Effect of Tension-Compression Asymmetry Response on the Bending of Prismatic Martensitic SMA Beams: Analytical and Experimental Study

Abstract

This paper aims to analytically derive bending equations, as well as semi-analytically predict the deflection of prismatic SMA beams in the martensite phase. To this end, we are required to employ a simplified one-dimensional parametric model considering asymmetric response in tension and compression for martensitic beams. The model takes into account the different material parameters in martensite twined and detwinned phases as well as elastic modulus depending on the progress of the detwinning process. In addition, the model considers the diverse slope of loading and unloading in martensite detwinned phases favored by tension and compression. To acquire general bending equations, we first solve the pure bending problem of a prismatic SMA beam. Three different phases are assumed in the unloading procedure and the effect of neutral fiber distance from the centerline is also considered during this stage. Then according to the pure bending solution and employing semi-analytical methods, general bending equations of an SMA beam are derived. Polynomial approximation functions are utilized to obtain the beam deflection–length relationship. To validate the attained analytical expressions, several three- and four-point bending tests were conducted for rectangular and circular SMA beams. Experimental data confirm the reasonable accuracy of the analytical results. This work may be envisaged to go deep enough in investigating the response of SMA beams under an arbitrary transverse loading and stress distribution during loading and unloading, as well as findings may be applicable to a good prediction of bending behavior.

Vectorized MATLAB Implementation of the Incremental Minimization Principle for Rate-Independent Dissipative Solids Using FEM: A Constitutive Model of Shape Memory Alloys

“…Due to the tension-compression asymmetry, its maximum tension was approximately 2/3 of the absolute maximum in compression, and the neutral plane shifted toward the compressed part of the material (cf. analytical computations in [46,51]). For comparison, the same computational simulation was performed at −25 • C (i.e., in the pseudoplastic regime of the material), and the distribution of the diagonal component of the stress tensor in the x direction is shown in Figure 6b.…”

Interface stress transfer model and modulus parameter equivalence method for composite materials embedded with tensile pre-strain shape memory alloy fibers

“…How to consider the substrate material and SMA discontinuities during modeling, as well as the stress and displacement transfer between the material interface at the micro level [14,15]. Secondly, SMAs have unique pre-strain properties and martensite austenite transformation properties [16][17][18], which not only help to improve the overall stiffness and dynamic properties of composite plates but also offer a fresh approach to designing and managing their vibration and acoustic radiation properties [19,20].…”

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“…Their model was then implemented as Euler-Bernoulli beam elements to simulate an SMA staple. Although using beam elements [31][32][33] may decrease the computation cost, it constitutes the drawback of being applied to more general loading types. For instance, in the case of four-point bending, under large amounts of deformations, the loading configuration between the inner rollers does not remain pure bending [34]; in such cases, an appropriate apparatus [34] or a 3D model is required.…”