The stress concentration factor for slightly roughened random surfaces: Analytical solution

We derive an analytical solution to the stress concentration factor (kt)(kt) for slightly roughened random surfaces. Topology is assumed to possess Gaussian distribution of heights and auto correlation length, ACL  . For our development, we combine Gao’s first-order perturbation method, the Hilbert transform, and an energy conservation principal related to the Parseval theorem.The root-mean-square (RMS) value of ktkt results in a function of the ratio RMS-roughness to ACL. The derived formula agrees with experimental results previously reported. The results provide insight for more efficient design.