Improvements to the notch stress method—effective stresses

New analyses have shown that the notch stress method, while it does include size effects, may be misleading especially in cases where the fixed radius for the notch is very sharp. For thinner sheets a detail weld with a fixed radius of 0.05 mm is recommended by standards, such as the IIW. This effect, shown in the following figure, becomes relevant when comparing results for weld roots and toes. [4, 5, 6] While the results split using the notch stress (left diagram), they fall into one scatter-band using the effective stress (right diagram). [6]

Fatigue Tests of Several Specimens with Failure in Root, Toe, and Weld End

The effective stress method uses Neuber's microscopic structural length ρ* to include the size effects on the notch. The structural length is used by Neuber to model the non-local effect in the notch in such a way that the effective stress value is averaged over the structural length (see the following figure), rather than analyzing the elastic notch stresses directly. This structural length is a material property that can be determined for steel and aluminum-based welds. The ratio between the effective stress and the elastic notch stress correspond to the ratio of Kf to Kt in traditional fatigue calculations. [4]

The Effective Stress Is the Average Stress Along the Microscopic Neuber's Structural Length ρ*

Analytical analysis, done in [6], shows that the correction factor due this effect depends on the radius of the notch, the opening angle, and the microscopic structural length. Under the assumption of V-shaped notches, it is even possible to analytically calculate the correction factors.

When using the Specialist Durability approach to calculate the notch stresses, the values of the radius and the opening angles are known (as shown in the following figure). This way it becomes possible to easily calculate the correction factors for each notch independently. Calculations, published in [7], on a real axle structure under several load conditions have shown that the new effective stress method is less dependent on the different failure locations and load situations.

Further advantages of the method of effective notch stress are that the weld SN-curve becomes independent of the used fictitious radius. This allows modeling the weld roots with a different radius than the toes. [4]

Influence on the Size Effect Factor: Radii (r), Opening Angles (ω), and Material Constant Structural Length (ρ*)

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Improvements to the notch stress method—effective stresses, Simcenter 3D 2021.1 Series

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