Materials Science and Engineering, A 160 (1993) 113-126 113

Origin and development of residual stresses in the Ni-NiO system: in-situ studies at high temperature by X-ray diffraction

Chun Liu Laboratoire de Microstructure et Mechanique des Materiaux (Unit~ de Recherche associde au 1219), Ecole Nationale Sup~rieure des Arts et M&iers, 151 boulevard de l'H6pital, 75013 Paris (France)

Anne-Marie Huntz Laboratoire de MOtallurgie Structurale (Unit~ de Recherche associ~e au CNRS 1107), B&iment 413, Universit~ Paris XI, 91405 Orsay C~dex (France)

Jean-Lou Lebrun Laboratoire de Microstructure et Mechanique des Materiaux (Unit~ de Recherche associ~e au CNRS 1219), Ecole Nationale Sup&ieure des Arts M~tiers, 151 boulevard de l'H6pital, 75013 Paris (France)

(Received May 4, 1992; in revised form July 31, 1992)

Abstract

In order to characterize the respective importance of the growth stresses, thermal stresses and stress relaxation developed in oxide scales, two high temperature chambers for X-ray diffraction were designed, allowing us to determine the stresses in both the oxide and the substrate with the sin 2 lp technique, at high temperatures or room temperature and during heating-cooling sequences. It was applied to Ni-NiO.

At room temperature after oxidation, NiO is subjected to compressive stresses whose level depends on the substrate thickness and on the oxidation time and temperature. In the substrate, compressive stresses are mainly due to internal oxidation. During oxidation at 900 °C, the oxide scale is subjected to slight tensile stresses which can be due partially to anionic diffusion, internal oxidation or the heating process. During heating-cooling sequences, the stresses in the scale decrease with increasing temperature and become negligible when the oxidation temperature is reached. The reversibility of the stress-temperature curve indicates that no stress relaxation occurs. The stresses found at room temperature are due only to thermal stresses and fit well the theoretical calculation of thermal stresses in NiO scale based on the newly deter- mined thermal expansion coefficients of Ni and NiO.

All these results show that the stresses found at room temperature are mainly generated during cooling and that the effect of the Pilling-Bedworth ratio or of factors playing a role during isothermal growth is negligible.

1. Introduction

Stress generation in the oxide scale developed on high temperature alloys may induce buckling, cracking and spalling of the scales, which, in turn, leads to the loss of protective properties and accelerates the degradation of materials. Because of the practical importance of the problem, review articles [1-7] provided information on the origins and development of the residual stresses in the metal-oxide systems. Although possible origins and sources have already been stated, the respective importance of growth stresses, thermal stresses, stress relaxation is not well distinguished. Attempts have been made in recent years to develop stress investigation techniques [6, 8]. Some of them, such as deflection techniques, acoustic emission and X-ray diffraction, allow determination either at room temperature or during heating-cooling

sequences, while others, such as the curvature method or the hole-drilling method, can give information only on stress at room temperature. Nevertheless, at this date, most of the studies on stress determination in metal-oxide systems have been performed at room temperature. It must be noted that, among all the mentioned techniques, X-ray diffraction allows one to determine the stress level in both the oxide scale and the substrate. In the last few years, interesting results have been obtained for both room temperature and high temperature studies, particularly on Cu20 [9-11], NiO [12-16], Cr20 3 [17-19] and A I 2 0 3 [20, 21] scales.

In order to characterize the respective importance of stress generation during the isothermal oxidation treat- ment (growth stresses) and during cooling (thermal stresses), and the part played by relaxation phenomena, two high temperature chambers for X-ray diffraction were designed [22-24]. Using the sin 2 ~p method, the

0921-5093/93/$6.00 © 1993 - Elsevier Sequoia. All rights reserved

1 14 C L iu et aL / Residualstresses in Ni -NiO

stress level can be determined in the scale and in the substrate at all steps of an oxidation process. The Ni-NiO system was chosen because only one oxide grows on nickel, the oxidation behaviour is well known [25-27], and residual stresses have already been deter- mined mainly at room temperature [ 12-15]. Theoreti- cal modelization of the stress development has also been performed recently on this system [28-30].

Our results will be discussed on the basis of the possible origins of stresses in such a system and by comparison with the experimental or modelization data in the literature.

mation on stress evolution during the "dead time", limited by the sin2q, method. For the direction (4, V)=( 0, 0) for example, the Bragg angle variation can be related to the stress state by

A[2Oo.o( hkl)] = s,( hkl)( o, + 02) - - 2

(2) cot 0

Such measurement provides information on the stress evolution when the diffraction is continuously recorded. Otherwise, the stress state cannot be deduced from a single unidirectional measurement.

2. Experimental details

2.1. Experimental method For X-ray stress analyses, the sin 2 ~0 technique was

used. Details of this method can be found in the litera- ture [31]. It can be summarized by the following expression for an isotropic material:

2 +s,(hkl)(o, + 0 2 ) - (1)

cot 0

with (4, ~0) the measurement direction, (hkl) the dif- fraction plane, A[20¢.,(hkl)] the Bragg angle stress- induced variation, ol and o2 the principal stresses, 0¢ the stress in the ~ direction, and ~sz(hkl) and sl(hkl ) the X-ray elastic constants.

Equation (1) relates the residual stresses in the material to the induced Bragg angle variation. ½s2(hkl) and s~(hkl) are the X-ray elastic constants which can be either calculated or measured. (4, ~0) is the measure- ment direction (Fig. 1). A complete tensor can be obtained when scanning in several directions. Using 15 ~p values currently, it takes about 10 min to deter- mine a stress value in a ~ direction. When the stress varies during the measurement time, the value thus obtained is an average value during the measurement.

The Bragg angle variation in a single direction (4, q') is also measured in this study in order to obtain infor-

Z incident measurement direction

• beam ~;-20 ~" (¢,V)

Fig. 1. Definition of the angles (in the ~ setting).

2.2. High temperature X-ray diffraction equipment The high temperature X-ray diffraction equipment

used in this study is composed of two high temperature chambers and of an improved computer-controlled Q- setting goniometer equipped with a position-sensitive detector. Both chambers, with X-ray transparent win- dows large enough for working at a large Bragg angle, enable us to use the sin 2 ~p technique with a ~p angle range greater than 70 °. In one of the chambers the sam- ple is heated by a Pt-10wt.%Rh resistance, reinforced with two hemispheric ceramic sheets. The working temperature of this chamber can reach 1100 °C. In the second chamber, the sample is directly heated by the Joule effect and the working temperature can reach 2100°C. For both chambers, the heating process is controlled with a digital temperature regulator. Heat treatment of samples can be made in room air, in a con- trolled atmosphere or in vacuum up to 10-3 Pa. Using this equipment, complete stress analysis can be per- formed within only a few minutes. Details of this high temperature X-ray diffraction equipment can be found elsewhere [22-24].

2. 3. Materials and sample preparation Nickel samples of two different purities were used in

this study. Their chemical compositions are given in Table 1.

For measurements at room temperature, the samples were mechanically polished with alumina up to 3 #m granulometry. The corresponding surface roughness R~ is equal to 0.03/~m. The surfaces were then cleaned in acetone and alcohol in ultrasound before oxidation. For high temperature in-situ measurements, samples were cold rolled in order to obtain different thick- nesses. The corresponding surface roughness Ra is found to be 0.4/~m. The sample surface was cleaned as described above before oxidation.

2.4. Experimental process 2.4.1. Oxidation treatment Various oxidation conditions were used in this study.

Oxidation treatments were conducted at a temperature

C Liu et aL / Residualstresses in Ni-NiO 115

TABLE 1. Chemical compositions of the nickel substrates

Element Amount (wt.%)

Nickel A" Nickel B (Ni-270)

Ni 99.7 99.97 Co 0.01 -- C 0.058 0.02 Si 0.01 0.001 S 0.003 0.001 Mo 0.084 0.001 Cu 0.005 0.001 Fe 0.01 0.005 Ti -- 0.001 Mn -- 0.001 Others -- --

"Provided by Imphy S.A., France.

TABLE 2. Material constants and X-ray diffraction conditions for the Ni-NiO system

Material Ni NiO Young's modulus (GPa) 200 220 Poisson's coefficient 0.30 0.30 Thermal expansion coefficient 17.5 14.5

(20-900"C)(x 10 -6 K- ') X-ray elastic constant ½s2 5.80 5.65

( xl0-6MPa -l) X-ray tube Cu Cr-Co Wavelength (nm) 0.15418 0.22909-0.17901 Filter Ni V-Fe Diffraction plane {420} {222}-{420} Bragg angle (*) (room T) 155.4 143.1-145.2 Average penetration depth in 12 5-9

bulk (/~m)

varying from 700 to 1130°C, under dry and wet oxygen and in room air. Nevertheless, most of the oxidation experiments were performed at 900 °C in air. The oxidation time varied from 15 min to 2 weeks. In most cases, the sample was furnace cooled (at about 300 °C h- 1).

2.4.2. X-ray diffraction Cr K a and Co K a radiations were used for the

room temperature and high temperature stress anal- yses of the oxide scale. The Cu K a radiation was used for the diffraction from the metallic substrate at room temperature. The X-ray diffraction conditions are collected in Table 2. Residual stresses were deduced using the mechanical X-ray elastic constants, which were calculated from the mechanical Young's modulus and Poisson's coefficient. The evolution of Young's modulus vs. temperature for NiO was taken from liter- ature [30]; its value at room temperature is equal to 220 GPa. Poisson's coefficient is equal to 0.3 and assumed to be constant with temperature.

As it takes 10 min to determine a stress value with the sin 2 ~0 method, a possible stress evolution during this measurement period cannot be directly observed. That is why experiments were also carried out by continuously measuring the Bragg angle variation for nickel and its oxide in a chosen (4, ~P) direction during high temperature oxidation. The Bragg angle of the {222} and {311} planes of NiO and the {220} plane of nickel were then used. Furthermore, with the position- sensitive detector used, the Bragg angles of both the NiO{311} and the Ni{220} planes were simultaneously recorded.

The sin 2 ~p method provides complete information on the residual stresses in the scale. As the measurement duration is too long for the observation of the stress evolution, especially in the first stage of oxidation, the stress evolution was also measured in a single given direction. This measurement, which is much more rapid, provides complementary informa- tion to the sin2~p method. However, it must be remarked that the stress information at the beginning of oxidation could not be easily obtained because the scale is thin and the temperature is unstable.

3. Experimental results

3.1. Oxidation Extensive studies on nickel oxidation and com-

parison with diffusion coefficients in NiO [26] have shown that grain boundary diffusion is an important mechanism during NiO growth. At 900 °C, cationic diffusion predominates and the scale grows according to the parabolic law

with A m the weight gain, S the oxidation surface, t the oxidation time, kp the parabolic constant and c con- stant.

The kinetic study of nickel oxidation is given in Figs. 2 and 3. Good agreement is observed with data in the literature [13, 14, 26]. It appears that the difference between the kinetic curves obtained in oxygen and in room air is not significant. The substrate thickness does not seem to have much influence on the oxidation rate, as shown by the behaviour of nickel A (Fig. 3). When we take this information into account, it can be said that the oxidation rate of nickel B is greater than that of nickel A (Fig. 3). Three suggestions can be put forward to explain this difference.

( 1 ) The difference in the initial substrate surface state: the crystalline defects due to cold rolling can increase the growth rate of the scale.

116 C L iu et al. / Residual stresses in Ni-NiO

5

,C ~ 4

3 m

m

Nickel A at 900*(2 ( sample thickness 4 mm)

"+ 1° Talm7 °Xm gaT; ' I I " 1"0 E ' ~ ) ~ ~'211"~"

f ~ ee• ••ee•j••el• . . . . . . .Hleon e•el•eoeo• ' = ~ n n ~ n n j m p c o o e e . . . . . .

i I i I i I i I J I

20 40 60 80 100

Oxidation time (hr)

Fig. 2. Kinetics of the oxidation of nickel A.

30 TABLE 3. Parabolic constants of nickel oxidation

20 2 Sample Oxidation

conditions Parabolic c o n s t a n t kp (mg 2 cm -4 h-1)

.o 10-S

,g

120

Ni A 900 °C, pure oxygen Ni A 900 °C, air Ni A 900 °C, primary vacuum Ni B 900 °C, pure oxygen Data from ref. 13 900 °C, air Datafrom ref. 14 900 °C, air

8.22 x 10 -2

8.57 x 10 -2

17.5 x 10 -2 (2.4-10.3) x 10 -t (1.7-5.2) x 10 -1

5 3( 900°C, Po2=l arm.

4 I + 4 - + + + + + + + + nickeIB I ~ . 4 - 4 -

+ ~ ~'Ly~ 4-4- 4- ÷" . , . ~ 4 - 4 ~ ~ "

~* 2 AAA~'itt aAA e al "~ 1 . A ~ t v ~ '~ % - nickel A 1(

.~ ~-r,- "%, 4- t=2.59 mm • ~. I ~ • t---4.1Orara .~ • t=1.36 mm

I I I I I I e I m 0

20 40 60 80 100 120 Oxidation time (h0

Fig. 3. Comparison of the oxidation kinetics of nickel A and B for various substrate thicknesses t.

(2) The surface roughness: as the surface roughness of sample B is greater than that of sample A, the real surface area of sample B is greater than its geometrical surface area, and the kinetic curve is hence overesti- mated.

(3) The impurity difference. It is found that the oxidation rate of nickel in pri-

mary vacuum is very low (Fig. 2). The scale thickness for an oxidation time up to 100 h is only about 2 #m. This allows us to conclude that the secondary oxida- tion effect during stress determination conducted under primary vacuum is negligible.

In Table 3, the oxidation parabolic constants obtained in this study or recently by other workers [13, 14] are collected. The differences found in these various studies are in the range of measured values reported for kp in the literature [26]. Indeed, the small- est value of kp in Table 3 leads to a k e value equal to 1.15 x l0 -H cm 2 s -1 and the greatest value to k c = 1.3 × 10-10 cm 2 s- 1. These differences in k c values could be due to the three factors mentioned above, i.e. to the surface roughness, to defects or to the impurity content and nature. This last parameter is not easy to discuss because analyses of impurities incorporated in the NiO scale were not performed in most cases.

Fig. 4. Cross-section after oxidation for 1 h at 900"C in air (cooling rate, 300 K h- 1).

Th e scale morphologies were observed by scanning electron microscopy on the surface and on transverse sections. In all cases (except for samples air quenched after oxidation), the scale is homogeneous but some defects (porosity and voids) are present a t t h e oxide S substrate interface, and internal oxidation occurs along the substrate grain boundaries (Figs. 4 and 5). For samples air quenched after oxidation, buckling (Fig. 6) and spalling are observed.

3.2. Stress determination at room temperature after oxidation

3.2.1. In the NiO scale Residual stresses in the NiO scale were studied after

oxidation at room temperature as a function of the oxidation conditions and of the sample thickness. The results are shown in Figs. 7-11.

It appears on Fig. 7 that, the higher the oxidation temperature, the greater are the absolute values of the stresses in the scale. In all cases, compressive stresses are detected.

C. Liu et al. / Residual stresses in Ni -NiO

-200

117

-300

-40O

-500

Z -600

~-700

-800 700

Nickel A 750°C. 116 h, room air 900°C, 1 h, pure Oxygen 1130"C, 0.5 h, room air

l ~ I t (substm__te)=3 mm

' ' 1'000 ' 800 900 1100 1200 Oxidation temperature (°C)

Fig. 7. Residual stresses at room temperature in the NiO scale as a function of the oxidation temperature.

Fig. 5. Nickel sample oxidized at 900 °C in room air for 55 h (cooling at 300 K h- l).

350 3xidation at 900"C • t=2.5 mm, Nickel A, air 250 ~. cnnwx ~,~r,~ * t=l.6 mm, Nickel A, air

. . . . . . . . . . . . . • " + 2 • ~ ,,--, 150 • concaves-ffa-- [ .l t=0.1 mm, NtckelB( ),O • " . .". ~ II, t=0.1 mm, Nickel B(-) 02

o e~ ~ 50 .: : suostrate thickness [ 1[* t--0.1 mm, Nickel B(+), air

~ ~o-150-50 I ~ - - - " ] ~ • t=0.1 mm, Nickel B,(-), air

'~ O-350 ¢~ Z - 4 5 0

-550 . . . . . . . . . . . .

-650 0 2.5 5 50 75 1001 325 350 375 400 Oxidation time (h)

Fig. 8. Residual stresses at room temperature in the NiO scale as a function of the oxidation time.

Fig. 6. Buckling of the NiO scale; nickel oxidized for 1 h at 900 °C in air and air quenched.

In Fig. 8, the stresses in the NiO scale for different substrate thickness and for nickel A or B are collected. For nickel B, owing to the small thickness (t = 0.1 mm),

• the samples were slightly curved after oxidation and determinations were per formed on both the convex and the concave surfaces. For short oxidation times, the absolute stress value increases; then the stress becomes stable and for longer oxidation times the stress slowly decreases. This has already been observed by Aubry [13]. It is important to note that, for nickel B, the stress level is much lower than for nickel

0.04 Oxidation at 900"C + : convex surface

: c o n c a v e s u r f a c e

~- : substrate thickness 0.03 r~

(D

.~ 0.02

• ",1 , ~ , 0.01 0 2.5 5 50

' " ' ° . l '

75 100

A t=2.5 ram, Nickel A, air I * t=l.6 mm, Nickel A, air I * t=0.1 mm, Nickel B(+),O2 I • t=0.1 ram, Nickel B(-), O21 , t=0.1 mm, Nickel B(+), air I • t=0.1 ram, Nickel B,(-), air I

I i i , i ,

325 350 375 400 Oxidation time (h)

Fig. 9. Diffraction peak breadth at room temperature as a func- tion of the oxidation time.

A and no significant differences between the stress values of the convex or concave surfaces of nickel B are observed. T h e peak breadth (defined by the peak breadth at two-fifths of its height) decreases rapidly with increasing oxidation time (Fig. 9).

T h e effect of the substrate thickness is verified in Fig. 10. U p to about 0.5 m m thickness a stress evolu- tion in the NiO scale is observed: the smaller the sub- strate thickness, the smaller is the stress absolute value,

118 C Liu et al. / Residual stresses in Ni-NiO

regardless of the oxide scale thickness. For larger substrate thicknesses, the stress becomes stable.

As shown in Fig. 11, the water vapor does not seem to have a significant influence on the residual stresses in the NiO scales.

As the average penetration depth varies according to the X-ray wavelength, two different X-ray tubes were used to study the stress gradient in the oxide scale. By X-ray diffraction, only residual stresses at the average penetration depth are measured, as schema- tized in Fig. 12. The results are given in Table 4. It is

200

100

~ -100

~ -200 Z .-= -300

~ -40o -500

~ - ~

-700

-800 0.0

Nickel A

Oxidation at 900°C, in room air, furnace cooling [ w 0.5h [

, , , , , , , I : , I I

0.5 1.0 1.5 2,0 6.5

Substrate thickness (rnm)

7.0

Fig. 10. Residual stresses at room temperature in the NiO scale as a function of the substrate thickness.

lOO o

• ~- -lOO

-300

N ~ -soo

-700 -800

0

N i c k e l A

O x i d a t i o n a t 9 0 0 ° C [

in room air for 5 h. I fu mac, e coolina:

i i i i | i • i . t . i , i

1 0 2 0 3 0

Vaporized water pressure (10 3 Pa) 40

Fig. 11. Residual stresses at room temperature in the NiO scale as a function of the vaporized water pressure.

shown that the residual stress distribution in the NiO scale depth is uniform. The result seems to agree with theoretical modelization of this system [29, 30]. How- ever, note that such a procedure does not allow one to detect a possible important variation in o near the oxide-metal interface.

3.2.2 In Ni substrate Residual stresses are determined in the substrate

using Cu K a radiation (Table 5). It appears that the stresses in the underneath substrate are small but always compressive, regardless of the oxidation condi- tions. This result does not seem to agree with theo- retical modelization [29, 30]. In both cases, it is suggested that the NiO oxide scale is subjected to com- pressive stresses and that the substrate is subjected to tensile stresses at room temperature. We shall explain this apparent contradiction between experience and theory later.

3.3. Stress determination at high temperature 3.3.1. During scale growth Residual stresses are studied in situ during high tem-

perature oxidation, as a function of time in isothermal conditions. Th e results are given in Figs. 13-15. It is

[ A: 900 *C. air, T ' /h B:~JO~C.~r.3~h ~ 20~ [[ L6mm

- - - O ' t a a v ~ ~ ' ~ ~...~

CoKa. averse , , ~

!

oxit~ I I

/--. . . . 401un

I I I

1.6 m

/I

B

oxide I I sube4ram

Fig. 12. Schematization of the average penetration depth accord- ing to the X-ray tube nature and to the scale thickness.

TABLE 4. Residual stresses in the NiO scale using different X-ray tubes

Sample Oxidation Substrate Scale conditions thickness thickness

(mm) (pm)

Residual stresses in NiO scale (MPa)

Using Cr Ka radiation ( r=5#m)

Using Co Ka radiation ( r=9#m)

Ni A 900 °C, room air, 1.6 20 77 h, furnace cooling

Ni A 900 °C, room air, 1.6 40 336 h, furnace cooling

- 385 + 22

- 268 + 23

-3 5 1 +1 2

-2 8 0 +2 3

C. Liu et al. / Residual stresses in Ni-NiO 119

TABLE 5. Residual stresses in the Ni substrate

Experimental conditions

Temperature Time Cooling rate (°C) (h) (Kh- ')

Residual stresses in Ni substrate (MPa)

900 l a =450 - 12_+87 900 1 ~ 300 - 15_+70 900 1 " 150 -2_+35 900 1 ~ 2xl04 -12_+109 900 0.5 b - 50 _+ 40

'~Ni A , t>0.4 mm. bData from ref. 13.

100

50

0

~- Nickel A

~, -50 I Oxidation at 900°C, room air, I substrate thickness 0.4 mm

. . . . . . !:. , ,

0 2 4 6 21 23 25 Oxidation time (h)

Fig. 13. Residual stresses in the NiO scale during growth.

shown (Fig. 131 that at 900 °C the oxide scale is sub- jected to slight but always tensile stresses during its growth. This result is obtained regardless of the sub- strate nature or its thickness and the same result was obtained for experiments conducted at 700 °C.

Studies using the sin 2 ~p method do not allow one to analyse a possible stress evolution during the measurement period. So, continued measurements of 20 variations in a single (4, ~P) direction were per- formed for large diffraction angles (Fig. 141. Moreover, simultaneous measurements on the Ni{2201 plane and the NiO{311} plane in a single direction (4, ~P) were also conducted in order to survey possible evolution in both the underneath substrate and the scale (Fig. 151. In all these experiments, no significant evolution is observed. The same results were obtained by oxidation at 1000 and 1100 °C.

3.3.2. During cooling and reheating In order to survey stress evolution during thermal

sequences, measurements were conducted during cool- ing to room temperature and during reheating to the oxidation temperature. The results for nickel A are presented in Fig. 16. A reversibility of the stress- temperature curve is observed. It is shown that, when reheating to the oxidation temperature, stresses in the oxide scale become negligible. The same effect is observed during cooling of a sample oxidized at 700 °C

138.5

Q 138.0 z

~ 137.5

Nickel B

I substrate thickness (1.1 mm

137.0 t t t t 0 5 10 15 20 25

Oxidation time (rain)

Fig. 14. Bragg angle variation at the beginning of oxidation.

130.50

130.48

130.46

o~ 130.44

130.42

0 130.40

130.38

130.36

130.34

130.32

130.30

Fig. NiO

Nickel B I Oxidation at 900°C, l '

I in room air ] _

I ~ - - ~

I 0 {220} Ni ! . {311} NiO

Substrate thickness 0.1 mm

. . . . II '

128.80

128.78

C ©

128.76 ~7

128.74 =~

128.72 ~

128.70 2 '~ 6 8 / 0

Oxidation time (h)

15. Simultaneous measurements of the Bragg angles of the scale and the nickel substrate during oxidation.

200 100 [ Oxidation at 900°C,[ Nickel A

+ 0 ~ -100 ~ -200 z -300 • -= -400

-500 ~ - [~_ Cooling -600 J . - 1 _r- I ° Re-heating -700 - 8 0 0 , I , I , I t

0 200 400 600 800 1000 Temperature (°C)

Fig. 16. Stress evolution, after 25 h oxidation at 900 °C, during cooling and during reheating to the oxidation temperature (nickel A).

(Fig. 17). Th e only difference is in the value of the stress reached at room temperature; after oxidation at 700 °C, residual stresses become equal to about - 350 MPa.

For nickel B samples of small thicknesses, the results are somewhat different, as shown in Table 6. Th e stress obtained at room temperature depends on the sub- strate thickness (see Figs. 8 and 10). This difference was not observed for a thickness equal to or greater than 0.4 mm (see Figs. 10, 16 and 181. Nevertheless, it can be observed that the a value obtained with thin samples is approximately equal to the stress value

120 C Liu et al. / Residual stresses in Ni-NiO

determined at room temperature for the same samples (see Fig. 10). Comparisons of the stress-temperature evolutions in vacuum for a pre-oxidized sample are given in Fig. 18. The stress-temperature curves are similar to that obtained by cooling at the end of the oxidation (see Fig. 16).

3.3.3. Stress evolution in isothermal conditions Nickel samples pre-oxidized for 1 h in air at 900 °C

and then furnace cooled were rapidly reheated at either 500 or 900 °C and maintained at this temperature in vacuum (Fig. 19). When heated at a given temperature, a stress evolution similar to that noted during an equiv- alent heating (see Figs. 16-18) is observed; at 500 °C, the stress becomes equal to - 200 MPa and at 900 °C it is equal to zero. Then, during the isothermal treat- ment, the stress keeps a constant value ( - 2 0 0 MPa and 0 MPa at 500 °C and 900 °C respectively).

4. Discussion

4.1. Growth stresses It is generally considered that the oxide scales grow

on a metallic substrate under compressive stresses when the Pilling-Bedworth ratio (PBR) is greater than 1, especially if the scale growth is controlled by pre- dominant anionic diffusion [5]. In the case of the Ni-NiO system, although cationic diffusion is pre-

~ 200

"~ -100 -200 -300

~ 4oo ~ -500

• ~ -7oo "~ -800

Oxidation at 700°C, I Ni lm~hy room air, 2I h, I substrate thickness I ~ , " .I. -

0 200 400 600 800 Temperature (°C)

Fig. 17. Stress evolution, after oxidation at 700 °C, during cool- ing and during reheating to oxidation temperature (nickel A).

dominant at 900 °C, anionic grain boundary or short- circuit diffusion is not negligible and, owing to the high value of PBR equal to 1.65, stresses would be expected to be compressive during NiO growth. In this study, it was shown that the NiO growth does not necessarily induce compressive stresses in the scales, nor stress evolution during scale growth (Figs. 13-15). The resid- ual stresses observed during oxidation are negligible compared with the stresses found at room temperature. This is confirmed by continuous measurements during

200 Nicke l A

z -4oo

a~ -800 subst ra te th i ckness 2 m m

sca e th ickness - 5 lain

-1000 ~ I ~ I ~ I ~ I 200 4 0 0 600 8 0 0 1000

Tempera ture ( °C)

Fig. 18. Stress evolution as function of temperature in a pre- oxidized NiO sample.

100

0

-100

~ - ~

z -300

~ -500

N -600

-700

-800

1

• i . i . i

1 2 3

l

S a m p l e p re -ox id ized a t 900 °C

in p u r e o x y g e n for I h

wi th subst ra te th ickness 1 m m

scale th ickness 5 pan

• i , i . i . | .

4 5 6 7

T i m e (h)

Fig. 19. Stress evolution in NiO scales treated in isothermal conditions.

T A B L E 6. Stresses measured at room temperature as a function of oxidation conditions, compared with theoretical calculation (oxidation in room air; cooling at 300 K h - ~ )

Type of stress Substrate thickness Scale thickness (mm) (/zm)

Stress (MPa) at the following oxidation temperatures

7 5 0 ° C 900°C 1130°C

Calculated thermal 1 5 - 410 - 540 - 680 Measured 1 5 - 385 - 550 - 720 Measured 0.2 5 - 235 Measured 0.1 5 - 104

C Liu etal. / Residualstresses in Ni -NiO 121

oxidation; the observed Bragg angles of both the oxide scale and the metallic substrate do not seem to vary with oxidation time (Figs. 14 and 15). Although slight, the stresses determined during oxidation at 900 °C are always tensile; this result agrees well with those reported by Homma and Pyun [9]. Their study indi- cated that, at 627 °C, the NiO scale grows under com- pressive stresses while, at 1027°C, the scale grows under tensile stresses. Using high temperature values of the mechanical X-ray elastic constant estimated by Touati et al. [30], the stress values observed by Homma and Pyun were recalculated; at 1027 °C, they are of the same order of magnitude as those obtained in the present study. The simultaneous measurement of Bragg angles on the two diffraction planes ({311} for NiO and {220} for the nickel substrate) at 900°C during oxidation confirms our previous measurement with {222} for NiO; no evident shifts in the diffraction peaks are observed for both the NiO scale and the nickel substrate during oxidation (Fig. 15).

However, the results obtained from in-situ measure- ments do not agree with the theoretical prediction of Bernstein [28], nor with the model proposed by Touati et al. [30], nor with the experimental observa- tion of Stout et al. [32]. Bernstein [28] proposed a stress generation model based on the PBR model for stress generation in the Ni-NiO system during high temperature oxidation. It was assumed in this model that the epitaxy relation between the substrate and the growing scale lasts only a few seconds. Residual stresses are essentially created by the volume differ- ence between the consumed substrate and the grown oxide. In this model, a correction factor ~o equal to 0.186 was introduced in order to keep stresses due to the volume difference reasonable; otherwise, residual stresses would not be realistic. In fact, neither this factor nor its value thus calculated is based on a physi- cal background. More recently, Touati et al. [30] tried to modelize stresses generation during isothermal oxi- dation. If the volume difference is taken into account, compressive stresses are generated in the scale during its growth, but they are rapidly relaxed at the oxidation temperature (after about 120 min oxidation). In our case, such evolution was not observed. Again, in this PBR-based model, a correction factor is needed and introduced. Stout et al. [32], using Mo K a radiation, studied the {111} peak of a thin (25 pm) nickel foil during oxidation at 900 °C. The results show changes in the lattice parameter during oxidation; the substrate is under strong tensile stresses during oxidation, and stress accumulation and relaxation are successively observed. It is, however, important to remark that in the experimental conditions used in this study, where the Bragg angle 2 0 is only about 20 °, the sensitivity of the Bragg angle shift to the lattice parameter changes is

low. Variations in the Bragg angle resulting from changes in the lattice parameter reported in this study seem very small compared with the resolution of the position-sensitive detector actually available. It is also important to note that the substrate thickness and purity are different from those used in our study. It is possible that, in our study, inner oxidation due to im- purities occurs and introduces compressive stresses in the substrate.

Three suggestions can be put forward to explain the slight tensile stresses in the NiO scale observed in our case during oxidation.

(a) Although cationic diffusion is predominant, anionic diffusion is not negligible [26] (particularly inward diffusion of the gaseous reactant through the scale (along microchannels)) and introduces compres- sive stresses in the newly formed oxide layer near the oxide-substrate interface. As the newly formed oxide grows under compression, tensile stresses are then generated in the outside oxide layers and in the under- lying substrate in order to maintain mechanical equilib- rium. It is known that, by X-ray diffraction, only stresses in the average penetration depth are measured [31]. In our study, the scale thickness varies from 3 to 15 pm, and the related average penetration depths are from 1 to 4 pm. So, only scale layers under tensile stresses are subjected to the X-ray diffraction analysis and measured values are hence tensile stresses. This idea is illustrated in Fig. 20.

(b) Inner oxidation of the substrate, especially in the grain boundaries, could introduce compressive stresses in the substrate and hence tensile stresses in the oxide layer. Compressive stresses can be estimated according

-i

5gm -]

~ lmm

average penetration depth

~ ~ , . . NiO scale

newly formed NiO layer

T=900"C ~ nickel substrate

J Fig. 20. Schematization of the NiO scale growth at 900 °C.

oxide scale

' , \ \ \ \ \ \ \ \ \ \ ' , ~ \ \ \ \ N N N \ \ \ \ /

~.- internal oxide ~ ~-- internal oxide--.~. 1'

4 1 1

substrate substrate

Fig. 21. Schematization of the internal oxidation.

122 C. Liu et aL / Residual stresses in Ni -NiO

to [17] (Fig. 21)

(PBR) 1/3 - 1 = (4)

R

with R the ratio of the distance between two inner oxide particles to the width of the inner oxide (R = 1/1' (Fig. 21)). With values taken from microscopic obser- vations (Fig. 5) (grain size, 100/~m; inner oxide width, 0.1/~m), the induced deformation is found to be equal to 2 x 10 -4, and the corresponding stress in the sub- strate resulting from this internal oxidation is equal to - 5 0 MPa. Additional deformation from cooling to room temperature can be calculated using the follow- ing equation in a simplified one-dimensional model (Fig. 21 ):

eadd = A a A T R - l (5)

with ead d the additional deformation during a tempera- ture change due to the difference between the thermal expansion coefficients, Aa the difference between the thermal expansion coefficients of the internal oxide and the substrate and A T the temperature change. Calculation indicates that the additional stresses during cooling are negligible for a typical temperature varia- tion of 1000°C. In fact, the calculated compressive stresses are of the same order of magnitude as those observed in the substrate at room temperature in our work or by other researchers [13, 14].

(c) A temperature gradient could exist through the scale as, in the case of samples heated by the Joule effect, the temperature is higher at the metal-oxide interface than at the outside surface. Stresses induced by a temperature difference of 10 °C can easily be as high as 20 MPa according to

Eox Oox- - - aox AT (6)

1 - Vox

So, the tensile stresses determined in the scale during oxidation can be due to the temperature gradient.

Recently, Bennett [19] reported that, in the Cr-Cr203 system, tensile stresses of about 200 MPa were found in the C r 2 0 3 scale at 875 °C, even after 23 h oxidation. In this system, all results [26] indicate that grain boundary diffusion is the predominant trans- port mechanism in the scale growth and that both outward chromium diffusion and also some inward oxygen diffusion are involved, as for NiO scales. The PBR for this system is equal to 2.07. So, it appears that a larger PBR does not induce compressive stresses in oxide scales during high temperature oxidation and has no particular effect on the stresses in the scales. This suggests that tensile stresses appear during scale

growth controlled by predominant cationic diffusion, at least in the outer part of the scale. In the very inner part of the scale, because of grain boundary diffusion, compressive stresses must be present. It would prob- ably be different if anionic diffusion was the predomi- nant transport mechanism. Our results and those reported by Homma and Pyun [9] on the Ni-NiO system indicate that for high temperature (900- 1000 °C) oxidation, the oxide scale grows under slight tensile stresses while mainly controlled by cationic diffusion, and for a lower oxidation temperature the oxide scale grows under slight compressive stresses under the control of anionic grain boundary diffusion. For predominant cationic diffusion, internal oxidation in the substrate may be responsible for tensile stresses through a mechanical equilibrium mechanism, while for predominant anionic diffusion the PBR may prob- ably be at the origin of compressive stresses in the scale because of the volume difference between the con- sumed metal and the grown oxide.

4.2. Thermal stresses Owing to the various observations, it seems reason-

able to suggest that stresses found at room temperature in the NiO scales are thermal stresses developed during cooling because of the differences between the thermal expansion coefficients of the scale and of the substrate. Thermal stresses can be calculated with the following equations which are modified from those proposed by Oxx [33] particularly in order to take into account the temperature dependence of the physical constants:

aox=_ f [Eox(T)/(1 -Vox)][aox(T)-am(T)] Tf l+(tox/tm)[Eo~( Z)/Em( r)][(1 - 'l,'m)/(1- ltox)]

dT

T, [Em( T)/(1 - Vm)][am(T) - - (/ox( T)]

O'm= - - l+(tm/tox)[Em( T)/Eox( T)][(1 - vox)/( 1 - Vm)]

(7 )

dT

(8)

with E Young's modulus, v Poisson's coefficient, tm the substrate thickness, tox the scale thickness, a the ther- mal expansion coefficient, and the subscripts m and ox referring to metal and oxide respectively.

As values of the thermal expansion coefficients t/Ni and aNi o in the literature differ from one study to another [14, 34-38], we measured the thermal expan- sion coefficients of nickel and NiO by both X-ray dif- fraction and dilatometry [8]. Good agreement was observed for the results obtained by both methods. Our measurements show that the average values between 20 °C and 900 °C for nickel and NiO are equal to 17.6 x 10 -6 K -l and 14.5x 10 -6 K -l respectively. The ratio tXNi/CtNi O is equal to 1.21, which is signifi-

C Liu et aL / Residualstresses in Ni-NiO 123

cantly different from the generally considered value of 1.03 [35].

With the thermal expansion coefficients measured in this study, the thermal stresses induced by cooling were calculated from several oxidation temperatures and compared with the stress values determined by X-ray diffraction at room temperature after cooling from the same oxidation temperature (Table 6 and Fig. 22). It is found that thermal stresses accumulated from 900 °C down to room temperature are equal to - 540 MPa for relaxation-free cooling. Calculation agrees well with experimental observations obtained with samples whose thickness is equal or greater than 0.4 mm. For thin samples (e.g. 0.1 mm), the experimental results are lower than the calculated values because of stress relaxation during cooling (see Figs. 8 and 10).

If we compare for several metal-oxide systems the stresses determined at room temperature and those calculated using eqn. (7) (i.e. thermal stresses (Table 7)), it appears that the residual stresses found at room temperature are mainly thermal stresses, created during cooling on account of the differences between the thermal expansion coefficients of the substrate and

200 Theoretical calculation with 4- Wa~1001.tm, tox=5~m , _

0 - x tm=2001.tm, tox=5.um . ~ -

-200 - ~

-400 ~ ] Experimental observation with

=.600:1 , - - ~ I~mo2000~,ox=s~m I ~, Pre-oxidation at 900°C,

in Oxygen for lh ] -800 • Heating

o Coo ng

-1000 i I I i I i I i

200 400 600 800 1000 Temperature (°C)

Fig. 22. Generation of thermal stresses: experimental observa- tions and theoretical calculations.

the oxide scale, regardless of the scale growth mecha- nism. Indeed, the results obtained on the MCrAI - Al203 system concern a scale whose growth is con- trolled by predominant anionic diffusion [21], while for the other systems, as said before, cationic diffusion predominates.

It can also be deduced from the above fact that, if stress relaxation occurs, it will not be important. A comparison of thermal stresses is given between theo- retical calculation and experimental observation for several metal-oxide systems (Table 7). One can see that in most cases, even if growth stresses appear during oxidation, they will not be significant compared with the thermal stresses. This may explain why spalling of oxide scales generally occurs during cooling sequences. It can also be deduced that stress relaxation for a typical cooling is not important. The scattering of the results and their differences f rom the theoretical pre- dictions must be mainly due to the differences in the experimental conditions and in the values of the physical and mechanical parameters used.

Th e same calculations (with eqn. (8)) can be carried out for the substrate. Owing to the important thickness difference between the scale and the substrate, it is found that the substrate thermal stresses are low (Fig. 23) and reach only about 50 MPa for thin (about 0.1 mm) nickel samples. As shown in Figs. 22 and 23, the metal-to-oxide-thickness ratio has a greater influence on the stresses in the substrate than on those in the scale. Such a calculation leads to tensile stresses in the substrate and could seem to disagree with our results (compressive stresses are obtained experimentally). This will be discussed later on, but note that, for sam- ples of 1 mm thickness or more, thermal stresses in the substrate are negligible.

4.3. Stress at room temperature In earlier studies at room temperature, it was found

that, for a given oxidation temperature, residual stresses in the scale vary with oxidation time [13, 14].

TABLE 7. Comparison between theoretical calculations of thermal stresses and experimental determinations of stresses at room temperature for several oxide scales

Stress (MPa) for the following systems

Ni-NiO NiCr-Cr203 Cr-Cr203 MCrAI-AI203

Theoretical calculation Theoretical calculation Experimental measurement Experimental measurement Experimental measurement Experimental measurement

- 540 ~ - 4000 ~ [81 - 820 ~ [8] - 5200g [21] - 640 h - 4500 b [29] - 1100 b [29] - 550 ~' - 2000" [17] - 400' [19] - 5700g [21] - 450 to - 650 [13, 14] - 3300 ¢ [18] < 300 h [20]

- 20 to - 7 0 c [ 1 6 ]

- 1 7 0 t o - 2 4 0 ~ [ 1 5 ]

~'This study, from 900°C. bThis study, from 1000 °C. CFrom 700 and 800 °C. dFrom 760 to 927°C. ~From 950°C. rFrom 875 °C. gFrom 1100 °C. hFrom 1150 °C.

124 C Liu et al. / Residual stresses in Ni-NiO

°L Theoretical calculation wilh

~ 50 1 - ' ~ x tm= 1001.tm, tox=5p.m [ " a ~ + tm=2001Jrn, tox=5l.tm I ~ ~ • un=420iam, tox=5pm

~ 4 0 1 - ~ . tm=2000pm, tOx=5!Lt m

~ 20 "

~ to

200 400 600 800 1000 Temperature (°C)

Fig. 23. Calculations of the thermal stresses created in the nickel substrate during cooling after oxidation.

The stress-oxidation time curves have a U-shape, as obtained in Fig. 8. The diffraction peak breadth (Fig. 9) decreases as the oxidation time increases. The diffrac- tion peak breadth is related to the microstructural defect concentration in the materials studied, and its decrease is due to the decrease in microstructural defect concentration. As the oxide scale grows predomi- nantly at the outer surface, and the X-ray diffraction is mainly due to the outer layers, it can be said that the outside oxide layer newly formed away from the scale-metal interface contains fewer microstructural defects than the oxide scale layers do near the inter- face. For the U-shape-like stress-oxidation time curve, it can be suggested that, for thin oxide scales, relaxation occurs when, for thick oxide scales, only the outer part of the scale is analyzed by X-rays, and the result does not take into account the layers near the substrate.

It is also found that the stress level at room tempera- ture in the oxide scale depends on the substrate thick- ness (see Fig. 10). The thinner the substrate, the weaker are the stresses in the oxide scale. However, from a given substrate thickness, the stress level in the oxide scale no longer varies with the substrate thick- ness. The decrease in stresses in the oxide scale formed on thin substrates is due to stress relaxation during cooling; a thin substrate creeps easily and enables stress relaxation to occur in the metal-oxide system. The critical substrate thickness for stress relaxation is found to be 0.4 mm for the Ni-NiO system.

In agreement with these observations, it was remarked (Table 5) that, for samples of thickness larger than 0.4 mm, the cooling rate has no effect on the stress level; no relaxation occurs for cooling rates between 450 and 1 5 0 K h -t. When the samples are air quenched (about 2 x 104 K h-t), buckling and spalling occur. This was discussed earlier [39] as a result of poor heat transfer at the interface due to the defect concentration at this interface (see Fig. 4). According

to the relation o c = K i J ( n c ) °'5 [40], the defect concen- tration at the oxide-metal interface can induce buck- ling (see Fig. 6) which leads to poor heat transfer. Therefore the substrate temperature could be higher than the scale temperature during cooling and this temperature gradient would induce additional tensile stresses in the scale and lead to scale spalling.

It is observed (Fig. 11) that the presence of vapor- ized water in the oxidation atmosphere does not change the stress level at room temperature. The same results were reported in the literature [14, 41]. It was verified that the presence of vaporized water does not modify the morphology of the NiO scale. However, the oxidation rate is somewhat greater than the oxidation rate in pure oxygen [41]. Moreover, we verified that the IR spectrum* of NiO is slightly modified when water vapor is present in oxygen. So, it appears that this parameter, although having an influence during iso- thermal growth, has no effect on the scale stresses. In the same way, it was verified in this work that the im- purities of the nickel substrate, although having an effect on the oxidation rate, do not influence the stress level in the scale. These observations can be general- ized by saying that factors playing a role during isother- mal growth do not act much on the stress level in the scale at room temperature because residual stresses in the scale are mainly generated during cooling, the growth stresses being negligible compared with thermal stresses. This is probably why no specific difference in the stress level was observed according to the oxidation conditions, i.e. to the microstructure of the NiO scale and/or to the predominant diffusion mechanism. Only defects leading to the formation of voids, cracks, buck- ling and spalling modify the stresses in the scale.

4.4. Stresses in the metall ic substrate It is found that at room temperature the nickel sub-

strate is subjected to slight compressive stresses regardless of the oxidation treatments. According to the mechanical equilibrium equation, tensile stresses would be expected as the oxide scale is subjected to strong compressive stresses after cooling. It is shown that the slight tensile stresses are due to inner oxidation of the nickel substrate. Internal oxides can be formed in the nickel substrate, especially along the grain bound- aries (Fig. 5), which create compressive stresses in the surrounding zone. Stresses introduced by internal oxidation were calculated with eqn. (4) and the stress level for a typical case is found to be - 50 MPa, a value higher than the expected compressive stresses due to thermal effect (Fig. 23). It is stated that the calculated

*IR experiments were performed by J. Roy in the Laboratoire de Matdriaux, M6tallurgie Physique, Ecole Nationale Sup6rieure de Chimie de Toulouse, Toulouse, France.

C. Liu et al. / Residual stresses in Ni -NiO 125

stress value is of the same order of magnitude as the experimental results (Table 5).

4.5. Stress distribution at room temperature According to our results, a scheme of the s t ress

distribution at room temperature can be proposed (Fig. 24). The stress distribution is more complicated than the distribution suggested by Barnes et al. [29] owing to the internal oxidation in the substrate which induces compressive stresses in the affected part of the sub- strate.

In fact, the same phenomena are observed in other metal-oxide systems such as NiCr-Cr203 [17, 18]. In these studies, compressive stresses as high as - 5 0 0 MPa are measured in the underlying substrate by both X-ray diffraction and the curvature method. It was reported that a sublayer in the substrate was made of internal oxide particles dispersed in the substrate.

The stress distribution in the scale is due to the thermal stresses, and compressive stresses are always detected in all scales. In the substrate, two different zones appear. The first, with a depth equal to the inter- nal oxidation penetration, is characterized by compres- sive stresses in both nickel and NiO particles. After this zone, on account of the mechanical equilibrium, tensile stresses must be present in the substrate. This zone is not analyzed by X-ray diffraction owing to the limited X-ray penetration.

5. Conclusions

The following conclusions can be drawn from the present study concerning the stress determination in the Ni-NiO system during all steps of oxidation treat- ments.

NiO scale thickness (I.tm)

0 ~ ] [ I , 1 ~ ~ [ J.J. Barnes et al

i i - 0 " " " ' " ' " I ~

I Our measurements with I x Cr Kct radiation

- " . . . . . . . . . "g • Co Kct radiation o Cu Kct radiation

J. J. Barnes et al

Interface |

Internal I NiO scale oxidation [ Ni substrate

zone I

Fig. 24. Schematization of the stress distribution in the Ni-NiO system at room temperature.

(1) The thermal stresses resulting from the differ- ences between the thermal expansion coefficients of the substrate and the scale are the main factor for the stresses observed at room temperature in the scale. So, the stress level in the scale at room temperature depends on the difference between the thermal expan- sion coefficients, the initial oxidation temperature, the mechanical properties of materials (Young's modulus etc.). Experimental results are in good agreement with theoretical modelization.

(2) Slight tensile stresses are found to be generated in the scale during its growth. Several factors, such as the internal oxidation of the substrate, the epitaxy relationship between the substrate and the scale, anionic grain boundary or short-circuit diffusion and the temperature gradient are considered as being pos- sibly the origins of the growth stresses. Their respective roles and degrees of importance remain to be clearly determined. In any case the growth stresses are very low compared with the thermal stresses. A model based on the PBR cannot explain the experimental observations.

(3) In the substrate, compressive stresses are also observed at room temperature. This is due to internal oxidation whose effect on the substrate stresses is higher than thermal stresses.

(4) Some parameters, such as the initial thickness of the substrate, the oxidation time and the temperature, can modify the stress level at room temperature. It seems that the stress level is modified through stress relaxation.

(5) Other parameters, such as impurities in the sub- strate or in the atmosphere, and oxidation conditions, which modify the growth rate and the scale morphol- ogy, do not seem to have much influence on the stress level as stresses are mainly generated during tempera- ture changes.

Some of the conclusions on the Ni-NiO system can be generalized to other systems. However, it would be interesting to study systems for which scale growth is controlled by predominant anionic diffusion in order to see whether, in such a case, a volumic deformation occurs, leading to significant growth stresses.

Acknowledgment

The authors acknowledge Centre Fran~ais Anti- Corrosion for its financial support for the high temper- ature equipment used in this study.

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