In a certain temperature range, NiTi and other shape memory alloys
show the so-called pseudoelastic effect. In the present study, the
pseudoelasticity of NiTi is experimentally investigated in tension
tests on thin-walled tubes. The observed phenomena are
modeled within the framework of continuum thermomechanics regarding a
geometric linear theory. The model is based on a free energy function
in order to represent the occurring energy storage and release
effects. Additionally, evolution equations for internal variables,
like the inelastic strain tensor and the fraction of martensite, are
introduced. The proposed system of constitutive equations represents
the observed history-dependent material behavior. To identify the
material parameters, the theory of neural networks is applied.
A thermomechanically consistent material model representing the multiaxial behavior of shape memory alloys is proposed in this article. The constitutive equations describe the one-way and two-way shape memory effect as well as pseudoelasticity, pseudoplasticity and the transition range between pseudoelasticity and pseudoplasticity. The material model is based on a free energy function as well as evolution equations for internal variables. In detail, the free energy function is introduced in order to describe the energy storage during thermoelastic processes, the energy difference between the regarded phases (austenite and martensite) as well as the energy storage due to the evolution of the residual stresses. In contrast to this, the evolution equations for the internal variables represent the observed inelastic behavior of shape memory alloys as well as the related thermomechanical coupling effects. Due to the description of the energy storage and release during the martensitic phase transitions by means of a mixture theory, one internal variable is the fraction of martensite. Others are the inelastic strain tensor and internal variables describing residual stresses. The viscous material behavior of NiTi shape memory alloys, which is experimentally observed, is represented by an inelastic multiplier of Perzyna-type. Numerical solutions of the developed constitutive equations for isothermal and non-isothermal strain and stress processes demonstrate that the material model represents the main effects of shape memory alloys. Additionally, the material model is able to depict the multiaxial material behavior as observed. Numerical solutions are compared with uniaxial and in particular biaxial experimental observations on NiTi shape memory alloys.
Tension and torsion as well as combined tension-torsion tests on NiTi Tubes are presented in this article. Two different specimens are used in the experiments: one is austenitic and the other is martensitic at room temperature. The experiments are performed at nearly isothermal conditions. However, non-isothermal effects occur as well because of the self-heating of the material during the phase transitions and the detwinning of the martensite. These effects can be excluded applying very small deformation rates. In contrast to this, the influence of the self- heating on the material behavior is investigated in other experiments, where temperature fields are measured by means of infrared thermography. This allows detailed observations of the temperature field on the surface of the specimen and leads to additional insight into the thermomechanical behavior of shape memory alloys. In simple tension and pure torsion experiments the various effects of the material behavior can be decoupled. In particular, relaxation and creep processes are observed as a result of self-heating, but also as a consequence of the viscosity of the material. The combined tension-torsion experiments make it possible to analyze coupling effects of the biaxial behavior. In this context, a proportional and non-proportional deformation path is carried out.
In this paper a thermomechanical material model for shape memory alloys is proposed. The model can depict the shape memory effect, the pseudo elasticity and pseudo plasticity as well as the transition region between pseudo elasticity and -plasticity. Moreover, the geometric non linearities are considered in the constitutive equations. For all thermomechanical processes, the CLAUSIUS-DUHEM inequality is fulfilled. Besides the phenomenological modeling, the finite element implementation of the constitutive equations at finite strains is developed. For simplification and in order to construct an efficient stress algorithm, only small elastic but finite inelastic strains are considered.
In this article we propose a material model for the representation of shape memory behavior based on a phenomenological thermoviscoplasticity theory. The constitutive model is thermodynamically consistent in the sense of its compatibility with the Clausius-Duhem inequality as a special formulation of the 2nd law of thermodynamics. Numerical solutions of the constitutive equations for isothermal and nonisothermal strain and stress processes demonstrate that the behavior of these materials, namely the one- and two-way shape memory effect, the pseudoelasticity and the pseudoplasticity as well as the transition region between pseudoelasticity and pseudoplasticity, is depicted as observed.