PSI - Issue 57

Yuki Ono et al. / Procedia Structural Integrity 57 (2024) 290–297 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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but the compressive residual stress stayed the same. As a result, there is no change in maximum stress compared to loading case 1. For the simulation result in Fig. 7 (c), applying compressive peak load before the tensile one influenced mean stress, like reducing maximum stress from 364 MPa to 177 MPa in the simplified geometry model. A more pronounced influence was seen on the actual geometry model, as shown in Fig. 7 (f); the tensile yielding is much more dominant in the elastic-plastic behavior, and then inducing the additional compressive residual stress. Consequently, most of the stress within the following CAL is below zero. It is also worth noting that after the peak-load cycle, one or two CAL cycles were taken until reaching stability for actual geometry model; see green color loops in Figs. 7 (e) and (f). The comparison of maximum stress in a depth of 5 μm (a representative for the start of short crack growth) and SWT parameter after the relaxation between the simplified and actual geometry models for all locations was made, as shown in Fig. 8. This figure also indicates the data at a depth of 100 μm (a representative for the start of long crack growth) to show how the material imperfection impacts the fatigue response below the surface. In Fig. 8 (a), the maximum stress at the depth of fatigue effective stress confirmed the large scatter due to the combination of residual stress relaxation and stress localization effect from the material imperfection. The degree of scatter highly varied with the loading condition and locations. At most 3.46-times difference in maximum stress between the two models was found on Location B and Case 2. The results for the 100 μm depth in Fig. 8 (b) showed the almost identical value between the two models due to less effect of material imperfection and at most 1.27-times difference for Location C and Case 1. The results for SWT parameter, as shown in Figs. 8 (c) and (d), gave certain increases of maximum errors when considering strain amplitudes. Other than that, there was almost the same trend in the variability of results as found by comparing the maximum stress. 5. Discussion This study investigates the effect of surface imperfection on residual stress relaxation and fatigue response when

Loading case 2

Loading case 1

Loading case 3

Max

Min Max

Max Min

…

…

…

Min

BL

AL

AL

BL

BL

AL

AL: After load

BL: Before load

Ϭ 0.00 500 1000 1500 ϱϬϬ ϭϬϬϬ ϭϱϬϬ

ͲϭϱϬϬ -500 -1000 -1500 ͲϭϬϬϬ ͲϱϬϬ Ϭ ϱϬϬ 0.00 500 1000 1500 ϭϬϬϬ ϭϱϬϬ ͲϭϱϬϬ ͲϭϬϬϬ ͲϱϬϬ -500 -1000 -1500 Ϭ 0.00 500 1000 1500 ϱϬϬ ϭϬϬϬ ϭϱϬϬ

ͲϭϱϬϬ -500 -1000 -1500 ͲϭϬϬϬ ͲϱϬϬ Ϭ ϱϬϬ ϭϬϬϬ ϭϱϬϬ ͲϭϱϬϬ ͲϭϬϬϬ ͲϱϬϬ Ϭ ϱϬϬ ϭϬϬϬ ϭϱϬϬ -500 -1000 -1500 0.00 500 1000 1500 0.00 500 1000 1500

σ eff,max = 177 MPa Δε = 0.0020

σ RS,BL = -357 MPa σ RS,AL = -544 MPa

σ eff,max = 415 MPa Δε = 0.0020

σ RS,BL = -357 MPa σ RS,AL = -307 MPa

σ eff,max = 364 MPa Δε = 0.0020

σ RS,BL = -357 MPa σ RS,AL = -358 MPa

Max

Max

Max

Min

Min AL

AL Min

BL

BL

BL,AL

ͲϭϱϬϬ ͲϭϬϬϬ -500 -1000 -1500 ͲϱϬϬ Stress, σ

Stress, σ

Stress, σ

ͲϬ͘Ϭϯ ͲϬ͘ϬϮ ͲϬ͘Ϭϭ Ϭ Ϭ͘Ϭϭ Ϭ͘ϬϮ Ϭ͘Ϭϯ -0.02 -0.01 0.00 0.02 0.03 0.01 -0.03

ͲϬ͘Ϭϯ ͲϬ͘ϬϮ ͲϬ͘Ϭϭ Ϭ Ϭ͘Ϭϭ Ϭ͘ϬϮ Ϭ͘Ϭϯ -0.02 -0.01 0.00 0.02 0.03 0.01 -0.03

ͲϬ͘Ϭϯ ͲϬ͘ϬϮ ͲϬ͘Ϭϭ Ϭ Ϭ͘Ϭϭ Ϭ͘ϬϮ Ϭ͘Ϭϯ 0.03 -0.03 -0.01 0.00 0.02 0.01 -0.02

Strain, ε

Strain, ε

Strain, ε

(a) Simplified geometry model Loading case 1

(b) Simplified geometry model Loading case 2

(c) Simplified geometry model Loading case 3

ͲϭϱϬϬ -500 -1000 -1500 ͲϭϬϬϬ Ϭ 0.00 500 1000 1500 ϱϬϬ ϭϬϬϬ ϭϱϬϬ

σ RS,BL = -295 MPa σ RS,AL = -318 MPa σ eff,max = 1093 MPa Δε = 0.0037

σ RS,BL = -297 MPa σ RS,AL = -302 MPa σ eff,max = 1132 MPa Δε = 0.0038

σ RS,BL = -311 MPa σ RS,AL = -1228 MPa σ eff,max = 40 MPa Δε = 0.0042

Max

Max

Max

Min

Min

AL

BL

BL,AL

BL

Stress, σ

ͲϱϬϬ Stress, σ

Stress, σ

Min

ͲϬ͘Ϭϯ ͲϬ͘ϬϮ ͲϬ͘Ϭϭ Ϭ Ϭ͘Ϭϭ Ϭ͘ϬϮ Ϭ͘Ϭϯ AL -0.02-0.01 0.00 0.02 0.03 0.01 -0.03

ͲϬ͘Ϭϯ ͲϬ͘ϬϮ ͲϬ͘Ϭϭ Ϭ Ϭ͘Ϭϭ Ϭ͘ϬϮ Ϭ͘Ϭϯ -0.02 -0.01 0.00 0.02 0.03 0.01 -0.03

ͲϬ͘Ϭϯ ͲϬ͘ϬϮ ͲϬ͘Ϭϭ Ϭ Ϭ͘Ϭϭ Ϭ͘ϬϮ Ϭ͘Ϭϯ -0.02 -0.01 0.00 0.01 0.02 0.03 -0.03

Strain, ε

Strain, ε

Strain, ε

(d) Actual geometry model Loading case 1 (f) Actual geometry model Loading case 3 Fig. 7 Stress-strain responses at the depth of fatigue effective stress for Location B (e) Actual geometry model Loading case 2