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.

本文介绍了功能梯度（FG）涂层对圆形截面钢筋在扭转力矩下被多个裂纹和空腔削弱的感应应力分布的增强影响。杆的整个横截面都承受着受圣维南原理约束的扭转载荷。假设FG涂层的剪切模量在径向方向上呈指数变化。解决方案的过程开始于使用傅立叶变换在带有FG涂层的圆形截面钢筋中找到与Volterra型螺钉位错相对应的应力场。之后，位错沿着裂缝和空洞的表面分布。利用位错应力场，根据裂纹和空洞表面上未知的位错密度函数，导出奇异积分方程，以评估具有任意图案的多个缺陷。这些积分方程是柯西奇异类型的方程，可以通过数值求解来确定缺陷表面上的位错密度函数。获得的结果用于计算所考虑区域的抗扭刚度，以及裂纹尖端处的III型应力强度因子（SIF）。最后，给出了几个数值示例，研究了FG涂层和任意图案的多个裂纹和空腔对裂纹和空腔对弱化钢筋的应力分布，应力强度因子（SIF）和抗扭刚度的影响。