PSI - Issue 75

Yuki Ono et al. / Procedia Structural Integrity 75 (2025) 176–183 Author name / Structural Integrity Procedia (2025)

180

5

CALseries (ΔS = 0.36f y andR=0.1)

Case 2 (with residual stress)

Case 3 (with residual stress + hardening)

Case 1

0.0000001

1E-11 CGR n , d 99% /N i,n (m/cycle) 10 -8 1E-10 1E-09 1E-08 10 -10

Effective strain amplitude, ε eff,a

Effective maximum stress, σ eff,max (MPa)

0.000001

Smooth Notch

10000

1E-12

0.001

1000

10 -6

0.1

0.01

10 -12

100

1000

10000

0.001

0.01

100

0.1

0.010 0.100 1.000 10.000

0.010 0.100 1.000 10.000

0.010 0.100 1.000 10.000

0.01

0.01

Short crack initiation

0.01

HL1

HL1

HL1

Short crack growth

HL2

HL2

HL2 HL3

0.1 10 Crack length, 0.01 + a n (mm) 0.2 1.0

0.1

0.1 0.2

HL3 BM

HL3 BM

BM

1.0

1.0

Long crack growth

10

10

Fig. 3 Estimated local fatigue response and crack growth rate, modified from Ono and Remes (2024).

Notch RS

Notch

step-by-step crack growth simulation from short crack initiation to final failure within a single FE model. The single model incorporates multiple sets of element deletion and loading steps. For instance, as shown in Figs. 2 (a) and (b), certain elements along the known crack path are manually pre-defined prior to the crack growth simulation. The example defines 26 steps, ranging from steps n = 0 to n = 25. At step n = 0, the model exists without fatigue crack growth, and a crack length is defined as a 0 = 0 μm. At step n = 25, the crack reaches a critical crack length of a cr = 2.3 mm, which corresponds to nearly full cross-sectional yielding at maximum loading. It should be noted that the y -axis in Fig. 2 (b) is adjusted to start at 0.01 mm for visualization purposes in the logarithmic scale graph, thereby avoiding a 0 = 0 mm. For simplicity, the increment intervals of crack length do not remain constant but vary relative to the crack length. In this example, intervals start at 1 to 2 μm in the beginning of crack growth, then expand from 5 to 25 μm up to a 0.1 mm crack size, and gradually increase further from 25 to 250 μm until reaching the critical crack length. Using finer Notch Notch RS Notch RS HL

Case 19 notch RS

Case 6 notch RS

Case 5 notch

HL

10000000 10 7

N i,0.2mm N p

%: Ratio for total fatigue life

100000 10 5 The number of cycle, N 57 % 43 % 1000000 10 6

94 %

90 %

10 %

6 %

10000 10 4

1 Case 1 Case 2 Case 3 2 3

Fig. 4 Estimated fatigue life, adapted from Ono and Remes (2024).

intervals at several short crack lengths aims to accurately capture local stress and strain states and their changes, which significantly affect the fatigue life estimation for high-performing welds. During each step, the loading history is always applied to average the stress components over the RVE length for calculating fatigue effective stress. Strain amplitudes for these averaged stresses are determined using a separate model known as the continuum-based single element model (CSEM) [Garcia (2020) and Niraula et al. (2024)], shown in Fig. 2 (c). The input load for CSEM consists of the history of averaged principal stresses. The primary objective for CSEM is to derive the fatigue effective strain corresponding to the fatigue effective stress based on the defined elastic-plastic material model. Therefore, this approach ensures to follow the stress-strain behavior and Hooke ’ s law. 3. Results 3.1 Numerical simulation result example for a notch model Fig. 3 displays the simulation outcomes for the notch model, highlighting how different surface conditions affect the fatigue damage process during short cracks [Ono and Remes (2024)]. The cases incorporate factors like residual stress and hardening layer sequentially. The results are broken down into effective strain amplitude, effective maximum stress, and crack growth rate as functions of crack length. The plots correspond to the results calculated after each modelling step in Fig. 2 (b). In Fig. 3 (a), Cases 1 and 2 show that the residual stress field does not alter the effective strain amplitude. In contrast, Case 3 reveals an increase in the effective strain amplitude due to the hardening