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

Alireza Ostadrahimi,Fathollah Taheri-Behrooz,Eunsoo Choi

doi:10.3390/ma14185415

Alireza Ostadrahimi, Fathollah Taheri-Behrooz + Show 1 more

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https://doi.org/10.3390/ma14185415

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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.

Highlights

One of the smart class of materials distinguished by its two well-known behavior and a highly nonlinear stress–strain curve is shape memory alloy (SMA)
Parametric Model to Describe Asymmetric Tension-Compression Behavior in Motivated by one-dimensional SMA model proposed by Auricchio et al [37] at low temperature, we present a parametric model for martensitic SMA beams to describe material behavior with asymmetric tension–compression response
The analytical results for martensitic beams having different responses in tension and compression are compared with experimental while having different responses in tension and compression are compared with experidata from four-point bending tests. tests

Summary

Introduction

One of the smart class of materials distinguished by its two well-known behavior and a highly nonlinear stress–strain curve is shape memory alloy (SMA). Since in many fields of engineering applications, SMAs devices are exposed to mixed loading states, such as global or local bending, clarifying how SMA beam behaves under transverse loadings recently draws a considerable attention [4]. This great motivation leads to researchers coming up with various bending analysis via several experimental, numerical, and analytical studies in literatures. In terms of experimental and numerical works, several researchers [5,6,7,8,9,10,11,12,13,14,15,16,17] predicted bending stress distribution of SMA beams

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