PSI - Issue 47

Stefano Rodinò et al. / Procedia Structural Integrity 47 (2023) 579–588 Carmine Maletta / Structural Integrity Procedia 00 (2018) 000–000

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TMf) and the austenite start and finish temperatures (TAs and TAf). In the past decade, SMAs became subject of considerable interest, both in scientific and commercial field. A large number of products based on these materials began to be used in sectors like automotive and aerospace [4 - 9], robotics [10 - 13] and structures [14 - 17], in addition also biomedical [18 - 21] applications are becoming more and more relevant. Beyond these considerations, SMAs are becoming more and more interesting as a functional material in active composites design. These classes of composite are suitable for light-weight applications and the shape morphing effect is ensured without the presence of moving parts, this allows to increase the reliability and to lower system maintenance costs. To develop active composites materials one can choose two different strategies. One of these consist in to directly embedding SMA wires into composite structures [22 - 27], by providing enough eccentricity from the neutral axis of the latter is possible to generate a bending moment that can perform a substantial deflection. Another common approached is an hybrid solution, that consists in non-embedding the SMA wire directly into composite structures [28 - 32], but out of it, by providing an appropriate distance from the outer surface. In the second approach, the adhesion between the composite structure and the SMA wires is not a requirement. During the design process for such active composites some important parameters of SMA actuators have to be investigated, such as maximum recoverable strain, wire diameter, stiffness and bandwidth and actuation capability. A critical point is also to provide a strong interfacial strength among the SMA actuators and the composite structure [33 - 34], several studies have been carried out and a reduction of the adhesion strength during the actuation was measured. Indeed, if the adhesion strength is not enough, during the actuation the load transfer among SMA actuator and composite structures won’t be efficient and will lead a low bending capability. Furthermore, adhesion strength must be strong enough to not be heat damaged, this can then have an impact on the wire's capability to act in succeeding cycles [35]. In this work, an appropriate analytical model was designed, with the aim to evaluate the bending of an active composite beam reinforced with SMA wires and activated by a thermal load. In the first section, the analytical model is explained in terms of thermo-mechanical implementation, by using an appropriate non-linear SMA model, following with the MatLab implementation. The discussion will follow with the comparison of the analytical model results against the results obtained from several FE simulations. Finally, some experimental validation will be discussed, by comparing the results measured on a 3D-printed prototype activation of the active composite designed in the previous phases, this will lead to final validation of the analytical model proposed. 2. Analytical model 2.1. SMA constitutive model The Brinson’s constitutive relation [36] is used to model the SMA behaviour: � � � � � � � Θ� �� � � � � (1) here � and � are the stress and strain in the active SMA layer, � is the reference temperature, � � � is the effective Young’s modulus, is the martensite fraction, Θ� � is related to the coefficient of thermal expansion and is the transformation stress component. This latter parameter can be related to the maximum recovery strain � : � � � � (2) The effective Young’s modulus � � � can be obtained by the Reuss formula: � �ξ� � � ξ � � 1 �ξ � � �� (3) Where � and � are the Young’s moduli of martenste and austenite, respectively.