F. Richter, G. Eggeler, O. Kastner, Ruhr-University Bochum, Bochum, Germany
The experimentally observed phenomenon of anti-buckling is a peculiar effect in shape memory alloys (SMA) and describes the astonishing observation that a SMA bar when first brought into the compressed martensitic state, then bent and unloaded by a lateral force is able to restore its initial straight configuration upon axial compression.This striking observation can be understood by the insight into the mechanics offered by the Müller-Achenbach-Seelecke (MAS) model for SMA. The model is interfaced with an Euler-Bernoulli-beam element available within the FEM program ABAQUS and starts out from a state of equal amounts of the two martensite variants.
The interpretation of the phenomenon by the MAS model resolves the stress and strain state as well as the distribution of martensite variants through the bar thickness and along the bar axis in the course of the deformation and arrives at a mathematical description akin to basic mechanics for elastic materials. These analytical formulas are in close accord with ABAQUS results.
The stress state through the thickness during lateral bending and unloading, including the occurrence of two stress-free layers while unloading, is corroborated by a formal interpretation of the stress-strain-diagram for an elastic–ideally plastic body when shifted along the strain axis.
With this model we are able to explain the anti-buckling effect by the superposition of axial (normal) stress and bending moments in the regime of stress-induced martensite-martensite transitions.
Summary: We are first to present FEM-simulations enlighting the process of the anti-buckling effect. This effect occurs when an initially detwinned, then curved martensite bar is axially loaded: under the axial load the straight reference shape is restored. This anti-intuitive phenomenon was experimentally observed and reported in the literature.
Here we explain the anti-buckling effect as the interplay of axial (normal) stress and bending moments in the regime of stress-induced martensite-martensite transitions.
