Fatigue tests were performed on thin-walled tubular specimens of S45C steel under tensioncompression, pure torsion, in-phase and out-of-phase axial-torsional loadings. The relationship between cracking behaviour and stress components on the crack plane was investigated. Measurement of microcrack density showed that microcracking was governed predominantly by the shear stress amplitude acting on the crack plane for all loading conditions. The failure crack was formed by coalescence of many cracks initiated near the maximum shear planes. The cracks grew turning their orientation to the direction perpendicular to the maximum normal stress. The transition of crack orientation occurred at relatively longer crack lengths at a higher stress ratio. The crack growth behaviour for all loading modes can be correlated using an equivalent strain intensity parameter based on shear and normal strains on the crack plane.Keywords-Multiaxial fatigue; Out-of-phase loading; Carbon steel; Crack orientation; Crack growth rate; Equivalent strain intensity range. NOMENCLATURE a = crack depth c = half surface crack length dc/dN = surface crack growth rate F,, F, = geometry factors k = a/c, aspect ratio E, G = axial and shear elastic moduli X(k), E(k) =complete elliptic integrals of the first and second kinds K O = equivalent stress intensity factor N/N, = cycle fraction a,, a, = phase angles of normal and shear strains on crack plane E,,, yo = applied axial and torsional strain amplitudes t = time ceC, ye,, A&$, Aye, = amplitudes and ranges of strain component on crack plane A K e = equivalent strain intensity range AK,* = modified equivalent strain intensity range 0 = angle of the normal to oblique plane relative to the specimen axis 8, = angular orientation of crack plane B, = angular orientation of crack growth 0, = angular orientation of om,, plane 8, = angular orientation of T, , , plane ; b = T~/ D , , , applied stress amplitude ratio v = Poisson ratio 5 = T,,/&,,, applied strain amplitude ratio uo, zo = applied normal and shear stress amplitudes ue, z, =normal and shear stress amplitudes acting on oblique plane oe,, T~~ = normal and shear stress amplitudes acting on crack plane 929 930 Chemical composition (%) Mechanical properties I. OHKAWA et al. C I Si I Mn I P 1 S j Cu Ni I Cr 0.45 I 0.18 1 0.67 10.027 IO.012 1 0.06 0.05 I 0 12 Yield stress in tension MPa 371 Tensile strength MPa 591 Elongation % 31 Contraction of area % 50 Yield stress in t,orsion MPa 243 Torsional strength MPa 663 ... z , , , = maximum shear stress amplitude g , , , = maximum normal stress amplitude 0, = normal stress amplitude acting on z , , , plane T, = shear stress amplitude along urnax plane 4 = phase difference between applied stresses o = angular frequency of applied stresses
