Issue 38

A. Niesłony, Frattura ed Integrità Strutturale, 38 (2016) 177-183; DOI: 10.3221/IGF-ESIS.38.24 180 af af af af 3 3 1.7321         (13) what is also valid for basic von Mises criterion in time domain, Eqs. (1) and (2). According to numerous reported experimental results such an equality is fulfilled only for few materials. Usually the ratio (13) varies between 1 and 2 for fatigue strength and fatigue limit as well. It is important to know how much influence have a deviation from the specified square root of three value (13) on calculated fatigue life. In order to present the scale of the problem fatigue life was calculated for round specimen under random, narrow-banded and Gaussian, pure torsion loading. In such a kind of loading the Probability Density Function (PDF) of amplitudes describe Rayleigh distribution [12]. On the Fig. 1a) PDF for shear stress amplitudes and equivalent tension amplitudes according EMS criterion were presented. It was also assumed that the Miner rule is applicable and constant amplitude SN curves for pure torsion and tension are known and described as follow m m a f a f N N S T N N 1 1 ,                       (14) where: S f and T f – fatigue limits for tension and torsion; N  and N  – number of cycles for knee points; m  and m  – slopes of the SN curves. On the Fig. 1b) two SN curve are presented which satisfy the S f / T f = 1.7321 condition, Eq. (13). Computed fatigue life T 1 according PDF of shear stress amplitudes and SN curve for torsion are equal to T 2 computed from PDF of equivalent tension amplitudes and SN curve for tension. For materials that do not meet the condition (13) computed fatigue life T 1 and T 2 differ significantly. Such a case is presented on Fig. 1c) for S f / T f = 1.5 what results in T 1 / T 2 = 3.16. Lack of Parallelism of the SN Curves Lack of parallelism is a special situation of the problem discussed in previous section. In this case the equality (13) cannot be fulfilled in whole range of cycles to failure. Depends on the m  and m  slopes of SN curves different deviation from T 1 / T 2 = 1 can be obtained. This effect was illustrated in Figs. 1d) 1e) 1f) where computed results obtained with the same procedure as described in previous section were presented. Abnormal Behaviour of the EMS Criterion under Biaxial Tension-Compression Biaxial tension-compression is a plane stress state where for specific reference axes only the shear component is constant and equal zero bi xx yy . [ 0 0 0 0 ]    S (15) Pure biaxial tension-compression is rarely found in practice but it is used for verification of multiaxial fatigue failure criteria. Such kind of stress state is released on so called cruciform specimens through loading of two sets of arms in perpendicular direction [13]. This two loading components can be of any type, for example in-phase, out-of-phase or random with given correlation coefficient. In biaxial tension-compression the PSD of equivalent stress can be computed as follow (16) Real part of cross spectral density Re[ G xx,yy ( f )] is equal 0 for fully uncorrelated loading components  xx ( t ) and  yy ( t ). There are some interesting results published in the literature which are showing basic biaxial fatigue behaviours of tested materials. Cláudio et al. [13] presenting results from which it appears that the EMS criterion does not fit the real behaviour of material. This can be observed on the Fig. 2 where EMS criterion for correlated data gives lower stress amplitudes and for out-of- phase loading higher stress amplitudes than expected. EMS xx xx yy yy xx yy G f G f G f G f , , , ( ) ( ) ( ) Re[ ( )]   