Analysis of L-shaped functionally graded viscoelastic shafts with longitudinal crack under torsion

The current analysis is concerned with longitudinal fracture in an L-shaped functionally graded shaft of circular cross-section. The shat is located in the vertical plane. The right-hand end of the horizontal member of the shaft is clamped. The vertical member of the shaft is supported also by a rotational spring located in the horizontal plane. The shaft is made of a material that is functionally graded along the radius of the cross-section. The material has non-linear viscoelastic behaviour. The upper end of the vertical member of the shaft is under an angle of twist that changes continuously with time. Thus, the vertical member is loaded in pure torsion, while the horizontal member of the shat is loaded in pure bending around the vertical axis. There is a longitudinal crack in the vertical member of the shaft. For this crack, the strain energy release rate is derived. The time-dependent energy balance is analyzed for verifying the solution of the strain energy release rate. The influences of various factors (L-shaped shaft geometry, parameters of loading, variation of material properties along the cross-section radius, rigidity of the spring support, etc.) are studied.