Grain size dependence of the strain rate sensitivity and activation energy of high temperature deformation of a microduplex stainless steel

Materials Science and Engineering, 54 (1982) 257 - 263

257

Grain Size Dependence of the Strain Rate Sensitivity and Activation Energy of High Temperature Deformation of a Microduplex Stainless Steel ADENIYI A. A F O N J A

Department of Metallurgical and Materials Engineering, University of Ife, lle-Ife (Nigeria) (Received January 7, 1980; in revised form November 17, 1981)

SUMMARY

The influence o f grain size on the high temperature deformation behaviour o f a microduplex stainless steel was investigated using tensile tests. The results show that a decrease in grain size increases the strain rates at which the material can be deformed without loss o f superplasticity. It was also shown that the grain size has a square relationship to the flow stress, an inverse square relationship to the strain rate and a linear relationship to the activation energy o f deformation.

1. I N T R O D U C T I O N

In the last 20 years or so, a great deal of research and developmental effort has been expended in m a n y countries on the phenomenon of superplasticity in metals. The ability of some metals and alloys to deform extensively over a range of temperatures and microstructural conditions offers considerable advantages in hot-forming practice, particularly for high strength alloys. The literature published on various aspects of the phenomenon is extensive and has been the subject of m a n y recent reviews [ 1 - 6]. Despite this, a sound theoretical understanding of the significant process and microstructural parameters or the deformation mechanisms has not yet been achieved. Some of the important issues which remain unresolved have been discussed recently in excellent detail by Mukherjee [6]. Among these are the differences between the shapes of the stress-strain rate curves for various alloys, the strong discrepancy between the measured values of the strain rate sensitivity parameter, and the interdependence of the primary process and microstructural variables. 0025-5416/82/0000-0000/$02.75

The objective of this work was to investigate the influence of grain size and temperature on the superplastic behaviour of a duplex phase stainless steel.

2. T H E O R E T I C A L CONSIDERATIONS

The results of numerous investigations have established clearly that a micrograin size of the order of 10 pm or less is an important prerequisite for superplastic behaviour. Hildebrand et al. [7] in their study of a Cr-Ni stainless steel concluded t h a t the grain size of the matrix is more important than that of the duplex structure. This appears to be logical because they studied a two-phase system in which the matrix ferrite was predominant (77% - 82%). It is unlikely that this conclusion applies to balanced systems. Most of the numerous theories on the mechanism of superplastic deformation that have been proposed [6] a t t e m p t to account for the effect of grain size but there is considerable inconsistency in the prediction of its influence on the flow stress or the strain rate. A summary of the most important theories is presented in Table 1. In general, the stress and strain rate dependence on grain size may be written in the forms oct

La

and 1 Lb respectively. The lack of agreement on the values of a and b predicted by various theories is evident from Table 1. The results of empirical studies have been even more divergent, as shown in Table 2. This is not surprising since © Elsevier Sequoia/Printed in The Netherlands

258 TABLE 1 Deformation mechanisms for superplastic deformation of metals

Deformation mechanism

e = f(o, L, T)

e = f(L)

o = f(L)

Activation energy Q

Nabarro--Herring vacancy creep (lattice diffusion)

B1VoD1 e- - L2kT

~ cc L - 2

o ¢c L 2

Self-diffusion (volume diffusion)

Coble-Jones creep (vacancy creep by grain boundary diffusion)

~ cc L - 3

a ~ L3

e-

Grain boundary diffusion

~ ¢c L - 1

02 ~ Le

Grain boundary diffusion

B2VOwDg b L3kT B3b2O2Dgb

Grain boundary sliding -

LGkT

B1, B2, B3, constants; V, atomic volume; D1, lattice diffusivity; Dgb, grain boundary diffusivity; L, grain size; k, Boltzmann's constant; T, temperature; o, applied stress; ~, strain rate; G, shear modulus; b, Burgers' vector; w, thickness of the grain boundary.

TABLE 2 Published values of constants relating grain size to stress and strain rate in superplastic deformation

Material

a

b

Reference

AI-Cu eutectic Ni- 26.2%Fe- 34,9%Cr IN-744 P b - S n eutectic A I - Z n eutectoid Fe-Mn

0.5

1 - 2.4 2 3 2.3 - 3 2 - 4.8 5

[4, 8 ] [4 ] [4] [ 4] [4] [9 ]

0.5 0.7 - 1.2

TABLE 3 Published values of activation energies for alloys

Material

Activation energy (kJ mo1-1 )

~-Fe 7-Fe ~-Fe Fe-Ni-Cr Fe-Cr P/M IN-100 AI-Zn-Mg Z n - A l eutectoid Sn-Pb eutectic

Self ~iffusion (volume diffusion)

Grain boundary diffusion

239-280 290-306 241 226-239 209-230 250 172 91 80

168-174 159-163

Superplastic deformation

Reference [10,11] [10,11] [11] [12-14] [15] [16-18] [19, 20] [21, 22] [23, 24]

220-280 397-470 80 61 48

80 - 105 59 - 61 40

TABLE 4 Chemical composition of the alloy

Element Amount (wt.%)

C 0.03

Cr 23.6

Ni 5.12

Ti 0.51

Si 0.63

Mn 0.59

Mo 1.48

Cu 1.03

N 0.143

S 0.007

P 0.006

Fe Balance

259 the grain size dependence of these parameters is likely to be significantly affected by the defect structure of the material, which in turn depends on other factors such as the thermal and strain history of the material and the deformation temperature. Another possible reason for the differences between the results of various studies is the fact t h a t several mechanisms m a y operate simultaneously during superplastic deformation and the relative effect of each mechanism m a y change during the process as a result of changes in microstructure, temperature or strain rate. A t t e m p t s are often made to determine the rate-controlling mechanism for superplastic deformation from measurements of the activation energy of deformation. Again there is considerable variation in the results, as shown in Table 3, probably for the same reasons outlined above. It is generally assumed t h a t the activation energy is not greatly influenced by the grain size but the results of a recent study by Hildebrand et al. [7] show that small variations in grain size can have a significant effect.

3. EXPERIMENTAL PROCEDURE

m u m temperature of 1500 K. The test specimen and grips were enclosed in a stainless steel tube through which argon was circulated. Provision was made for water quenching the specimen in situ. The stability of the alloy at elevated temperatures and prolonged exposure periods was verified by testing a specimen with a grain size of 3.2/~m at 1220 K and a strain rate of 10 -4 min -1 until a strain of about 20% was achieved and by then quenching with water. This combination of variables was considered to be the most favourable for possible grain growth or phase transformation in the range investigated. A microstructural examination of the material revealed no significant change in the phase ratio but the grain size increased to about 5 pm. In the main experiments, each test piece was heated slowly to the test temperature in the equipment and held at the peak temperature for 30 min before straining. The test was stopped after a strain of about 20% had been achieved and the specimen chamber was flushed with chilled water. Tests were carried out at three temperatures and five to eight different strain rates.

3.1. Materials

The stainless steel was supplied in the form of bars 25 m m in diameter h o t forged at 1473 K from 100N ingots. The chemical composition of the alloy was as given in Table 4. The as-forged grain size was about 15/~m. The bars were warm worked by swaging and annealed at temperatures between 1200 and 1400 K; this was followed by quenching in chilled water. By varying the a m o u n t of deformation, annealing temperature and time, four grain sizes between 3 and 10 /~m were obtained. The grain sizes were determined by the Hilliard circle technique and the relative proportions of the phases were evaluated by point counting. The average ratio of ~ to c~ phase was 1.03. Tensile test specimens of 5 mm diameter and 25 mm gauge length were made from the rods and polished.

3.2. E q u i p m e n t and test p r o c e d u r e

The tests were carried out on a tensiletesting machine fitted with a variable-speed control unit and a tube furnace with a maxi-

4. DISCUSSION OF RESULTS 4.1. D e t e r m i n a t i o n o f strain rate s e n s i t i v i t y

The strain rate sensitivity m was determined from the expression a = K~ rn

where o is the flow stress, e the strain rate and K a constant. The flow stress (maximum stress) was obtained from the stress-strain curve for each strain rate, temperature and grain size. Graphs of log o against log e were plotted as shown in Figs. 1 - 3 and m was obtained from the slope of the curves. The values for all the test conditions are shown in Table 5. All the log o versus log e curves are linear within a range of strain rates, indicating superductility. The m values which range from 0.35 to 0.51 are also consistent with superplastic behaviour. At strain rates below about 10 - s min -1, there is a significant decrease in the slope of the curves for the two

260

1.6

1.6,

~E

~,E 1 . 2 .

E 1.2 z

z

o.s

,~o.s .J

8

0.4

JO.4

0

-s

0

-'4

-3

-'2

-~

-1

Fig. I. Log(stress) vs. log(strain rate) curves for tests carried out at 1120 K for various grain sizes: X,

9.8 #m; [], 7.4 pro; o, 5.1 #m; e, 3.2 pro.

-'3

-', LOG,

LOG STRAINRATE ( MIN- I )

-2

STRAINRATE

-'1 (MIN-I)

Fig. 3. Log(stress) vs. log(strain rate) curves for tests carried out at 1 2 2 0 K for various grain sizes: X, 9.8 p m ; G, 7.4/Jm; o, 5.1 p m ; e, 3.2 p m .

TABLE 5 Grain size and temperature dependence of strain rate sensitivity 1.6

7~

sl.2. z

~

0.8

Grain size

Strain rate sensitivity

(mm)

At1120

9.8 7.4 5.1 3.2

0.35 0.41 0.42 0.44

K

(m)

At1170 K

At1220 K

0.37 0.42 0.42 0.44

0.45 0.50 0.51 0.50

0.4

0

-5

-'4

-'3

'

'

LOG STRAIN RATE2 (MIN-171

Fig. 2. Log(stress) v s . log(strain rate) curves for tests carried out at 1 1 7 0 K for various grain sizes: x, 9.8 #m; D, 7.4 pm; o, 5.1 # m ; ¢, 3.2 p m .

finest grain sizes at the three temperatures, the change being most prominent for the 3.2 #m material tested at 1220 K. A microstructural examination of these specimens revealed some grain coarsening, the grain size of the finest-grained material having increased to 6.1 #m. The increase in the 5.1 #m material was less, the final grain size being 6.3 #m. Again, there was no significant change in the ratio of ~, to a phase. Similar results have been reported for both ferrous and non-ferrous metals [7, 8, 12, 25]. This agrees with the results of many investigations which show a

sigmoidal relationship between the logarithms of stress and strain rate [26, 27]. Rai and Grant [8] have shown that for AI-Cu alloy the shape of the curve is significantly strain dependent and that the sigmoidal shape is only evident when, at very low strains, there is inherent grain growth of the very fine grains. Several researchers have suggested that the sigmoidal shape is due to the presence of a threshold stress but this is not supported by the results of other investigations [8, 28, 29]. Mukherjee [6] has suggested that the presence of a threshold stress may be due to impurity atom segregation in the grain boundaries which lock grain boundary dislocation movements and consequently alter the deformation and accommodation characteristics at the grain boundaries. It is also possible that the change in the slope of the curve at very low strain rates is due to intergranular oxidation o t t o the precipitation of a new phase.

261

4.2. Grain size effect It is evident from Figs. 1 - 3 and Table 5 that the grain size influences the strain rate sensitivity of the material in the range of conditions investigated. The material with the finest grain structure had the highest strain rate sensitivity. Also, the effect of decreasing the grain size from 9.8 to 3.2 # m on the strain rate sensitivity is a b o u t the same as increasing the test temperature of the coarser material from 1120 to 1220 K. Furthermore, the rate at which the material can be strained without loss of superplasticity increases with decreasing grain size. This has an important practical implication since the highest possible forming rate is desirable in industrial processes. The relationships between the grain size L and stress o and between the grain size L and strain rate e are shown in Figs. 4 and 5 respectively. In effect,

1220 K 40 ¸

mEE 30. Z

20.

u.

10

0

25

45

6~

8~

1~0

SQUARE OF GRAIN SIZE ( MICRONS )

Fig. 4. Relationship b e t w e e n f l o w s t r e s s a n d g r a i n s i z e (strain rate, 10-2min-1).

o o= L 2

and ~ccL -2

These relationships suggest that volume diffusion is the predominant deformation mechanism (see Table 1). The activation energy Qy of deformation at constant stress and the activation energy Qx of deformation at constant strain rate were determined from the Arrhenius plots for the superplastic region and are shown in Figs. 6 and 7 respectively. Q~ values range from 306 to 359 kJ mo1-1, higher than published values for self-diffusion in F e - N i - C r systems (see Table 3). Qy is also significantly grain size dependent. A plot of Qy versus L (Fig. 8) shows an approximately linear relationship. The same relationship was obtained by Hildebrand et al. [7] for a similar alloy but their activation energies are considerably lower. The relatively high values obtained in this study m a y arise because the alloy contained approximately equal proportions of ferrite and austenite. The alloy studied by Hildebrand et al. contained only 18% - 22% austenite. Activation energy values for self-diffusion in ~-Fe and 7-Fe structures cited in the literature are given in Table 3 and show that the value for ~/-Fe is higher. Padmanabhan [30] has suggested that Qy is greater, and Q= is less, than the real activation energy Q0. This is supported by the results of our study (see Figs. 6 and 7). Another

~5

x

-: 4. v ua 3 '

/

117o K

z2'

1.

0

2 4 6 8 INVERSE SQUARE OF GRAIN SIZE

10 (MICRONS x 102)

Fig. 5. Relationship between strain rate and grain size

(flow stress, 15.9 N ram-2).

conclusion that emerges from his analysis is that Q= is closer to Q0 than Qy is. The value of Q= obtained in our investigation is a b o u t 242 kJ mol -x and is of the same order a s values published for self-diffusion in F e - N i Cr alloys. This is further evidence that the rate-controlling mechanism for superplastic deformation in our alloy is lattice diffusion.

5. CONCLUSIONS

(I) The strain rate sensitivity of microduplex F e - N i - C r stainless steel is significantly

262

A

Jj33Kmo SKmol/

-8

'T z

'

v

z -4

2" -2

z.s

8".0

d.s

TEMPERATURE -1 x

104 (

~.o K )

Fig. 6. Arrhenius plot of strain rate us. temperature for various grain sizes (flow stress, 15.9 N ram-2): x, 9.8/Jm; o, 7.4 #m; o, 5.1 pm; o, 3.2 pm; 4, 5.0 p m [25].

~38C i

-4,

36~

-3

a4c

~

-1

32C

30C 8.0 TEMPERATURE -

1

x

104

(

GRAIN

K )

Fig. 7. Arrhenius plot of flow stress vs. temperature (strain rate, 10 - 2 min-1).

influenced by the grain size. The finer the grain structure, the higher is the strain rate sensitivity, except when the microstructural and process conditions favour grain growth. (2) A decrease in grain size increases the rate at which the material can be deformed without loss of superplasticity. (3) In the superplastic region the strain rate varies inversely and the flow stress varies directly as the square of the grain size. (4) The activation energy of deformation is of the same order as the values measured for self-diffusion in F e - N i - C r alloys and varies approximately linearly with grain size.

SIZE

( MICRONS )

Fig. 8. The effect of grain size on activation energy (flow stress, 15.9 N ram-2).

(5) There is a significant reduction in the strain rate sensitivity of the materials for grain sizes below about 5 pm at very low strain rates because of grain coarsening.

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