The long rectangular bar is made from a material whose fracture toughness is 60 MPa√m. During routine maintenance, a 20 mm deep edge crack is found. Assuming LEFM, is it safe to return the bar to service without repair ?

The load is not central here and we do not have the Y-factor for this geometry /loading. However we note that tension and bending are present, and that for each of these we do have the configuration factor. So, exploiting the inherent linearity between stress (load) and stress intensity, we use superposition and calculate the stress intensities for the tensile and bending components separately, then combine ( add) them :-

The computed stress intensity is greater than the fracture toughness - though theoretically it can't be, but such an inaccuracy is typical of Fracture Mechanics. Nevertheless, it is clear that the bar was inspected just in time and will have to be repaired.