Low cycle fatigue data evaluation for a high-strength spring steel

Int. J. Fatigue Vol. 19, Nos 8-9, pp. 607-612, 1997 © 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0142 1123/97/$17.00+.00

ELSEVIER

PIh S0142-1123(97)00074-1

Low cycle fatigue data evaluation for a highstrength spring steel D. M. Li*, K. W. Kim and C. S. Lee

Department of Materials Science and Engineering, Pohang University of Science and Technology, Pohang, 790-784 Korea (Received 11 May 1997; accepted 28 May 1997) In the present investigation, low cycle fatigue (LCF) behavior is studied using the cylindrical smooth specimens under strain-controlled fully-reversed pull-push conditions for a high-strength spring steel heat-treated to different strength levels. During strain cycling the steel exhibits continuous softening independent of the applied strain levels and heat-treatments. Under the circumstances the saturation of the plastic strain energy density per cycle proves to be a valid criterion to determine the stable hysteresis loops for the cyclic stress-strain (CSS) curve formation. The strain-life curve calculated on the basis of the CSS relationship is in good agreement with the experimental counterpart, indicating a fine consistency between data from the CSS approach and from the strain-life approach. Then the LCF properties are discussed with regard to their dependence on the heat-treatments or strength levels of the steel. © 1997 Elsevier Science Ltd. (Keywords: low cycle fatigue; high-strength steel; cyclic stress-strain correlation; strain-life correlation)

Despite the fact that low cycle fatigue (LCF) behavior has been studied for many decades and become a rather classic topic, some of its fundamentals still need to be clarified systematically in order to have a better understanding of the LCF mechanism. Just as in the monotonic loading condition, an appropriate determination of the cyclic stress-strain (CSS) relationship is also of key importance in the description of basic cyclic deformation behavior. As a conventional practice, the cyclic stress-plastic strain relationship is generally expressed in a power-law equation as l 0",, = K ' ( E p a ) n'

not a unified definition for the 'stable' state. For instance, with the single-step method, a 'half-life' criterion is conventionally adopted in which the hysteresis loop at 50% life cycles is assumed as the stable oneL For a material that does not reach a (stress or strain) saturation state before specimen failure, however, this criterion becomes arbitrary and hence, has little physical implication. Moreover, different methods usually result in divergent ~CSS curves for a definite material 26. On the other hand, the strain-life relationship is one of the major issues to study, either for the LCF damage analysis or for engineering design. Simply combining Basquin's formula v for the elastic component with Coffin-Manson's formula s,9 for the plastic component, the total strain amplitude, Eta, can be expressed in correlation with the strain reversals to failure, 2Nr, as

(1)

where oa and %. are stress amplitude and plastic strain amplitude, respectively, and K' and n' are constants for the best-fit of data, and are considered the cyclic deformation properties of a material. While obtaining the monotonic stress-strain curve is quite straightforward by tensile tests, the experimental determination of the CSS curve is largely dependent on experiences as well as assumptions. The most frequently adopted methods are the single-step or companion samples method, the multiple-step method and the incremental step method2-% Common to these methods is that the tips of the stable hysteresis loops are connected to form the CSS curve. Then the criterion for the stable hysteresis loop becomes a crucial issue while there is

E,a = ~O-r'(2N/)h + Er,(2Nr)"

(2)

in which E is Young's modulus, and the four constants, of', ~f', b and c are termed fatigue strength coefficient, fatigue ductility coefficient, fatigue strength exponent and fatigue ductility exponent, respectively, and are also considered fatigue properties of a material. A theoretical consistency between properties obtained from the strain-life data and from the CSS data should be maintained ~,m because they represent the cyclic properties of one single material. However, since the CSS relationship and the strain-life relationship are experimentally determined individually via different approaches, this consistency cannot always be maintained adequately in practice.

*Author for correspondence at: c/o Professor W. Bleck, Institut ftir Eisenhtittenkunde, RWTH Aachen, Intzestral3e 1, 52072 Aachen, Germany.

607

608

D . M . Li et al.

In the present investigation, the LCF behavior of a high-strength spring steel is approached both experimentally and analytically. It is aimed at establishing an appropriate criterion for the determination of the stable state of the LCF deformation and at examining the consistency between data of the CSS and the strainlife approaches.

EXPERIMENTAL DETAILS The steel used for the present investigation was received from Pohang Iron and Steel Co. Ltd (POSCO, Pohang, Korea) in the form of rolled bars having a nominal diameter of 12.3 mm. The steel had a chemical composition, in weight percent, of: 0.59 C, 2.49 Si, 1.98 Ni, 0.54 Cr. 0.50 Mn, 0.18 V and balance Fe. The heat-treating procedures were selected to get different microstructures as well as various strength levels. The steel samples were austenitized at 900°C for 40 min and quenched in oil. Then the samples were tempered for 30min at 300, 350, 400, 450 and 500°C in a salt-bath furnace. The microstructure was composed basically of tempered martensite regardless of different tempering temperatures. Due to the high temperingresistance of the steel, the typical lath configuration of the tempered martensite was maintained up to the tempering temperature of 450°C, with slightly coarsening of the tempered martensite occurring in the steel tempered at 500°C. A detailed observation of the tempered microstructure was made under a transmission electron microscope (TEM), and reported elsewhere ~. A cylindrical smooth bar specimen was used for the present LCF tests. It had a gauge diameter of 6 mm and a gauge length of 8 mm. Before the fatigue testing the gauge length and the fillet areas of the specimens were polished using abrasive papers with their final powder No. being 1500, in order to minimize the roughness-induced early crack initiation from specimen surface. The LCF tests were conducted at room temperature in ambient air in an Instron 8501 dynamic testing machine. Both the process control and the data acquisition were realized by a computer equipped with a specialised dynamic testing program package 'Flaps 5'. Its data acquisition speed could reach as high as l kHz (103 points s 1). To ensure a tight contact between specimen and its holder in the tensile-compressive cycling, considerable efforts were made in the design of a jig which was capable of accommodating off-alignment by its wedged surface contact. The total strain amplitude control mode were adopted and the sine-wave input form was used. The total strain amplitude ranged between _+ 1 and _+ 2.5% and the strain ratio was - 1 , that is, completely reversed tensile compressive strain cycling. Since strain rate might have some influence on the LCF behavior, the strain wave frequency was selected according to the strain amplitude in such a way as to maintain a constant strain rate of 0.2% s t. And, the data acquisition rate was also regulated according to the strain wave frequency to maintain a uniform data system. From this testing system, a detailed load-strain history of the whole LCF process was available, from which various data postprocessing was realized. The monotonic tensile tests were also carried out using the same specimens to provide necessary data source for the analysis of the

LCF results. Principal properties obtained from these tests are listed in Table 1. RESULTS AND DISCUSSION In the present study, the single-step method was adopted for the determination of the CSS curve since enough specimens were available as they were tested for the strain-life correlation. In order to use this method, the state of the stable hysteresis loop has to be decided. Under the strain-controlled condition, the variation of stress amplitude during cycling has to be examined to check if the material is cyclically softening, hardening, stable or exhibits mixed behavior. It is observed that, for each applied strain amplitude (Ea), the stress amplitude oa decreases continuously as the strain cycling proceeds. All the five groups of specimens exhibit the same trend of this variation, with Figure 1 showing representative examples. Therefore the steels behave as cyclically softening independent of their specific microstructures. This is in agreement with the cyclically softening behavior reported for some other high-strength steels ~2. As is noted earlier, in the case where no stable stress is reached during cycling, defining the stable hysteresis loop by the 'half-life' criterion is somewhat artificial or is not physically based. On the other hand, from a viewpoint of damage accumulation, the strain energy-based criterion has been proved to be more consistent in describing the LCF behavior ~3. Then, the variation of the plastic strain energy density, as measured by the area of the hysteresis loop in the true stress-true strain plot, has to be checked. Figure 2 shows the plastic energy density per cycle, AW~,, as a function of cycle N for specimens with different strain amplitude Ea. It provides data for the steels tempered at 300 and 500°C but is representative of all groups of steels studied. As is seen from Figure 2, the value of AWe first increases with increasing N and then saturates to a stable value when N reaches a critical value. For the present case, this critical value of N ranges between 10 and 20 cycles. In view of this experimental trend, the stable hysteresis loop for the determination of the CSS curve is chosen as the one at the critical cycle when AWp reaches a stable value. For each specimen group, the stable hysteresis loops were selected according to the above criterion, and the tips of these loops were connected, to form the CSS curve. All the CSS curves determined by this procedure are given in Figure 3, in comparison with their counterparts obtained in monotonic tension. It is indicated that, for all groups of specimens, the CSS curve lies beneath the corresponding monotonic stress-strain curve, confirming the cyclic softening behavior as is reflected in the variation of the stress amplitude

(Figure 1). In the evaluation of the LCF life, the number of strain (or stress) reversals to failure, 2Nf, rather than the number of cycles to failure, Nt-, is used for the convenience of correlating experimental data directly with some well-established basic equations like Equation (2). In the present study, the total strain amplitude vs reversals to failure (Ca-2Nf) relationship was obtained directly from experimental data for each group of steel, since the present LCF tests were total strain-controlled.

609

Low cycle fatigue data evaluation for a high-strength spring steel Table 1

M o n o t o n i c tensile properties

T e m p e r i n g temperature

Yield strength (MPa)

Tensile strength (MPa)

Elongation (%)

Reduction o f area (%)

(°C)

300 350 400 450 500

2175 2170 2120 1875 1810

2505 2420 2295 2065 1930

34.9 39.5 42.2 43.0 37.4

13.6 14.8 16.0 16.4 14.1

2600 80

2500

.-''--

"

g ~

2.46%

2.31%

," 2.31%

2400 -797

2300

- - -

2.15%

70

2.01%

2.15%

1.83%

2.01% 2200

..........

- .... - -.

-

I. 83%

....

o

50

' : .......

1.1"66%55%

v

40

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i. 33%

g

2100

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i

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1.66% 1.5o%

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v

~

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20

1800 1700

T 6 ~ p e r e d a t 300 °C

160o0o~

,

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1

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*

i03

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(a) ,

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i

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103

N (Cycles) .

2000

at 300 °c

Te~per~

.........

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.

.

.

.

.

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.

. . . . . . . . _

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ga =

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1900

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60

2.34%

2.16%

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1.84%

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1.84%

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1.66%

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1500

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1400

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20

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(b)

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N (Cycles)

F i g u r e I Variation o f stress amplitude o-. with c y c l e N and strain amplitude E. for the s p e c i m e n s tempered at: (a) 300°C; and (b) 5 0 0 ° C

Figure 4 gives the log-log plots of the experimental data of e~-2Nf correlation. As is evidenced in this figure, the slope of the Eta-2Nf curve changes as the strength level, or the tempering temperature, of the steel changes: the slope increases with decreasing the strength level of the steel. In consequence, the E,,-2Nf curves for steels with different strength levels intersect, rather than shift, to each other, approaching a pivoting configuration. More specifically, the stronger steel has a longer life at low strain amplitude, whereas the softer (tougher) steel has a longer life at high strain amplitude. This phenomenon has also been documented in some previous investigations for typical SAE steels H. For those steels corresponding to the pivoting position is located at the reversals ca 2 x 103 (or 103 cycles) and at a strain amplitude of ca 10 2 or lower ~4. By contrast, the number of reversals corresponding to the pivoting position in our case (Figure 4) ranges 300400 but at a higher strain level of 1.6 x 1 0 - 2 . This upper-left shift of the Eta-2Nf curve pivoting is probably due to the markedly higher strength level (ca 2 GPa)

°1oo

(b)

,

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,

,

,

, ,

10,

.

"1)

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.

.

.

.

.

lO,

N (Cycles)

F i g u r e 2 Variation o f plastic strain energy density per cycle, AWe, with c y c l e N and strain amplitude ~ for the steels tempered at: (a) 300°C; and (b) 5 0 0 ° C

of the steel in the present study. Information provided by the data of Figure 4 establishes a base on which the performance of a steel can be tailored flexibly according to the particular concern of its application by changing its microstructure, which is in turn controlled by appropriate heat-treatments. To examine if there exists a consistency between data of the CSS approach and of the strain-life approach, the elastic and plastic strain amplitudes, Eta and ev,, were calculated using the stress-strain relationship, summed and compared with the experimental data of Eta, as functions of 2Nf for each group of steels. To be specific, Eea and eva were independently calculated by the value of %, at the energetically-stable cycle as defined in the previous section, using Hooke's law (Ee, = O'a/E ) and Equation (1) [eva = (o'JK')l/"], respectively. Then, they were summed to form the calculated value of the total strain amplitude, Et,, plotted against 2Nf and compared with the corresponding experimental data. This is demonstrated in Figure 5 for all the five

D . M . Li

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et al.

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(b)

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1.7 1.6

10_2 •

....... ~o~.~ ~ . . . . ~

1.9 1.8

........................ - -

:

~ i ~

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at 500 :C

T~r~d

1.6

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./.

,

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0,015

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. . . . . 0.025

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~

~

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iO~

5xlO3

(a)

Figure 3 The CSS curves (mainly plastic components) in comparison with the monotonic counterparts for specimens with different heat-treatments

3xlO 2

i0_2 • 3x10 -2 r

2xl 0 .2

i0:

~pa

2Nt

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300 °C

v

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8xl 0 .3 10 ~

.......

in

.......

i'~

.......

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2Nf

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groups o f specimens. It is found from Figure 5 that the calculated curve (dashed line) is in g o o d agreement with the experimental data. Undoubtedly this agreement would not have been possible if the 'half-life' criterion had been adopted in the determination o f the CSS curve, since the stress amplitude used for the calculation would have been evidently lower. The impor-

Low cycle fatigue data evaluation for a high-strength spring steel 3x10

I0

2

:

-

gta

i 3xlO

(calculated)

g~ (measured)

S .5xiCr

V]'!

2xl0 3

(e) Figure 5 Calculated elastic, plastic and total strain amplitude, ec~, ET,~, and e,~ in comparison with the experimental e,., against the reversals to failure, 2Nr, for different steel groups (with tempering temperature as indicated)

tance of the agreement is twofold. On one hand it is implied that the criterion for the stable hysteresis loop to determine the CSS curve is thereby justified as the one at which the strain energy density reaches a stable (or saturated) value. On the other hand, it implies that there should be a sound consistency between data of the CSS relationship and the strain-life relationship, although these two relationships were determined independently. To further substantiate the effectiveness of the strain energy criterion, the saturated (stable) value of the plastic strain energy density per cycle, AWp, is plotted against the reversals to failure, 2Nr, as shown in Figure 6. Comparing Figure 6 with Figure 4, it is clearly indicated that the AWp-2Nr curves and the Eta-2Nr curves follow the same trend regarding their responses to tempering temperature (or strength level) of the steels. That is, they intersect each other in such a manner that the slope increases with increasing tempering temperature or with decreasing strength of the steels. In an energetic sense it is implied that the softer (tougher) steel is more resistant in the applications where greater plastic energy is dissipated (plasticity-dominated situation), whereas the stronger steel is superior in surviving the applications where strain energy dissipation is mostly elastic and recoverable (strength-dominated situation). Therefore, a consistency exists between the strain-based criterion and the energy-based criterion for the evaluation of the present LCF behavior. . . . . . . . .

Tempered

•

10:

i

. . . . . . . .

,

5x10 °

%\~

400 ~

"~

soo °c

. . . . . . . . i0

,

at

---o--- 450 °C -o--

. . . . . . . .

"-,. ~

. . . . . . . .

l0 s

J I0 3

. . . . . . . .

611

As is shown in Figure 5, at high strain amplitudes the 6ta-2Nf curve approaches the plastic component (Epa-2Nf) and the behavior is plastically dominant, while at low strain amplitudes the E~,-2Nf curve approaches the elastic component (Eoa-2N0 and the behavior is elastically dominant. At a transition fatigue life, 2N,, the elastic and plastic components are equal. The higher the 2N,, the longer life cycle would a steel spend in plastic strain regime, and vice versa. Thus 2N, can also be indicative of the relative resistance of the steel to plasticity-dominated failure (in the case of high 2N,) or to strength-dominated failure (in the case of low 2Nt). For the present case, 2Nt increases with increasing tempering temperature or with decreasing strength level of the steels. It is also noted that the data of both the elastic and the plastic components suggest a single and fairly linear relationship on the log-log plot (Figure 5). By contrast, in some austenitic steels, dual-phase steels or A1-Li alloys, it has been found 15 ~'~ that there is a transition in the %,-2Nr plot and hence a bilinear Coffin-Manson relationship exists. The mechanisms for this bilinearity have been explained as a change in the cyclic hardening behavior iS, an inhomogeneous distribution of a high density of intergranular carbide and the formation of planar arrays of dislocations jr, a transition of fracture morphology with increasing strain level iT, and environmentally assisted degradation processes4~'l% These observations provide a hint that the LCF process in our cases should be dominated by a single mechanism of cyclic deformation and fatigue damage accumulation, at least in the strain regime studied. This has been confirmed by the observations by the present authors on the deformation substructural variation during cycling, and is to be detailed in a separate article. CONCLUSIONS For the present high-strength spring steel under quenched and tempered conditions, the following conclusions can be drawn regarding its LCF behavior: 1. In the case where no stress-strain saturation is found, the saturation of the plastic strain energy density per cycle, AWp, can serve as an effective criterion for the determination of the stable hysteresis loops to obtain the CSS curve. 2. There exists a good consistency between data obtained from the CSS approach and from the strain-life approach so that the strain-life curve calculated according to the CSS relationship agrees well with the experimental data. . A pivoting phenomenon is found in the strain amplitude-reversals to failure (E,~-2Nr) curves for different strength levels: the slope of the eta-2Nr curve increases with increasing tempering temperature or with decreasing strength of the steel. The same trend is confirmed by the AWp-2Nr curves. In consequence, the transition life (2Nt) prolongs as tempering temperature increases or as the strength of the steel decreases.

r 10 4

2x10 4

2Nf

Figure 6 Experimental data of plastic strain energy density per cycle. AWp, against strain reversals to failure. 2Nr. for the steels with different heat-treatments

ACKNOWLEDGEMENTS The authors address their gratitude to the financial support by Pohang Iron and Steel Co. Ltd. (POSCO) to the present work.

D . M . Li et al.

612

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12 13 14 15 16 17 18 19

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