19.8 : 円形シャフトの塑性変形

When materials are subjected to stresses exceeding their yield strength, plastic deformation occurs, causing a permanent strain. In the case of circular shafts, plastic deformation changes its configuration.

An accurate assessment of plastic deformation necessitates the determination of stress distribution within the circular shaft.

If the maximum shearing stress in the material is known, then plotting a shearing-stress-strain diagram gives the corresponding maximum shearing strain.

Recall that the shearing strain varies linearly with the distance from the axis of the shaft. The relationship between shearing strain and radial distance is established by substituting the maximum shearing strain value. Further, the relationship between shearing stress and radial distance is obtained.

Using the integral relation and substituting for the elemental area and the polar moment of inertia in terms of shaft radius, the ultimate torque that causes shaft failure can be determined by maximizing the value of the material's ultimate shearing stress.

The corresponding fictitious stress is called the modulus of rupture in the torsion of the given material.