S-N curve slope exponent

Physical-Chemical Mechanism of Action

The Wöhler curve describes the relationship between stress range Δσ and the number of cycles to failure N. In a double logarithmic plot, this becomes a straight line: log N = log C - m · log Δσ. The slope exponent m is the slope of this line. It shows how sensitive the material is to changes in stress. A large m value means a steep line: if stress increases only slightly, fatigue life drops sharply. Physically, what's behind this is: higher stresses drive microcracks through the structure faster. The crack tip experiences more energy per load cycle, so the crack grows disproportionately.

Metallurgical Relevance & Risks in Welding

Welded joints have different m values than the bare base material. Typical values: m = 3 for welds under normal stress, m = 5 for base material. The smaller m value of the weld means: fatigue life drops less steeply with increasing stress than for the base material. However, the entire Wöhler curve for the weld lies significantly lower. Causes are notches at the weld transition, welding residual stresses, and microstructural changes in the heat-affected zone. These factors act like pre-damage. As a result, the weld can only withstand a limited number of cycles even at low stresses. A wrongly chosen m value in the calculation leads to dangerous misjudgments of fatigue life.

Workshop Practice & Action Guidelines

Determine the applicable m value from the relevant standard (e.g., Eurocode 3 for steel structures). Use m = 3 for welds under normal stress, and m = 5 under shear stress. For variable amplitudes, use linear damage accumulation according to Palmgren-Miner. Actively reduce the stress range: halving the stress extends fatigue life by a factor of 8 for m = 3, and by a factor of 32 for m = 5. Dress the weld transition by grinding or TIG remelting to reduce notches. Control welding residual stresses by stress relief annealing or mechanical straightening. This shifts the Wöhler curve upward and gains fatigue life.