On the actual three-dimensional stresses in notches and cracks

Abstract

It has been known in aeronautical engineering for over 60 years that the stresses in regions of notches in plates are three-dimensional and the stress in the thickness direction is not negligible. However, for various reasons, the concept of a generalized plane stress state has been widely accepted in analytical mechanics and was adapted in general engineering design and testing, including various procedures of experimental stress analysis, mainly photoelasticity. As a result, various technically important concepts, such as geometric stress concentration factors for notches in plates, or stress intensity factors in-plane fracture mechanics, have been developed on the basis of the concept of average stresses. The empirical evidence presented in this paper shows that in regions of notches and cracks in plates all components of a three-dimensional stress state exist and depend also on the thickness coordinate. This evidence has been produced using the resistance strain gages and isodyne techniques. The actual stresses and their major functions, such as the equivalent stresses, are 20–30% higher than generally assumed. A new concept of the three-dimensional stress concentration factor for plates is suggested. The presented evidence pertains to structures made of homogeneous materials and—essentially—of composite materials as well.