PSI - Issue 57

Boris Spak et al. / Procedia Structural Integrity 57 (2024) 445–451 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

450

6

1

n

 = i 1

D

=

.

(6)

f i N ,

To identify the critical location, a loading simulation is performed. The forming history of the process simulation is preserved in the strip and used to initialize the loading simulation, with all settings kept the same as in the process simulation. The material behavior is described directly using elastic-plastic stress-strain relationship, without invoking a reevaluation accordingto Neuber’s rule (1961). A schematic of the angled strip and the applied boundary conditions are presented in fig. 4, on the right hand side. Two cyclic loading regimes are chosen, differing in the stress ratio: R = 0.1 and R = -1. Four levels of peak forces F max in the range between 600 N and 1200 N are chosen, with three loading cycles simulated in each simulation run. The failure location is assumed to coincide with the area of the maximum equivalent stress. For each of the angled strips, the initial stress tensor in the failure location in the inner radius is retrieved and a summary of the individual stress tensor components is compiled in table 4. Table 4. Stress components (residual stresses) in failure location for each variant as result of the process simulation.

Stress component in failure location / MPa

σ xx

σ yy

σ zz

σ xy

σ xz

σ yz

σ 1

σ 3

σ eqv

Variant 1 Variant 2 Variant 3

-88 -36

21

-192 -120

11

-125

-98

83 84

-294 -176

332 228 390

-17 207

-72

88 66

36

33

37

69

178

347

-79

By comparingthe equivalent stresses of each variant,one could assume that variant 3 would show the lowest fatigue life due to higher residual stress value. Especially, if it is assumed that the sign of the absolute value of the principle stresses determines whether residual stresses are of compressive or tensile nature. Variant 3 would be attributed tensile residual stresses with | σ 1 | ≥ | σ 3 |, while the residual stresses in variant 1 and 2 could be assumed as compressive due to | σ 1 | ≤ | σ 3 |. A thorough investigation of the stress history during cyclic loading revealed a significant residual stress relaxation within the first loading cycle in tension with the applied boundary conditions in all variants. This observation is supported by existing experimental with thin specimen results presented by Zaroog et al. (2011). Fig. 4 presents the fatigue life estimation for both cyclic loading regimes for R = 0.1 and R = -1 in terms of Wöhler curves. Variant 1 and 2 show an almost identical performance. Variant 3 on the other hand exhibits a higher number of cycles up to crack initiation, even though the initial residual stresses are higher if compared to the other two variants. This effect can be attributed firstly to the relaxation of residual stresses in the first cycles, and secondly to the overall greater cold working on the surface of the angled strip which leads to a slightly smaller stress amplitudes during cyclic loading.

Fig. 4. Fatigue life estimation with LSA for all three variants under cyclic loading with R = 0.1 (left) with failure location in the inner radius of the angled strip, and R = -1 (right) with failure location on the outer radius of the angled strip.