The dynamics of cyclic plastic deformation and fatigue life of low carbon steel at low temperatures

Materials Science and Engineering, 26 (1976) 157 - 166

157

© Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands

The Dynamics of Cyclic Plastic Deformation and Fatigue Life of Low Carbon Steel at Low Temperatures

J. POL~K and M. KLESNIL Institute of Physical Metallurgy, Czechoslovak Academy of Sciences, Brno (Czechoslovakia)

(Received April 7, 1976)

SUMMARY The cyclic plastic stress-strain response and fatigue life of a low carbon steel at low temperatures was studied. The cyclic hardening/ softening curves and cyclic stress-strain curves at different temperatures were measured. Two components contributing to the cyclic flow stress were resolved, i.e., the internal stress and the effective stress. The effective stress c o m p o n e n t was found to be strongly dependent on the temperature and independent of the strain amplitude. The internal stress component was found to be dependent on the plastic strain amplitude and nearly independent of temperature. An analytical form of the cyclic stress-strain curve suitable for the analysis of the temperature and strain rate dependence of the cyclic plastic stress-strain response is proposed. The Manson-Coffin curves were found to be independent of temperature down to 113 K. A tendency to lowering the fatigue life was observed at the lowest temperature and highest strain amplitude only, and was connected with the appearance of brittle fracture, originated from short fatigue cracks.

1. INTRODUCTION The interest in low-temperature fatigue properties of metallic materials has arisen in connection with aircraft materials working under fluctuating loads at sub-atmospheric temperatures [ 1 - 3 ]. The approach to this problem relied on the WShler's curve concept. In investigations of pure metals made by

McCammon and Rosenberg [4] the WShler's curves at different temperatures were measured, too. With the exceptions of Fe and Zn, which became brittle, the effect of low temperatures resulted in a shift of the WShler's curve to higher stresses or higher fatigue lives. The low cycle fatigue of metals has attracted much attention in recent years. The Manson-Coffin law was applied as a new life criterion and its validity has been proved both in low cycle- and high cycle regions [5, 6]. Also, the importance of the cyclic stressstrain behaviour has been recognized and m a n y room-temperature cyclic stress-strain investigations have been performed. Temperature and strain rate significantly influence both the stress-strain behaviour and the fatigue life of metals, especially those with b.c.c, structure. Though there are many investigations on the dynamics of the unidirectional straining [7, 8], the dynamic aspects of the cyclic plastic deformation have begun to be investigated only recently. Information concerning the effect of low temperatures on the cyclic stress-strain behaviour and fatigue life are meagre, too. ' The effect of low temperatures on the cyclic plasticity and fatigue life was studied in f.c.c, metals. Laird and Feltner [9] strain cycled polycrystalline copper and Cu--7.5%A1 alloy in the temperature interval 78 - 293 K. In copper the Manson-Coffin curve was independent of temperature, in Cu-7.5%A1 alloy the shift to higher fatigue lives with decreasing temperature was observed. Holt and Backofen [10] stress cycled the same material at 293, 78 and 4.2 K. They obtained the plastic strain amplitude in the saturation region. In the range of fatigue lives 104 - 106 cycles, the

158 Manson-Coffin curves for both materials are shifted to higher fatigue lives with decrease of temperature. The dislocation arrangement in copper cyclically strained at low temperatures is characterized by a cell structure with the average cell size decreasing with decreasing temperature [11]. However, a plot of the stress amplitude vs. average cell size was independent of temperature [12]. The low temperature fatigue life of b.c.c. metals was studied by Ferro and Montalenti [13]. They cycled Fe and Fe-5%Si wires in cyclic torsion at temperatures of 293, 78, and 4.2 K in the range of fatigue lives 1 0 3 107 cycles. They found temperature dependence of the WShler's curve, in agreement with the previous results [4]. From the internal friction measurements they estimated the plastic strain amplitude and obtained MansonCoffin curves. Contrary to f.c.c, metals, the curves were shifted to lower fatigue lives with decreasing temperature. There have been few investigations on the dynamics of cyclic plastic deformation in b.c.c, metals. Abdel-Raouf e t al. [14 - 17] investigated the effect of the strain rate and higher temperatures on the cyclic plasticity of pure iron and low carbon steel. Miura and Umeda [13] measured the changes of the effective and internal stress of cyclically strained a-zirconium. Swearengen and R o h d e [19] compared the microdeformation parameters obtained from monotonic and cyclic straining of iron at room temperature. According to the microscopic theory of plastic deformation, the contributions to the flow stress may be of various origins. Usually, two components are found, i.e., the stress necessary to overcome the long range stress fields, which is identified with the mean internal stress, oi, and the stress necessary to overcome the short range obstacles, the effective stress, oe. The different contributions to the flow stress cannot be superimposed linearly always [8], however, as shown by Li [20], in the case of long range internal stress fields and short range obstacles the linear superposition is a good approximation. As the thermal fluctuations can help to overcome short range obstacles, the effective stress depends on the temperature and strain rate. The plastic strain rate, ~p, is proportional to the mobile dislocation density, Pro, and to

the average dislocation velocity, v, according to the Orowan relation ~p ~-

fbPm V,

(1)

where f is the geometrical factor and b is Burger's vector. The dislocation velocity will be limited by the time spent before the obstacle [7]. Supposing the overcoming of the barrier can be thermally activated, the average velocity is v = v~ exp [ - - A G / k T ] ,

(2)

where Vc is the limit velocity and AG is the free activation enthalpy. The dependence of AG on the effective stress can be expressed with the help of the activation area, A, e

AG = A G o - b

A (oe, T)doe,

(3)

0 where AGo is the free activation enthalpy for (/e ~ 0 .

In order to be able to express the effective stress dependence of the dislocation velocity, the dependence A = A ( % ) must be known. This dependence can be deduced from theoretical models [8]. Experimental investigations of the dynamics of plastic deformation resulted in an experimental relation of the form [21, 22] ~p = te1 o~"~,

(4)

where kl is a constant, and n~ is the strain rate sensitivity exponent. The temperature dependence of the strain rate could be expressed using the Arrhenius Law. Due to these facts the "operational parameters" are deduced from experimental data. These are the strain rate sensitivity exponent, defined more generally as n~

= (Olndp I , \ Oln% I T

(5)

and the effective activation energy Q =

1

~ln (--~--~

= kT

\ OlnT]Oe

(6)

o~

Using the theoretical models and/or some simplifying assumptions, the operational parameters can be related to the physical quantities characterizing the thermally-activated

159

dislocation motion, e.g., activation area, A, or activation enthalpy, AH. In order to divide the applied stress into the internal and the effective stress components the stress relaxation method was applied. Assuming that the effective stress dependence of the strain rate can be described b y relation (4), Li [21] derived, for the time dependence of the applied stress, the following relationship: 1

o = o i + h 2 ( t + A ) he-l,

(7)

where k 2 is a constant. The integration constant, A, can be deduced by plotting do~dr vs. log t. Analysing the dependence a vs. time according to relation (7), the internal stress component, oi, and the strain rate sensitivity exponent, ne, can be deduced. The theory of the thermal activation was developed and experimentally verified for unidirectional straining. In principle it can be applied also to low temperature cyclic straining. However, different contributions to the cyclic flow stress can vary not o n l y within individual cycles, but also with the number of cycles in dependence on the strain rate, strain amplitude, etc. The aim of the present work is to investigate the effect of low temperatures on the low cycle fatigue behaviour of low carbon steel. Cyclic hardening-softening curves and cyclic stress-strain curves are measured. The temperature dependence of the cyclic flow stress is found, and experimental and theoretical procedures for the analysis and identification of the individual contributions to the cyclic flow stress are proposed and verified. The dislocation structures produced by cyclic straining at low temperatures are observed and discussed in connection with the temperature dependence of the flow stress. The effect of lowering temperature on the Manson-Coffin plot is discussed.

length. The symmetrical-triangle-shape strain cycle with constant strain rate was chosen. The sensitivity of the strain measurement was higher than 10-5; the strain amplitude was held constant within + 10 -4. The error of the stress measurement was always less than + 5 MPa. However, the relative changes could be" followed with a sensitivity an order of magnitude higher. The low-temperature environment was produced in a cryostat [23] modified for cyclic loading [24]. The specimen and the inductive gage were placed in nitrogen vapor. The specimen temperature was controlled and measured with iron-constantan thermocouples placed above and below the gage length. The setting and control of the temperature was performed within +1 K; in relaxation experiments within + 0.4 K. The temperature gradient was dependent on the temperature and the type of the cooling coil. Down to the temperature 213 K the gradient within the gage length was smaller than 1 K. Dislocation substructures were investigated in thin foils by transmission electron microscopy with an Hitachi HU 11A electron microscope.

3. R E S U L T S

Cyclic hardening-softening and cyclic stressstrain curves In Fig. 1 the stress amplitude oa vs. number of cycles for constant total strain amplitude e a = 9.6 X 10 -a and strain rate ~ = 10 -2 s-1 at three different temperatures is shown. Rapid hardening is observed and saturation is reached quickly, especially at low temperatures. The rapid hardening stage is completed

&

T=148K

600

bo

jT= 213K 400

~

2. E X P E R I M E N T A L

-

\'T=295K co=9 6x103 ~o=1 O* 102s1

200

Cylindrical specimens o f 10 mm diameter were produced from weldable low carbon steel (0.2% C). They were cycled in an electrohydraulic testing machine ~operated in a closed loop. The strain was controlled and measured with an inductive type gage on a 10 mm gage

-

1

10

102

103 a ~cyctes]~

Fig. 1. Cyclic h a r d e n i n g curve~, at d i f f e r e n t t e m p e r a tures.

160 within 1% of the fatigue life for all amplitudes and temperatures. The majority of the fatigue life is characterized by negligible hardening which can be considered, to a good approximation, as saturation of the stress amplitude. That is why the cyclic stress-strain behaviour can be characterized by a stress-strain curve. Cyclic stress-strain curves obtained from constant amplitude tests at three different temperatures are shown in Fig. 2 in a log-log plot. Within the experimental scatter, a power law can be fitted to each set of the data. The parameters of the power law relation Oa ----K

t

n r

Cap,

(8)

i.e., the cyclic strength coefficient, K ' , and the cyclic strain hardening exponent, n', were obtained from least squares fit for each temperature and are shown in Table 1. In addition, the conventional monotonic parameters obtained from stress-strain curves at a strain rate g = 1.3 X 10 -3 S- 1 a r e presented.

Hysteresis loops and stress relaxation In order to divide the flow stress or stress amplitude into internal and effective compo-

I 6oo b~ 500

40O

30O 10-3

10-2

Fig. 2. Cyclic s t r e s s - s t r a i n curves at d i f f e r e n t t e m p e r a tures.

nents, the stress relaxation m e t h o d was used in conjunction with the record of the hysteresis loop. In order to avoid the inherent scatter in the data due to different specimens, the experiments were performed with a single specimen. The specimen was cycled at room temperature into the saturation region to obtain a steady dislocation structure. The temperature was successively lowered to 2 5 3 , 2 1 3 , 168 and 113 K, and at each temperature three hysteresis loops were recorded. The strain rate was held constant at ~ = 10 -3 S- 1 . At zero strain both in the tension and compression parts of the cycle the stress relaxation was recorded. Afterwards the specimen was heated to room temperature and again the loops were recorded with the relaxation at zero strain. The hysteresis loops and the stress relaxation were identical before and after cooling the specimen to low temperatures. It indicates that in a specimen cycled into saturation a few cycles at low temperatures did n o t change the internal stress; only the temperaturedependent c o m p o n e n t of the flow stress, i.e., the effective stress, was changed reversibly. In Fig. 3 the hysteresis loops in coordinates stress vs. plastic strain at the same plastic strain amplitude and different temperatures are shown. Except for o values at % close to -+cap the effect of temperature on the hysteresis loops is to reduce the shift in the direction of the stress. This finding indicates that the effective stress within the major part of the cycle does n o t depend on strain. With decreasing temperature, the magnitude of the effective stress increases and the rate of relaxation decreases. At temperatures close to room temperature the rate of relaxation was too high to record the commencement. At the lowest temperatures the relaxation was too slow, and therefore it was difficult to ensure long term temperature stability. The plot of the stress vs. time at the

TABLE 1 M o n o t o n i c a n d cyclic p a r a m e t e r s of t h e steel at d i f f e r e n t t e m p e r a t u r e s

T (°K)

OKt (MPa)

opt (MPa)

O~ (MPa)

ef

K' (MPa)

n'

e~

295 213 148

244 334 515

440 531 641

901 1067 1124

1.05 1.02 0.87

1013 1155 953

0.182 0.199 0.110

0.998 0.471 0.451

c

--0.625 --0.527 --0.565

o~ (MPa) 1008 1008 874

b

--0.114 --O.106 --0.062

161

113K

r

~. soo

10

o

.~.

o

~E

~1~,

b

C

~

o

i

4

-05

o o

0

1 ~pl{ap--

0 5

O1

001

__,

___,

1

10

100

~500

t Is]-

5. Time dependence of stress rate relaxation.

Fig.

Fig. 3. Hysteresis loops at different temperatures.

T

"~'

~o

:E a. 310

A =Is /'JOoo i

300

5

=260MPQ n, 7 0

/

290

0 280

200 50

100

150

250

200

t

[s]

Fig. 4. Time dependence of stress relaxation. o p t i m a l t e m p e r a t u r e , i.e., at 213 K, is s h o w n in Fig. 4. T h e r e l a x a t i o n e x p e r i m e n t s were h a n d l e d using the e f f e c t i v e stress c o n c e p t a n d t h e p o w e r law r e l a t i o n s h i p , eqn. (4), b e t w e e n t h e strain r a t e a n d t h e e f f e c t i v e stress a c c o r d i n g to Li [ 2 0 ] (see eqn. (7)). T w o o p e r a t i o n a l param e t e r s w e r e e s t i m a t e d ; strain rate sensitivity e x p o n e n t , n~, a n d e f f e c t i v e a c t i v a t i o n e n e r g y , Q. In Fig. 5 t h e r a t e o f stress d r o p vs. the logar i t h m o f t i m e is s h o w n . F o r s h o r t t i m e s t h e d e p e n d e n c e deviates f r o m linear d e p e n d e n c e ; t h e i n t e g r a t i o n c o n s t a n t , A = 1 s, was e s t i m a t e d . F r o m t h e slope o f the s t r a i g h t line, t h e strain rate sensitivity e x p o n e n t , n~ = 7, was determ i n e d . In Fig. 6 t h e q u a n t i t y - - ~ o / ~ l n ( t + A ) vs. e f o r A = 1 s is p l o t t e d . E x t r a p o l a t i n g to zero, t h e value o f t h e i n t e r n a l stress, oi = 2 6 0 MPa, was f o u n d . F r o m t h e s l o p e o f the straight line t h e value o f ne = 7 was d e d u c e d . F r o m t h e r e l a x a t i o n at t h e t e m p e r a t u r e 253 K t h e s a m e value o f t h e i n t e r n a l stress,

300

350

o" [M P4--

Fig. 6. Determination of internal stress and exponent n e from stress relaxation. TABLE 2 Strain rate sensitivity exponent, ne, and effective activation energy, Q, at different temperatures T

11e

(°K) 113 213 253

Q

(10 --20 J) 20 7 5

4.5 7.2 6.7

oi = 2 6 0 MPa, was derived. H o w e v e r , f r o m t h e d a t a at 113 K, o i c o u l d n o t be f o u n d with s u f f i c i e n t precision t h o u g h the value oi = 2 6 0 MPa is close t o t h e c e n t r e o f t h e s c a t t e r b a n d . If we a s s u m e t h a t we can fix ei = 2 6 0 MPa f o r all t e m p e r a t u r e s , t h e values o f ne c o u l d be f o u n d w i t h high precision (Table 2). S u b t r a c t i n g oi f r o m t h e flow stress, t h e t e m p e r a t u r e d e p e n d e n c e o f ee was o b t a i n e d (Fig. 7). T h e s m o o t h curve was f i t t e d t o e x p e r i m e n t a l d a t a and f r o m t h e slope o f this

162

t

L400

'-2 6oo (3_

~P

bo

b" 300

4OO

200

200 0

100

0

•

T

178

K

T

= 213

K

•

T

=

= 253

K

O T

= 295

K

i

I

L

5

10

15

i

20 ~ap[lO"3]

0

lOO

200

300 T [K'I~

Fig. 7. T e m p e r a t u r e d e p e n d e n c e o f t h e effective stress, a e.

dependence and from ne values the effective activation energy was calculated (Table 2). I n c r e m e n t a l step test

Using hysteresis loop records and stress relaxation the flow stress at one amplitude has been divided into internal stress and effective stress components. In order to find the strain amplitude dependence of these components many tests would be necessary. Moreover, considerable experimental scatter is inherent in these experiments due to scatter in material properties of different specimens. Therefore, to find the strain amplitude dependence of the effective stress c o m p o n e n t the incremental step-test procedure for the cyclic stress-strain curve determination [25] was used. In order to stabilize internal stresses and simultaneously the dislocation structure, the specimen was cycled into saturation at high strain amplitude. Later, one block of the increasing and decreasing strain amplitudes was applied to the specimen at each of the decreasing temperatures. Afterwards the specimen was heated again to r o o m temperature and the incremental step test was repeated. The average of the rising and falling portion of the block is the cyclic stress-strain curve obtained at an approximately constant level of the internal stress. The approximate constancy of the internal stress structure during this block loading at various temperatures is proved by the fact that the repeated stress-strain curve at 295 K is only 10 MPa lower than the original one. Therefore only the original curve is shown in Fig. 8. Figure 8 shows that the cyclic stress-strain curves at different temper-

Fig. 8. Cyclic s t r e s s - s t r a i n curves at d i f f e r e n t t e m p e r atures as f o u n d f r o m i n c r e m e n t a l step test m e t h o d .

atures can be made to coincide by merely shifting in the direction of stress (except values of oa for the smallest e~p). This suggests that the temperature dependent part of the cyclic flow stress is, to the first approximation, independent of the strain amplitude. Dislocation s t r u c t u r e s

The dependence of the dislocation structures in the saturation region on the temperature and plastic strain amplitude was investigated. In Fig. 9 the dislocation structures of the material cycled with a saturated plastic strain amplitude, eap= 10-2, at three temperatures are shown. The typical cell structure is observed in all cases. Although no detailed investigation of the dislocation arrangement or a statistical evaluation of the average cell size was performed, no systematic dependence on the temperature of cycling was found. The cell boundaries became more diffuse and the number of dislocations within the cells increased with decreasing temperature. The result of the investigation of the dislocation structure on the plastic strain amplitude is in agreement with other findings [12, 14]. For constant cycling temperature the cell size decreases with increasing plastic strain amplitude. The cell boundaries become wider for small plastic strain amplitudes. Fatigue life curves

The saturated plastic strain amplitude eap vs. the number of reversals to fracture, 2N~,

at different temperatures is shown in Fig. 10. The full line is the least-squares fit to about twenty-five experimental points obtained for the power law dependence at room temperature [26]

163

t

104

--

T = 295 K

o T = 213 K • T = 148 K

102

• •

%

i

• °!°

o

103 I

102

103

10 ~'

10 s 2N+

(a)

--

Fig. 10. Saturated plastic strain amplitude, number of reversals.

t

600

"•

;

o 50O

G a p , VS.

• o o

•

, •

o

•

°°

•

40O o o o o T= 2 1 3 K 300

(b)

~

o °

• T= 148 K

102

103

104

105 2Nf

Fig. 11. S a t u r a t e d reversals.

stress amplitude,

Oa,

vs.

number

of

11). T h e full line is t h e least squares fit o f Basquin's relation O a = OPf ( 2 N f ) b

(c) Fig. 9. Dislocation structures of 11423 steel cyclically strained at different temperatures into saturation with the strain amplitude e a = 1.1 × 10 -2. (a) T = 295 K; (b) T = 213 K; (c) T = 148 K.

Gap = G~f ( 2 N f ) C ;

(9)

e~ is t h e fatigue d u c t i l i t y c o e f f i c i e n t a n d c is the fatigue d u c t i l i t y e x p o n e n t . R e l a t i o n s h i p (9) was f i t t e d to e x p e r i m e n t a l d a t a at low t e m p e r a t u r e s , a n d p a r a m e t e r s e~ a n d c are s h o w n in T a b l e 1. We h a v e also p l o t t e d t h e s a t u r a t e d stress a m p l i t u d e s vs. t h e n u m b e r o f reversals t o f r a c t u r e , 2Nf, at d i f f e r e n t t e m p e r a t u r e s (Fig.

(10)

f o r t h e r o o m t e m p e r a t u r e data. o'f is t h e fatigue s t r e n g t h c o e f f i c i e n t a n d b is t h e fatigue s t r e n g t h e x p o n e n t . T h e p a r a m e t e r s o'f a n d b, o b t a i n e d f r o m a least squares fit o f r e l a t i o n s h i p (10) t o l o w - t e m p e r a t u r e e x p e r i m e n t a l data, also are s h o w n in T a b l e 1. Fracture surfaces F a t i g u e f r a c t u r e in s p e c i m e n s strain c y c l e d at r o o m t e m p e r a t u r e and d o w n t o 213 K was d u e to p r o p a g a t i o n o f the m a i n c r a c k to a c o n s i d e r a b l e length (over h a l f o f t h e s p e c i m e n d i a m e t e r ) f o l l o w e d , f o r higher strain amplitudes, b y s u d d e n f r a c t u r e . H o w e v e r , cycling at 148 K r e s u l t e d in v e r y s h o r t fatigue c r a c k length (less t h a n 0.5 m m ) a n d final f r a c t u r e was d u e t o brittle f r a c t u r e . O b s e r v a t i o n o f the f r a c t u r e surface s h o w e d t h a t o v e r 95% o f the f r a c t u r e surface c o r r e s p o n d e d to brittle frac-

164

ture. This fact was not studied quantitatively; however, it may account for the decreased fatigue life, especially at high strain amplitudes.

4. DISCUSSION

Cyclic stress-strain response Fatigue hardening curves obtained from low-temperature reversed cycling with constant strain amplitude show a pronounced saturation region at all temperatures. The cyclic stress-strain curves obtained from these tests show considerable scatter. Within this scatter the power law dependence, eqn. (8), can be fitted to experimental data. However, the investigations of the dynamic aspects of the cyclic straining have proved that the total flow stress can be separated into an effective stress and an internal stress c o m p o n e n t within a single hysteresis loop as well as for stress amplitudes. The effective stress c o m p o n e n t was found to be independent of the strain within the loop, and also independent of the strain amplitude in the incremental step test. Therefore, the total cyclic flow stress can be separated into two components. o = Oe[~p,T,h(pm)

] + o i [ e p , h ( P t , T , ~ p ) ].

(11)

The effective stress, oe, depends on the plastic strain rate, ip, the deformation temperature, T, and the strain history through the mobile dislocation density, Pro. The internal stress, ai, depends on the magnitude of the reversed plastic strain, ep, and on the strain history through the total dislocation density, Pt, as well as on the dislocation arrangement, both of which can be influenced by the temperature, T, and the strain rate, g. From this general expression and from our experimental observations an expression suitable for the analysis of the cyclic stress-strain curve can be derived. We can deduce that the internal stress in the saturation region is only feebly dependent on the temperature and strain rate. This is supported by the fact that the difference of the saturated stress amplitude, Oa, at low temperature and at room temperature is equal to the difference of the effective stresses at these temperatures. The observed independence of the scale of the dislocation structure on temperature also favours this conclusion. The internal stress amplitude depends predominantly on the plastic strain amplitude.

The effective stress c o m p o n e n t strongly depends on temperature and strain rate. As the loops in the saturation region are nearly cycle independent, the changes in the mobile dislocation density can be considered negligible. Therefore, to a good approximation, the saturated stress amplitude is a sum of two components Oa = Ga, e ( e p , T ) + Ga,i(eap ).

(12)

Until now only room temperature investigations of the low-cycle fatigue in b.c.c. metals have been performed. The cyclic stressstrain curves were analysed using expression (8). As this expression is a function of the plastic strain amplitude only, it can very well describe the plastic strain amplitude dependence of the internal stress. Therefore, an analytical expression suitable for the analysis of the effect of the temperature and the strain rate on the cyclic stressstrain curve is: r

a a = B + g~ eab.

(13)

The parameter B = B(T, gp) is temperature and strain rate sensitive. K1 and nl are cyclic hardening parameters that are, to a first approximation, temperature and strain rate insensitive. By fitting expression (8) to the cyclic stressstrain curves the strain hardening exponent, n', decreases with decreasing temperature (see Table 1). If eqn. (13), however, is used for the analysis, a good fit to the cyclic stress-strain curves at various temperatures is obtained for a constant value of n~ and different values of B, dependent on the temperature. Data on cyclic stress-strain response obtained from the multiple step-test procedure are subject to much smaller scatter. The observed shift of the cyclic stress-strain curves with decreasing temperature (Fig. 8) justify the use of eqn. (13). The effect of lowering the temperature results in different parameters of B. Dynamics o f cyclic straining The results of low-temperature cyclic straining have been missing until now, apparently. In this investigation we have checked whether the experimental methods and type of analysis used for unidirectional straining can be applied in an investigation of cyclic straining. It was found that the record of the hysteresis

165 loops and stress relaxation are a valuable tool for the determination of the operational parameters. The values of the strain rate sensitivity exponent, ne, at different temperatures (Table 2) can be compared with the value ne = 5.5 for T = 300 K found by Abdel-Raouf et al. [16] for cyclically strained pure iron and low carbon steel, and with the room-temperature values obtained by Swearengen and Rohde [18] from relaxation experiments on unidirectionally (n~ = 3.3) and cyclically (n~ = 2.6) strained iron. At lower temperatures, ne was measured for unidirectional straining only. Spitzig and Keh [27] found a steep rise of n e with decreasing temperature. At the temperature T = 110 K, n~ values were around 30 for different single-crystal orientations of iron. The drop in n~ with increasing temperature is in qualitative agreement with our results. Effective activation energies were not measured systematically; however, t h e y fall in the interval 3 - 11 × 10 -20 J found for unidirectional straining of iron single crystals [27] and depend on ee. As the mobile dislocation density was held constant and the temperature dependence of the pre-exponential factor in eqn. (2) can be neglected [8], the effective activation energy equals the activation enthalpy, AH, connected with the glide of dislocations in cyclic straining of the low carbon steel. Our experiments in this area are of a preliminary nature. Therefore we do not a t t e m p t to decide between various proposed mechanisms of the thermally-activated slip in b.c.c, metals as, e.g., the thermal overcoming of the PeierlesNabarro stress [28] or the thermally-activated glissile-sessile transformation of the screw dislocation [29].

Fatigue life Experimental data concerning fatigue lives as expressed in the Manson-Coffin plots show only very feeble temperature dependence in the measured temperature interval. Only at the lowest temperature (T = 125 K) is there a tendency to decrease the fatigue life at the highest plastic strain amplitudes. This was found to be connected with the very short fatigue crack length and subsequent brittle fracture. With decreasing temperature the stress amplitude increases and the critical

value of KliS reached for very short crack lengths, especially at higher strain amplitudes. It has frequently been proposed that low cycle fatigue life is controlled by fatigue crack propagation under general yield conditions [5]. Our findings support this hypothesis. Provided that the fatigue crack propagates across the greater part of the specimen, the fatigue life will be controlled by the plastic strain amplitude, whatever is the stress amplitude. The plastic strain amplitude is related to the stress amplitude through the cyclic stress-strain curve. The cyclic stress-strain curve depends on temperature mainly due to the effective stress component. Therefore, the effective stress c o m p o n e n t can be considered as a non-damaging component of the stress amplitude that compensates for the reduced help of thermal activation due to the drop in temperature. This consideration is valid for b.c.c, metals with high stacking fault energy, and therefore easy cross slip, in which the dislocation structure and therefore the amplitude of the internal stress is to a first approximation temperature independent. In f.c.c, metals, especially in those with low stacking fault energy, the amplitude of the internal stress is strongly temperature dependent. The decrease of temperature leads to the improvement of fatigue life in the Manson-Coffin plot of Cu-7.5%A1 alloy, though the Manson -Coffin plot of pure copper was not affected [9]. CONCLUSIONS (1) The cyclic hardening of low carbon steel at low temperatures does not qualitatively differ from that at room temperature. The saturation of the stress amplitude is reached very quickly and the cyclic stressstrain curves can be found at all temperatures. (2) Two components contributing to the cyclic flow stress can be resolved, i.e., the internal stress and the effective stress. The internal stress depends on the plastic strain amplitude but is nearly independent of temperature. The effective stress is approximately independent of the strain amplitude and is strongly temperature dependent. (3) The microscopic parameters characterizing the dynamics of the cyclic plastic straining can be acquired using the methods c o m m o n in unidirectional straining.

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(4) Fatigue life curves expressed in the form of a Manson-Coffin plot were found to be independent of the deformation temperature, provided that the fatigue crack propagated through a considerable part of the specimen cross section.

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