In micromechanics, the definition of the optimum Representative Volume Element (RVE) that represents the microstructure of the considered composite material is still an ongoing research subject. Therefore, depending on the required accuracy of the micromechanical model predictions, the size and number of realizations that define the RVE, must be determined through a systematic study. In the present work, an RVE based study is conducted on precipitation hardened NiTi Shape Memory Alloys (SMAs) with Ni4Ti3 precipitates. The considered RVEs consist of a homogeneous SMA matrix with periodically arranged precipitates. The precipitates are assumed to have ellipsoid shape and are arranged in random position and orientations, ensuring the periodicity at the boundaries. The non-linear constitutive behavior of the precipitated SMA, is solved by means of a recently developed Fast Fourier Transform variational approach for SMAs. An extensive study is conducted considering RVEs with changing volume fraction and increasing number of precipitates.
Shape memory alloys (SMAs) are unique materials with the ability to generate and recover moderate to large inelastic deformations. Due to their aforementioned ability, SMAs are suitable for applications in aerospace, oil and gas and automotive industries, where compact actuators with high actuation energy density are required. The current work presents a modeling framework that links the heat treatment of SMAs with their effective response and aims to accelerate the discovery of new high temperature SMAs with optimal performance. Thus a finite element based, multi-field micromechanical framework is developed to capture the constitutive response of precipitation hardened Ni-Ti-Hf SMAs. A representative volume element of precipitated polycrystalline SMAs is considered which contains randomly distributed non-overlapping precipitates, while periodic boundary and geometric conditions are maintained. The SMA matrix is assumed to behave isotropic as a result of random texture while the precipitates are considered as linear elastic solids. The effect of the lattice mismatch between the precipitates and the matrix, and the effect of the Ni and Hf depletion during precipitation on the thermo-mechanical response of the material are taken into consideration. The Fickian diffusion law is used to predict the Ni and Hf concentration field in the vicinity of the precipitates, which results in substantial SMA transformation temperature shifts. Finally, the predictive capability of the developed framework is assessed through correlations with experimental results.
Current efforts towards the identification of suitable processing parameters of shape memory alloys (SMAs) that enhance
their actuation performance, are based on semi-empirical approaches. This is largely due to a lack of models able to predict
the macro-mechanical response of SMAs as function of given composition and the temperature and time of an imposed
heat treatment. The present work aims for the development of multi-field Finite Element (FE) based models, for the NiTiHf
SMA material system, adequate to address these challenges and able to simulate materials macro-mechanical response
including transformation strain, hysteresis and transformation temperatures. Representative Volume Elements (RVEs)
with periodic geometry and boundary conditions are used to model materials microstructure. Randomly placed precipitates
are considered in the NiTiHF matrix, while eigenstrains corresponding to the lattice mismatch between the precipitates
and the matrix are introduced in order to model the residual stress and strain fields. The Hf concentration field is taken into
consideration in addition to the displacement field in order to capture the Hf diffusion process through the adoption of
Fickian diffusion law. To this end the composition of NiTiHf in the vicinity of the precipitates is computed thus resulting
in substantial SMA transformation temperature shifts. The developed framework is validated based on correlations with
experimental results.
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