A one-dimensional constitutive model for the thermomechanical behavior of shape memory alloys is developed based on previous work by Liang and Tanaka. An internal variable ap proach is used to derive a comprehensive constitutive law for shape memory alloy materials from first principles without the assumption of constant material functions. This constitutive law is of such a form that it is well suited to further practical engineering applications and calculations. A separation of the martensite fraction internal variable into temperature-induced and stress- induced parts is presented and justified, which then allows the derived constitutive law to accurately represent both the pseudoelastic and shape memory effects at all temperatures. Several numerical ex amples are given that illustrate the ability of the constitutive law to capture the unique thermome chanical behavior of shape memory alloys due to their internal phase transformations with stress and temperature.
Here we will present a simplification of the form of one popular shape memory alloy (SMA) constitutive model. This simplification allows a more compact written form and hence easier calculations with the one-dimensional SMA constitutive law first developed by Tanaka, later modified by Liang and Rogers, and again by Brinson. In addition, a new derivation of the model will be given based on micromechanics. In this context, comparisons between the Tanaka and two other models will be presented and implications discussed. It will be shown that the constitutive models are in fact quite similar, and that the important distinction between these SMA models is primarily in the formulation of the transformation kinetics. Several examples will be presented utilizing the models.
In this paper, a macro-scale, phenomenological constitutive model for shape memory alloys is used in conjunction with energy balance equations to study the evolution of temperature and deformation profiles seen in SMA wires under specific thermal and mechanical boundary conditions. The general, fully coupled thermo-mechanical problem is formulated and analytical solutions are determined for the decoupled case and limit cases. Results for two specific initial/boundarv value problems are presented here: 1) resistive heating of an SMA wire-initial detwinned martensite leads to strain recovery (contraction) on heating; 2) deformation wave in a semiinfinite, initially austenitic SMA wire cooled at the boundary-deformation zone propagates and expands as the wire transforms to martensite (expansion). In both cases, the region and extent of transformation is identified, indicating the magnitude of actuation obtained. Implications of the modeling for the active control of structures are discussed.
In this paper the active control of beam deflection through heating and cooling of Shape Memory Alloy (SMA) wires is examined. A phenomenological constitutive law for SMA wires is coupled with beam theory to provide predictions of beam shape upon temperature change in the SMA actuator. Both the linear and nonlinear beam theory are presented, enabling calculation of large deflections. Examples for a single wire attached at the tip of a uniform beam are given, but the procedure can easily be generalized for other configurations and utilized in control algorithms. Issues of design constraints for shape control with shape memory wires are addressed and the model is qualitatively verified by experiments.
To help address the lack of engineering data on the time-dependent behavior of advanced polymeric composites, a combined experimental and analytical research program was initiated to investigate the similarities and differences of the effects of physical aging on creep compliance of IM7/K3B composite loaded in tension and compression. Recently developed novel experimental apparatus and methods were employed to test two matrix dominated loading modes, shear and transverse, for two load cases, tension and compression. The tests, run over a range of sub-glass transition temperatures, provided material constants, material master curves and aging related parameters. Assessment of these new results indicated that although trends in the data with respect to aging time and aging temperature are similar, differences exist due to load direction and mode. An analytical model proposed previously by the authors for tension loading was used for predicting long-term tension and compression behavior using short-term data as input. These new studies indicated that the model worked equally as well for the tension or compression loaded cases. Comparison of the loading modes indicated that the predictive model provided more accurate long-term predictions for the shear mode as compared to the transverse mode. Parametric studies showed the usefulness of the predictive model as a tool for investigating long-term performance and compliance acceleration due to temperature.
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