Three-dimensional elastic stress fields ahead of notches in thick plates under various loading conditions

• 3D elastic stress distributions ahead of notches in finite thick plates.
• The governing system is given by a bi-harmonic and a harmonic equation.
• The first equation provides the solution of the corresponding plane notch problem.
• The second equation provides the solution of the out-of-plane shear notch problem.
• The analytical frame is applied to a number of notched geometries.

The paper discusses the features of three-dimensional elastic stress distributions ahead of notches in finite thick plates under different loading conditions. It is proved that, under certain circumstances, the three-dimensional governing equations of elasticity can be reduced to a system where a bi-harmonic equation and a harmonic equation have to be simultaneously satisfied. The former provides the solution of the corresponding plane notch problem, the latter provides the solution of the corresponding out-of-plane shear notch problem. The analytical frame is applied to a number of notched geometries, and its degree of accuracy is discussed comparing theoretical results and numerical data from 3D FE models. Practical consequences on the expected crack paths are also documented for one of the considered models.