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• The effects of precrack lengths and material yield stress on crack closure development are examined. • A new master curve equation is proposed for the cyclic R-curve. • The fatigue thresholds of materials with defects are successfully derived. A strip-yield model modified to leave plastically deformed stretch in the wake of the advancing crack tip is applied to simulate the development of plasticity-induced crack closure with crack extension from precracks with various lengths under the stress ratio R = 0. The effects of precrack length and yield stress on fatigue thresholds were systematically examined. Because of a sharp increase of crack opening stress with crack extension, the effective stress intensity range Δ K eff drops initially and then turns to increase. Assuming the threshold value of Δ K eff for steels, a master curve equation is proposed for the cyclic R-curve. The effects of precrcrack length and material yield stress on fatigue thresholds are successfully derived. [ABSTRACT FROM AUTHOR]

The resistance-curve ( R-curve) method was applied to the prediction of the fatigue thresholds of notched components under in-phase and out-of-phase combinations of cyclic torsion and axial loadings. The prediction was compared with the experimental data obtained from thin-walled tubular specimen of medium-carbon steel with a hole. The stress was completely reversed and the mean stress was zero. The crack was nucleated at the position of the maximum range of the circumferential stress on the periphery of a hole, and propagated almost straight for all cases examined. The experimental data of the thresholds for crack initiation and fracture agreed well with the predictions for in-phase and for out-of-phase loadings with 45° phase difference. For out-of-phase loading with 90°, the threshold for fracture was close to the crack initiation limit, because of the reduction of crack closure due to crack face rubbing by mode II shear cycling. [ABSTRACT FROM AUTHOR]

Single-edge notched specimens of a unidirectional SiC long fibre reinforced titanium alloy, were fatigued under four point bending. The propagation behaviour of short fatigue cracks from a notch was observed on the basis of the effects of fibre bridging. The branched fatigue cracks were initiated from the notch root. The fatigue cracks propagated only in the matrix and without fibre breakage. The crack propagation rate decreased with crack extension due to the crack bridging by reinforced fibres. After fatigue testing the loading and residual stresses in the reinforced fibres were measured for the arrested cracks by the X-ray diffraction method. The longitudinal stresses in the reinforced fibres were measured using high spatial resolution synchrotron radiation. A stress map around the fatigue cracks was then successfully constructed. The longitudinal stress decreased linearly with increasing distance from a location adjacent to the wake of the matrix crack. This region of decreasing stress corresponded to the debonding area between the fibre and the matrix. The interfacial frictional stress between the matrix and the fibre could be determined from the fibre stresses. The bridging stress on the crack wake was also measured as a function of a distance from a notch root. The threshold stress intensity factor range, corrected on the basis of the shielding stress, was similar to the propagation behaviour of the monolithic matrix. Hence the main factor influencing the shielding effect in composites is fibre bridging. [ABSTRACT FROM AUTHOR]

Fatigue tests of crack propagation from a precrack in thin-walled tubular specimens made of a medium-carbon steel were performed under cyclic torsion with and without superposed static or cyclic axial loading. The stress ratio of cyclic loading was−1. The fatigue crack-propagation path from a precrack was compared with the predictions based on the maximum tangential stress criterion. The direction of fatigue crack propagation follows the direction of the maximum of the range of the tangential stress,Δσ*θ max, near the crack tip determined from the stress intensity factor (SIF) which was calculated by considering the contacts of crack faces at the minimum load. The SIF calculated from the actual crack path by using the body force method (BFM) showed that the mode II SIF range quickly approached zero after a small amount of crack extension. The crack-propagation rate decreased first and then increased with crack extension. The initial dip of the crack-propagation rate was caused by the development of crack closure with crack extension. As cracks extended a long distance, the propagation rate was faster than the uniaxial data. This acceleration of crack propagation was caused by excessive plasticity near the crack tip. [ABSTRACT FROM AUTHOR]

ABSTRACT The crack propagation law was derived from the S–N data in the very high cycle fatigue of a bearing steel. The propagation rate, da /d N (m/cycle), of surface cracks was estimated to be a power function of the stress intensity range, Δ K (MPa√m) with the coefficient C s = 5.87 × 10 -13 and the exponent m s = 4.78. The threshold stress intensity range was 2.6 MPa√m. The crack propagation from internal inclusions was divided into Stages I and II. For Stage I, the coefficient of the power law was C 0 = 3.44 × 10 -21 and the exponent m 0 = 14.2. The transition from Stage I to II took place at Δ K = 4.0 MPa√m. For Stage II, the coefficient was C i = 2.08 × 10 -14 and the exponent m i = 4.78. The specimen size and loading mode did not influence the surface fatigue life, while the internal fatigue life was shortened in larger specimens and under tension–compression loading. For ground specimens, the surface fatigue life was raised by the compressive residual stress, while reduced by the surface roughness introduced by grinding. For shot-peened specimens, fatigue fracture did not take place from the surface because of a high surface compressive residual stress. The internal fatigue life was reduced by the tensile residual stress existing in the interior of the specimens. [ABSTRACT FROM AUTHOR]

The crack closure behaviour of microstructurally small fatigue cracks was numerically simulated by combining the crack-tip slip band model with the plasticity-induced crack closure model. A Stage II crack started to propagate from an initiated Stage I crack. When the plastic zone was constrained by the grain boundary or the adjacent grain with higher yield stresses, the crack opening stress increased with crack extension, and the effective component of the stress range decreased. The crack-tip opening displacement range (ΔCTOD), first decreased with crack extension due to the development of the residual stretch, then increased until the tip of the plastic zone reached the neighbouring grain boundary. When the plastic zone was blocked by the grain boundary, ΔCTOD began to decrease. The arrest condition of cracks was given by the threshold value of ΔCTOD. At the fatigue limit, the arrest of small cracks takes place just after the Stage II crack crosses the grain boundary when the grain boundary does not act as a barrier. Only when the grain boundary has a blocking strength and the yield stress of adjacent grains is not so high, the arrest of Stage II cracks takes place before the crack reaches the grain boundary. The fatigue limit decreases with the mean stress. The predicted relation between the fatigue limit and the mean stress is close to the modified Goodman relation. [ABSTRACT FROM AUTHOR]