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 In which � � refers to polar coordinates of points in the problem domain referenced to the crack tip location. As the plate’s dimensions are sufficiently large compared to the notch size, the reference solution, � ���. , (Yau, Wang, and Corten 1980; Paris and Sih 1965) given for plate for mode I SIF can be used as follows: � ���. � � � √ . (8) In which θ is the angle of the notch corresponds to the tensile loading direction and � stands as the nominal uniaxial stress. 3. Analysis and results In this work, a MT specimen containing the slant crack in the central section was designated following the ASTM E647 Standard Test Method Measurement for fatigue crack growth rates (E647-15e1 2015). The geometrical characteristics are as follows: plate width, � � �0 ���� , initial notch, � � � ���� , crack length, � 7 ���� and the plate thickness, � � � ���� . A 1-mm-precrack has been machined by a saw. The experimental test has been performed by an Instron® tensile testing machine ��1000� with a load capacity of 1.00 � � (c.f. Fig. 1-a). The experiment was conducted with a 3D DIC system, to analyze the deformation change around the cracked region due to the tensile loading condition. Thus, two-2048×2048-pixel cameras were positioned in front of the target respecting a nominal distance of 700 � � and 60 mm f/4 C-Mount Rodagon lenses. Halogen lamps were used to illuminate the specimen surface (c.f. Fig. 1-b). DIC provides the full deformation field in the observed specimen. Therefore, the normal and shear strain components were extracted for a set of points respecting their polar coordinates � � referenced to the crack tip. It must be noticed that the extracted points covered an area of 5-by-5 (mm 2 ) in the vicinity of the notch tip. This area is known as the problem domain where the results are analyzed. According to Hooke’s law and LEFM theory, it is conceivable to transform the strain into the stress field considering the following material properties: Young’s modulus, � � ���0 ����� and Poisson’s ratio, � � 0.�7 . A series of images has been captured during the mechanical testing and the acquired data has been processed by the correlated solution software (VIC 3D 2012 © ). 221 4

(a)

(b)

Fig. 1. (a) MT specimen with the slant crack with θ = 45° respecting loading direction; (b) DIC setup standing in front of the tested specimen, dimensions are in mm.

Geometrical characterisation of the stress dead-zone region, has been analytically formulated in the former study (Farahani, de Melo, da Silva Tavares, et al. 2020). Therefore, an arbitrary interest region was defined around the cracked region; see the trapezoid area in Fig. 2-a). Besides, the DIC field of view representing the facet field and speckle size is indicated in the same figure. Numerically, the problem was modelled by FEM formulation in ABAQUS © . The whole model includes a total number of 20930 nodes and 20638 linear quadrilateral elements, S4R. A denser FE mesh was built on the arbitrary interest region including 12738 nodes and 12464 elements, see Fig. 2-b).