A B S T R A C TThe strain-life approach is standardized and widely accepted for determining fatigue damage under strain-controlled low cycle fatigue (LCF) loading. It was first extended to non-isothermal cases by introducing an equivalent temperature approach (ETA). The paper presents its extension that is the damage operator approach (DOA) enabling online continuous damage calculation for isothermal and non-isothermal loading with mean stress correction. The cycle closure point, cycle equivalent temperature, threshold temperature and separate rainflow counting obligatory for the ETA are not necessary for the DOA any more. Both approaches are equivalent for the second and subsequent runs of block loading if temperature is constant. However, for non-isothermal cases, the DOA is within the worst and the best case scenarios of the ETA. The approaches are compared to the simple stress histories and several thermo-mechanical fatigue (TMF) cycle types. = cyclic stress-strain curve i = data point index j = fictive yield stress index, fictive yield damage parameter index k = temperature index K (T) = cyclic hardening coefficient K P = limit load ratio n p = index of the top fictive yield damage parameter n r = index of the top fictive yield stress n T = index of the top temperature n (T) = cyclic hardening exponent N f = number of cycles to failure p j = fictive yield damage parameter P , P (t i ) = damage parameter P a (t i ) = damage parameter amplitude P o (t i ) = damage parameter origin r j = fictive yield stress S * = nominal stress Correspondence: M. Nagode.
A B S T R A C TThe isothermal strain-life approach is the most commonly used approach for determining fatigue damage, particularly when yielding occurs. Computationally it is extremely fast and generally requires elastic finite element analyses only. Therefore, it has been adapted for variable temperatures. Local temperature-stress-strain behaviour is modelled with an operator of the Prandtl type. The hysteresis loops are supposed to be stabilized and no creep is considered. The consequences of reversal point filtering are analysed. The approach is finally compared to several thermo-mechanical fatigue tests and the Skelton model. E = Young's modulus i = data point index j = spring-slider segment index k = temperature index K = cyclic hardening coefficient n = index of the top data point n = cyclic hardening exponent n q = index of the top fictive yield strain n T = index of the top temperature q j = fictive yield strain t = time T = temperature α j = the Prandtl density ε = total strain ε αj = spring strain ε qj = slider strain q = fictive yield strain class width σ = total stress σ j = spring-slider stress
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