Constitutive modeling of pseudoelastic NiTi and its application to structural problems
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Nearly equiatomic NiTi exhibits the unique characteristic of pseudoelasticity, i.e. it can be deformed to strain levels of several percent that is fully recoverable on unloading. Under tension, the phase transformation results in strain of nearly 7% and inhomogeneous deformation while the stress remains essentially constant. By contrast, under compression, transformation occurs at a much higher stress, the induced strain is nearly one-half and deformation is essentially homogeneous. These material nonlinearities interact with structural instabilities to produce hitherto unknown intriguing structural responses. A constitutive modeling framework based on J₂-type kinematic hardening is developed to address the tension/compression asymmetry of pseudoelastic NiTi, including inhomogeneous versus homogeneous deformations. Its performance is then evaluated in the numerical studies of four nonlinear NiTi structures that were previously investigated experimentally. The first problem considered is the buckling and recovery of an axially compressed NiTi tube. The modeling efforts reproduce the major events observed, including onset of axisymmetric wrinkling, collapse by progressive development of buckling lobes with three circumferential waves, erasure of the lobes and recovery of deformation upon unloading. The study shows that the tension/compression asymmetry plays the key role in bringing the calculated response close to the experimental one and addition of plastic deformation further improves the results. The second problem involves a NiTi strip under tension. The constitutive model properly accounting for softening in the tensile response reproduces the closed hysteresis with two stress plateaus with correct levels and extents, as well as localization of deformation into inclined bands that propagate in the specimen. In the third problem, the constitutive model is used to analyze the tension test of a NiTi tube. The simulation reproduces a closed hysteretic response with two stress plateaus close to the measured one. The tubular geometry of the specimen imposes helical and multi-pronged localization patterns. The last problem studied is the bending of a NiTi tube. The simulation reproduces the major features of the experimental results: the hysteretic moment-end rotation response with two plateaus; localization of curvatures; progressive development of diamond patterns of higher strain on the tensioned side and the nearly homogeneous deformation on the compressed side.