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A quantitative model has been proposed which predicts the extent of lifetime scatter in low-cycle fatigue due to the influence of bending caused by load misalignment. The main components of the model are the mechanism of bending, the type of extensometer used to control strain and the fatigue characteristics of the material being assessed. Three mechanisms of bending have been studied and it is F. A. KANDIL and B. F. DYWN tb = maximum bending strain tbx = bending strain at point x cbe = maximum bending strain at axial compressive peak strain tb, = maximum bending strain at axial tensile peak strain cC = control-strain amplitude t, = strain amplitude at point x L,, = strain amplitude at the centre of testpiece t , = maximum strain amplitude t2 = minimum strain amplitude A6 = strain range Atb = bending strain range ( = t b t f k ) = control-strain range Act = elastic strain range AcP = plastic strain range Au = stress range ub =bending stress 8 = angle in the circular cross-section between the intersections of the maximum bending plane and the extensometer plane

Models for predicting scatter bands due to bending have been applied to four alloys, namely AISI 316L, Nimonic 101, 9 Cr-l Mo, and IN 718. The alloys were tested extensively by 26 laboratories in an international round robin exercise sponsored by the Community Bureau of Reference (BCR) of the EC. After initially selecting data for analysis on the basis of their confirmed conformance to the ASTM bending criterion, it has been shown that in all four materials a major fraction of the data scatter could be attributed to bending. Furthermore, at the lowest strain range the predicted bending component represents the highest proportion of the experimental interlaboratory scatter. Many laboratories did not report any measure of bending and so could not be used in the initial analysis. However, a further interesting deduction from the models is that the entire BCR data-set can be encompassed within a scatter band based upon a bending criterion that is twice the allowable ASTM limit. Differences in the extent of scatter between materials at a given total strain range can be attributed to the gradient of the logarithmic plot of total strain range as a function of lifetime. NOMENCLATURE c = distance from neutral axis C, C' = material constants e = lateral offset E = Young's modulus E, = cyclic modulus ( = Ao/A€) f= extensometer factor = 1 for dual extensometer = 2 for single extensometer F = total axial force through testpiece I = moment of inertia of the cross-section K = material constant 1 = testpiece length L = total length of machine's cross-beam M = bending moment Nrl = repeatability minimum-cycles-to-failure Er2 = repretability maximum-cycles-to-failure IVr, = reproducibility minimum-cycles-to-failure Nr2 = reproducibility maximum-cycles-to-failure NF = number of cycles to failure under no bending A F f = range of repeatibility scatter-band (= Nr2;Nrl 1 AN, = range of reproducibility scatter-band (= Nr2-NfI ) r = testpiece radius R = radius of curvature z = distance CL, a' = exponents = slope of log A6 and log N f curve 529 530 F. A. KANDIL and B. F. DYWN y = angular offset; angle of deflection tb = maximum bending strain tbx = bending strain at point x tk = maximum bending strain at axial compressive peak strain cb, = maximum bending strain at axial tensile peak strain c, = control-strain amplitude t, = strain amplitude at point x to = strain amplitude at the centre of testpiece t , = maximum strain amplitude t2 = minimum strain amplitude At = strain range Ac,, = bending strain range ( = t b , -tb) Atc = control-strain range Ate = elastic strain range Acp = plastic strain range Au = stress range u,, = bending stress 0 = angle in the circular cross-section between the intersections of the maximum bending plane and the extensometer plane

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