Cyclic deformation of the alloy Cu-35%Ni-3.5%Cr in the homogenized condition

Int J Fatigue 15 No 5 (1993) pp 423-428

Cyclic deformation of the alloy Cu-35%Ni-3.5%Cr in the homogenized condition G . - X . Wang, H . Bomas, R. B6schen and P. M a y r

The cyclic deformation behaviour of the planar slip mode alloy Cu-35%Ni-3.5%Cr in the homogenized condition has been investigated at constant stress amplitudes. During cycling at stress amplitudes higher than the cyclic yield strength, an initial cyclic hardening followed by a cyclic softening was observed. TEM studies revealed that cyclic hardening is due to an increase of dislocation density and cyclic softening is mainly introduced by energetically favourable rearrangements of dislocations. The smallest plastic strain amplitude during cycling corresponds to a saturation dislocation density, which increases with increasing stress amplitude. The lifetime of this alloy can be correlated not only with the stress amplitude, but also with the smallest plastic or total strain amplitude.

Key words: cyclic deformation; copper alloy; dislocations; lifetime The cyclic deformation behaviour of wavy slip mode metals has been studied extensively in the past. For these materials the correlation between microstructure and cyclic deformation behaviour is fairly well understood. The onset of saturation in single crystals oriented for single slip is related to the flow stress of persistent slip band (PSBs), whereas the saturation stress for polycrystals corresponds to the cell formation) The dislocation structure consisting of thick dislocation bundles in the matrix and a dislocation ladder structure in the PSBs is also well known for wavy slip materials. 2-s In contrast, only a few investigations are known for planar slip mode materials which generally exhibit a pronounced shortrange o r d e r : It is reported that PSBs do not exist in planar slip Cu-31wt %Zn. 7 More recent work s-~° has, however, found PSBs in Cu-16 at%Al, a planar slip mode alloy. Because these PSBs differ entirely from those of wavy slip materials like Cu, AI and Fe, these bands were named persistent Liiders bands (PLBs). s-*° Therefore it has to be concluded that the understanding of cyclic deformation in planar slip materials is insufficient compared with that of wavy slip mode materials. In this paper the cyclic deformation behaviour of the planar slip mode alloy C u - 3 5 % N i - 3 . 5 % C r , which exhibits spinodal decomposition, is reported for the solution-treated state. The influence of spinodal hardening on fatigue of C u - 3 5 % N i - 3 . 5 % C r is shown in a separate paper; .2 the tensile properties are discussed by Heerens) *

Experimental Rolled sheets, 5 mm thick, with 34.7 wt% Ni and 3.5 wt% Cr (balance Cu) were solution treated and quenched (1050 °C, 1 h, ice water). After this treatment the alloy had a mean grain size of 102 -+ 6 ~m. Specimens with a rectangular net section (4 x 8 mm) were machined from the heat-treated sheets. The specimens were carefully electropolished in order to remove the surface layer which was affected by machining. Tensile tests were performed at a strain rate of 0.002 s -*. Stress-controlled tension-compression tests were performed

in a servohydraulic test equipment using a triangular load-time function with a zero mean stress and a frequency of 2 s -1 for stress amplitudes Gr, I> 150 N mm -2 and 10 s -1 for stress amplitudes or, < 150 N mm -2. In addition to continuous tests at different stress amplitudes to establish cyclic deformation and S - N curves, fatigue tests which had been interrupted after definite numbers of cycles were carried out to get specimens with different microstructures. The microstructures resulting from cyclic deformation were studied by transmission electron microscopy (TEM). Thin foils were prepared parallel to the loading axis from near-surface regions using the double-jet polishing method. The dislocation density was determined using the line intersection method 13 and the foil thickness was measured with the convergent-beam diffraction method./4

Results Mechanical tests The tensile test revealed a 0.2% yield strength of 190 -+ 8 N mm -2 an ultimate tensile strength of 466 -+ 13 N mm -2 and an elastic modulus of 161200 -+ 21800 N mm -2. Figure 1 shows the plastic strain amplitude %, as a function of the number of cycles N and the corresponding number of cycles to fracture Nf for different stress amplitudes ~,. All curves show an initial cyclic hardening followed by a cyclic softening. The rates of hardening and softening increase with increasing stress amplitude. The rate of cyclic hardening, -d~pa/dN, is very large at the beginning of each test (for example -dEpa/d/~r ~ 1.8 X 10 -3 at ~, = 245 N mm -2) and decreases rapidly to zero with increasing number of cycles. The cyclic softening is not very pronounced, with a rate of d~pa/dN ~ 10 -6 for ~, ~ 245 N mm -2. The arrows in Fig. 1 indicate the steep gradient of the curves caused by fatigue cracks generated in the gauge length. An increase of plastic strain amplitude can correspond to material softening or crack opening. To separate material

0142-1123/93/050423-06 © 1993 Butterworth-Heinemann Ltd Int J Fatigue September 1993

423

1.4

.

\\

/~ 2q512800

1.2

300

oa(N/mm2)/ Nf

oooo

/ ~ . ~ q . _ °a- ~:pa,rn~.,, %- C:ta,min

1.0

200

0.8

. t 220/12000

\

E E 7

8.0.6

ca

k 0.g

~-

0

~- 10o

--%'oZoo

0.2

1

I

I

I

2

3

4

150/1~5600 6

"~,

5

7

log N Fig. 1 Cyclic deformation curves and corresponding number of cycles to fracture at different stress amplitudes

2.0

I

I 1

I 2

e,

eta,min, epa,min (%o1

0

I 3

q

Fig. 4 Unidirectional (~r-e) and cyclic (~r.--et=.m,n, O'a--ep~,min) stress-strain curves

O

1.6 5

1

.5

semilogafithic plot. Each data point represents a single test. The fatigue limit has been determined to ~= = 100 N mm -2. For stress amplitudes in the limited-life region the number of cycles to fracture N~ can be related to the stress amplitude by

1.2 ca

0.8

logN~ = 8.871 - 0.022 or=

0.4 O

0

I

I

1

2

I 3

g

5

log N Fig. 2 Cyclic deformation curve of a notched specimen as the strain was measured in the hatched zone where a nominal stress amplitude of 210 N mm -= was active

sketched;

softening from crack opening the strain response of a notched specimen with notches outside the gauge length was investigated (Fig. 2). In a surface examination by light microscopy after the test only a very few microcracks were detected in this region. Therefore it is concluded that the strain increase is due to material softening. The S - N curve of the material is shown in Fig. 3 in a

(1)

In Figs 1 and 2 it can be seen that for each applied stress amplitude a minimum plastic strain amplitude %=,rain and a corresponding total strain amplitude •==,rainexist. As will be discussed later, this strain amplitude coincides with a saturation dislocation density and this is characteristic for the cyclic deformation of the investigated material. Figure 4 therefore shows curves of o,= v e r s u s •pa, min and Gra versus •ta, min~ and Fig. 5 curves of Iog%=.min versus logN~ and log• .... in versus logNf. A comparison of the cyclic O'a--%a,min curve and the unidirectional or• curve in Fig. 4 reveals that the amount of cyclic hardening, defined as the difference between the unidirectional strain and the minimum total strain amplitude Aep =

•

--

•

(2)

. . . . in

increases with increasing stress amplitude. The cyclic yield

300 .E - 2 . 0

E

t0

¢z -2.5 ca 200

O~

o

o

-3.0

-¢

E E Z

T= -3.5 100

w 01 o

3X

log Nf = 8.871-0.022 oa

"c

-q.O -4.5

E pa,min

.

~

~. - 5 . o 0

103

I

I

I

I

10q

105

106

107

108

Nf Fig. 3 Number of cycles to fracture Nf in relation to the stress amplitude ~ro

424

hi O'1 _?

-5.5

I

I

I

I

q

5

6

7

log

Nf

Fig. 5 Lifetime as a function of the minimum strain amplitude

Int J Fatigue September 1993

strength, below which no measurable plastic strain appears, is about 150 N mm -2 (see the O'a--Epa,min Curve in Fig. 4). As shown in Fig. 5, the lifetime of the investigated material can be correlated with the minimum plastic and total strain amplitude, respectively. According to E. . . .

in =

E. . . .

(3)

i n - - ~-pa, m i n

the log~,min-logNf curve, as indicated with the dashed line in Fig. 5, can be established. The plastic strain amplitude Epa, min according to the accuracy of the equipment used, could only be measured for lifetimes Nf < 3 x 105, which corresponds to a cyclic yield strength of about 150 N mm -2 (see Figs 3 and 4). For lifetime Nf > 3 x 10s, a plastic strain amplitude Epa.min cannot be detected and the alloy shows predominantly an elastic deformation behaviour. TEM

investigations

TEM investigations were first performed on specimens fatigued at ~, = 220 N mm -2 at different stages of lifetime to study the development of dislocation structure during cyclic loading. Lateron specimens have been cycled until fracture at different stress amplitudes to examine the dependence of the dislocation structure on the stress amplitude. The results of this investigation are described below. Development o f dislocation structure at stress amplitude era = 220 N m m -2 The dislocation structure after heat treatment is shown in Fig. 6(a), which corresponds to a beam direction [112]. After 1000 cycles, a significant increase in dislocation density is visible (Fig. 6(b)). Most of the dislocations are arranged parallel or vertical to the (110) direction with a homogeneous distribution. In the sample, fractured after about 12000 cycles, a structure as in Fig. 6(c) was observed using a beam direction [1i0]. Slip bands with several dislocation groups are oriented parallel to each other in the [112] direction. These bands can be associated with the {111} slip planes. The dislocation density between these bands is relatively low as well as between the dislocation groups inside of one band. A comparison of Fig. 6(c) and Fig. 6(b) shows that a clustering of dislocations has taken place during the period 1000 < N < 12000. At low magnifications a structure similar to the surface slip bands is visible in the TEM (Fig. 7). Figure 7 was taken from the same region as Fig. 6(c). The dark bands correspond to those in Fig. 6(c) with dislocation groups. The dislocation density at ~= = 220 N mm -2 as a function of the number of cycles is shown in Fig. 8. Before loading, the alloy shows a dislocation density of 1.4 x 109 cm -2, which then remains almost constant for the rest of the lifetime. In other words, the dislocation density has already reached its saturation value at the appearance of the minimum plastic strain amplitude (Fig. 1) in the first 1% of the lifetime. Influence o f stress amplitude on dislocation structure Figure 9 shows the dislocation structures of samples fatigued with Gr, = 175 N mm -2 and Gr, -- 200 N mm -z until complete fracture. The dislocations in both cases are distributed fairly homogeneously, and no clustering of dislocation such as shown in Fig. 6(c) could be detected. At stress amplitudes between 220 and 245 N mm -2 clustering of dislocations was observed, being most distinct at cr, = 220 N mm -2 (Fig. 6(c), Fig. 7 and Fig. 10). Significant cell formation could not be

Int J F a t i g u e S e p t e m b e r

1993

Fig. 6 Evolution of dislocation structure during cycling at ~ro = 220 N mm-=; U = beam direction, g = arrow orientation. (a) N = 0, U = [112], g = [312]; (b) N = 1000, U = [001], g = [110]; ( c ) N ~ 12000, U I = [110], g = [112]

425

Fig. 7 TEM image s u r v e y i n g the band structure s h o w n

in

Fig. 6(c)

I .q x 1010 1.2 x 1010 1 . 0 x i 0 I0 0 . 8 x 1010 E u

0.6 x 1010 0.qxl010 0.2 x 1010'

rl/i///I/'t'~

0

o a = 220 N mm-2

I

i

I

I

1

10

100

1000

I

10000 100000

N Fig. 8 Change o f dislocation density during cycling at or, = 220 N mm -2

Fig. 9 Dislocation structure in broken specimens f a t i g u e d at (a) or, = 175 N mm -2 and ( b ) ~ = = 220 N mm -2

detected in samples fatigued at stress amplitudes lower than or equal to 245 N mm -2 because planar slip dominates, owing to limited cross-slip of screw dislocations. As shown in Fig. 11, the square root of dislocation density in fractured specimens is proportional to the stress amplitude, according to

~= = 110 + 9 . 5

X 104

x pl/2

(4)

with ~, in N mm -2 and p in cm -2.

Discussion In fatigue experiments with stress amplitudes above the cyclic yield strength, an initial cyclic hardening followed by a cyclic softening was observed (Fig. 1). To understand this deformation behaviour, TEM studies of the associated microstructural changes in the bulk of the material were performed. At a constant stress amplitude of 220 N mm -2 the dislocation density has increased considerably during cyclic hardening and a saturation value occurs just at the transition from cyclic hardening to cyclic softening, corresponding to a minimum plastic strain amplitude. It seems reasonable to correlate cyclic hardening at this stress amplitude with the

426

Fig. 10 Dislocation structure after fracture in a sample fatigued at or, = 245 N mm -2

Int J Fatigue September 1993

270 250

I

I

•

I I

230 WE 210 E ~9o

150 130

.••a=110

+ 9.5 x 10 -g p½

170 :

/

-

i

5x10 q

:

i

10x!0 q

i

15x10 q

20x10 q

Cpa

p ½(cm-1 )

P'= <0

Fig. 11 Relationship between stress amplitude and dislocation density after fracture

aN

iI

r--- >0 @N log N

increase in dislocation density. The same is expected for other stress amplitudes higher than the cyclic yield strength (~- 150 N mm -2, see Fig. 4). Inserting the dislocation density before loading of 1.4 x 109 cm -2 into Equation 4 leads to a stress amplitude of 145 N mm -2 which is lower than the cyclic yield strength. At this amplitude the formation of new dislocations as well as the cyclic hardening is expected to be very low, which is in agreement with the strain measurement (see Fig. 1). After the saturation dislocation density is reached, two processes can take place. First, the dislocations will cluster together to reduce their interaction energy. During this process the dislocations move from areas of low density to areas of high density, with a reduction of the free energy of the system. The clustering of dislocations enables the dislocations at the border of these groups to move easily over the distance between two neighbouring dislocation groups. Because of this the free path of their movement is enhanced by clustering (see Fig. 6(b) and Fig. 6(c)). The second process is the mutual annihilation of dislocations with opposite sign. Since the dislocation density remains constant when the cyclic softening takes place (see Fig. 1 and Fig. 8), it is necessary to assume that the annihilation, even if it takes place, is compensated by simultaneous dislocation production and has thus no significant contribution to cyclic softening in Cu-35%Ni-3.5% Cr. From these considerations it can be concluded for the solution-treated C u - 3 5 % N i - 3 . 5 % C r that the initial cyclic hardening is due to the increase of dislocation density, and the following cyclic softening is mainly correlated with the energetically favourable clustering of the dislocations. At a= < 200 N mm -2 the cyclic softening is very small. Accordingly, no apparent clustering of dislocations such as shown in Fig. 6 could be detected (Fig. 9). Samples fatigued at 220 N mm -2 ~ ~ 245 N mm -2 exhibit considerable cyclic softening and undergo the above-mentioned clustering of dislocations (see Fig. 6(c) and Fig. 10). This confirms the conclusion that the clustering of dislocations is the major origin of cyclic softening inCu-35%Ni-3.5%Cr. Figure 12 sums up the above conclusions about the cyclic deformation behaviour of the investigated material and its microstructural mechanisms. It should finally be pointed out that the dislocation structure after the clustering is very similar to the ladder structure of PSBs in fatigued wavy slip mode materials. Since this structure allows a more intensive cyclic plastic deformation

Int J Fatigue September 1993

Fig. 12 Schematic description of the cyclic deformation behaviour and its mechanisms

than a homogeneous distribution of dislocations, the dislocation structure shown in Fig. 6(c), Fig. 7 and Fig. 10 can be regarded as PSBs in Cu-wt35%Ni-3.Swt%Cr. Since the overall dislocation density decreases with decreasing stress amplitude (see Fig. 11), which also means a decreasing of the driving force for the rearrangement of dislocations, the probability of PSB formation will be reduced at lower stress amplitudes. However, the formation of PSBs is impeded at high stress amplitudes. Two reasons are worth mentioning. First, at high stress amplitudes fatigue cracks can be created very early. After crack formation the further deformation process takes place only in the plastic zone at the crack tip. The time for the to-and-fro dislocation movement in the specimen volume is therefore not sufficient for PSB formation. Second, with increasing stress amplitude at the specimen surface a deformation-induced topography will develop, which makes TEM investigations of the microstructure near the surface of fatigued specimens more difficult. According to the observations of Pohl s the probability of finding PSBs decreases with increasing distance from the surface. Both reasons seem to explain the less intense PSB formation at ~, = 245 N mm -2 in this work.

Acknowledgement The authors are grateful to the GKSS Research Centre in Geesthacht for financial support of this work.

References 1.

Plumtree, A, 'Correlation between microstructure and cyclic behaviour' in K.-T. Rie (ed) Low Cycle Fatigue and Elasto-Plastic Behaviour of Materials (Elsevier Applied Science Publishers, 1987) pp 19-30

2.

Laird, C., Charsley, P. and Mughrabi, H. 'Low energy dislocation produced by cyclic deformation' Mater Sci Eng 81 (1986) p 433-450

3.

Wang, R. and Mughrabi, H. 'Secondary cyclic hardening in fatigue of copper monocrystals and polycrystals' Mater Sci Eng 63 (1984) pp 147-163

4.

Rasmussen, K.V. and Pedersen, O.B. 'Fatigue of copper polycrystals at low plastic strain amplitudes' Acta Metal/ 28 (1980) pp 1467-1478

5.

Pohl, K., Mayr, P. and Mecherauch, E. 'Persistent slip

427

6. 7, 8.

9.

10.

428

bands in the interior of fatigued low carbon steel' Scr Metall 14 11 (1980) pp 1167-1169 Gerold, V. and Kernthaler, H.P. 'On the origin of planar slip in f.c.c, alloys' Acta Metal137 8 (1989) pp 2177-2183 Lukaa, P. and Klesnil, M. 'Dislocation structures in fatigued Cu-Zn single crystals' Phys Stat Sol 37 (1970) p 833-842 Yen, B.D., Cheng, A.S., Buchinger, L., Stanzl, S. and Laird, C. 'The cyclic stress-strain response of single crystals of Cu-16at%AI alloy - Part 1: Cyclic hardening and strain localization' Mater Sci Eng 80 (1986) pp 129-142 Laird, C., Stanzl, S., De La Veaux, R. end Buchinger, L. 'The cyclic stress-strain response of single crystals of Cu-16aWoAI a l l o y - Part 2: Polycrystalline behaviour' Mater Sci Eng 80 (1986) pp 143-154 Buchinger, L., Cheng, A.S., Stanzl, S. and Laird, C. 'The cyclic stress-strain response of single crystals of Cu-16at%AI alloy - Part 3: Single crystals fatigued at low strain amplitudes' Mater Sci Eng 80 (1986) pp 155-167

11.

Heeren$, J. 'Zusammenhang zwischen Ausscheidungsstruktur und stabilem Ril~wachstum in einer Kupfer-NickeI-Chrom-Legierung' Dipl thesis (University of Hamburg, Germany, 1983)

12.

Wang, G.-X. 'ErmOdungsverhalten der Legierung Cu-35%Ni-3.5%Cr in unterschiedlichen Entmischungszust~inden' Doctor thesis (University of Bremen, Germany, 1990)

13.

Hem, R.K. 'The determination of dislocation densities in thin films' Phil Meg 6 (1961) p 1183

14.

Kelly, P.M., Jostsons, A., Blake, R.G. and Napier, J.G. 'The determination of foil thickness by scanning electron microscopy' Phys Stat Sol 31 (1975) pp 771-780

Authors

The authors are with the Institiit fiir Werkstofftechnik, Bremen, Federal Republic of Germany. Received 2 January 1993; accepted 4 March 1993.

Int J Fatigue S e p t e m b e r 1993