Effect of elastic matrix constraint on the tensile deformation of NiTi superelastic fiber

In this paper we study the effect of elastic matrix constraint on the tensile deformation of an active NiTi shape memory alloy fiber, which, when no matrix constraint is present, will experience stress-induced phase transformation by nucleation and growth of a macroscopic martensite band. The effect of the constraint is measured by two factors: the relative Young's modulus (by dimensionless parameter E⁽²⁾/E⁽¹⁾) and the relative dimension (by dimensionless parameter h/a) of the fiber and the matrix. The transformation process of the fiber through the martensite band growth under tension is modeled as an embedded elastic fiber containing growing cylindrical transformation inclusions. By Love's stress function, the elastic solutions of the inclusion-fiber-matrix system as well as the internal elastic energy during the transformation are obtained. Analytical expressions of the free energy of the system during the transformation are also formulated for the case of uniaxial tension. After introducing the band nucleation and growth criteria, the growth capability of a martensite band is examined. The results demonstrate that, depending on the magnitude of the matrix constraint, three distinct deformation patterns of the fiber exist: (1) with weak matrix constraint, single band growth dominates the transformation process of the fiber; (2) with intermediate matrix constraint, sequential bands nucleation and growth prevails in the fiber; and (3) with strong constraint, numerous bands form and grow, and macroscopically the fiber tends to deform homogeneously. Parametric studies on the macroscopic stress-strain response of the fiber-matrix system are performed and the obtained results are discussed.