Propagation and Closure of Short Fatigue Cracks at Notches Under Compressive Mean Stresses

Abstract

Single-edge-notched specimens of a low-carbon steel were fatigued under cyclic in-plane bending with compressive mean stresses. The development of crack closure with crack growth was studied both experimentally and theoretically. The relation between the crack opening stress and the crack length was a function of the minimum (compressive) applied stress, irrespective of the maximum stress. The efl-ective stress intensity range was a unique parameter in correlating the crack growth rate, even if the crack wdS embedded in the compressive plastic zone. Under a constant minimum stress, the length of nonpropagating cracks became longer with increasing maximum applied stress. A theoretical model was proposed for predicting the crack opening stress on the basis of the compressive stress distribution at the minimum applied stress. The predicted value agreed fairly well with the experimental result. The model gave upper bounds of the crack growth rate and the length of nonpropagating Fatigue cracks within the plastic zone. NOMENCLATURE a =crack length including notch depth u', c'. n' =coefficients of the stress-strain relation c =crack length from the notch-tip c,. c,. cnp = mean, surface and non-propagating crack length dc/dN =crack propagation rate F. F , , F2 =geometrical correction factors for the stress intensity factor (SIF) K = SIF value due to applied stress K,,,, K,,, = SIF value due to minimum and maximum applied stress Kop = SIF value at crack opening K,, = SlF value due to residual stress Kr = stress concentration factor K*. K:," = true SIF value and SIF value calculated from the stress distribution at minimum applied nominal stress AKen, AK,,, =effective SIF range and its threshold value M = weight function R = ratio of minimum to maximum stress I = notch depth W = specimen width x =distance from the edge of specimen to load point p = notch-root radius 6 = von Mises equivalent stress u, = applied nominal stress amplitude u, = applied nominal mean stress = von Mises equivalent plastic strain urnax. u,,, = maximurn and minimum applied nominal stresses u:," =stress at minimum applied nominal stress u, = applied nominal stress uy = yield stress w, w * = plastic zone size at urnin and reversed plastic zone size at umrl 343 344 Y. AKINIWA er a1

Bending fatigue behaviour and microstructure in welded high-strength bolt structures

“…This agreed with the fact that the crack initiated from the region R u of the bolt under-head that was opposite to the weld bead side in the full-circled sample as shown in Figure 5, because the cracks generate and propagate preferentially from the tensile side but not from the compressive side. 7,15,16 Accordingly, the strength decrease of 15% of the full-circled sample comparing with the bolt-only sample was mainly due to the tensile residual stress in the bolt under-head, because their fracture mechanisms were comparable as mentioned in the above section.…”

“…The crack initiated from the right as well, but the propagated distance was shorter and is presumed to have met with the crack that propagated from the left and reached breakage at point F. From the beach marks and the distance to the point F, the left side was the first starting point of the crack and the right side was the second. 11,15…”

Fatigue limit and life evaluation formulae for compressive mean stress states

“…where the test constant C and even the exponent m might be dependent on mean stress or stress ratio. Equation (6) in fact is only a mathematical expression of the linear part of a S-N curve, as it is illustrated in Figure 4. It cannot be applied to cases that the stress amplitude is near the fatigue limit, and more inconveniently, constants C, m have to be determined individually by a large number of tests under the corresponding mean stress or stress ratio state.…”

“…Generally, with the increase of tensile mean stress, both the fatigue limit and life would decrease rapidly. On the effect of compressive mean stress, some empirical expressions of fatigue limit and life-based on test results [5][6][7][8][9] can also be found. It has been found that fatigue limit increases with the absolute value of compressive mean stress [10][11][12][13], but it cannot be predicted at all by the well-known empirical formulas such as Goodman's or Gerber's relationships.…”

Measurement of Stress Distribution Near Fatigue Crack in Ultra-Fine Grained Steel by Synchrotron Radiation

“…In the calculation, the model is infinite plate. The experimental results agree well with the solid curve.When the measured residual stress is approximated by appropriate functions, the crack opening SIF can be calculated[9].…”