PSI - Issue 47

Robert Eriksson et al. / Procedia Structural Integrity 47 (2023) 227–237 R. Eriksson, A. Azeez / Structural Integrity Procedia 00 (2023) 000–000

230

4

Fig. 2. Standard CT25 specimen.

The weight function used here is by Eder and Chen (2021) where x is defined as in Fig. 2 and the coe ffi cients, β , are given in Table 2.

Table 2. Coe ffi cients for the weight function. a / W β 1

β 2

β 3

β 4

0.2 0.3 0.4 0.5 0.6 0.7 0.8

2.00 2.00 2.00 2.00 2.00 2.00 2.00

3.3270 4.9886 7.2610 10.4356 15.1033 22.6834 37.2393

1.4351 1.7280 2.7054 5.2943 11.3700 26.0237 69.1970

-0.4652 -0.4130 -0.4570 -0.7632 -1.6671 -4.0924 -11.7568

In the strip-yield approach, the crack surface pressure is set constant to the negative of the yield strength, p ( x ) = − σ ys , and is only applied over a virtual extension of the crack, ρ . The solution then becomes

a + ρ  a

h ( x ) dx

K ρ = − σ ys

7 2  

π  

= − σ ys 

a a + ρ 

3 

a a + ρ 

5 

a a + ρ 

7 

a a + ρ 

 β 1  1 −

1 2

3 2

5 2

2( a + ρ )

β 2

β 3

β 4

+  (3) where the notation K ρ has been introduced for a stress intensity factor calculated from the crack face pressure on the virtual crack extension ρ (which will later be taken as equal to the plastic zone size). 1 − + 1 − + 1 −

3.2. Material model

In the strip-yield approach, the material is assumed ideally plastic. In the current work, however, a “quasi-ideal plastic” model is used by which is meant:

1. When the material is loaded, the average plastic zone strain, ϵ pz , is estimated from displacements determined from the stress intensity factor (further explained below). 2. Based on estimated plastic zone strain, the flow stress, σ flow , is calculated from a simple one dimensional com bined linear isotropic / kinematic hardening model (described in Appendix A). 3. The so determined σ flow is taken as the yield stress, σ ys , in an ideal plastic model and used in the strip yield model, i.e. σ ys = σ flow ( ϵ pz ). The procedure is illustrated in Fig. 3.