Finite-Element Simulation of the Anti-Buckling-Effect of a Shape Memory Alloy Bar

Abstract

Shape memory alloys (SMA) are characterized by an intricate stress-strain curve modified by temperature, posing thermomechanically coupled problems. A model able to address this feature is the Mü ller-Achenbach-Seelecke (MAS) model which had been ported into the user material interface in the finite-element (FEM) simulation software ABAQUS. The literature on this model mainly focuses on pseudo-elasticity of SMA at elevated temperature. We address a numerical investigation in the low-temperature pseudo-plastic regime. The present publication deals with the little-known anti-buckling effect which occurs in de-twinned and pre-bent martensitic bars under axial compression. It was experimentally demonstrated by Urushiyama et al. (JSME (The Japan Society of Mechanical Engineers) Int. J. Ser. A, Solid Mech. Mater. Eng., 2003, 46(1), p 60-67). This study reveals that the origin of this effect roots in an interplay of inhomogeneous stress states and mechanically induced twin-twin phase transformations. The proper explanation of the anti-buckling effect can be inferred from the explicit knowledge of the martensitic phase composition of the bar during the process. We show that the MAS model is capable to resolve this matter in detail, hence addressing the reliability of this particular model also in the pseudo-plastic regime of SMA. The study thereby implies that the MAS model is an excellent modeling tool for the analysis of complex, thermomechanically coupled processes.

Ni-Ti SMA bars behaviour under compression

“…They concluded that the transformation of typical SMA phases affected the solution to the problem. Finally, Richter et al [41] numerically analyzed the phenomenon so-called anti-buckling effect reported by Urushiyama et al [42] Table 1 shows the list of tests with the number of test speci-239 mens, the total bar length L total , the free length of each test L and mechanical slenderness L=k (where k ¼ D=4 and D is the bar diameter). A total of 30 steel bars and 6 Ni-Ti bars were tested.…”

Analytical solution for twinning deformation effect of pre-strained shape memory effect beam-columns

“…Due to the initial pre-strain, the trends of the stressstrain diagram during loading in tension and compression are not the same (Richter et al, 2010). Therefore, after complete removal of the bending moment, the SME beam-column remains deflected and inhomogeneous stress distribution across the cross section occurs (Figure 3(e)).…”

“…In the latter, the deformed shape of the structures can be recovered by applying axially compressive load; it is named ''Twinning Deformation effect'' (TD-effect) by Urushiyama et al (2003). The origin of this effect roots in the inhomogeneous stress states and mechanically induced twin-twin phase transformations (Richter et al, 2010;Urushiyama et al, 2003;Watkins and Shaw, 2018).…”

“…When a deformed SME beam-column is under axially compressive load, it has the tendency to recover some inelastic strains and to become straight before buckling (anti-buckling). Follow-up to this work, Richter et al (2010) used a finite element model to capture TD-effect behavior of SME beam-columns in the martensite phase, and successfully simulated this effect under axial loading. Although there have been several studies on the TDeffect, no analytical studies on TD-effect are existed.…”

Unbuckling of superelastic shape memory alloy columns

“…It (a) Balloon inflation (adapted from [Alexander 1971]) (b) Sheet wrinkling in tension (adapted from [Nayyar et al 2014]) (c) Martensitic SMA column straightening (adapted from [Urushiyama et al 2003]) should also be noted that the mechanical behavior of SMAs in the martensite phase differs from that of superelastic SMAs (which are examined here), although both exhibit the seemingly necessary stiffening at large strains for unbuckling to occur. As a follow-up to this work, Richter et al (2011) used a finite element model to capture the behavior of SMA columns in the martensite phase, successfully simulating this straightening behavior during compression.…”