M. R. Aziz, German University in Cairo, New Cairo city, Egypt; H. Ahmed, Materials Innovation Institute (M2i), Techincal University of Delft, Delft, Netherlands; J. Rödel, German University in Cairo, New Cairo City, Egypt
Modeling of shape memory alloys thermo-mechanical behavior has become a major requirement in order to design increasingly complex components utilizing shape memory alloys. In this research, a physically-based mathematical model was developed and coupled to finite elements, to predict the thermo-mechanical behavior, namely shape memory effect and pseudoelasticity, of shape memory alloys including Cu-Al-Ni. The model accounts for phase transformations occurring as a function of temperature, responsible for the unique properties of shape memory alloys. The phase transformation is described thermodynamically, by deriving an explicit free energy expression from micromechanics incorporating two state variables, namely: (i) the overall martensite volume fraction and (ii) the mean transformation strain. The chosen behavior is implemented using the commercial finite element software ABAQUSTM, where the material properties were defined using UMAT subroutine. The predicted load-displacement and phase transformation as a function of temperature and applied stress is validated against experimental results obtained employing nano-indentation. The verified model will help in understanding the thermo-mechanical behavior of shape memory alloys at various loading conditions and temperatures.
Summary: Finite element modeling of phase transformation in Shape Memory Alloys
M. Aziz, H. Ahmed, J. Röedel Cairo, Egypt micheal.aziz@student.guc.edu.eg
Shape memory alloys are metallic alloys that can undergo martensitic phase transformation as a result of applied thermo-mechanical loads and are capable of recovering permanent strains when heated above certain temperatures [1; 2; 3; 4]. These shape memory alloys find applications in industry such as, micro-electro-mechanical systems [5], novel medical devices [6] and aerospace applications [7]. The uses of shape memory alloys include being utilized as coating materials for tribological problems where their unique constitutive behavior can be used to ameliorate surface damage accumulation mechanisms in fatigue and wear. These applications utilize the ability of shape memory alloys to recover inelastic strains upon heating or stress removal. Thus, in order to be able to design the future shape memory alloys based applications and improve their functionality for a small scale material system, it’s necessary to develop the knowledge of the microscopic deformation of these alloys. The design of shape memory based systems relies on the development of shape memory alloy models that can predict the response of the material to a given thermo-mechanical loading. This research work is aimed at creating a physically based mathematical model coupled with finite elements to predict the behavior of shape memory alloys, including Cu-Al-Ni at various temperatures and loading conditions. The results obtained are verified against experimental work utilizing nano-indentation. The authors believe that the developed and verified model will be of great interest to the industry. It can be utilized to investigate the range of operating conditions of an application utilizing shape memory alloys. The fact that the model can correlate the occurring phase transformation during loading at various temperatures to the pseudo-elastic and shape memory effect can be used to optimize the loading conditions. Thus, the developed model along with the results verified with experimental work can be utilized as a powerful tool to optimize and design new shape memory alloy industry.
References
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