PSI - Issue 26

Christos F. Markides et al. / Procedia Structural Integrity 26 (2020) 53–62 Ch. F. Markides et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Η΄

C ΄

ε xx

ε yy

Η΄

C ΄

C ΄

Η΄

Fig. 5. Experimental (Kourkoulis et al. 1999) (left) versus analytic (right) data for the ε xx and ε yy strains along a portion of the y-axis.

In this paragraph, different geometry and material (from those adopted in the previous one) were adopted in order for the deformed scheme of the notched beam to be clearly seen. In this context, the material of the beam was Poly Methyl Methacrylate (PMMA) with a Young’s modulus E=3.2 GPa and Poisson’s ratio ν=0.36. The dimensions of the beam were, ℓ o =10 cm, b=1 cm, h=5 cm, the length of the notch was 1 cm and its width BD=4 mm. The two loads P/2, applied at points F, G were at distances d=ℓ o =10 cm from the supporting cylinders at the lower side of the beam. For an overall load P=10 kN, the deformed configuration is shown in Fig.6. In this figure the unstressed state is shown with the black discontinuous line, whereas the red and black lines correspond to the deformed schemes of the notched and the intact beams, respectively. A detailed magnified view of the area of the parabolic notch shows, also, the deformation tendency of the material. As it is seen, the deformed sides of the notched and the intact beam almost coincide, confirming the initial assumption that a notch of moderate dimensions does not significantly influence the beam boundaries. That is seen to be violated for a higher load level in Fig.7, where an overall load of 20 kN was applied. Considering, however, that such a load is rather unrealistic (a pre-notched beam with the particular dimensions would have split into two parts well before 20 kN), it seems that the analytic solution may be effectively used in cases of moderate notch dimensions and loading levels.