Simulation of fatigue life of constructional steels within the mixed modes I and III loading

Abstract

A B S T R A C TThe authors analysed influence of a component of the torsional moment M as under the complex loading state, that is under bending with torsion, on fatigue life during initiation and propagation of fatigue cracks. Simulation of specimen life was performed according to the relationships describing the crack propagation rate and including the equivalent stress intensity factor range K eq . Under complex loading, increase of amplitude of the torsional moment M as for a given initial value of the resultant moment M aw0 caused a higher fatigue life of specimens made of 10HNAP and 18G2A steels. This fatigue life increase was described by a nonlinear equation, the parameters of which had been determined from the experimental results. The fatigue lives estimated according to the assumed models were compared with those obtained from tests.Keywords bending with torsion; equivalent stress intensity factor range; fatigue life; mixed mode loading. N O M E N C L A T U R Ea = crack length a e xpi = crack length obtained while tests a max e xpi = maximum crack length a k = the critical crack length a p = the initial length of crack a o bli = calculated crack length b = width of the specimen d i = minimal length of the interval E = Young's modulus G = strain energy release rate G eq = equivalent strain energy release rate G I = strain energy release rate for mode I G III = strain energy release rate for mode III h = height of the specimen k 2 and k 3 = coefficients dependent on side ratios b/h K eq = equivalent stress intensity factor K I = stress intensity factor for mode I K III = stress intensity factor for mode III M ag and M as = amplitudes of the bending and torsional moments M g = bending moment M K I , M K I I I = shape correction coefficients for modes I and III M mg and M ms = mean values of the bending and torsional moments (constant) M s = torsional moment

Influence of non‐proportional bending with torsion on fatigue life of 10HNAP steel within the range of crack initiation and propagation

“…In such a case, two tangent components of stresses occur: τ yz = τ h and τ xz = τ b . Their values are different and dependent on the length of the side where they occur 22 where M s is the torsional moment, b is the width of the specimen, h is the height of the specimen, k 2 and k 3 are coefficients dependent on the ratio b/h .…”

“…Also the Forman model is often applied for the determination of fatigue life of machine elements 13,22,31,32 . After integration of that relationship between the initial crack length a p and the critical crack length a k we obtain the following expression for the fatigue life determination where C 2 and m 2 are experimental constants.…”

“…Paris called them the material constants. However, they depend not only on a material type, but also on some other parameters as well, for example cycle asymmetry 13,27 or loading kind 22,23 . Thus, the name experimental constants seems to be better.…”

“…Under the complex stress state, in Eqs and the stress intensity factor range ΔK is replaced by a range of the equivalent stress intensity factor ΔK eq which takes the following forms for the plane stress state (PSS) and the plane strain state (PSTS) 13,22,25,33 where: ΔK I,II,III are the ranges of the stress intensity factor for modes I, II, III, respectively, and ν is the Poisson ratio.…”

“…As for fatigue crack initiation and propagation, there are not many papers on the influence of non‐proportional complex loading on the fatigue life 6,18,19 . Special attention should be paid to the papers presenting tests of specimens subjected to non‐proportional cyclic tension and torsion 20,22 . The authors of the paper 20 verified the Dowling model describing the fatigue crack propagation rate – they tested specimens made of S460N steel and aluminium alloy Al5083.…”