PSI - Issue 57

Kalle Lipiäinen et al. / Procedia Structural Integrity 57 (2024) 32–41 Lipiäinen et al. Structural Integrity Procedia 00 (2019) 000 – 000

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3

Quality

CX HT

a

b

Geometric notch root

Neuber’s Hyperbolas

Stress

Stress

MS1 & CX

Quality

Geometric

Cyclic

R close to 0

Quality

Cyclic R < 0

Cyclic R << 0

Load

Nominal

Local strain

Local strain

Quality

Load

Fig 1. Schematic local cyclic behaviour with (a) MS1 and as-built CX, (b) heat treated CX.

TCD evaluation with point method (PM, effective stress at the critical distance) was used in this study. The process is described with equations 1-8 and the schematic workflow is illustrated in Figure 2. ( ) f,PM tcd K a  = , (1) k k f tcd nom ( ) 1 K a R     = = − , (2) where K f effective fatigue notch factor, a tcd is critical distance, is combined stress from nominalstress and SCFs and R is the applied stress ratio of external loading. The material behaviour at the notch root is described the Ramberg Osgood (R-O) materials models (monotonic, and cyclic with the kinematic hardening rule): (4) where σ and ε are the true stress and true strain values, E is the modulus of elasticity, H is the strength coefficient and n is the strain hardening exponent of the plastic strain. In Eq. (6), the variables are the same but correspond to the range values. The computed linear-elastic notch stresses at a notch or crack can be converted to the elastic-plastic behaviour applying Neuber’s rule. For the monotonic and cyclic behaviour , respectively, the Neuber’s rules can be written as follows: 2 ( ) k res E     + = , (5) 2 k E      =  , - (6) where σ res is the residual stress. To account for the local elastic-plastic behaviour at the notch in fatigue assessment, the local stress ratio is computed: min local max R   = , (7) In the fatigue assessments using the stress-life ( S - N ) model, the mean stress corrected reference stress is obtained 1 n E H     = +      , (3) 1 n 2 E H       = +      ,