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By means of classical molecular-dynamics simulations we investigate the solid–solid phase transition from a bcc to a close-packed crystal structure in cylindrical iron nanowires, induced by axial strain. The interatomic potential employed has been shown to be capable of describing the martensite–austenite phase transition in iron. We study the stress versus strain curves for different temperatures and show that for a range of temperatures it is possible to induce a solid–solid phase transition by axial strain before the elasticity is lost; these transition temperatures are below the bulk transition temperature. The two phases have different (non-linear) elastic behavior: the bcc phase softens, while the close-packed phase stiffens with temperature. We also consider the reversibility of the transformation in the elastic regimes, and the role of the strain rate on the critical strain necessary for phase transition.