Size effect in beams with rounded-tip V-notch

Stresses and strains in a beam with a single-edge rounded-tip V-notch subjected to bending were analyzed by the method of finite elements by using nonconforming quadrilateral elements under the assumption that the material is linearly elastic. We studied the influence of the depth of the notcha, its radius of curvature ρ, the angle of the notch ω, and the height of the beamh on the stress intensity factorKt. It is established that the relative depth of the notch ζ=a/h causes practically no influence if the notch angle ω lies within the range 0°–135°. The influence of the notch rapidly weakens as the relative radius of curvature ρd=ρ/h increases from 0.01 to 1.0 and becomes insignificant for ρd ≤ 1. For small ρd (ρd ≤ 1), the quantityKt attains its maximum value provided that ζ lies within the range 0.1–0.3. As the height of the beam increases, the quantityKt first remains practically constant, then increases, and finally, ash infinitely increases, approaches a certain constant value.