This question is designed to demonstrate why one uses the semi-minor axis to assess the criticality of surface defects and to indicate that cracks tend towards a stable aspect ratio (2c/a). It requires some thought in interpreting the table of geometry correction factors but is straightforward and should take about 10 minutes to complete.
A thin leaf spring experiences unidirectional bending and develops a semi-elliptic crack on the tensile surface. The crack has an initial aspect ratio of 0.2 when found. The plane of the crack is perpendicular to the direction of applied bending stress. As the spring undergoes repeated deflection, the crack grows by fatigue.
Using the K solution and geometry correction factors for tensile loading, given in the table below, determine whether the ellipticity ratio of the crack will increase or decrease. The figure below shows the crack geometry.
Fracture Mechanics
