Issue34

Z. Marciniak et alii, Frattura ed Integrità Strutturale, 34 (2015) 1-10; DOI: 10.3221/IGF-ESIS.34.01 5 Fig. 2 compares calculated life values and experimental values for variance and damage accumulation [12]. a) b) Figure 2 : Comparison of calculated and experimental fatigue lives with critical planes determined according to: a) variance and b) damage accumulation methods [14]. Strain fatigue criterion [3] expressed as   max ( ) ( ) ns n t b t k t q     (12) is another proposal to formulate multiaxial random fatigue in the field of strains, where ε ns (t) and ε n (t) are shear and normal strain in critical plane, respectively; and a, b, k, q – constants for the selection of a given criterion version. In 1991, Macha, Grzelak and Łagoda [14] attempted to apply spectral method to determine fatigue life. Studies on these issues were continued further in cooperation with Niesłony [15]. In these studies, assuming linear effort criteria, a generalised spectral method was formulated for determining fatigue life of materials put to multiaxial loading, using the function of power spectral density in the field of frequency. Multiaxial state of stress is reduced to uniaxial state, and accumulation of damage is carried out using standard material characteristics. The study proves that the results for lives assessed using spectral method in the field of frequency and cycle counting method in the field of time are much the same. Whereas, determination of expected critical plane position using variance method for time histories gives results equivalent to the function of power spectral density. Then, Professor Macha focused his attention on stress distribution in notch root. Like in Neuber [16] and Molski-Glinka [17] criteria, Łagoda-Macha [18] proposed an energy equation for determining the state of stresses in notch bottom as 1 2 max max max 1 2 1 n LM n W E n K                 , (13) where: n  - exponent of cyclic strain curve, K  - coefficient of cyclic strain curve. Experimental verification proved that the values obtained through this relation are between the results obtained using Neuber and Molski-Glinka relations. Tab. 1 contains sample calculation results for the above three models [19].