The critical influence of some �tiny� geometrical details on the stress field in a Brazilian Disc with a central notch of finite width and length

Abstract

The role of some geometrical characteristics of the notches machined in circular discs, in order to determine the mode-I fracture toughness of brittle materials, is discussed. The study is implemented both analytically and numerically. For the analytic study advantage is taken of a recently introduced solution for the stress- and displacement-fields developed in a finite disc with a central notch of finite width and length and rounded corners. The variation of the stresses along strategic loci and the deformation of the perimeter of the notch obtained analytically are used for the calibration/validation of a flexible numerical model, which is then used for a parametric investigation of the role of geometrical features of the notched disc (thickness of the disc, length and width of the notch, radius of the rounded corners of the notch). It is concluded that the role of the width of the notch is of critical importance. Both the analytic and the numerical studies indicate definitely that ignoring the accurate geometric shape of the notch leads to erroneous results concerning the actual stress field around the crown of the notch. Therefore, it is possible that misleading values of the fracture toughness of the material of the disc may be obtained.

Keywords

• brazilian disc
• central notch
• analytical solution
• numerical analysis
• finite elements