A constitutive mathematical model has been developed that predicts the nonlinear thermomechanical behaviors of shape-memory alloys (SMAs) and of shape- memory-alloy hybrid composite (SMAHC) structures, which are composite-material structures that contain embedded SMA actuators. SMAHC structures have been investigated for their potential utility in a variety of applications in which there are requirements for static or dynamic control of the shapes of structures, control of the thermoelastic responses of structures, or control of noise and vibrations. The present model overcomes deficiencies of prior, overly simplistic or qualitative models that have proven ineffective or intractable for engineering of SMAHC structures. The model is sophisticated enough to capture the essential features of the mechanics of SMAHC structures yet simple enough to accommodate input from fundamental engineering measurements and is in a form that is amenable to implementation in general-purpose structural analysis environments.

SMAs exhibit thermoelastic martensitic transformations. The interaction of temperature and stress applied to an SMA can be used to exploit the shape-memory effect. An SMA can easily be deformed in the low-temperature (martensitic) state and, if not mechanically constrained or restrained, can be returned to its original shape and size by heating through its reverse-transformation temperature range; recovery in this mode is denoted free recovery. If recovery of the original size and shape is completely prevented by mechanical constraint, then the heating results in a large stress and the recovery is said to be constrained. If the SMA is neither completely free nor constrained but, instead, disposed to perform work by deforming under load, then the recovery is said to be restrained.

The model expresses the nonlinear thermoelastic nature of an SMA in the form of an effective coefficient of thermal expansion (CTE). This form enables representation of shape-memory behavior, on the basis of either (1) measurement of the effective CTE or (2) inference of thermal strain from measured values of the recovery stress and the modulus of elasticity. The model captures the thermoelastic nonlinearity of the SMA implicitly and provides a simple means of including nonlinear thermoelastic effects of a matrix material in an SMAHC structure. The model can predict constrained and free recovery implicitly and the combination of this model with a model of nonlinear elasticity can predict restrained recovery.

The constitutive equations for a given SMA, SMAHC, or a larger structure that incorporates an SMAHC as a substructure can be derived, using the present model as a basis, following a mechanics-of-materials approach or other suitable approach. The present constitutive model, in combination with classical lamination theory, has been incorporated into a finite-element mathematical model and computer code to enable modeling of static and dynamic responses of panel-type SMAHC structures subjected to static and dynamic thermal and mechanical loads. Loads that have been considered include acoustic pressures, acceleration forces, and concentrated forces. Phenomena that have been investigated include control of thermal buckling, thermal post-buckling, random vibration, and acoustic transmission/radiation responses of structures under constrained recovery. The constitutive model and structural response formulation have been validated against experimental measurements of thermal buckling/post-buckling and random vibration responses.

This work was done by Travis L. Turner of Langley Research Center. LAR-16274.


NASA Tech Briefs Magazine

This article first appeared in the February, 2004 issue of NASA Tech Briefs Magazine.

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