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Abstract
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This paper presents the reinforcement impact of a functionally graded (FG) coating layer on the induced stress distribution of circular cross-section bars weakened by multiple cracks and cavities under torsional moment. The entire cross-section of the bar is under torsional loading governed by Saint-Venant’s principle. The shear modulus of the FG coating layer is assumed to vary exponentially in the radial direction. The solution procedure begins by finding the stress field corresponding to a Volterra-type screw dislocation in a circular cross-section bar with an FG coating layer using the Fourier transform. After that, the dislocations are distributed along the surfaces of cracks and cavities. The dislocation stress field is employed to derive singular integral equations in terms of the unknown dislocation density function on the surface of cracks and cavities for the evaluation of multiple defects with arbitrary patterns. These integral equations are of the Cauchy singular kinds and are solved numerically to determine the dislocation density functions on the surface of defects. The obtained results are employed to calculate the torsional rigidity of the domain under consideration, and the mode III stress intensity factors (SIFs) at the crack tips. Finally, several numerical examples are presented to study the effects of the FG coating layer and multiple cracks and cavities with arbitrary patterns on the stress distribution, stress intensity factors (SIFs) and torsional rigidity of weakened bar by cracks and cavities.
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