12
I. A. Volkov et al.
1.3.3 Hard Block-Type Asymmetric Low-Cycle Loading
Further studies present the numerical results of cyclic plastic deformation process and
fatigue damage accumulation during hard (controlled strains) block-type asymmetric
low-cycle loading. Experimental studies have been performed on the samples made
of stainless 12X18H9 steel under conditions of hard (controlled strains) uniaxial
tension–compression at room temperature in the laboratory for testing the physical and mechanical properties of structural materials of the Research Institute for
Mechanics of Lobachevsky State University of Nizhny Novgorod. The test program
consists of two blocks, including monotone and cyclic loadings (Mackenzie 1950):
• in the first block, the sample is compressed up to strain of e 11 = 0.01, and then
stretched up to strain of e 11 = 0.05;
• in the second block, the sample is subjected to asymmetric hard cyclic loading
with the strain amplitude of e 11 = e
(+)
11 − e
(−)
11 = 0.01 up to failure (N f = 850).
Here, the setting of the plastic hysteresis loop takes place (Fig. 1.5) and after the
500th loading cycle the loop becomes practically symmetrical.
Tables 1.4, 1.5 and 1.6 present the main physical–mechanical characteristics of
12X18H9 steel and the material parameters of the MDM model, determined from the
results of the basic experiment (Volkov and Korotkikh 2008; Mitenkov et al. 2015),
used in calculations.
Figure 1.7 depicts the deformation process of 12X18H9 steel in the second loading
block (the 500th cycle). The experimental and numerical data agree both qualitatively
and quantitatively.
Table 1.4 Physical–mechanical characteristics and material parameters of the MDM model of
12X18H9 steel
K
G
C o
p , MPa g 1 , MPa g 2 g 3 , MPa g 4 k 1 , MPa k 2 a 1 a 2 W a W f
165.277 76.282 190
24.090 286 800
2 10.000 0.2 5 0 0
800
Table 1.5 Cyclic hardening modulus Q 1 (ρ max )(MPa) for 12X18H9 steel (Q 2 = 0)
Q 1 , MPa
190
205
210
215
220
225
225
ρ max , MPa
0
20
40
60
80
100
120
Table 1.6 Monotone hardening modulus q 1 (MPa) for 12X18H9 steel (q 2 = 0)
q 1 , MPa
−5000
−4471
−4188
−3859
−2460
−182
888
χ
0
0.002
0.004
0.006
0.008
0.01
0.015
q 1 , MPa
1531
1274
913
913
913
χ
0.02
0.03
0.04
0.05
0.06
I. A. Volkov et al.
1.3.3 Hard Block-Type Asymmetric Low-Cycle Loading
Further studies present the numerical results of cyclic plastic deformation process and
fatigue damage accumulation during hard (controlled strains) block-type asymmetric
low-cycle loading. Experimental studies have been performed on the samples made
of stainless 12X18H9 steel under conditions of hard (controlled strains) uniaxial
tension–compression at room temperature in the laboratory for testing the physical and mechanical properties of structural materials of the Research Institute for
Mechanics of Lobachevsky State University of Nizhny Novgorod. The test program
consists of two blocks, including monotone and cyclic loadings (Mackenzie 1950):
• in the first block, the sample is compressed up to strain of e 11 = 0.01, and then
stretched up to strain of e 11 = 0.05;
• in the second block, the sample is subjected to asymmetric hard cyclic loading
with the strain amplitude of e 11 = e
(+)
11 − e
(−)
11 = 0.01 up to failure (N f = 850).
Here, the setting of the plastic hysteresis loop takes place (Fig. 1.5) and after the
500th loading cycle the loop becomes practically symmetrical.
Tables 1.4, 1.5 and 1.6 present the main physical–mechanical characteristics of
12X18H9 steel and the material parameters of the MDM model, determined from the
results of the basic experiment (Volkov and Korotkikh 2008; Mitenkov et al. 2015),
used in calculations.
Figure 1.7 depicts the deformation process of 12X18H9 steel in the second loading
block (the 500th cycle). The experimental and numerical data agree both qualitatively
and quantitatively.
Table 1.4 Physical–mechanical characteristics and material parameters of the MDM model of
12X18H9 steel
K
G
C o
p , MPa g 1 , MPa g 2 g 3 , MPa g 4 k 1 , MPa k 2 a 1 a 2 W a W f
165.277 76.282 190
24.090 286 800
2 10.000 0.2 5 0 0
800
Table 1.5 Cyclic hardening modulus Q 1 (ρ max )(MPa) for 12X18H9 steel (Q 2 = 0)
Q 1 , MPa
190
205
210
215
220
225
225
ρ max , MPa
0
20
40
60
80
100
120
Table 1.6 Monotone hardening modulus q 1 (MPa) for 12X18H9 steel (q 2 = 0)
q 1 , MPa
−5000
−4471
−4188
−3859
−2460
−182
888
χ
0
0.002
0.004
0.006
0.008
0.01
0.015
q 1 , MPa
1531
1274
913
913
913
χ
0.02
0.03
0.04
0.05
0.06