PSI - Issue 47

Robert Eriksson et al. / Procedia Structural Integrity 47 (2023) 227–237

232

6

R. Eriksson, A. Azeez / Structural Integrity Procedia 00 (2023) 000–000

LCF

LUCF

a)

WPS plastic zone

WPS plastic zone

P 1

T 1

P 1

T 1

σ ys1

σ ys1

σ ys1

σ ys1

P 1

P 1

ρ

ρ

a

a

b)

WPS plastic zone

WPS plastic zone

WPS reversed plastic zone

T 1

P 2 = P 1

T 1

P 2

σ 2

σ 2 = σ ys1

σ ys1 σ ys1

σ 2 = σ ys1

σ 2

P 2 = P 1

P 2

≈ ρ

ρ

a

a

ρ

c)

WPS plastic zone

WPS plastic zone

plastic zone

plastic zone

P

T

T

P

σ ysf

2

2

σ ysf

σ res σ res

σ ysf

σ ysf

P

P

< ρ

< ρ

a

a

d)

WPS plastic zone

WPS plastic zone

plastic zone

plastic zone

T

P=P f

T 2

P=P

σ ysf

2

f

σ ysf

σ res σ res

σ ysf

σ ysf

P=P f

P=P f

= ρ

a

= ρ

a

Fig. 5. The overall procedure for establishing the plastic zone size for the LCF and LUCF cycles: a) WPS load ( P 1 ) at T 1 , b) unloading to P 2 ; for LCF P 2 = P 1 , for LUCF residual stresses are introduced, c) temperature is dropped to T 2 , the load starts to increase, d) fracture at load P f as the plastic zone reaches the same size as the plastic zone from step a).

1. A plastic zone forms at T 1 during WPS load ( P 1 ). 2. The stresses in the plastic zone is retained during cooling to T 2 as the load is kept constant. 3. At T 2 , some additional load must be added to cause plasticity just outside of the WPS plastic zone since the yield strength is higher at T 2 compared to T 1 . Fracture occurs as the plastic zone at T 2 just barely extends outside of the WPS plastic zone. Figure 5 illustrates the procedure. For the LUCF cycle the procedure is a bit more involved; the unloading to P 2 < P 1 will leave some residual stresses that needs to be accounted for. The procedure becomes: 1. A plastic zone forms at T 1 during WPS load ( P 1 ). 2. The load is dropped to P 2 < P 1 ; residual stress from P 1 remains. (How these are estimated is explained below.) 3. Stresses from P 2 as well as residual stresses in the plastic zone are retained during cooling to T 2 . 4. At T 2 , fracture occurs when the sum of residual stresses and stresses from P f causes the plastic zone at T 2 to just barely extends outside of the WPS plastic zone. Figure 5 illustrates the procedure.