Cumulative Damage in Fatigue: A Step towards Its Understanding

Abstract

A method is described which uses changes of apparent dynamic modulus and damping during fatigue cycling, for estimating accurately the fatigue lives of stainless steel (Rex 535) specimens. This technique for estimating well in advance of failure the fatigue lives of individual specimens avoids the usual difficulties caused by scatter of fatigue results, and has enabled a more precise quantitative investigation to be made of cumulative fatigue damage (i.e. damage due to multi-level loading) than would have been possible using conventional experimental methods. By estimating the remaining life of a specimen at one stress amplitude before measuring the equivalent remaining life at a second stress amplitude by cycling to failure, it was possible to determine lines of equal damage on a plot of stress amplitude versus remaining fatigue life. These lines of equal damage were used to predict the fatigue lives of specimens subjected to programmes of multi-level loading, and the accuracy of these estimates, when compared with the subsequent experimental results, is much better than has been achieved hitherto. Depending on the stressing programme chosen, Miner's linear damage rule is shown to be very good, rather pessimistic, or very dangerous.

The Influence of Load Misalignment During Uniaxial Low‐cycle Fatigue Testing—i: Modelling

“…This is not current practice, and therefore reported values of percent bending [ 15-1 71 or the so-called "precision of alignment" [ 18,191 at arbitrary elastic-loading conditions are of little value. The present work suggests that there should be a reappraisal of the British Standard BS 7270:1990 [20] and ASTM Standards E606-80 and It can be seen that equations (24) to (30) predict that there will be no effect on fatigue life due to a non-reversed bending (angular or lateral offsets, Fig. 1) since At, = zero, despite the mean strains caused by bending.…”

“…When calculating scatter bands, according to equations (24) to (30) the slope fl should ideally be obtained from tests with no bending. However, in practice any set of data with a reasonable level of bending (i.e.…”

“…Similarly, the maximum number of cycles to failure N,, is For a single laboratory, the repeatability limits Nrl and Nf2 will therefore depend on the angle 8, which is expected to be approximately constant. According to equations (24) and (25), the mid-point fatigue life is the repeatability scatterband [Nf, = $N,, + N,,)] will not be constant and will be dependent on 8. The interesting conclusion to be drawn is that, contrary to intuition, the mid-point (and also, the mean, mode, or median) values of a data-set obtained from a single test system will not generally represent the "true" material behaviour N: obtained under the condition of zero bending.…”

“…The reproducibility limits (between laboratories) of Nfl and N,, are fir, and fir, and given respectively by the absolute minimum of N,, in equation (24) and the absolute maximum of Nf2 in equation (25). These occur when 8 = 180" and 8 = O", respectively.…”

“…Therefore Rfl=N: 1 + 2 -i and For a sufficiently large number of laboratories, the median of the reproducibility range will approximate to N : . A shorthand for equations (24) to (27) which is convenient for tabulation purposes is and Equations for repeatability and reproducibility limits of fatigue life due to bending can be calculated in the same way for other combinations of material model and extensometer type: all combinations are given in Table 1. The important features to note are that (a) the repeatability limits are the same as the reproducibility limits only when a dual extensometer is used, (b) repeatability scatter is zero for a material whose behaviour conforms to material model 1, regardless of the type of extensometer used, and (c) the largest reproducibility scatter occurs when a single extensometer is used in conjunction with material model 2.…”