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Keywords:Torsional fatigue Mean stress effect Haigh diagram Multiaxial fatigue criteria A B S T R A C TThis study provides a theoretical and experimental investigation of the effect of static shear stresses on the highcycle fatigue behaviour of a 34CrNiMo6 high-strength steel under quenched and tempered conditions. Torsion S-N curves under different mean shear stresses were obtained. Experimental results show that an increase in mean shear stress yields a gradual reduction in shear-stress amplitude that the material can withstand without failure. The results for this steel agree well with the Smith's hypothesis for ductile steels, which states that the effect of the torsional mean stresses on the torsional fatigue limit is negligible as long as the maximum shear stress is within the torsional yield strength. Taking into account the results collected from the literature and the experimental results on torsional fatigue of 34CrNiMo6 steel, an extension of the theory of Crossland is proposed to include the mean-shear-stress effect. Its application to the torsional fatigue case with mean shear stresses can be interpreted in terms of a balance of the energy of distortion. Macro-analyses of the specimen fracture appearance were conducted to obtain the fracture characteristics for different mean-shear-stress values under torsion fatigue loading.

The present study consists of a theoretical and experimental investigation of the effect of axial mean stresses on the high cycle fatigue behaviour of DIN 34CrNiMo6 high strength steel in quenched and tempered conditions. The axial S-N curves under 4 different stresses ratios were obtained. Experimental results show that increasing the value of the tension mean stresses gradually reduces the axial stress amplitude the material can withstand without failure. Moreover, the compressive mean stresses show a beneficial effect in terms of the axial fatigue strength, resulting in a non-symmetrical Haigh diagram. A historic review of the axial mean stress effect is presented, showing the shape of the Haigh diagrams for ductile metals and presenting the most-known empirical and physical theories. The results for this steel are compared with the physical theories of Findley based on the critical plane; the Froustey's and Marin's methods, based on energetic theories; and the Crossland invariants method based on the Gough's theory of fatigue damage. Taking into account the experimental results, a physical fatigue function based on energetic considerations is proposed. Its application to the fatigue case with mean stresses can be interpreted in terms of a balance of elastic energies of distortion and volume change. Macro-analyses of specimen fracture appearance were conducted in order to obtain the fracture characteristics for different mean stress values.

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