Issue 33

M.Kurek et alii, Frattura ed Integrità Strutturale, 33 (2015) 302-308; DOI: 10.3221/IGF-ESIS.33.34 303 materials. The paper also compares the calculation and experimental results for fatigue strength of specific materials, using multiaxial fatigue criteria and various methods for determining critical plane orientation that take into account the ratio of fatigue limits. F ATIGUE STRENGTH ALGORITHM o estimate calculation fatigue life used standard model, which consists of several stages. The first step includes measurement, generation or calculation of component of stress tensor, according to the following equations: ( ) sin( ) t t xx a     (1) ( ) sin( ) t t xy a       (2) where: σ a – amplitude of normal stress induced by bending, τ a – amplitude of shear stress induced by torsion, ω – angular frequency, φ – angle of phase shift, t - time. In the discussed model, the course of normal stress σ xx (t) refers to stress induced by bending, while τ xy (t) refers to torsion- induced stress. The next step involves determination of the orientation angle of the critical plane, which can be done using one of three established methods: weight functions, damage accumulation or variance. In this paper, the orientation of the critical plane was determined using damage accumulation method. If the criterion proposed by Carpinteri et al. [2] is used, the inclination angle of the critical plane is increased by the angle 2 2 3 1 1 45 2 B                   (3) with respect to the angle determined by maximum normal stress, where: 2 af af B    (4) where σ af , τ af are fatigue limits for bending and torsion respectively. The relationship (4) was proposed for some selected constructional materials, and the group for which this relationship is constant was determined. In such a case, hypotheses allow to calculate the fatigue life. As for other materials, there is no one universal criterion of fatigue life calculation because it is necessary to include variation of the ratio σ a /τ a depending on a number of cycles to the fatigue failure [5, 16]. There is a number of multiaxial fatigue criteria. Here, we are discussing the group based on the critical plane concept. Macha [8] has formulated the criterion of maximum normal and shear stress in fracture plane which can be generalised for the scope of random loading of numerous criteria. The general form can be written down as ( ) ( ) ( ) eq s t B t K t        (5) where: B, K – constants used for selection of specific criterion form [7] In this paper, in order to verify the highest conformity of results, three different criteria of multiaxial fatigue were used: 1. Criterion in the maximum normal stress plane, in the following form 1 ( ) ( ) ( ) eq s t B t t        (6) where: B 1 – constant depending on material type, σ η (t) is the course of normal stress orientated at angle α towards σ xx , expressed by the following equation 2 ( ) ( )cos ( )sin 2 t t t xx xy         (7) Whereas τ ηs (t) is the course of shear stress 1 ( ) ( )sin 2 ( )cos 2 2 t t t s xx xy          (8) T