PSI - Issue 23

Lucie Malíková et al. / Procedia Structural Integrity 23 (2019) 487–492

490

Lucie Malíková et al. / Structural Integrity Procedia 00 ( 2019) 000 – 000

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behavior and can be used for calculation of the effective fracture toughness. The idea is based on the theory that the effective crack length represents such a crack length that would correspond to the same stiffness if the ideally linear elastic material was considered.

3.2. Searching for the effective crack length via finite element method

In order to be able to find the effective crack length, experiments on real specimens had to be carried out. Three granite specimens have been chosen for the study presented in this paper. From CB tests, load – displacements and/or load – CMOD (Crack Mouth Opening Displacement) curves have been obtained and the important values of the maximum loading force and corresponding CMOD can be together with basic dimensions of the specimens found in Tab. 2.

Table 2. Basic dimensions of the Silesian granite specimens considered in this study.

Parameter

11964/17

11964/19

11964/20

Diameter of the cylinder, D [mm] Depth of the initial notch, a 0 [mm] Span between the supports, S [mm] Maximum loading force, F max [N]

49.5 7.12 163

49.3 6.95 163

49.3 7.30 163

2531.3

2547.4

2565.7

CMOD when F max occurs, CMOD F max [mm]

0.032035

0.027891

0.025517

The data from the measurements have been used as inputs for finite element (FE) simulations when the bending of the chevron notch specimen has been modelled. From FE simulations, dependences between the loading force and the CMOD have been obtained for several crack lengths a , see Fig. 2. Then, the loading force obtained from FE simulations for a = 0 was replaced by the value F max obtained experimentally and similarly the other values of the loading forces were recalculated according to the same ratio for increasing crack. The value of the CMOD for the zero crack was calculated from the initial stiffness obtained from the load-displacement experimental curve. Additionally, the CMOD values for other crack lengths could be calculated from the same ratio between CMOD from FE simulations and CMOD from experiment. Thus, a new load – CMOD diagram was obtained taking into account the idea described at the beginning about the equality of the stiffness of the real quasi-brittle specimen with an initial notch a 0 and a virtual ideally elastic specimen with an effective crack length a eff . To find the value of a eff , the intersection point between the recalculated load-CMOD diagram and the line representing the stiffness when the F max is reached in the experiment is found and the corresponding effective crack length is calculated from the CMOD eff value, see Fig. 3. More details about the approach can be found for instance in Halfar (2018) or Halfar et al. (2018).