The cyclic stress-strain properties, hysteresis loop shape, and kinematic hardening of two high-strength bearing steels
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Table I.
Material AISI 1070 AISI 52100
Mechanical Properties of the AISI 1070 and 52100 Steels
Cro (0.02 Pct) (MPa) 1080 1020
HRC 60 to 61 62
stress-strain curve of the ELKP model. Equations [ 1] and [2] (Table II) show that Oreand Orcd e c r e a s e with increasing strain amplitude and can take on values less than zero. Another distinguishing feature of kinematic hardening is that an initially unbalanced strain cycle tends to become fully reversed (Figure 1). To quantify this feature, n r , t h e nonreversibility of the cycle, is defined here in terms of r, the reversibility: n r -~ 1 -
[6]
r
and [7]
r - - A E P R / A E pF
~ro (0.2 Pct) (MPa) 1650 1660
~rz (MPa) 3110 3040
e/ 0.0387 0.026
It shows that the results obtained for the two steels are generally within the scatter of the measurements. Only the oi values of the 1070 grade are significantly higher than the values of the 52100 steel. Both of the kinematic hardening parameters, o'k and M, are relatively insensitive to the strain amplitude, while the more conventional yield properties, orc and ore, decrease substantially with strain amplitude, taking on values less than zero at the larger strain amplitudes. The results in Figure 11 compare the actual loop areas with the bilinear representation for which the loop area U ' = 2AEPOrk. They show that the ELKP model yields values within a few percent of the actual plastic work at
where A e PF and A e PR are the plastic strain ranges produced by the larger stress (forward) and smaller stress (reverse) portions of the cycle, respectively. IlL
R E S U L T S AND DISCUSSION
The variation of the loop parameters (Table II) with number of cycles is shown in Figures 8 and 9. Both of the steels display 15 to 30 pct increases in the stress amplitude during the first 100 to 1000 cycles, but both trc and Ore d e c r e a s e in this range of N. Figure 9 illustrates that although the different loop parameters are still varying with N at failure (N: = 783 in this case), they may be beginning to approach a steady state after N = 103. Thus, the near end-of-life values, summarized in Table HI and in Figures 10 through 12, currently serve as an approximation to the values appropriate for much larger numbers of contacts. Figure 10 compares the strainamplitude dependence of the different loop parameters.
Tin-
0
I
0.01 $HEA~
I STRAIN
(a) arsI STANDARD GAGE SECTION
io7o
SHORT GAGE SECTION
1.000 + 0.001 OD 0.500 + 0,001
1.000 + 0.00t OD ID
A (GAGE DIA)
0 . 5 0 0 _+ 0.001 ID
D (GAGE DIA)
D I M E N 8 1 O N 8 (~.)
i I" i i
II [
_
~
A B C D E F
- 0.650 + 0.001 1.000 ~ 0.010 - 0.250 radius - 0.650 + 0.001 0.250 ~ 0.005 - 0.172 radius
"iI
i
3:%
I
0.01
I
"fro m O
SHEAR STRAIN
(b) AISI 52100 Fig. 4 - - T o r s i o n test specimens. 656--VOLUME 21A, MARCH 1990
Fig. 5 - - E x a m p l e s of the shear stress-strain hysteresis loops displayed by (a) AISI 1070 steel and (b) AISI 52100 steel. METALLURGICAL TRANSACTIONS A
[
1500
'
t--
0.035% (0.02%)
1
2
7"a
(2 0",)
f
-t50-"t.5
-t
-0.5
0.5 SHEA
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