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

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Load-controlled fatigue tests were conducted on smooth tubular specimens of an annealed medium carbon steel under fully-reversed torsion with superimposed static torque or tension. Effect of mean stress on initiation and growth of short crack was studied in the intermediate life regime. Microcracks initiated around the maximum shear stress amplitude planes rather than the planes of maximum shear stress, irrespective of mean stress conditions. The dominant crack grew accompanying coalescence of the shear cracks initiated in the early stage of life and the preferential growth direction was different depending on the type of mean stress. The increase of the crack growth rate and the reduction of the fatigue life with application of mean stress were slight in the present material. The relatively smaller mean stress effect appeared to be resulted from the decrease of the plastic shear strain amplitude with static loading. Therefore, two-stage short crack growth model proposed by Hobson and Brown was modified incorporating the effects of mean stress acting on the crack planes and the hardening/softening of material. The model showed a satisfactory estimation of fatigue lives in torsion under various mean stress conditions.

This paper discusses the stress-based evaluation of fatigue life under both in-phase and outof-phase combined loading conditions. Load controlled fatigue tests were performed on a low carbon steel under combined push-pull and completely reversed torsion in the intermediate to high cycle reg

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