PSI - Issue 47

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

229

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

3

the specimen was unloaded to P 2 = 0 . 5 kN and then the furnace was turned o ff . For both cycles, the specimens were left to cool in the furnace overnight. Two minimum temperatures were tested: 20 ◦ C and 50 ◦ C. Once the specimens had properly cooled, they were pulled to fracture in crosshead displacement control at 1 mm / min. The maximum temperatures used were 100–400 ◦ C and the applied loads were 40–60 kN. The tests are summarized in Table 1

Table 1. Performed WPS tests. No. Cycle

T 1 , ◦ C

T 2 , ◦ C

P 1 , kN

P 2 , kN

1 2 3 4 5 6 7 8 9

LCF LCF LCF LCF LCF LCF LCF LCF LCF LCF LCF

100 200 200 300 300 300 300 300 300 400 400 200 300 300 300 400

50 50 50 40 50 50 50 50 60 50 50 50 40 50 60 50

20 20 50 20 20 20 50 20 20 20 50 20 20 20 20 20

50 50 50 40 50 50 50 50 60 50 50

10 11 12 13 14 15 16

LUCF LUCF LUCF LUCF LUCF

0.5 0.5 0.5 0.5 0.5

3. Model description

Most mechanisms contributing to the WPS e ff ect (i.e. residual stresses, crack tip blunting and increase in yield strength) depend on the amount of plastic deformation at the crack tip. It seems reasonable that a parameter that de scribes the amount of plastic deformation at the crack tip should quantify, at least indirectly, all relevant mechanisms causing the WPS e ff ect. The crack tip plastic zone size should work as such a parameter. A convenient way of estimat ing the plastic zone size is the fracture mechanics based strip-yield model. Therefore, a modified strip-yield approach was used to develop a model that describes the WPS e ff ect. The following sections outline the model.

3.1. Solutions for the stress intensity factor

Stress intensity factor solutions for a standard CT specimen are readily available in various handbooks; it is

3 2

4

13 . 32

a W

a W

a W

+ 14 . 72

− 5 . 6

a W

2 +

2

3

a W −

P √ BB N W

K I =

0 . 886 + 4 . 64

(1)

1 − a

W

with the specimen width, W , and the crack length, a , as defined in Fig. 2. B is the specimen thickness and B N is the thickness at the side grooves (if present). The stress intensity factor can also be obtained by integrating the weight function, h ( x ), and the crack face pressure, p ( x ), over the crack length

a 0

5 2

1 √ 2 π a

x a

x a

x a

x a

β 1 1 −

+ β 2 1 −

+ β 3 1 −

+ β 4 1 −

− 1 2

1 2

3 2

K I =

h ( x ) p ( x ) dx , h ( x ) =

(2)