Temperature–stress–strain trajectory modelling during thermo‐mechanical fatigue

Abstract

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

Identification of material parameters from low cycle fatigue, thermomechanical fatigue and creep tests for damage prediction of thermomechanically loaded Ni-resist Type D-5S

“…This procedure is presented in Nagode and Fajdiga. 24 True stress sðt i Þ and elastoplastic strain e ep ðt i Þ contribute to the fatigue damage…”

Coupled elastoplasticity and viscoplasticity under thermomechanical loading

“…The strain‐controlled spring‐slider model 15 is capable of modelling elastoplastic hardening solids and nonlinear kinematic hardening for isothermal or non‐isothermal cases. The model can be extended to the nonlinear Maxwell model by adding a nonlinear damper in series, as depicted in Fig.…”

“…Next, the abrupt move to point 3 makes it possible to gain the elastoplastic strain (thin solid line) from the known total strain (thick solid line) where ɛ vp ( t 1 ) = 0 if σ(0) = 0. Finally, stress σ( t i ) can be expressed in a form 15 for 0 ≤ t 1 ≤ t 2 ≤⋯≤ t i ≤⋯, where ɛ αj ( t i ) is the play operator with general initial value Presumably, there is no residual strain initially, so ɛ αj (0) = 0 and σ(0) = 0. The Prandtl densities α j ( T k ) in the range j = 0, …, n q and k = 0, …, n T are gained from the available cyclically stable cyclic stress–strain curves for , where σ −1 ( T k ) =σ 0 ( T k ) = 0.…”

“…The Prandtl densities α j ( T k ) in the range j = 0, …, n q and k = 0, …, n T are gained from the available cyclically stable cyclic stress–strain curves for , where σ −1 ( T k ) =σ 0 ( T k ) = 0. Fictive yield strains 15 q j are usually dispersed equidistantly with constant fictive yield strain class width Δ q between zero strain and the maximum expected strain (see Fig. 7).…”

“…The second use viscoplastic strain solely 16 . Although the unified framework has been developed extensively in the last two decades, 17,18 simpler solutions 10,13,14,15,19 have been searched for to reduce computational times and experimental demands.…”