PSI - Issue 40

A.V. Zinin et al. / Procedia Structural Integrity 40 (2022) 470–476

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A.V. Zinin at al. / Structural Integrity Procedia 00 (2022) 000 – 000

Fig. 5 Initial and secondary fatigue curves during loading with "training" of 10G2S1 steel under tension-compression – (a) and bending with rotation (b), as well as 14Kh2GMR steel (c) : 1 – primary curve; 2 - ε a = 0.2%, N low = 5; 3 - ε a = 0.2%, N low = 80; 4 - ε a = 0.2%, N = 1500; 5 - ε a

= 0.5%, N low = 5; 6 - ε a = 0.5%, N low = 80. 3.4. Fatigue damage accumulation

To assess the effect of low-cycle overloading on the degree of material damage under non-stationary cyclic loading, a linear Miner-Palmgren damage accumulation model corresponding to two-stage loading with low-cycle overloading in the form of

low n n

high

low high      D D D

N N

1 (1) where D Σ – the present value of damage at failure under the combined action of the overload and low-cycle fatigue loading; D low – damage (or hardening) made the low-cycle stage at severe loading; n low – the number of hard loading cycles; N 1 – lifetime under low-cycle loading; D high – damage under high-cycle loading; N 2 – lifetime with a control voltage on the primary curve; n high – the ultimate lifetime with a control voltage of the sample subjected to overload (for secondary curve). For the loading of cyclically hardening steel with training in the elastoplastic region with a strain amplitude ε a = 0.2% at N low = 5 and 80 cycles, the calculated value of the total destructive damage D Σ > 1 is obtained, i.e., low cycle overloads contribute to the hardening of the material. An increase in the strain level and the number of overload cycles leads to softening of the material – in this case when summing up the damage according to dependence (1) D Σ <1. For cyclically softening steel, a deviation from the linear law of damage summation ( D Σ = 0.13 ... 0.70 < 1) was observed under all modes of preliminary low-cycle overloads, which indicates the softening effect of the preliminary elastoplastic strain. To quantify the effect of combined cyclic loading regime with repeated overloading on the damaging and lifetime of different types of materials, the ratio of change in the total lifetime K D =F( ε a , N low , σ a ) , which depends on the amplitude of strain under overloading, the number of cycles of low-cycle loading, and the stress level under subsequent fatigue loading, is proposed: 2

1

high D

D 

low

K



D

.