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 R-C being the radius. R-C 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 R-C 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/R-C ratio. A scatter band is obtained whose mean value does not depend on R/R-C, 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/R-C (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.