The effect of the boundary conditions on in-plane and out-of-plane stress field in three dimensional plates weakened by free-clamped V-notches

Dealing with the material microstructure an analytical multiscale model has recently been developed by Sih. Physically, the different orders of the stress singularities are related to the different constraints associated with the defect thought as a microscopic V-notch at the tip of the main crack. Irregularities of the material microstructure tend to curl the crack tip being the clamped-free boundary conditions the more realistic and general representation of what occurs on the microscopic V-notch. As a result, mixed mode conditions are always present along the V-notch bisector line. It is known for a long time that at the antisymmetric (mode II) stress distribution ahead of the crack tip generates a coupled out-of-plane singular mode. Recent theoretical and numerical analyses have demonstrated that this out-of-plane mode due to three-dimensional effects occurs also in the case of large V-notches where the mode II stress field is no longer singular. In addition, when the notch opening angle is non-zero, the three-dimensional singular stress state is strongly influenced by the plate thickness. The aim of this paper is to investigate the effect of free-fixed boundary conditions along the notch edges in three dimensional plates weakened by pointed V-notches and quantify the intensity of the out-of-plane singularity occurring under this constraint configuration. For the sake of simplicity a macronotch is considered rather than a micronotch. A synthesis of the magnitude of the stress state through the plate thickness is carried out by using the mean value of the strain energy density over a given control volume embracing the notch tip. The capability of the strain energy density to capture all the combined effects due to the out-of-plane mode make it a powerful parameter at every scale levels.