PSI - Issue 28

Behzad V. Farahani et al. / Procedia Structural Integrity 28 (2020) 218–225 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2019) 000–000

222

5

This study aims at extraction of the strain variation in the interest region in addition to evaluating the dead-zone area. Thus, the unloaded region (which is practically the dead zone) and the loaded region (which is ahead of the notch tip) would be investigated and therefore the region dimensions proposed by the former work could be verified. Furthermore, the strain distribution must conform to LEFM fundamentals and Griffith theory. Using FEM formulation, the cracked model has been solved through an explicit shell model and as a result, the � ��� was calculated on ten contour integrals ahead of the notch tip according to the maximum SERR criterion. Boundary conditions were applied in accordance with experimental conditions. Therefore, a tensile force with a magnitude of � � ���� � � was applied. As a result, the � was calculated from all studies as reported in Table 1. To draw a comparison and assessment on the robustness of the supporting methodologies, the deviation values (in percentage) were thereby computed amongst all results according to the below equation: � � � ��� � � � � �. (9)

(a)

(b)

Fig. 2. Detail on the arbitrary interest region in which dead zone was predicted in, (a) DIC representing the problem domain, step size and speckle pattern characteristics; (b) FEM.

As stated, the deviation accounted for a maximum value close to 6%, which verifies the supporting methodologies are robust and reliable, especially the stress dead-zone concept. It can be concluded that the compliance formulation has been properly adopted and extended to the fracture analysis of the finite plates containing slant cracks.

Table 1. SIF calculation obtained from experimental, numerical, stress-dead zone (SDZ) concept compared to the reference solution.

����√ � DIC

Absolute Deviation (%)

Crack orientation

REF. & DIC

REF. & FEM

REF. & SDZ

� � ���

REF. 26.05

FEM 26.86

SDZ 25.18

25.53 3.34 At a closer view to obtained results, the normal strain in y -direction �� �� � has been monitored on the interest region predicting the stress dead-zone. The profiles were extracted from DIC and FEM, as Fig. 3 shows. The acquired strain profiles are smooth and the numerical result has been validated by the experimental outcome. Fig. 3 clearly shows the unloaded region (the area in purple), “dead-zone” at the centre of the depicted area, along with the loaded region around the notch tips; see the area highlighted in red. The unloaded area can be neglected in the structural design, and stress computation, which proved the stress dead-zone hypothesis. The notch tip corresponds to the maximum strain locally concentrated in the region. Moreover, according to Equation (3), the stress dead zone (parallelogram) was dimensioned as �� � ��.�� ���� and � � �� ���� , (Farahani, de Melo, Tavares, et al. 2020). 2.00 3.11