Ziad Moumni

Fatigue analysis of shape memory alloys: energy approach

The purpose of this paper is to define a low cycle fatigue criterion for NiTi shape memory alloys (SMAs) in order to perform numerical calculations necessary for designing structures made of SMA and subjected to cyclic loading. For this purpose, fatigue tests are performed in a temperature and deformation regime in which the alloy exhibits pseudoelasticity. A behavior similar to plastic shakedown is observed; during the first cycles a hysteresis loop with a varying size which eventually stabilizes is obtained. Therefore, by analogy with plastic fatigue (low cycle fatigue), it is shown that the dissipated energy of the stabilized cycle is a relevant parameter for the estimation of lifetime.

Non-linear dynamic thermomechanical behaviour of shape memory alloys

The non-linear dynamic thermomechanical behaviour of superelastic shape memory alloys is investigated. To this end, the Zaki–Moumni model, initially developed for quasi-static loading cases, is extended to simulate the uniaxial forced oscillations of a shape memory alloy device. First, the influence of loading rate is accounted for by considering the thermomechanical coupling in the behaviour of NiTi shape memory alloy. Comparisons between simulations and experimental results show good agreement. Then, the forced response of a shape memory alloy device is investigated at resonance. Both isothermal and non-isothermal conditions are studied, as well as non-symmetric tensile-compressive restoring force. In the case of large values of forcing amplitudes, simulation results show that the dynamic response is prone to jumps, bifurcations and chaotic solutions.

Modeling Tensile-Compressive Asymmetry for Superelastic Shape Memory Alloys.

In this article, the Zaki-Moumni (ZM) model for shape memory alloys is extended to account for tensile-compressive asymmetry over a wide temperature range. To this avail, a mathematical framework recently developed by Raniecki and Mróz is utilized to define new yield functions that are sign-sensitive. With respect to the original ZM model, the modifications are essentially made to the expressions of the Helmholtz free energy and of the internal constraints. The model is shown to properly simulate the asymmetric behavior of shape memory alloys both for martensite orientation and pseudoelasticity.

Direct Numerical Determination of the Asymptotic Cyclic Behavior of Pseudoelastic Shape Memory Structures

The design of shape memory alloys (SMAs) structures against fatigue requires the computation of the stabilized mechanical state. The classical computation method, based on a plasticity-like algorithm, requires a step-by-step calculation, leading to prohibitive computation time to reach this stabilized state. To overcome this issue, we propose to extend the direct cyclic method (DCM), for elastoplastic structures, for use with the Zaki-Moumni (ZM) model for SMAs. DCM is a large time increment method in which a periodicity condition is enforced on the state variables. Comparison with the classical incremental approach shows considerable reduction in computation time.

Two-dimensional analysis to improve the output stress in ferromagnetic shape memory alloys

Most existing experiments investigating the martensite-variants reorientation (switching) of ferromagnetic shape memory alloys (FSMA) are in a simple 1D condition: An axial compressive stress and a transverse magnetic field. To obtain field-induced variant switching, however, the compressive stress (output stress) is limited by a small blocking stress (<10 MPa, mainly governed by the materials’ magnetic anisotropic energy). In this paper, to overcome the stress limit, we suggest using the materials in two-dimensional (2D) configurations: Two (axial and transverse) compressive stresses and a magnetic field. Based on a 2D magneto-mechanical energy analysis, it is found that only the difference between the two stresses is limited; each of the two stresses can be larger than the blocking stress. The energy analysis is also incorporated into the field-stress phase diagrams (including hysteretic effect) to study the variant switching in different loading paths: rotating/non-rotating field-induced strain and fie...

Reversible-strain criteria of ferromagnetic shape memory alloys under cyclic 3D magneto-mechanical loadings

Recent researches revealed that ferromagnetic shape memory alloys (FSMA) in 2D/3D configurations (with multi-axial stresses) had much more advantages (e.g., higher working stress and more application flexibility) than that in 1D configuration (with uniaxial stress). In literature, however, there is no simple criterion to judge whether a cyclic 3D magneto-mechanical loading can induce a large reversible strain (via martensite reorientation in FSMA). In this paper, a 3D magneto-mechanical energy analysis is proposed and incorporated into a phase diagram in terms of deviatoric stresses (including mechanical and magneto-stresses) to study the path-dependent (hysteretic) martensite reorientation in FSMA under 3D cyclic loadings. Based on the phase diagram (a plane graph), general criteria for obtaining reversible strain under cyclic magneto-mechanical loadings are derived, which provide basic guidelines for FSMA’s applications under multi-axial loadings. Particularly for FSMA actuators driven by cyclic magneti...

Energy-based fatigue model for shape memory alloys including thermomechanical coupling

This paper is aimed at developing a low cycle fatigue criterion for pseudoelastic shape memory alloys to take into account thermomechanical coupling. To this end, fatigue tests are carried out at different loading rates under strain control at room temperature using NiTi wires. Temperature distribution on the specimen is measured using a high speed thermal camera. Specimens are tested to failure and fatigue lifetimes of specimens are measured. Test results show that the fatigue lifetime is greatly influenced by the loading rate: as the strain rate increases, the fatigue lifetime decreases. Furthermore, it is shown that the fatigue cracks initiate when the stored energy inside the material reaches a critical value. An energy-based fatigue criterion is thus proposed as a function of the irreversible hysteresis energy of the stabilized cycle and the loading rate. Fatigue life is calculated using the proposed model. The experimental and computational results compare well.

Shakedown based model for high-cycle fatigue of shape memory alloys

The paper presents a high-cycle fatigue criterion for shape memory alloys (SMAs) based on shakedown analysis. The analysis accounts for phase transformation as well as reorientation of martensite variants as possible sources of fatigue damage. In the case of high-cycle fatigue, once the structure has reached an asymptotic state, damage is assumed to become confined at the mesoscopic scale, or the scale of the grain, with no discernable inelasticity at the macroscopic scale. Using a multiscale approach, a high-cycle fatigue criterion analogous to the Dang Van model (Dang Van 1973) for elastoplastic metals is derived for SMAs obeying the Zaki–Moumni model for SMAs (Zaki and Moumni 2007a). For these alloys, a safe domain is established in stress deviator space, consisting of a hypercylinder with axis parallel to the direction of martensite orientation at the mesoscopic scale. Safety with regard to high-cycle fatigue, upon elastic shakedown, is conditioned by the persistence of the macroscopic stress path at every material point within the hypercylinder, whose size depends on the volume fraction of martensite. The proposed criterion computes a fatigue factor at each material point, indicating its degree of safeness with respect to high cycle fatigue.

A simple 1D model with thermomechanical coupling for superelastic SMAs

This paper presents an outline for a new uniaxial model for shape memory alloys that accounts for thermomechanical coupling. The coupling provides an explanation of the dependence of SMA behavior on the loading rate. 1D simulations are carried in Matlab using simple finite-difference discretization of the mechanical and thermal equations.

Energy Dissipation of Martensite Reorientation in NiMnGa Single Crystals under Biaxial Compression

Experiments of biaxial compression were conducted to study the energy dissipation (stress-hysteresis) of martensite reorientation in NiMnGa single crystals. From the experiments, the observed stress-hysteresis consists of two parts ― the material intrinsic friction due to martensite reorientation, and the external friction between the loading clampers and the sample surfaces. It is found that the former one is independent of the 2D stress state while the latter one strongly depends on the 2D stress levels. Both kinds of friction are important and need to be considered in real applications.