PSI - Issue 18

Johannes Scheel et al. / Procedia Structural Integrity 18 (2019) 268–273 J. Scheel et al. / Structural Integrity Procedia 00 (2019) 000–000

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resulting in relations interpreting the near field solution at specific points of the crack faces in the FE analysis, thus being akin to the classical DIM.

3. Numerical verification and discussion

The FE calculations were performed using ABAQUS and for comparison the crack tip loading is not only calculated using the EMCCI but also the MCCI, the CTEM and the DIM, where for the extrapolation of the DIM di ff erent node sets were used. In all node sets, node C (Fig. 1) is the closest to the crack tip while the other nodes follow the crack face in the opposite direction. The first node set (node set 1) continues to the 4th node behind the crack tip , the second node set (node set 2) continues to the 9th node behind the crack tip and in the last node set (node set 3) all nodes are within five percent of the crack length. In Fig. 3 the relative errors of the SIF calculated with the di ff erent methods are plotted vs. element edge lengths. The reference value for the relative error is the SIF from the ABAQUS interaction integral for an element edge length of 0.1 mm. In each model, all elements have the same size and are 8-node bi quadratic quadrilateral elements (except for the CTEM calculations) and plane strain conditions are assumed. The results show that only using node D in Eq. (13) yields very accurate results for the finest mesh applied, exceeding

20

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a)

b)

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−10 relative error of K I [%] −5 0 5

c) relative error of K I [%] relative error of K I [%] 5 0 −5 −10 −15 −20 0.1 −10 −5 0 5 10 15 20

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−20

0.25

0.5

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element edge length [mm]

element edge length [mm]

DIM: Node set 1 DIM: Node set 2 DIM: Node set 3 EMCCI: Node C EMCCI: Node D EMCCI: Nodes CD

CTEM MCCI

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element edge length [mm]

Fig. 3. Relative errors of the SIF calculated with di ff erent methods vs. element edge lengths. a) DCB, b) three-point-bending, c) tension bar specimen, see Fig. 2 .