PSI - Issue 14

Nikolay A.Makhutov et al. / Procedia Structural Integrity 14 (2019) 199–206 N.Makhutov et al./Procedia Structural Integrity 00 (2018) 000 – 000

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key problems in ensuring structural integrity and safety. Such assessment should be carried out not only for the cases of normal loading regimes that cause elastic ( ε < ε Y ) and limited elasto-plastic ( ε < ε lp = 5ε Y ) response of the material in the notch zone (regions I and II of the stress-strain curve, fig.1), but also for the cases of extreme loading that causes extensive plastic strains and general yielding of the cross section (region III fig.1 when maximum local strains tend to fracture values that can reach up to ε f ~50  70% or 20 ε Y ). This will allow one to estimate residual strength and remaining lifetime of highly damaged structures.

Nomenclature E - elasticity modulus E S - secant modulus at the notch root F – correction function in generalized Neuber rule

K ε – strain concentration factor K σ – stress concentration factor K t – theoretical (elastic) stress concentration factor m – strain hardening exponent W n - energy density due to nominal stress and strain W ε strain energy orm at the notch root ε f – fracture strain ε lp – limited plastic strain ε n – nominal strain ε max k - maxim local strain at the notch root ε e-f -pseudoelastic (fictitious) strains at the notch root ε p -f - pseudoplastic (fictitious plastic) strains at the notch root ε Y – yield strain

σ max k - maxim local stress at the notch root (maximum notch stress) σ e -f - pseudoelastic (fictitious elastic) stresses at the notch root σ p -f - pseudoplastic (fictitious plastic) stresses at the notch root σ n – nominal stress σ n norm - nominal stress due to normal loading σ n extr -nominal stress due to extreme loading σ Y – yield stress Φ – transformation that maps pseudoelastic or pseudoplastic states to actual stress-strain states at the notch zone The accumulation of strain in post-yielding situation is a complicated task. Closed form solutions are only available for a relatively small number of specific cases. Three types of approaches are used in notch mechanics: experimental strain measurements, numerical simulations (FEM), and approximate analytical methods also known as stress-strain conversion rules. Neuber rule is a widely used as an approximate analytical method for estimation of the stress-strain behavior of notched components upon local yielding occurs (Neuber,1961). This method tends to overestimate local strains, but proved to be useful in predicting maximum local strains and stresses in case of limited plasticity when the extent of the plastic zone around the notch tip is small in comparison with the elastic area surrounding the plastic zone (about 0.1 - 0.2 of the elastic area width surrounding the notch tip). However, the accuracy of the method drops considerably when extensive plastic strains develop. The paper describes a modification of the Neuber rule that allows one to assess elasto-plastic material response at the notch root to extreme loading regimes when maximum notch strains are close to fracture strain values and general yielding over the entire cross section occurs (Makhutov, 1981; Makhutov, 2008). Φ N – Neuber transformation Φ M – Makhutov transformation