Tarak Ben Zineb

Constitutive Law for Ferroelastic and Ferroelectric Piezoceramics

The focus of this paper is to investigate the nonlinear behavior exhibited by ferroelectric and ferroelastic ceramics under high electromechanical loading. External loads, such as electric field and stress, can induce a remanent strain or polarization due to domain switching. Two internal variables are introduced in order to capture the history dependance and dissipation that characterize ferroelectricity and ferroelasticity. Two loading surfaces are introduced so that associated flow rules provide the evolution laws of the internal variables. In addition, these variables must verify kinematical constraints that may depend on the stress state since experiments indicate that tensile and compressive states have to be considered in this order. Then, dielectric, butterfly, and ferroelastic hysteresis are represented. Mechanical depolarization is also captured. All the tangent operators are expressed so that a resolution with a finite element method can be achieved.

Effect of Hydrogen on the Tensile Strength of Aged Ni–Ti Superelastic Alloy

Because of its good corrosion resistance and biocompatibility, superelastic Ni–Ti wire alloys have been successfully used in orthodontic clinics. However, delayed fracture in the oral cavity has been observed. The susceptibility of a Ni–Ti shape-memory alloy toward hydrogen embrittlement has been examined with respect to the current densities and aging in air at room temperature. Orthodontic wires have been cathodically hydrogen charged using a different current density of 5, 10, and 20 A/m2 from 2 to 24 h in 0.9% NaCl aqueous solution at room temperature. The critical stress for the martensite transformation under a monotonous tensile test has been 20–90 MPa higher than that without hydrogen charging. In addition, embrittlement takes place in the austenite–martensite transformation plateau. For a short period of charging, the Ni–Ti alloy conserves its superelastic behavior. However, after 24 h of aging in air at room temperature, fracture at the austenite–martensite transformation plateau takes place earlier.

Finite Element analysis of a shape memory alloy actuator for a micropump

Abstract This paper deals with a Finite Element (FE) behavior analysis of a shape memory alloy actuator for a micropump. It is composed of two membranes of NiTi shape memory alloy (SMA) in a martensitic state at room temperature. They have an initial flat shape and are bonded together with an intermediate spacer. The thermal loading allows the actuator to move up and down in the membrane normal direction. A detailed analysis of sensibility to material and geometric parameters of the SMA actuator is undertaken by FE method. The actuation capability and reliability are studied in order to lead to optimal parameters set providing a higher stroke (deflection) with a low heating temperature. The shape memory effect exhibited by these membranes is simulated by means of the phenomenological constitutive law based on Chemisky–Duval model [1] , [2] , and implemented in the Abaqus® FE code. The obtained numerical results were detailed proving the ability of the proposed modeling to reproduce the actuator behavior under thermal loading. This analysis showed that it is possible to provide a large stroke for a minimal geometry of the actuator.

Hydrogen effect on the austenite–martensite transformation of the cycled Ni-Ti alloy

Because of its biocompatibility, superelastic Ni-Ti wire alloys have been successfully used in orthodontic clinics. The susceptibility of Ni-Ti shape memory alloys toward hydrogen embrittlement has been examined with respect to the residual stress after a few number of cycles in air at room temperature. Orthodontic wires have been cycled until having an imposed deformation of 2.1%, 4%, and 7.7% between 1 and 50 cycles and then have cathodically been charged by hydrogen with a current density of 10 A/m2 for 4 h in a 0.9% NaCl aqueous solution at room temperature. Throughout cycling, a residual strain has been formed and has increased by the number of cycles and the value of the imposed deformation. After hydrogen charging, the critical stress enhances when the number of cycles is great and the value of the imposed deformation is high. In addition, an embrittlement occurs for the specimen submitted to 50 and 30 cycles with an imposed strain of 2.1% and 4%, respectively. Nevertheless, no embrittlement has been detected after 50 cycles until 7.7% of the imposed deformation. The results of this study imply that the embrittlement could be related to the discontinuity in the distribution of defects created by partial superelastic cycling.

A constitutive model for Fe-based shape memory alloy considering martensitic transformation and plastic sliding coupling: Application to a finite element structural analysis

In this article, we propose a finite element numerical tool adapted to a Fe-based shape memory alloy structural analysis, based on a developed constitutive model that describes the effect of phase transformation, plastic sliding, and their interactions on the thermomechanical behavior. This model was derived from an assumed expression of the Gibbs free energy taking into account nonlinear interaction quantities related to inter- and intragranular incompatibilities as well as mechanical and chemical quantities. Two scalar internal variables were considered to describe the phase transformation and plastic sliding effects. The hysteretic and specific behavior patterns of Fe-based shape memory alloy during reverse transformation were studied by assuming a dissipation expression. The proposed model effectively describes the complex thermomechanical loading paths. The numerical tool derived from the implicit resolution of the nonlinear partial derivative constitutive equations was implemented into the Abaqus® finite element code via the User MATerial (UMAT) subroutine. After tests to verify the model for homogeneous and heterogeneous thermomechanical loadings, an example of Fe-based shape memory alloy application was studied, which corresponds to a tightening system made up of fishplates for crane rails. The results we obtained were compared to experimental ones.

An original pure bending device with large displacements and rotations for static and fatigue tests of composite structures

As composite structures, flexible structures have, for pure bending loading, significant displacements and rotations. The design and the dimensioning of these structures require good material characterization beyond the small deformations domain. This paper thus proposes a new original device making pure bending loading possible in large transformations. The sample is embedded at each end using a sleeve with a rigid body movement. The applied bending moment is perfectly controlled during the loading. A behavior model of the bench based on the beam theory for large transformations is developed, making it possible to dimension and design this bench. An experimental campaign using glass/epoxy composite samples has validated this new device in static and fatigue states. This device was used for identification of a fatigue model dedicated to flexible composite structures.

A FSDT–MITC Piezoelectric Shell Finite Element with Ferroelectric Non-linearity

A shell finite element based on the Reissner/Mindlin first-order shear deformation theory and integrating a bi-dimensional phenomenological ferroelectric constitutive law for domain switching effects is proposed. An electric switching function is considered to indicate the onset of domain switching. Only one internal variable (the remanent polarization) is used in the model. An implicit integration technique based on the return-mapping algorithm is adopted. The shell element is implemented into the commercial finite element code Abaqus ® via the subroutine user element. Some linear (piezoelectric) and non-linear (ferroelectric) tests are considered to validate first, the element formulation and second, the implementation of the bi-dimensional ferroelectric model. It is shown by studying a complex example (the spiral actuator) that the Reissner/Mindlin kinematic hypothesis (no variation of the displacement across the thickness or no thickness variation) is not sufficient for some electromechanical applications for which the d33 effect is of major importance.

Numerical tool for SMA material simulation: application to composite structure design

Composite materials based on shape memory alloys (SMA) have received growing attention over these last few years. In this paper, two particular morphologies of composites are studied. The first one is an SMA/elastomer composite in which a snake-like wire NiTi SMA is embedded into an elastomer ribbon. The second one is a commercial Ni47Ti44Nb9 which presents elastic–plastic inclusions in an NiTi SMA matrix. In both cases, the design of such composites required the development of an SMA design tool, based on a macroscopic 3D constitutive law for NiTi alloys. Two different strategies are then applied to compute these composite behaviors. For the SMA/elastomer composite, the macroscopic behavior law is implemented in commercial FEM software, and for the Ni47Ti44Nb9 a scale transition approach based on the Mori–Tanaka scheme is developed. In both cases, simulations are compared to experimental data.

Contribution of industrial composite parts to fatigue behaviour simulation

The dimensioning of composite structures presents the problem of behaviour modelling. This problem comes not only from the specific nature of the involved materials, but also from the reproducibility of the process both on the series scale as well as on the specimen characterisation level, which enables determination of the modelling parameters. In the case of static dimensioning with or without damage, the reproducibility of the mechanical parameters is satisfactory overall, regardless of the implemented experimental procedure. In fatigue dimensioning, the two aspects; process influence and procedure of identification play a major role in the application of the lifetime predictive models. This research has, as a medium-term objective, to partially answer the problems raised previously. The damage model used is based on generalised standard material thermodynamics. This model, coupled with the finite element method, allows simulation of the fatigue behaviour of composite parts.

Numerical study of the influence of material parameters on the mechanical behaviour of a rehabilitated edentulous mandible.

OBJECTIVES The study dealt with full dental prosthetic reconstruction on four implants. The aim was to analyse the influence of material parameters on the mechanical behaviour of the restored mandible compared to the natural mandible. METHODS A finite element model of an edentulous mandible with prosthetic rehabilitation was established. Four materials were investigated for the framework of the prosthesis (zirconia, titanium, gold and nickel-titanium (NiTi)), as well as three cortical bone thicknesses. Various muscles were employed to simulate the main stages of mastication. Three distinct phases of mastication were modelled: maximum intercuspation, incisal clench and unilateral molar clench. RESULTS The zirconia framework demonstrated the highest stresses and NiTi the weakest. The highest stresses in the framework were obtained during maximum intercuspation. The highest stresses at the bone-implant interface were recorded on the working axial implant during unilateral molar clench and on tilted implants during maximum intercuspation. The influence of the frameworks material stiffness on the stresses at the bone-implant interface was insignificant for axial implants (except the right implant during unilateral molar clench) and slightly more significant for tilted implants. Mandibular flexion decreased with an increase of the cortical bone thickness and the stiffness of the prosthetic frameworks material. CONCLUSIONS Among all materials, NiTi allowed a better preservation of the mandibular flexure, during all the mastication stages. Compared to stiffer materials, NiTi also permitted physiological mechanical conditions at the bone/implant interface, in almost all mastication stages.