A Mohr-circle graphical method for stress intensity factors in cracked plates under different loadings

Abstract

The concept of the stress intensity factor circles (SIF circles) was introduced in this paper, as well as the correlation of these circles with Mohr's circles. The main advantage of this graphical representation is the facility in establishing a one-to-one correlation between the values of the angle of a slant crack in a cracked plate submitted to a biaxial normal loading at infinity and different loading modes at infinity. Moreover, the definition of a general transformation of any biaxial state to another equivalent one, such that the stress intensity factors remain invariant in both states, was also established and discussed. The special cases where the reduction of any biaxial state to that of equal tension-tension at infinity, or uniaxial tension, or equal tension-compression, are also investigated. The method yields the possibility of replacing biaxial tests in cracked plates, which are difficult to be executed with the appropriate accuracy and convenience, with uniaxial ones, which are much easier and accurate than the biaxial ones. Examples indicate the validity and the simplicity of the method.