PSI - Issue 28

Michael Jones et al. / Procedia Structural Integrity 28 (2020) 2078–2085 Author name / Structural Integrity Procedia 00 (2019) 000–000

2081

4

Images were captured every two seconds and then matched up to the force vs time data output from the test machine. Images were postprocessed using darktable to further improve contrast, and then thresholded to give a binary black and white image. This allowed for clear determination of the specimen edges. Examples of a raw image, a postprocessed image and a thresholded image are shown in Figure 3 (a) to (c). These images were analysed by means of a MATLAB script to determine the minimum specimen diameter and notch radius of curvature. These parameters could then be used in Equations Errore. L'origine riferimento non è stata trovata. to Errore. L'origine riferimento non è stata trovata. to determine the strains and level of triaxiality within the sample. 3. Finite Element Analysis Axisymmetric models were used for all three notch geometries. Since the double notched bars were symmetric around their mid-height, y -symmetry conditions were applied to the bottom edge of each model. A floating node was kinematically constrained to the top edge of the model and the load was applied to this node. Geometric nonlinearity was considered in the model. The load profile against time was taken from one of the experimental tests for each notch geometry, and from this a load amplitude was defined. The models were loaded to the maximum tensile load from the experiment. The meshes used for the three geometries are shown in Figure 4 (a) to (c). The mesh details for the three geometries are given in Table 1. (a) (b) (c)

y

r

Figure 4(a)-(c) – The mesh used for (a) the small notch, (b) the medium notch and (c) the blunt notch

Table 1 - Mesh details for the notched bar FEA models

Notch type

No. of elements No. of nodes

Element type

Small

5840 7643

6042 7805

CAX4R CAX4R CAX4R

Medium

Blunt

15234

15584

The material behaviour was modelled using experimental uniaxial tensile data. The triaxiality values were calculated in every element by means of an Abaqus user defined field subroutine (USDFLD). Five values were then taken at approximately equidistant points across the cross-sectional radius of each sample, as shown in Figure 5(a)-(c). The positions have been named ‘Centre’, ‘2 nd ’, ‘3 rd ’, ‘4 th ’ and ‘Edge’ as shown in the Figures. Values for the strain in the y direction were also taken at these same points.