Issue 59

S.K. Kourkoulis et alii, Frattura ed Integrità Strutturale, 59 (2022) 405-422; DOI: 10.3221/IGF-ESIS.59.27

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-1.0 The σ θ stress (normalized over Pc) along part of the notch’s perimeter (0 o ≤θ ≤60 o ) The normalized σ θ stress along part of the perimeter of the notch with 0 o ≤ θ≤60 o -0.5 0.0 0.5 0 20

-2.0 The σ θ stress (normalized over Pc) along part of the notch’s perimeter (0 o ≤θ ≤60 o ) The normalized σ θ stress along part of the perimeter of the notch with 0 o ≤ θ≤60 o 0.0 2.0 4.0 0 20

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Angle θ in the ζ-plane [deg], corresponding to the θ=constant hyperbola in the z-plane Angle θ in the ζ-plane [deg], correspondin to the θ=constant parabola in the z-plane

Angle θ in the ζ-plane [deg], corresponding to the θ=constant hyperbola in the z-plane Angle θ in the ζ-plane [deg], correspondin to the θ=constant parabola in the z-plane

(b) (c) Figure 3: (a) The locus along which the stresses are plotted (red line); (b, c) The variation of the transverse stress σ θ (normalized over the amplitude, P c , of the parabolic distribution of radial stresses exerted on the disc) along the part of the perimeter of the notch shown in Fig.3a, for w=5 mm (b) and w=0.5 mm (c). practical use inflexible and time consuming. In this direction, it was thought that one could take advantage of the analytic formulae in order to validate a numerical model, which, in turn, could be used for thorough parametric investigation of the geometric factors. In this context, a three-dimensional numerical model is designed using the finite elements method and employing the commercially available software ANSYS-19, as it is described in next sections. Reference numerical model A disc of diameter equal to 100 mm and thickness equal to 10 mm, with a central notch of 50 mm length and 5 mm width, was chosen as the reference model. The radius of curvature at the notch’s corners was set equal to 0.33 mm. The disc was assumed to be squeezed between the curved loading platens suggested by the ISRM standard. The whole complex consisting of the disc and the two loading platens was modelled (Fig.4), in an attempt to approach the actual loading scheme developed along the disc-loading platen interface (without any additional assumption for this issue). The disc was considered to be made of plexiglass (modulus of elasticity and Poisson’s ratio equal to 3.2 GPa and 0.36, respectively) while the mechanical properties of steel (modulus of elasticity and Poisson’s ratio equal to 210 GPa and 0.30, respectively) were assigned to the loading platens. The coefficient of friction between the plates and the disc was set equal to 0.01, in order to approach the assumptions adopted in the analytic solution, where the role of friction was ignored. The volumes of the model were meshed using the SOLID185 element while the TARGE170 and CONTA173 elements were used for the two material interfaces between the platens and the disc. The final meshing (Fig.5) was decided based on a thorough convergence analysis carried out as a first step of the numerical study.

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