Nonlocal Superelastic Model of Size-Dependent Hardening and Dissipation in Single Crystal Cu-Al-Ni Shape Memory Alloys

Abstract

We propose a nonlocal continuum model to describe the size-dependent superelastic effect observed in recent experiments of single crystal Cu-Al-Ni shape memory alloys. The model introduces two length scales, one in the free energy and one in the dissipation, which account for the size-dependent hardening and dissipation in the loading and unloading response of micro- and nanopillars subject to compression tests. The information provided by the model suggests that the size dependence observed in the dissipation is likely to be associated with a nonuniform evolution of the distribution of the austenitic and martensitic phases during the loading cycle.

Anomalous Plasticity in the Cyclic Torsion of Micron Scale Metallic Wires

“…Some portion of plastic work is not dissipated but stored in the deformed materials through GNDs or other polarized structures [36]. This is the physical basis for the strain gradient plasticity (SGP) theories [18,[37][38][39] with both energetic and dissipative length scales. It is beyond the scope of this Letter, but we will present elsewhere a nonlocal kinematic model within a SGP framework that captures the size effect, the BE, and plastic recovery.…”

Transition from many domain to single domain martensite morphology in small-scale shape memory alloys

“…propagate along the sample axis [16]. Nonlocal continuum modeling of Cu-Al-Ni nanopillars, furthermore, related the size effect to the non-uniform evolution of the phase transformation [23]. However, the above works offered these explanations for the size effect as hypotheses, which are strongly related to an assumed morphology of the phase transformation, without the benefit of any direct observations that speak to the morphological evolution of martensite in any SMA in this size range (~5 -500 µm).…”

Investigation of the role of Ti oxide layer in the size-dependent superelasticity of NiTi pillars: Modeling and simulation

“…Combining these two equations leads to The group of parameters S 0 2 e has the effect to enhance the strain-hardening rate for nonuniform phase transformations [22]. In this study, the values, S 0 2 e = 0.01 nm 2 E A and 1 nm 2 E A , will be adopted to study this effect.…”

“…10, the strain-hardening rate extracted from the finite element simulations with For the finite element simulations with S 0 2 e /E A = 1 nm 2 , it can be seen that starting from large pillar sizes, the strain-hardening rate first increases for decreasing pillar size, and at about 200 nm it starts to decrease with further decrease in the pillar size, which is consistent with the experimental observations. It has been shown in [22] that for pure SMA, the hardening effect increases for decreasing pillar size due to the nonlocal term in the free energy and the constraint of phase transformations. However, because of the presence of the TiO 2 layer, in smaller and smaller pillars, the strain-hardening rate eventually drops as it approaches the perfect plastic response.…”