Brittle failures from U- and V-notches in mode I and mixed, I + II, mode: a synthesis based on the strain energy density averaged on finite-size volumes

A large bulk of static test results carried out on notched specimens are presented in a unified way by using the mean value of the strain energy density (SED) over a given finite-size volume surrounding the highly stressed regions. In plane problems, when cracks or pointed V-notches are considered, the volume becomes a circle or a circular sector, respectively, with RC being the radius. RC depends on the fracture toughness of the material, the ultimate tensile strength and the Poisson's ratio. When the notch is blunt, the control area assumes a crescent shape and RC is its width as measured along the notch bisector. About 900 experimental data, taken from recent literature, are involved in the local SED-based synthesis. They have been obtained from (a) U- and V-notched specimens made of different materials tested under mode I loading; (b) U- and V-notched specimens made of polymethyl-metacrylate (PMMA) and an acrylic resin, respectively, tested in mixed, I + II, mode; (c) U-notched specimens made of ceramics materials tested under mode I. The local SED values are normalized to the critical SED values (as determined from unnotched specimens) and plotted as a function of the R/RC ratio. A scatter band is obtained whose mean value does not depend on R/RC, whereas the ratio between the upper and the lower limits are found to be about equal to 1.6. The strong variability of the non-dimensional radius R/RC (ranging here from about zero to around 1000) makes stringent the check of the approach based on the mean value of the local SED on a material-dependent control volume.

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