Probabilistic relationships between strain range, stress range and loading cycles. Application on ASTM A969 steel

Abstract

Fatigue life estimations can be made by considering the -N or -N curves. Reliable estimations allow engineers designing save stress levels in structures or machines. In this paper, the Weibull distribution is combined with the Stüssi function to model the quantiles of the -N and -N curves and the Ramberg-Osgood relationship. The nonlinear Stüssi function offers a good geometric approach to model the relationship -N or -N and the Weibull distribution is the most adequate to handle lifetime magnitudes as load cycles N. To show the application of the proposed model, simulated and experimental data of ASTM A969 steel are evaluated.

Low cost estimation of Wöhler and Goodman–Haigh curves of Ti‐6Al‐4V samples by considering the stress ratio effect

“…The modified Stüssi function proposed by Toasa Caiza and Ummenhofer in 32 will be considered in order to model the Wöhler curves. This function is given by where stress range during the fatigue test number of load cycles up to failure or up to end of the test ultimate tensile strength fatigue or endurance limit corresponding to the stress ratio R . geometrical parameters stress ratio Stüssi function. …”

“…In this case, together with the Ramberg–Osgood relationship allow to model curves of the type Δ ϵ − N , see. 32 …”

“…The modified Stüssi function proposed by Toasa Caiza and Ummenhofer in 32 will be considered in order to model the Wöhler curves. This function is given by…”

“…If the goal is estimating in ULCF or LCF regimes, where the plastic behavior prevails, a better accuracy in the estimation can be achieved by considering the strain. 32 Assuming that the fatigue endurance Δσ ∞ is known, may be controversial, but it can be estimated by applying the Weibull model proposed by Castillo and Fernandez-Canteli. 25 Nevertheless, the existence of the fatigue limit is still an open debate.…”

“…However, since the fatigue strength estimation based on the stress is relevant in HCF and VHCF regimes, this assumption does not harm the goal of this work. If the goal is estimating in ULCF or LCF regimes, where the plastic behavior prevails, a better accuracy in the estimation can be achieved by considering the strain 32 . Assuming that the fatigue endurance Δ σ ∞ is known, may be controversial, but it can be estimated by applying the Weibull model proposed by Castillo and Fernandez‐Canteli 25 .…”