Research ArticleNo Access

Finite element analysis on the effect of martensitic transformation and plastic deformation on the stress concentration factor in a thin notched superelastic NiTi ribbon

Pejman Shayanfard

http://orcid.org/0000-0001-7847-0369

Institute of Physics of the Academy of Sciences, Na Slovance 2, Prague 18221, Czech Republic

Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, CZ-61669 Brno, Czech Republic

E-mail Address: [email protected]

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Petr Šittner

Institute of Physics of the Academy of Sciences, Na Slovance 2, Prague 18221, Czech Republic

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Luděk Heller

Institute of Physics of the Academy of Sciences, Na Slovance 2, Prague 18221, Czech Republic

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, and

Pavel Šandera

Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, CZ-61669 Brno, Czech Republic

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https://doi.org/10.1142/S1793604720510285Cited by:2 (Source: Crossref)

Abstract

The severe nonlinear behavior caused by the martensitic transformation (MT) and subsequent plastic deformation (PD) of detwinned martensite leads to a complex local stress redistribution at the location of stress risers of superelastic shape memory alloy (SMA) components. Nevertheless, in the literature, the simple linear elastic fracture mechanics (LEFM) equations are widely used in the evaluation of the fracture response of superelastic components which has resulted in obvious conflicts between the conclusions regarding the effect of MT on the fracture parameters, i.e. stress intensity factor (SIF) and material toughness. Furthermore, the linear elasticity method is frequently used in the literature to calculate the stress intensity range ( $Δ K$ ) when the fatigue crack growth rate dependence on $Δ K$ ( $d a ∕ d N - Δ K$ ) is being evaluated. Moreover, the PD followed by MT is poorly considered in the fracture mechanics of SMAs. This paper presents a numerical investigation on the role of both MT and PD, as well as the notch acuity, on the evolution of notch-tip stresses and strains and stress concentration factor ( $K_{tn}$ ) upon the incremental application of the macroscopic tensile load on a thin NiTi notched superelastic ribbon, to mimic the effects of MT and PD on the SIF of superelastic parts. It is revealed that MT results in drastic deviations of the notch-tip stress, as well as the stress concentration factor ( $K_{tn}$ ), from that obtained in LEFM. Due to the heterogeneous evolution of MT, the trend of the deviations is not regular and unique upon monotonic external loading. Accordingly, the results represent the ineffectiveness of the LEFM method in the evolution of the stress concentration factor (hence, the SIF) and toughness in monotonic loading, as well as the stress intensity range ( $Δ K$ ) under fatigue loading in SMA components.

Keywords:

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