Surface Roughness-Induced Stress Concentration
B. N. J. Persson
Abstract
Abstract When a body is exposed to external forces large local stresses may occur at the surface because of surface roughness. Surface stress concentration is important for many application and in particular for fatigue due to pulsating external forces. For randomly rough surfaces, I calculate the probability distribution of surface stress in response to a uniform external tensile stress with the displacement vector field parallel to the rough surface. I present numerical simulation results for the stress distribution $$\sigma (x,y)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>σ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and show that in a typical case the maximum local tensile stress may be $$\sim 10$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>10</mml:mn> </mml:mrow> </mml:math> times bigger than the applied stress. I discuss the role of the stress concentration on plastic deformation and surface crack generation and propagation. Graphical Abstract