Issue 35

R. Sepe et alii, Frattura ed Integrità Strutturale, 35 (2015) 534-550; DOI: 10.3221/IGF-ESIS.35.59 541 The first term on the left-hand side of Eq. (1) is the octahedral shear stress, τ oct :                 2 2 2 1, 2, 3, 1, 2, 1, 3, 2, 3, 2 ( ) 3 oct a a a a a a a a a (2) where σ 1 , σ 2 and σ 3 are the amplitudes of the alternating principle stresses. The second term on the left-hand side of Eq. (1) is a hydrostatic stress term, σ H,m :              1, 2, 3, , 3 m m m H m (3) where σ 1,m , σ 2,m and σ 3,m are the amplitudes of the mean principle stresses; λ = is material constant proportional to reversed fatigue strength; k = is a numerical material constant, which gives variation of the permissible range connected to the hydrostatic stress. The constants λ and k may be easily determined from fatigue tests with a large R-ratio difference. For example, in a fully reversed uniaxial test (R-ratio = -1), Eq. (1) gives:    1, 2 3 a letting    1, , a f a it is obtained:    , 2 3 f a where  , f a is the amplitude of reversed axial stress that would cause failure at the desired cyclic load. For pulsating load from 0 to  max (R-ratio = 0) it is obtained:    1, 1, a m and Eq. (1) may become:      1, 1, 2 1 3 3 a m k Letting    1, , a p a it is obtained:             , , 2 1 f a p a k where  , p a is the amplitude of fluctuating stress that would cause failure at the same cyclic life as  , f a . For computer calculations, a convenient notation introduces the von Mises equivalent stress so the Sines criterion Eq. (1) becomes:                        , , ( ) 1, 2, 3, , , 1 f a eq a vonMises m m m f a p a (5)