PSI - Issue 46

Jakub Šedek et al. / Procedia Structural Integrity 46 (2023) 69–74 Jakub Šedek / Structural Integrity Procedia 00 (2021) 000–000

72

4

B= 1.25 mm B= 2.5 mm B= 5 mm B= 10 mm B= 20 mm B= 1.25 mm B= 2.5 mm B= 5 mm B= 10 mm B= 20 mm B= 1.25 mm B= 2.5 mm B= 5 mm B= 10 mm B= 20 mm

2.2

0.5 0.75

2

1.8

1.6

Pl. Strain Pl.Strain ‐ CW Pl. Strain Pl.Strain ‐ CW Pl. Strain Pl.Strain ‐ CW Pl.Stress

α gS (‐)

1.4

1.2

2a/W = 0.25

1 000 0.5 0.75 2a/W=0.25

1

0

1

0.001

0.1

10

1000

B/r p

2 (mm ‐1 )

Fig. 2. Constraint factor α gS in M(T) specimens with different thickness in dependence on the ratio B/r p 2 ; for plane stress plot used B =1e-4 mm; a – half crack length, B - specimen thickness, W - width of the specimen, r p - size of plastic zone in x axis and CW – restrained displacements on width edges in FE model. 3. Strip Yield Model The strip yield model (SYM) according to Newman (1981) was used to utilize FE-determined constraint factor α gS as an input. The model is based on a crack solution according to Dugdale (1960). The crack is divided into 3 zones: elastic neighbourhood of the crack, plastic zone at the crack tip and the crack wake. The latter two zones are built by 1D elements that can be plastically deformed. During monotonic loading of virgin crack, the crack wake does not act and only elements in plastic zone are deformed. The plastic wake is formed by the crack advance, but presently it is not the scope of this work.

COD/2a (‐)

0.004

Δσ

COD/2a (‐)

0.003

0.003

Δσ

0.002

0.002

0.001

0.001

0

0

0.95 0.97 0.99 1.01 1.03 1.05

0.95

0.97

0.99

1.01

1.03

1.05

x/a (‐)

x/a (‐)

0.134 0.317 0.45 1.9 1.5 1.36 1.9 1.5 1.4

α, SYM, ν =0.3 α, FEM‐Dugdale, Pl.Strain σ/σ flow , FEM‐elpl.

0.134 0.228 0.318 1.49 1.26 1.2

α, SYM, ν =0 σ/σ flow , FEM‐elpl.

a)

b)

Fig. 3. COD for FEM and SYM during monotonic loading; (a) plane strain; (b) B =1.25 mm.