PSI - Issue 46

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

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Fig. 1. One-eighth FE model of M(T) specimen; 2a/W = 0.5; a – crack length, B – specimen thickness, L – specimen length, sym. – symmetry applied on xy , xz and yz planes.

The global constraint factor α g generally defined by equation (2) for whole specimen is computed from FE model by discrete expression (3). A T denotes the projected area in the crack plane for all elements which have yielded and A i denotes the projection area of an element. Contrary to α g definition in Newman (1993), where A i is the element that yielded, the A i is actually the element laying on a crack plane ahead of a crack tip located inside or under the plastic zone. In order to distinguish the process of determination, the global constraint factor by latter method is denoted α gS in this work. 1 g A T dA A     (2)

0     yy    

1 N



A

g 



(3)

i

A

1



T i

i

The dependence of the constraint factor on the ratio of thickness B over the squared crack size ahead of the crack tip is shown in Fig. 2. The values for low load levels are situated at higher part of the graph with maximum α gS ≈ 2 dropping left-down to α gS ≈ 1.15 when plane stress appears while load is increasing. On the right side of the figure, there are shown results for pure plane strain and plane strain boundary conditions with constrained specimen’s side ahead of the crack tip (denoted as - CW ). Results show decrease of constraint with increasing load also under pure plane strain, while - CW case shows relatively stable α gS slightly under 2 and only at high loads, when plastic zone spreads over uncracked ligament, the constraint decreases. The pure plane stress conditions were analysed using 2D FE problem with plane stress elements. The constraint value of α gS corresponds to 3D solution at low B/r p 2 ratios with α gS = 1.15.