۱- Introduction

۲- Materials and experiments

۳- Model formulation

۴- Model implementation

۵- Numerical results

۶- Conclusions

References

Abstract

The one-way and two-way shape memory effects (SMEs) as well as the thermal hysteresis represent fundamental properties when dealing with the design of detachable and thermally-stable connection systems based on shape memory alloys (SMAs). Such properties can be induced and tuned by thermo-mechanical processes that include thermal treatments and severe pre-deformation in martensitic state, causing the onset of plastic strains. In such complex conditions, material modeling is of great importance to support the design. This paper proposes a generalization of the three-dimensional phenomenological constitutive model by Souza et al. (1998), in order to describe the behavior of severely pre-strained NiTi-based SMAs. The proposed model allows to describe pseudoelasticity, one-way and two-way SMEs, as well as additional physical phenomena evidenced experimentally, such as transformation temperatures’ evolution, thermal hysteresis, phase transformations at low stresses, thermal strains, and phase-dependent elastic properties. Several numerical simulations, ranging from uniaxial tests to the finite element analysis of two case-studies, are performed. Model results are in good agreement with the results of a performed experimental campaign and allow to discuss SMA behavior under such complex loading conditions.

Introduction

Shape Memory Alloys (SMAs) are widely applied in various fields of engineering and medicine thanks to their unique strain recovery capabilities (Jani et al., 2014; Otuska and Wayman, 1998; Duerig et al., 1990), that can be obtained either by heating or by stress release, through the so-called Shape Memory Effect (SME) and Pseudoleastic Effect (PE), respectively. SME and PE are due to reversible solid-state microstructural transitions, the so-called thermoelastic martensitic transformations (TMT), between the parent body-centered cubic austenitic phase (B2) and the product monoclinic martensitic one (B19’). TMT can be induced either by temperature changes (TIM, ThermallyInduced Martensite) or by mechanical loads (SIM, Stress-Induced Martensite), providing the SME and PE, respectively. B2 phase is stable at high temperature and low stress, while B19’ is stable at low temperature and high stress. Thanks to TIM, the material is able to change its microstructure reversibly when varying the temperature between the so-called Transformation Temperatures (TTs). Direct transformation (B2-B19’) can occur when cooling the material below the martensite TTs, while reverse transformation takes place during heating above the austenite TTs. The difference between martensite and austenite TTs, namely ΔTT, is regarded as the thermal hysteresis of the material. Thermal hysteresis, and the associated stress-strain hysteresis, is a limiting phenomenon in SMA-based fast actuation systems, as it represents a source of inefficiencies due to the increased energy loss and time response. Nevertheless, thermal hysteresis could be a beneficial feature when a large thermal stability range is needed, such as in some fasteners or connectors operating in constrained recovery mode (Jani et al., 2014; Duerig et al., 1990; Humbeeck, 2001). In such systems recovery forces are generated as the SMA element, previously deformed in martensitic state, is heated up to the austenite TTs in a constrained shape, i.e. against a mechanical obstacle. This is due to the so-called One-Way Shape Memory Effect (OW-SME) and it is the basic principle of many successful systems, e.g. permanent fasteners, couplers, or SMA hybrid composites (Humbeeck, 2001; Duerig et al., 1990; Jani et al., 2014; Kirkby et al., 2008).