Saeidreza Mohebpour

A dislocation solution to evaluate the mode III stress intensity factors (SIFs) of the crack tips, torsional rigidity and the hoop stress around the cavities in an infinite rectangular cross-section bar coated by an FG layer under torsion is developed based on the Saint-Venant theory. The solution of the rectangular cross-section with the FG coating weakened by a screw dislocation under torsion was first obtained in terms of the dislocation density function. Then, the problem is transformed into a group of Cauchy integral equations in the rectangular cross-section bar with the FG coating layer via the distributed dislocation approach. The singular integral equations are reduced to a set of algebraic equations to evaluate them numerically. After solving the integral equations, the stress intensity factors of the crack tips, the hoop stresses around the cavities and the torsional rigidity of the entire domain is found. The obtained solution is validated by performing comparison studies in multiple cases. It is shown that the interaction between the cracks, the cracks length, variation of the shear module of the FG coating layer, and distance of the crack tips from stress-free surfaces can significantly affect the stress intensity factors of crack tips and torsional rigidity of the rectangular cross-section bar coated by an FG layer.