Pseudoelastic Hysteresis Loop Research Articles

Finite Strain Elastoplastic J<sub>2</sub>-Flow Model for Automatically, Accurately Simulating Pseudo-Elastic Effects of SMAs

Finite strain elastoplastic J2-flow equations are established toward the purpose of automatically, accurately simulating pseudo-elastic effects of SMAs. The uniaxial responses derived from these equations in each loading-unloading cycle exactly produce a closed stress-strain curve of any given shape. Then, any given test data for pseudo-elastic hysteresis loops of SMAs may be accurately fitted by means of a new technique for combining linear spline functions into a unified, smooth interpolating function, in a sense with no need to identify any unknown parameters.

An explicit simulation of arbitrarily-shaped pseudo-elastic hysteresis loops in shape-memory alloys

A new and explicit approach is proposed for accurately simulating pseudo-elastic hysteresis loops of any shape in shape-memory alloys (SMAs). For this purpose, new finite strain elastoplastic J2-flow equations are established for modeling finite strain behavior of SMAs. A stress-strain loop of any given shape in each uniaxial loading-unloading cycle is derived exactly from these equations. Then, a new technique is further introduced toward integrating usual piecewise linear splines into a single smooth interpolating function in a unified form. With the proposed equations and technique, test data for SMA hysteresis loops of any shape may be automatically fitted with high accuracy based on a single-parameter identification.

Modelling Bonded Shape Memory Alloy Vibration Attenuators Elements Using the Finite-Element Method

Shape memory alloys (SMAs) present the capability to develop large forces and displacements with low power consumption. Due their special characteristics, SMAs have been used in many different applications. Pseudoelastic hysteresis loop observed in austenitic SMAs is associated with energy dissipation. Therefore, pseudoelastic SMA elements can be used as vibration attenuators. Joining methods present some technological challenges for the use of these elements. Welding can strongly affect the properties of the alloy. Mechanical joints using rivets and screws are commonly used but promote stress concentration effects. The use of adhesives offers some benefits, being an alternative to be investigated. This work presents a numerical model based on the finite-element method and experimental procedures to study the behaviour of bonded vibration attenuators with SMA elements. The proposed model considers the pseudoelastic behaviour of SMA elements, and a cohesive zone model was used to study the union between absorber and an aluminium plate. Finally, several loading conditions were analysed with the proposed models to assess the capability of bonded pseudoelastic SMA elements to dissipate energy. The proposed geometry allows the elements to actuate as an efficient vibration attenuator, in particular when submitted to axial loading.

A time-domain modeling of systems containing viscoelastic materials and shape memory alloys as applied to the problem of vibration attenuation

It is widely known that traditional damping materials such as elastomers present a number of interesting characteristics when applied for vibration mitigation, such as inherent stability and good damping performance in relatively broad frequency bands, besides cost effectiveness. However, the behavior of those materials is highly dependent upon environmental and operational parameters such as excitation frequency and temperature. Another typical drawback is the added weight entailed by viscoelastic treatments. Especially regarding environmental influences, uncontrolled temperature variations and moisture can jeopardize the damping capacity and endurance of viscoelastic dampers. On the other hand, shape memory alloys present potential advantages in vibration damping due to their large pseudoelastic hysteresis loop in stress–strain relationship and can be used both as a damping material and structural elements in various engineering applications. Thus, it becomes apparent the convenience of combining both types of materials in such a way to explore the advantageous features of each of them. In this paper, a time-domain modeling procedure of structures containing both viscoelastic materials and shape memory alloys is addressed. The main goal is the development of a finite-element-based methodology intended to perform the analysis of engineering structures treated by passive constraining layer damping and pseudoelastic shape memory alloy wires for vibration mitigation. The viscoelastic behavior is modeled by using a four parameter fractional derivative model. To model the hysteresis response of the shape memory alloy, a phenomenological simplified model suitable for performing the parametric study of such dynamic system is used. After the discussion of various theoretical aspects, the time-domain responses are calculated for a three-layer sandwich beam containing viscoelastic materials and shape memory alloy wires and the main features of the modeling methodology are highlighted.

Pseudo-elastic hysteresis in shape memory alloys

Observations of pseudo-elastic hysteresis loops in the shape memory alloy CuAlNi are presented. Particular emphasis is laid on the interior of the overall loop and the phenomena of internal yield and recovery and internal loops are discussed. A thermodynamic argument is presented which may afford an interpretation of the observed phenomena in terms of interfacial energies.

Strain Self-Sensing Property and Strain Rate Dependent Constitutive Model of Austenitic Shape Memory Alloy: Experiment and Theory

By using both the pseudoelasticity and strain self-sensing ability of shape memory alloy (SMA) material, an innovative smart SMA-based damper can be developed. This damper has comprehensive energy dissipation and strain self-sensing abilities (i.e., electric resistance versus applied strain relationship) simultaneously. Before shaking table test on a building installed with such SMA-based dampers, the tests were conducted on the hysteresis stress–strain-electric resistance relationship of SMA wires (diameter 1.2mm). These tests were carried out under sinusoidal excitations with different loading frequencies at different ambient temperatures, to investigate the energy dissipation ability and strain self-sensing property of SMA wires. The sensitivity coefficient of electric resistance versus applied strain of the SMA wires was identified to be 5.948 from the test results, which is larger than that of the conventional strain gage and is independent of loading frequency. The experimental results indicate that the pseudoelastic hysteresis loops of the SMA wires are dependent on loading frequencies, particularly in the case of lower frequency. Further tests aimed at revealing the mechanism of the strain rate dependence of pseudoelasticity of SMA wire were conducted. The results indicate that the phase transformation temperature is dependent on strain rate, i.e., both the martensitic phase transformation finish temperature and the austenitic phase transformation start temperature decrease with increasing of strain rate. Based on the results of these tests, a one-dimensional strain rate dependent constitutive model of SMA wires was developed. This model predicts pseudoelastic behavior of SMA under various loading frequencies. Finally, a numerical simulation using the proposed model was performed, and the simulated pseudoelastic hysteresis loops agree well with test results presented not only by writers but also by other researchers.

Simulation of pseudoelastic behaviour of SMA under cyclic loading

A simple modification to an existing constitutive model for SMA materials is proposed to include the effects of loading frequency. The proposed model is based on the behaviour of experimental results of SMA wires subjected to cyclic strains. Numerical simulations based on the modified constitutive model show good qualitative agreement with experimental results. The influence of loading frequency, temperature, static strain offset and strain amplitude on pseudoelastic hysteresis loops and energy dissipation is studied. Dynamic response of a single degree of freedom system with an SMA element is examined by using the modified constitutive model and Newmark’s time integration method. Basic features of the displacement and SMA element stress time histories are studied. The frequency–response curve of a SDOF is investigated.

The use of shape memory alloys for passive structural damping

Experimental results on the dynamics of a beam constrained by shape memory wires are presented. It is observed that the damping increases significantly when the shape memory wires are stressed such that they lie within the pseudoelastic hysteresis loop. Theoretical models of the inner hysteresis loop are considered, and modal analysis is used to obtain the dynamic response of the system. Simulations of the system using these models give theoretical values of damping which agree well with those observed experimentally. The proposed models of the pseudoelastic hysteresis loop are adequate for providing an estimate of the initial increase of damping due to the use of prestressed shape memory wires in structures. These results demonstrate that pseudoelasticity of shape memory wires can be used to augment passive damping significantly in structural systems.

Pseudoelastic toughening of a shock-resistant composite with transformable reinforcement

A macromechanical approach and scientific principles of the construction of two-phase pseudoelastic composites with pseudoelastic hardening are formulated in the present work for the first time in the case where SMA particles are coherently embedded in the elastic matrix. It is shown that a pseudoelastic hysteresis loop may appear in the macroscopic load-unload cycle as a consequence of microstresses caused by direct and inverse martensite transformations in the SMA particles. We also analyze the process of hardening of the new structure and deduce a theoretical formula for estimation of the crack-growth resistance of pseudoelastic materials.

Experimentelle und theoretische Untersuchungen des Last - Verformung-Verhaltens von CuZnAl- und CuAlNi-Einkristallen

When a stress is applied to a shape memory alloy in the martensitic state, the deformation proceeds by the movement of intervariant boundary, while the deformation at higher temperature is caused by the stress-induced martensitic transformation. The load deformation behaviour is investigated at different temperatures. Comparing the results with the Landau-Devonshire model we find that the pseudoelastic hysteresis loops are not in agreement with this model. The thermodynamic analysis shows that the size of the hysteresis loops is determined by a coherence energy which is measured in CuZnAl and CuAlNi singlecrystals. This energy is a material constant and independent of temperature

The Interior of the Pseudoelastic Hysteresis

AbstractAn interesting problem within the research on shape memory is provided by the investigation of the pseudo-elastic hysteresis loop that accompanies the strain-induced austenitic-martensitic phase transition. Miller [1] suggested by thermodynamic arguments that the size of that loop should be related to the coherency energy at interfaces between martensite and austenite. That proposition received a boost when Müller & Xu [2] showed that the same thermodynamic arguments predicted the onset of internal yield and recovery inside the hysteresis loop on a well-definqd line of unstable phase equilibrium. Recently Fu, Müller and Xu [3] have reported results with improved specimens and methods of observation that may help to understand the nature of metastability inside the hysteresis loop.