Vincent Legrand

Direct numerical determination of stabilized dissipated energy of shape memory alloys under cyclic tensile loadings

When shape memory alloys are subjected to cyclic loadings, the stabilized dissipated energy is an effective parameter in studying their performance, for instance, the fatigue life. However, thermomechanical coupling in the behavior of shape memory alloys under cyclic loadings causes the amount of stabilized dissipated energy to be obtainable once the responses of all transient cycles are determined. In this article, direct formulae are proposed to numerically evaluate stabilized dissipated energy of a shape memory alloy under cyclic tensile loadings as a function of maximum and minimum applied stresses as well as the loading frequency. A one-dimensional fully coupled thermomechanical constitutive model with a cycle-dependent phase diagram is utilized to be able to directly predict the uniaxial stress–strain response of a shape memory alloy in a specified cycle with no need of solving the previous cycles. The results are experimentally assessed for NiTi and CuAlBe specimens. Since the backward transformation in CuAlBe is realized to more gradually occur than that in NiTi, an enhanced phase diagram is proposed in which different slopes are considered for the start and finish of backward transformation strip. The numerical predictions of the present approach are shown to be in a good agreement with the experimental findings for cyclic tensile loadings.

A comprehensive energy approach to predict fatigue life in CuAlBe shape memory alloy

Stabilized dissipated energy is an effective parameter on the fatigue life of shape memory alloys (SMAs). In this study, a formula is proposed to directly evaluate the stabilized dissipated energy for different values of the maximum and minimum applied stresses, as well as the loading frequency, under cyclic tensile loadings. To this aim, a one-dimensional fully coupled thermomechanical constitutive model and a cycle-dependent phase diagram are employed to predict the uniaxial stress-strain response of an SMA in a specified cycle, including the stabilized one, with no need of obtaining the responses of the previous cycles. An enhanced phase diagram in which different slopes are defined for the start and finish of a backward transformation strip is also proposed to enable the capture of gradual transformations in a CuAlBe shape memory alloy. It is shown that the present approach is capable of reproducing the experimental responses of CuAlBe specimens under cyclic tensile loadings. An explicit formula is further presented to predict the fatigue life of CuAlBe as a function of the maximum and minimum applied stresses as well as the loading frequency. Fatigue tests are also carried out, and this formula is verified against the empirically predicted number of cycles for failure.

Mechanical Behavior of a NiTi Endodontic File During Insertion in an Anatomic Root Canal Using Numerical Simulations

Abstract Superelastic NiTi shape memory alloys (SMA) have biomedical applications including rotary endodontic files. These alloys are used thanks to their flexibility, which is due to solid-solid martensitic transformation. Unfortunately, the intracanal file separation can occur during canal preparation. To avoid this problem and to have a good idea of the mechanical behavior of these instruments, finite elements simulations taking into account the real shape of root canals are proposed in this study. This is possible by using a well-adapted model describing all the particularities of SMA and representative limit conditions. The behavior model has been validated in previous studies under complex loadings. It is implemented in ABAQUS® finite elements software. The anatomic shapes of root canals are extracted by microtomography using a real tooth. They are applied as limit conditions in realized simulations to be as near as possible to clinical conditions. The mechanical behavior of an endodontic file is then simulated during insertion in a root canal without and with rotation. This permits to obtain different information like the loading applied to the instrument during its use, the stress, and the phase transformation fields through the file. This is useful not only for clinical use but also for new NiTi endodontic instruments design.

Rotary bending fatigue analysis of shape memory alloys

In this work, a one-dimensional constitutive model is used to study rotary bending fatigue in shape memory alloy beams. The stress and strain distributions in a beam section are driven numerically for both pure bending and rotary bending to show the basic differences between these two loading types. In order to verify the numerical results, experiments are performed on NiTi specimens with an imposed bending angle using a bending apparatus. Since the specimens show significant stress plateau for forward and backward transformation in their stress–strain response, an enhanced stress–temperature phase diagram is proposed in which different slopes are considered for the start and finish of each transformation strip. In order to study low cycle fatigue of shape memory alloys during rotary bending, the stabilized dissipated energy is calculated from numerical solution. A power law for variations of the fatigue life with the stabilized dissipated energy is obtained for the studied specimens to predict their fatigue life. The numerical predictions of the present approach are shown to be in a good agreement with the experimental findings for rotary bending fatigue. Uniaxial tensile fatigue tests are further performed on the studied specimens to investigate effect of loading type on the fatigue lifetime.

Mechanical Behavior Study of NiTi Endodontic Files Taking into Account Anatomic Shape of Root Canals

Superelastic NiTi SMA is the base of endodontic files. The flexibility of these instruments permits the preparation of root canals. Unfortunately the intracanal file separation can occur. To have a good idea of the mechanical behavior of these instruments, we propose in this study the finite elements simulations taking into account the real shape of root canals. This has been possible by using a well adapted model describing all the particularities of superelastic SMA and by using representative limit conditions.