stresses near the

interface with the bond coat. A decrease of the stress level is observed along the cross section towards the surface. The residual stresses

increase after annealing, however, have smaller variations after thermal shock.

The elastic properties were evaluated by Brillouin scattering: the scattering of laser light by acoustic waves in the GHz frequency range.

The spectra at different depths indicate that in the annealed condition the acoustic velocity increases when approaching the external surface.

D 2004 Published by Elsevier B.V.

Keywords: Thermal barrier coatings; Residual stresses; Young’s modulus; Zirconia

1. Introduction

Zirconia (ZrO2) stabilized with 8 wt.% Y2O3 is the most

common material to be applied in thermal barrier coatings

(TBC) owing to its excellent properties: low thermal

conductivity; high toughness and high thermal expansion

coefficient, good wear and erosion resistance.

Due to these properties and combined with protection

from oxidation, sulfidation and hot corrosion of the

structural Ni or Co based super alloys, thermal barrier

0257-8972/$ - see front matter D 2004 Published by Elsevier B.V.

doi:10.1016/j.surfcoat.2004.08.014

* Corresponding author. Tel.: +351 253 510465/400; fax: +351 253

510401.

E-mail address: vasco@fisica.uminho.pt (V. Teixeira).

coatings are widely used to protect gas turbines components

(vanes, blades, shrouds, etc.) and diesel engines, and

improve performance at high temperatures [1–3], allowing

higher inlet temperatures for the same cooling rates or even

reducing and simplifying the cooling systems.

Each time higher operation temperatures are required and

in order to obtain systems of coatings that allow its range of

temperatures it is necessary to develop new materials for

coatings or new architectures for the existing materials.

These new concepts of TBCs should have lower thermal

conductivity, and be more stable at higher temperatures than

the conventional ones [4–7].

The residual stresses in TBCs systems have an important

influence in the behavior, performance and lifetime of the

188–189 (2004) 120–128

A. Portinha et al. / Surface & Coatings Technology 188–189 (2004) 120–128 121

coated parts. In fact, the integrity and performance of

coatings applied with different purposes (corrosion, thermal

and hard protection) are strongly dependent on the nature

and magnitude of the residual stresses. In the case of high

tensile stresses, film cracking will be present and in an

excessive compressive stress field a film decohesion caused

by buckling will be installed. It is important to consider two

different origins for the residual stresses in the TBCs [8],

one is the coating deposition process and another is the

service conditions on the coated parts. One source of

intrinsic residual stress of as-sprayed ceramic top coating by

plasma spraying is the thermal residual stress that arises

from the nature of the plasma spraying process associated

with the quenching effect of the splashed molten droplets

arriving to the cool substrate or with lower temperature of

the solidified coating during the coating growth.

The other is due to the different coefficients of thermal

expansion (CTE) and/or temperature gradients of the

ceramic top layers, the bond coats and metallic components.

After heat treatments or during service, the stress states of

the as-sprayed condition can be largely changed due to

stress relaxation during high temperature operation. Besides

the residual stress changes, an additional thermal growth

oxide (TGO) also causes an interface stress field. The

overall stresses are responsible for delamination or fracture

of the material at the interface between the thermal growth

oxide (TGO) and the ceramic top layer [9–11].

At the surface of the as-sprayed coatings, the residual

stresses are almost zero or have lower tensile state [1,12].

However, within the coatings in the plane parallel to the

interface the stress state shows a biaxial compressive stress

distribution with a gradient across the section.

X-ray diffraction (XRD) is a nondestructive technique that

can be used to determine stresses at the near surface region of

materials. XRD can be used to measure the strains within the

coatings and from there one can determine the residual

stresses. The state of the elastic strain promotes changes in the

lattice plane spacing when compared with the ones free of

stresses allowing for the determination of the stress state in

the material. The most commonly used process is the sin2wmethod [13,14]. If one needs to evaluate the stress state as a

function of depth along the cross section of the coatings, one

can use a destructive approach and remove layer by layer.

Micro-Raman spectroscopy is a powerful technique to

study the structural changes in the coatings because Raman

scattering depends on electron–phonon interactions that are

very sensitive to local environments [15,16] and due to its

sensitivity it is a suitable technique to identify and study

small changes in the stress states of the coatings [12,17,18].

The Brillouin scattering technique is an optical method to

probe the elastic properties: the inelastic scattering of light

by ultrasonic waves of sub-micrometric wavelength is

observed. This provides a contact-less and nondestructive

way to measure the acoustic properties, with a spatial

resolution of tens of micrometers. While X-ray and Raman

techniques are most sensitive to local order at the atomic

scale, Brillouin scattering probes the behavior of sub-

micrometric acoustic waves, and is therefore sensitive to

the structure at a mesoscopic scale, comparable to the

characteristic sizes of ceramic grains and of porosity.

This contribution presents the results of residual stresses in

plasma sprayed coatings: (i) for as-sprayed condition, (ii)

after thermal shock (100 cycles, heating at 1000 8C in air

during 1 h and then cooling down in water), (iii) after annea-

ling at 1100 8C in air during 100 h. This study was well done

at the surface and along the cross section in order to under-

stand the residual stresses gradient through the interface to-

wards the surface of the ceramic top coat and was also related

with the porosity gradient. By Brillouin measurements, the

elastic properties for the TBCs were also evaluated.

2. Experimental

2.1. Preparation and characterization

The TBC have been produced by depositing a conven-

tional NiCoCrAlY bond coat deposited by vacuum spraying

on an Inconel 738 LC substrate, followed by an atmospheric

plasma sprayed top coat of ZrO2–8wt.%Y2O3 with a

porosity gradient along the cross section. The coatings

porosity levels were quantitatively evaluated by mercury

intrusion technique and by image analysis. The porosity

increases from the bond coat interface towards the surface of

the top coat. In as-sprayed condition, the porosity increases

typically 8% near the interface to 18% at the surface. After

annealing condition, we observe a significant reduction in

its variation due to the sintering effects at high temperature

[19]. The details of deposition parameters and process

characterization are extensively explained elsewhere [19].

X-ray measurements in the mode h–2h angles in the range

of 20–808 using Cu Ka (40 kV, 30 mA) radiation in steps of

0.02 were performed in order to access the structural

characterization of the coatings. The average crystallite

dimension of coatings was determined by the Scherrer

equation after full with at half weight of maximum intensity

(FWHM) determination. Residual stresses were determined

by X-ray diffraction using the sin2w technique, using the

high resolution diffractometer Hotbird at ITN (Cu Ka1, 40

kW, 200 mA) with a beam of 0.4�1 mm2. Measurements on

[620] lattice plane of ZrO2 were performed to obtain the

coatings surface strains. The diffraction angle for this plane

occurred at about 2h=144.58. The w angle was scanned from

�258 to 258 by steps of 58 in order to get the interplanar

distance dw (the main parameters are listed in Table 1). The

biaxial stresses in the plane parallel to the interface were

calculated considering an isotropic biaxial stress distribution

with r33=0 (see Fig. 1).

The XRD spectra were acquired for the as-sprayed

coatings at three different depths, after annealing at 1100 8Cin air during 100 h and after 100 cycles thermal shock at

1000 8C with quenching in water.

Fig. 2. Cross section example of thermal barrier coating indicating the

positions where the Raman residual stresses were measured (A, B, C).

Table 1

XRD parameters used in the residual stress measurements

Diffractometer Hotbird (at ITN)

Anode current (mA) 200

Anode power (kW) 40

Radiation Cu Ka1

Lattice plane in analysis [620]

Range of measurement, 2h (8) 138 to 150

w range (8) �25 to 25

A. Portinha et al. / Surface & Coatings Technology 188–189 (2004) 120–128122

Raman spectroscopy measurements have been done

using an HeNe laser line at 633 nm wavelength with 1

mW power in order to obtain the Raman shift for the

coatings at various states as described before. A laser spot

(with a size of 2 Am) was positioned and scanned along the

cross section of the sample as represented in Fig. 2, in order

to collect the spectra at different depths of the coating. In

our case, we use the shift for the tetragonal ZrO2 Raman line

located at about 640 cm�1 to calculate the residual stresses.

This technique requires a previous calibration [12] and for

our material each cm�1 corresponds to 220 MPa.

Brillouin spectra were recorded at different depths on the

cross section of an annealed coating. Measurements were

performed in backscattering, with the 515.5 nm line of an Ar

ion laser. The focusing spot is of the order of 10 nm, and the

spectrum is analyzed by a 3+3 passes tandem Fabry–Perot

interferometer of the Sandercock type [20]. The fine-grained

ceramic structure, not completely opaque and rich of

internal surfaces, introduces a strong elastic scattering and

multiple scattering effects. These show up in the spectra as a

strong background noise and a peak broadening, which limit

the obtained information. In particular, peaks due to surface

acoustic waves could not be observed, while peaks due to

bulk waves were measured and characterized. As discussed

below, the probed acoustic wavelength is around 120 nm.

3. Theoretical background

3.1. X-ray residual stresses

3.1.1. h–2h mode

There are numerous experimental techniques to deter-

mine accurately the residual stresses in coatings and the

methods based in X-ray diffraction are well suitable for the

Fig. 1. Model of the in-plane elastic residual stresses (method sin2w).

assessment of the stress states in thin or thick films. In

general, the coatings have stresses in two or three directions

(principal stresses, r11, r22 and r33) forming orthogonal

angles called the principal directions [13,14]. In the surface

of the coatings usually a biaxial stress state is considered

where the r33 component perpendicular to the surface is

zero.

For this stress state, the strain perpendicular to the

surface, e33, being different of zero is calculated by:

e33 ¼ � vðe11 þ e22Þ ¼ � v

Er11 þ r22Þð ð1Þ

the e33 strain component is determined measuring the dhklinterplanar spacing of planes parallel to the surface:

e33 ¼dhkl � d0

d0ð2Þ

Combining Eqs. (1) and (2) and considering that

r11=r22=rc, we obtain the value of the residual stress

parallel to the surface, which is given by:

rc ¼ � E

2v

dhkl � d0

d0ð3Þ

where dhkl is the measured plane spacing of the coatings,

and d0 is the standard plane spacing from X-ray diffraction

files (2.96 2) for h111i planes of the ZrO2 tetragonal phase.

However, this method gives only approximate values due to

the uncertainty d0 and high diffraction angles should be

used. The so-called sin2w method is largely used for precise

quantitatively stress measurements.

3.1.2. Sin2w method

Considering Fig. 1, for a biaxial stress in the irradiated

layers of the surface TBC coating the lattice strains are

related to the stress by:

e/;w ¼ d/;w � d0

d0¼ 1þ v

Er/sin

2w � v

Er11 þ r22Þð ð4Þ

where d0 is the unstressed lattice spacing, d/,w is the lattice

spacing under stress, r/ is the stress present in the /direction defined in the plane of the coating, w is the tilt

angle, r11 and r22 are the stresses along the principal

directions, E is the Young’s modulus and t is the Poisson’s

ratio of the material. Eq. (1) predicts a linear relationship

A. Portinha et al. / Surface & Coatings Technology 188–189 (2004) 120–128 123

between d/,w and sin2w, and the stresses can be obtained

from a least squares fit of experimentally determined d-

spacing measured at a number of tilts, see Fig. 5.

The r/ stress is given by:

r/ ¼ r11cos2/ þ r22sin

2/ ð5Þ

and for w0=0 the strain in the perpendicular direction e33come as:

e33 ¼d/;w¼0 � d0

d0¼ � v

�e11 þ e22

�¼ � v

Er11 þ r22Þð

ð6Þ

Relating Eqs. (5) and (6), we get the following relation:

d/;w � d/;w¼0

d0¼ 1þ v

Er/sin

2w ð7Þ

which means that the strain difference between two

directions on a material under stress is only dependent of

the stress applied in this plane.

From this equation, we can calculate the r/ stress along

the / direction by the following equation:

r/ ¼ E

1þ vð Þsin2wd/;w � d/;w¼0

d0

��ð8Þ

Eq. (8) allows to calculate the stress in any direction on

the plane and the stresses in the / direction can be obtained

directly from the slope of a least-squares line fitted to

experimental data, measured at various w (see Fig. 5). If d0is not available, dw=0 can be used; this change normally

introduces an error lower than 0.1% in the stresses values

[14].

3.2. Raman stresses

The micro-Raman spectroscopy is also a powerful

technique to determine the phase structure and the residual

stresses of materials. This technique allows measurements in

very small areas (micrometer range) for the assessment of

the residual stresses in the coatings cross section as well in

the thin interlayer such as the thermal growth oxides in

TBCs [21]. The stress state evaluated by Raman spectro-

scopy requires a previous calibration curve where a stress

value determined by other technique is usually assumed.

Using this calibration sample, the relation between the

Raman shift and imposed external bending stress is

determined in order to obtain the calibration curve. The

shift in the peak position versus the intensity of the applied

stress is based on a linear fit of the experimental data. For

the ZrO2–8wt.%Y2O3 plasma sprayed coatings, Teixeira et

al. [21] found a linear relationship between the applied

stress and the peak shift and each cm�1 shift corresponds to

220 MPa. It is well known that the Raman shifts towards

higher wave numbers corresponding to an increase in the in-

plane compressive residual stresses and, in the inverse order,

a tensile residual stress.

3.3. Brillouin scattering

Brillouin scattering by longitudinal bulk waves was

observed. In a homogeneous medium of refractive index n,

mass density q and tensor of elastic constants Cij, back-

scattering of light of wavelength (in vacuum) k0 exchanges a

wave vector 2(2p/k0)n. Acoustic waves having wavelength

k=k0/2n are thus probed. The velocity of longitudinal bulk

waves [22] being vl ¼ffiffiffiffiffiffiffiffiffiffiffiffiC11=q

p, such waves have frequency

f ¼ffiffiffiffiffiffiffiffiC11

q

s2n

k0ð9Þ

and give, in the Brillouin spectrum, a peak at this frequency

shift. If the values of q and n are known, the elastic constant

C11 is measured. For an isotropic medium C11 is given, in

terms of Young’s modulus E and Poisson’s ratio m, by

C11=E(1�m)/(1+m)(1�2m).In the application of the method to a porous medium like

the TBC, the pore size distribution has to be carefully

considered. In general, for the propagation of a wave in a

porous (or, more generally, inhomogeneous) medium, the

waves sees the pores (much) smaller than the wavelength

only by an averaged effect: the wave propagates in an

effective equivalent homogeneous medium, whose proper-

ties are an average of the solid and pore properties. The

pores being much larger than the wavelength are seen as

external surfaces instead of pores, which simply reflect the

wave, while the pores of intermediate size diffract the wave,

dispersing its direction. In the TBC, since the laser wave-

length is k0=514.5 nm and the refractive index is of the

order of 2 (see below), the probed optical wavelength is

~250 nm, and the acoustical wavelength is half of it.

Therefore, the total porosity (void fraction) p can be

decomposed as p=p1+p2+p3 where p1 is due to dsmallTpores, below ~100 nm, p2 is due to dmediumT pores,

between ~100 nm and ~2 Am, and p3 is due to dlargeT pores,above ~2 Am. While dlargeT pores are seen by both optical

and acoustical waves considered here as external surfaces

which cause reflections only, dmediumT pores contribute to

diffraction, implying spectral peak broadening. Only the

dsmallT pores, being smaller than wavelength, are seen by

both types of waves as contributing to the properties of the

equivalent homogeneous medium in which they propagate.

Brillouin spectroscopy therefore probes the properties

of this equivalent medium formed by the compact

ceramics of properties nV, qV and CV11, and only the

fraction p1 of the porosity. The properties of such a

medium are q=qV(1�p1) (by definition) and CV11cC11(1�p1)

2/3; thus for acoustic waves vlcvVl(1�p1)�1/6.

For optical waves, a detailed analysis [23] gives the implicit

result 1� p1 ¼ ð1�n2ÞðnV2þ2n2Þ3n2ð1�nV2Þ ; for nVV3 and p1V0.15, the

decrease of n due to porosity remains below 0.3; the simple

average weighted by volume fractions ncnV(1�p1)+

p1=nV[1+(1/nV�1)p1] predicts this decrease to within 0.005

(absolute difference) and is therefore acceptable in this

A. Portinha et al. / Surface & Coatings Technology 188–189 (2004) 120–128124

range. Eq. (9) therefore gives ( fVis the frequency given by

nV, qVand CV11)

fcf Vð1� p1Þ�1=61þ 1

nV� 1

�p1

� �;

ð10Þ

Computation of df/dp gives Df/fV=(1/nV�5/6)p1; with

nVc2.2 this means Df/fVc�0.38p1: a 1% porosity in small

pores implies a 0.38% decrease in spectral peak frequency.

Fig. 4. Raman spectra of the coatings at various conditions (as-sprayed,

annealed and thermal cycled).

4. Results and discussion

4.1. Structural analysis and phase transformation

The structural analysis was performed to determine the

structure for all coatings and to determine the volume of

phase modification. Fig. 3 shows some typical XRD patterns

at lower angles and at high angles for the ZrO2–8wt.%Y2O3

plasma sprayed coatings in condition: as-sprayed, annealed

and thermal cycled coatings. All the as-sprayed coatings

present a polycrystalline tetragonal structure where the main

diffraction peak corresponds to the h111i planes. After

annealing and thermal shock for some of the tested samples,

a very small amount (less than 1–2%) of themonoclinic phase

was observed. The main diffraction peaks correspond to the

mh111i and mh�111i planes and due to the magnification

Fig. 3. XRD patterns of the coatings for the different conditions: (a) at

lower angles and (b) at high angles.

used in the plots these peaks are not visible. In Fig. 3b, the

high temperature tetragonal phases, which are well identified

as h004i and h400i peaks, are shown. After heat treatments,

no significant changes were observed which means a good

thermal stability of the coatings even after thermal cycling

exposure at high temperatures. TBCs during service at high

temperature the nontransformable tetragonal phases tend to

transform to the cubic phase and after cooling down, a

transformation to the monoclinic phase occurs [24]. It is well

known that the presence of monoclinic phase in TBCs should

be avoided because it reduces TBCs lifetime due to the 3% to

5% volume increase during the tetragonal to monoclinic

transformation inducing coating failure. A small shift in the

XRD peak positions, which can be explained by the changes

in the thermal stresses after heat treatments, is well observed.

Using a Pseudo-Voigt function, the main peaks were

fitted and determined for each peak the Gaussian and

Lorentzian components that represent the micro-strain and

grain size, respectively [25]. The grain size was determined

using the Scherrer equation. An increase in the grain size

after heat treatments was observed. These values are 31 nm

for the as-sprayed coatings, 68 nm for annealed and 60 nm

for the thermal cycled samples.

Fig. 4 shows the micro-Raman spectra of the ceramic top

layer of the TBCs studied where the typical Raman bands

for the tetragonal phase of stabilized zirconia coatings (146,

260, 320, 470, 612, 640 cm�1) are present. No monoclinic

bands were observed which confirms the results obtained by

XRD and no changes were observed after thermal cycling.

The principal Raman bands of zirconia tetragonal phase are

at 260 and 640 cm�1 and are related with the stretching

modes of Zr–OII and Zr–OI, respectively. Considering the

Raman band at about 640 cm�1, some shifts are observed

due to the presence of different in-plane stress states.

4.2. Residual stresses analysis

The low stress intensity in the plasma sprayed ZrO2–

8wt.%Y2O3 top coat can be understood by its low stiffness,

Fig. 5. d-spacing of the tetragonal h620i crystallographic planes of ZrO2

function of the sin2w measured at the surface of the coatings. Three

measurements are presented, each one for each condition of the samples. By

these slopes, it is shown that there is an increase in compressive stresses

with the heat treatments.

A. Portinha et al. / Surface & Coatings Technology 188–189 (2004) 120–128 125

which arises from its typical microstructure containing inter-

splat porosity and an intralamellar micro-crack that leads to

a high strain tolerance. After annealing and thermal cycling,

due to the sintering effects and microstructural changes, the

stiffness of the ceramic top coats increases which develops

higher stresses and a higher probability to failure [26].

The main factor affecting the lifetime of TBCs is the

resistance of the coatings to spallation after thermal

exposure due to the residual stresses generated [27,28].

During heat treatments or/and in service, a TGO grows

between bond coat and top coat and the sintering of the top

coat microstructure changes the stress states and reduces the

fracture toughness.

The average values of the residual stresses at the surface

obtained for the samples by various techniques are in Table 2

for the different conditions of the samples at room temper-

ature. An increase in the compressive residual stresses after

thermal cycling and annealing treatments can be seen.

Tensile stresses at the surface of the coatings are mainly

due to the rapid quenching of the splashed plasma sprayed

droplets, arriving to the substrate and to the surface of the

coating in growth process which is at lower temperature

than the molten sprayed particles. Fig. 5 represents the d-

spacing of the tetragonal h620i crystallographic planes of

ZrO2 versus sin2w measured at the coatings surface. These

data were used to calculate the stresses presented in Table 2.

The changes in the slopes indicate an increase in compres-

sive stresses with the heat treatments. For the as-sprayed

samples, a lower tensile stress at the surface due to the

typical growth of the coatings and quenching effects is

observed. The stresses are more compressive near the

interface and decrease towards the surface. After annealing,

the residual stresses increase in compression as expected,

due to relaxation at high temperature. The in-plane

compression stress state is related with an increase in the

elastic modulus of the material due to the sintering effects

like homogeneity of the pores and reduction in the cracks

width. After thermal cycling, the state of tensile stress also

increases in compression but reaches lower values than for

the annealed samples. This difference can be explained by

some relaxation effects due to quenching. This rapid cooling

develops some micro-cracks within the coatings that have

an opposite effect to the sintering process developed during

the exposure at high temperature.

At high temperature, a residual stress relaxation on the

ceramic top layers is observed. After cooling down to room

temperature, a higher compressive stress is developed

Table 2

Residual stresses measured at the surface determined with different

techniques

Sample condition Measurement method

XRD (MPa) XRD–sin2w (MPa) Raman (MPa)

As-sprayed �92 37 c0

Annealed �404 �22 �594

Thermal cycled �37 �14 �462

within the coatings due to the differences between the

coefficients of thermal expansion of substrate and coatings.

Another factor which influences the residual stresses at the

interface between the top coat and bond coat is the growth

of the thermal growth oxide developed at high temperatures,

which is mainly a-Al2O3.

As it is presented in Fig. 6a, the residual stresses

evaluated by micro-Raman spectroscopy along the cross

section in the annealed samples increase in compression

from a small traction at the free surface towards the interface

near the TGO where a value of 660 MPa is reached.

Measurements inside the TGO were also performed but it

was not possible to assess the residual stresses due to the

background of the spectra which was high enough to absorb

any peak of the TGO. These results are in agreement with

the theory [29].

Fig. 6. Residual stresses evolution along the cross section: (a) for the

annealed samples determined by Raman analyses; (b) for the as-sprayed

samples determined by XRD–sin2w, and the residual stresses for the

annealed and thermal cycled samples at the surface is also represented by

this method.

A. Portinha et al. / Surface & Coatings Technology 188–189 (2004) 120–128126

In Fig. 6b, the values of the residual stresses measured by

XRD–sin2w method for the samples in the three conditions

studied are plotted. These values are plotted for the surface

position and for the as-sprayed condition the evolution of the

residual stresses along the cross section towards the interface

with bond coat is also plotted. These measurements along the

cross section have been done after successive remotion of

material by polishing which means that these values can be

affected by the stresses imposed with the polishing process;

however, this operation had been done carefully and at very

low loads. The residual stresses for the as-sprayed condition

change gradually within the coating with the maximum in-

plane compressive stresses at the interface and very low

values at the free surface. These results are in agreement with

the modeled residual stresses done by Teixeira et al.

[1,21,30] which show a gradient in the residual stresses

with higher compressive stresses at the interface decreasing

to very low values of the stresses on the surface.

The results plotted in Fig. 6 show a similar behavior in

the evolution of the residual stresses through the cross

section for the coatings after deposition and after annealing

in a furnace at 1100 8C during 100 h. From the theoretical

concepts, the residual stresses increase in compression

towards the interface with the bond coat for the annealed

samples. The differences in the values before and after

annealing can be justified by the stress relaxation, sintering

effects, mismatch of thermal expansion coefficients between

the top layer and the metallic part. Near the interface the

residual stresses can be affected by strains developed during

TGO growth. For the as-sprayed samples, the values of the

residual stresses can be affected by the preparation

technique because the material layer removing after layer

tends to increase slightly the compressive stresses due to

some densification promoted by the low pressure polishing

of the surface.

The results plotted in Fig. 7 relate the residual stresses

with the porosity. It is well observed that for the lower

Fig. 7. Changes in the residual stresses as function of the porosity contents

along the cross section for the as-sprayed coatings (measurements

effectuated by sin2w).

porous structure the residual stress increase in compression.

This effect means that the control on the level of porosity

within the coatings could be used to produce graded

coatings in porosity in order to control the residual stress

distribution. This is in agreement with theory because

coatings with lower porosity have higher elastic modulus

and also higher stiffness which predicts higher levels in

compressive residual stresses; nevertheless, this alone is not

the only reason for compressive stress. The porosity level

and the shape of porous have an important influence in the

elastic modulus. In fact, an adequate porosity control

enables to obtain an optimized lifetime of thermal barrier

coatings [30].

4.3. Elastic properties

The main findings from Brillouin spectra are as follows:

a single peak is observed, which is due to a bulk wave

because its frequency does not change with the incidence

angle (the frequencies of peaks due to surface waves scale

as the sine of the incidence angle). Since in backscattering

peaks due to transverse waves are much weaker, this peak is

attributed to the longitudinal bulk wave. The first result is

that the frequency of this peak is around 17 GHz,

throughout the thickness. From Eq. (9), assuming for the

effective medium, due to small pores only, qc5500 kg/m3

and nc2, this frequency gives C11c26 GPa; assuming

mc0.23 (the value of tetragonal zirconia) this means for

Young’s modulus Ec22 GPa. The precision of this value is

limited by the precision of the measured frequency of the

spectral peaks, and of the estimates of values of q and n due

to small pores only, not to the total porosity. This is a

relatively low stiffness, and could be attributed to defects at

grain boundaries, implying nonperfect adhesion among

grains, and also to the influence of the boundaries

themselves. The grain size being of the order of 60 nm

(half of the acoustic wavelength), even if boundaries are

defect free they contribute to scattering and diffraction of

the acoustic wave, possibly affecting the effective prop-

agation velocity.

The second finding comes from the comparison of the

spectra at different depths. Residual stresses are non-

influential, because their effect on the acoustic velocity is

only through the third order elastic constants; porosity

instead changes with depth. Experimentally as it is plotted in

Fig. 8, in an outer layer of approximately 20% of the TBC

thickness, peaks are relatively sharp and well defined; in the

rest of the thickness peaks become significantly weaker and

broad (they extend from 13 up to 18 GHz, their weak and

noisy aspect making rather erratic a statistical fit to attribute

a more precise frequency). Light scattering and diffraction

by small pores and internal surfaces tend to broaden the

peaks toward lower frequencies, because light emerging

from scattering events not perfectly in backscattering (and

therefore of lower frequency) can, by successive elastic

scattering, be deviated and collected. The sharper peaks in

Fig. 8. Brillouin spectra measured in the cross section of an annealed TBC,

close to the external surface (dots) and at mid-depth (crosses). Continuous

lines are smoothed interpolants. (The anti-Stokes part is shown, while

interpolation is performed on the average of Stokes and anti-Stokes parts.)

A. Portinha et al. / Surface & Coatings Technology 188–189 (2004) 120–128 127

the outer layer therefore suggest a lower fraction of dsmallTand dmediumT pores in the outermost layer. This is

consistent with the indication coming from frequency:

although for spectra from deeper layers the peak frequency

cannot be precisely attributed, these broad peaks tend to be

at slightly lower frequencies than those measured from the

outer layer. According to the analysis presented above, an

increase of porosity in dsmallT pores induces a decrease in

spectral peak frequency.

In conclusion, a precise analysis of Brillouin data is not

possible because of the poor quality of spectra, due to the

nature of ceramic materials; the YoungTs modulus turns to

be around 22 GPa, and there are consistent indications

(although not a conclusive evidence) that in the annealed

specimen the porosity due to either dsmallT pores (below

~100 nm) or dmediumT pores (below ~2 Am) decreases

towards the outer surface, although the overall porosity

increases due to the dlargeT pores.

5. Conclusions

The residual stresses and elastic properties of graded

plasma sprayed ZrO2–8wt.%Y2O3 coatings have been

measured at room temperature for the as-sprayed coatings,

annealed and thermal cycled.

It was demonstrated that both X-ray diffraction and

micro-Raman spectroscopy are powerful techniques to

determine the microstructure and the residual stresses in

the coated parts.

Brillouin scattering detects bulk acoustic waves only,

allowing an estimation of Young’s modulus; since it is a

dmesoscopicT technique, it gives an indication on the

structure and porosity at the ~100 nm scale.

The coatings presents a tetragonal phase with a preferred

orientation on the h111i direction and no significant changesoccurs after thermal exposure. The most important change

was the grain size growth after heat treatments which

increase from 31 to 68 nm.

These graded thermal barrier coatings presents a tensile

stress state at the free surface which increase in compression

towards the interface. The residual stresses show an increase

in compression after annealing; however, for thermal

shocked samples, this increase is smaller.

It has been shown that the residual stresses increase in

compression when the porosity levels decrease; however,

more detailed studies are being performed in order to detect

or not the real physical correlation between coating gradient

porosity and residual stress distributions.

Acknowledgments

This work was financially supported by FCT-Portuguese

Foundation for Science and Technology under the project

POCTI/EME/39316/2001: bPVDCOAT—Composite and

multilayered protective coatings for efficient energy sys-

temsQ. The cooperative work is also supported by German-

Portuguese Cooperative Programme ICCTI-DAAD and

European Commission-DG-XII under contracts: ICCTI-

DAAD/423/2000, bComposite coatings for high temper-

ature applicationsQ and COST 522, WP2/SP2-1999/01:

bResidual stresses and failure in multilayered and function-

ally graded coatings for advanced energy systemsQ (projectsleader: V. Teixeira). A. Portinha is grateful for the Research

Grant supported by F.C.T.-Portuguese Foundation for

Science and Technology.

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