Brittle fracture occurs when the maximum stress in the material reaches a critical value. As well known, it is favoured by
the presence of a notch, which induces a local stress and strain concentration. This causes the easy nucleation of a microcrack
and induces a local stress triaxiality that prevents microcrack blunting. In order to explain the premature brittle fracture of
the pinion under investigation, an evaluation of the stress level at the thread root is necessary. It is to be understood that the
calculation is approximate, since the intention is to obtain an understanding of the problem and not the exact solutions.
The principal tensile stress distribution in the plastic region at the thread root can be simply calculated using the slip-line
field theory [7,8]. If the local strain hardening is neglected (which is a correct approximation, given the martensitic nature of
the microstructure at the notch root), the maximum principal tensile stress is given by the following relation: