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Thermal Diffusivity Measurement of a NiTi Shape Memory Alloy Using a Periodic Temperature Field

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Abstract

The aim of this study is to estimate the thermal diffusivity of martensitic and austenitic microstructures of a NiTi SMA. To this end, an experimental apparatus supported on the Angstrom’s method was designed, where one face of a cylindrical sample is subjected to a periodic heat flux and the other face is kept at a constant temperature. This apparatus was developed to provide the three fundamental requirements of the applied method: (1) uniformity of the thermal field in any cross section of the medium; (2) complete damping of the heat wave before it reaches the face at a prescribed temperature; (3) thermophysical properties independent of temperature within the adopted measurement range. Fourteen thermocouples are fixed at specific locations on the side of the sample, for measuring the amplitude and phase-lag of the thermal wave supplied from periodic heating at a certain frequency. The measurements of these parameters, carried out on a permanent periodic regime, are replaced into a mathematical model, in order that the thermal diffusivity can be determined by linear regression. The results obtained for the two microstructures showed good agreement with the literature, with absolute deviations below 8.5 %, proving the effectiveness of the experimental arrangement. The estimated thermal diffusivity of austenite is 48.21 % higher than that of martensite. The uncertainty quantification, assessed by the Monte Carlo Method, indicates a low dispersion, below 1.5 %, which delivers high precision and reliability to the estimated thermophysical property.

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Abbreviations

SMA:

Shape Memory Alloy

SMM:

Shape Memory Material

DSC:

Differential Scanning Calorimetry

AWG:

American Wire Gauge

JCGM:

Joint Committee for Guides in Metrology

MCM:

Monte Carlo Method

LPU:

Law of Propagation of Uncertainties method

PDF:

Probability Density Function

PPR:

Periodic Permanent Regime

\(\alpha\) :

Thermal diffusivity (m2·s−1)

\(k\) :

Thermal conductivity (W·m−1·K−1)

\(\rho\) :

Density (kg·m−3)

\({c}_{p}\) :

Specific heat (J·kg−1·K−1)

\({\alpha }_{M}\) :

Thermal diffusivity of martensite (m2·s−1)

\({\alpha }_{A}\) :

Thermal diffusivity of austenite (m2·s−1)

\({A}_{S}\) :

Start temperature of austenitic transformation·(°C)

\({A}_{F}\) :

Finish temperature of austenitic transformation·(°C)

\({M}_{S}\) :

Start temperature of martensitic transformation·(°C)

\({M}_{F}\) :

Finish temperature of martensitic transformation·(°C)

\(H\) :

Latent heat (J·kg−1)

\({k}_{A}\) :

Thermal conductivity of austenite (W·m−1·K−1)

\({k}_{M}\) :

Thermal conductivity of martensite (W·m−1·K−1)

\(u\) :

Speed of the boundary phase change (m·s−1)

\(\xi\) :

State of M-A transformation

\(L\) :

Sample length (m)

\(x\) :

Spatial coordinate (m)

Ra :

Surface roughness (μm)

\(T\) :

Temperature (°C)

\(t\) :

Time (s)

\(A\) :

Amplitude ratio

\(A\left(x\right)\) :

Amplitude of the thermal wave at x position (°C)

\(A\left(L\right)\) :

Amplitude of the thermal wave at (x/L) = (°C)

\(\omega\) :

Angular velocity (rad·s−1)

\(\phi\) :

Phase-lag (rad)

\(\varepsilon\) :

Reference phase angle (rad)

\(f\) :

Thermal wave frequency (Hz)

\(\delta\) :

Relative difference between measurement temperatures (%)

\(U\) :

Measurement uncertainty (%)

\(N\) :

Number of iterations of the Monte Carlo Method

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Acknowledgements

The authors would like to thank the Brazilian financing agencies Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Fundação de Amparo à Pesquisa de Minas Gerais (FAPEMIG) for supporting the development of this research. The authors would like to thank Prof. Arthur Alves Fiocchi, Ph. D, and Walter Motta Neto, Ph. D student (Manufacturing Research Center, Faculty of Mechanical Engineering, Federal University of Uberlândia, MG, Brazil), for their support in surface roughness measurements.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Federal University of Uberlândia, João Naves de Ávila Avenue, 2121, Uberlândia, MG, Zip Code 38900-402, Brazil

    José Ricardo Ferreira-Oliveira

  2. Postgraduate Program in Process Engineering, Federal University of Campina Grande, Aprígio Veloso Street, 882, Campina Grande, PB, Zip Code 58429-140, Brazil

    Paulo César Sales da Silva

  3. Department of Mechanical Engineering, Federal University of Campina Grande, Aprígio Veloso Street, 882, Campina Grande, PB, Zip Code 58429-140, Brazil

    Luiz Roberto Rocha de Lucena, Carlos José de Araújo & Celso Rosendo Bezerra Filho

  4. Department of Engineering and Technology, Federal Rural University of the Semi-Arid, Francisco Mota Avenue, 572, Mossoró, RN, Zip Code 59625-900, Brazil

    Rômulo Pierre Batista dos Reis

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  1. José Ricardo Ferreira-Oliveira
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  3. Luiz Roberto Rocha de Lucena
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Contributions

JRFO: Conceptualization, Methodology, Validation, Investigation. PCSS: Conceptualization, Methodology. Investigation. LRRL: Conceptualization, Methodology. RPBR: Conceptualization, Software. CJA: Resources, Supervision. CRBF: Formal analysis, Supervision, Project administration.

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Correspondence to José Ricardo Ferreira-Oliveira.

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Ferreira-Oliveira, J.R., da Silva, P.C.S., de Lucena, L.R.R. et al. Thermal Diffusivity Measurement of a NiTi Shape Memory Alloy Using a Periodic Temperature Field. Int J Thermophys 42, 147 (2021). https://doi.org/10.1007/s10765-021-02900-2

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