Int J Thermophys DOI 10.1007/s10765-014-1661-x

Thermal Diffusivity of Reduced Activation Ferritic/Martensitic Steel Determined by the Time Domain Photoacoustic Piezoelectric Technique Binxing Zhao · Yafei Wang · Chunming Gao · Qiming Sun · Pinghuai Wang

Received: 30 October 2013 / Accepted: 16 June 2014 © Springer Science+Business Media New York 2014

Abstract The thermal diffusivity of reduced activation ferritic/martensitic steel (CLF1), which is recognized as the primary candidate structural material for the test blanket module of the international thermal-nuclear experimental reactor, has been studied by the time-domain (TD) photoacoustic piezoelectric (PAPE) technique. The TD PAPE model based on a simplified thermoelastic theory under square-wave modulated laser excitation is presented, relating the TD PAPE signal to the modulation frequency, thermal diffusivity, and other material parameters. Thermal diffusivities of reference samples such as copper and nickel were measured and analyzed, by which the validity of the technique is verified. The thermal diffusivity of the CLF-1 sample was measured to be 8.2 mm2 ·s−1 , which is at a medium level among the ordinary steel materials (3 mm2 ·s−1 to 14 mm2 ·s−1 ) and has decent heat-dissipation ability. The results show that the TD PAPE technique can provide a fast and economic way for the investigation of the thermophysical properties of fusion reactor structural materials. Keywords Reduced activation ferritic/martensitic steel · Thermal diffusivity · Time-domain photoacoustic piezoelectric technique 1 Introduction Finding high performance structural materials for use in the test blanket module (TBM) of the International Thermal-nuclear Experimental Reactor (ITER) is one of the key

B. Zhao · Y. Wang· C. Gao (B) · Q. Sun School of Opto-electronic Information, University of Electronic Science and Technology of China, Chengdu 610054, China e-mail: [email protected] P. Wang Southwestern Institute of Physics, Chengdu 610041, China

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factors to achieve commercial application for fusion energy [1–4]. Reduced activation ferritic/martensitic (RAFM) steel, which has good resistance to irradiation swelling, good thermophysical and mechanical properties, and good compatibility with major cooling and breeding materials can be used as structural material for the TBM of the ITER [3,4]. In China, RAFM steel (CLF-1) is made by the Southwestern Institute of Physics of China [3,4]. The thermal diffusivity is one of the most important properties of fusion reactor structural materials, which can influence the structure design of the TBM. Measurement of the thermal diffusivity of RAFM steel is, therefore, mandatory. However, conventional measurement methods are complex, slow, and expensive. Hence, an effective, fast, simple, and low-cost technique is required. The photoacoustic piezoelectric (PAPE) technique has been proven to be an effective method to determine the thermal diffusivities of many materials, including metals, composites, and biological tissues [5–13]. However, the conventional PAPE technique for thermal-diffusivity determination is a frequency-domain (FD) method relying on a frequency scan, which is complex, slow, and expensive for actual application. The time-domain (TD) PAPE technique, which does not need a lock-in amplifier, could provide an effective, fast, simple, and low-cost method for thermal-diffusivity measurements. In this paper, the thermal diffusivity of the RAFM steel CLF-1 has been studied by the time-domain (TD) photoacoustic piezoelectric (PAPE) technique. First, the PAPE model based on thermoelastic theory is introduced, and the TD PAPE signal under square-wave-modulated laser excitation is derived, by which the dependence of the signal on time, modulation frequency, and material parameters including the thermal diffusivity are obtained. Second, the measurement method and the corresponding experimental system are setup, and the thermal diffusivities of reference samples such as copper and nickel are measured, by which the TD PAPE technique is verified. Finally, the TD PAPE technique is employed to measure the thermal diffusivity of CLF-1 steel.

2 Theory The principle of the TD PAPE technique is as follows: a periodic heat source caused by an intensity-modulated (square wave) laser generates thermal waves; the thermal waves propagate in the sample and cause thermoelastic strains; and the periodic thermoelastic strains are detected by a PZT attached to the back side of the sample. The model is shown in Fig. 1a. The geometry of the sample is a plate, with a PZT attached to the back side. l, R, k, ρ, and c are the thickness, radius, thermal conductivity, density, and specific heat of the sample, respectively; and L is the thickness of the PZT. Based on Blonskij’s simplified thermoelastic model that uses the thin plate theory to simplify the sample vibration problem, neglecting the influence of PZT on the strains in the sample, and considering the strong absorption case βl → ∞, where β is the absorption coefficient, the FD PAPE signal is [5] V (ω) = −

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2Pα klσ 2

 1+

 3 (1 − cosh σ l) , σ l sinh σ l

(1)

Int J Thermophys

Fig. 1 (a) Theoretical model of TD PAPE technique and (b) schematic of the experimental system

where σ 2 = iω/D, p = 2I π b2 eL/εS, α is the linear thermal expansion coefficient, D is the thermal diffusivity, ω is the modulation frequency, I is the laser intensity, b is the laser radius, S is the surface area of PZT, e is the piezoelectric modulus, and ε is the permittivity. When the laser intensity is square-wave modulated, the thermal source has the form, Q = Iβe−r

2 /b2

e−β(l/2−z) Re ( f (t)) ,

(2)

 2 sin (2m−1)π −i (2m−1)π 2 2 where f (t) = 21 + ∞ ei(2m−1)ωt . m=1 (2m−1)π e According to Eqs. 1 and 2, the TD PAPE signal under square-wave-modulated excitation (neglecting the dc term) is  ∞  2 sin (2m−1)π −i (2m−1)π i(2m−1)ωt 2 2 e V ((2m − 1) ω) e . V (ω, t) = Re (2m − 1) π 

(3)

m=1

Equation 3 shows the dependence of the TD PAPE signal on the modulation frequency and material parameters. Under the thermally thick condition for the sample, with the known thickness and frequency, the TD PAPE signal is only determined by the thermal diffusivity and a normalized factor. By fitting the theoretical experimental data to experimental results (both normalized to the range of −0.5 to 0.5), the thermal diffusivity can be obtained.

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Fig. 2 (a) Experimental data and theoretical fit for reference samples (frequencies are 31 Hz for copper and 29 Hz for nickel) and (b) experimental data and theoretical fit for RAFM steel CLF-1 (frequency is 31 Hz)

3 Experiments The experimental setup of TD PAPE detection is shown in Fig. 1b. The sample and PZT are well attached. The argon-ion laser (wavelength of 514 nm, power of 200 mW) is modulated by an acousto-optic modulator driven by a function generator, and induces periodic thermal waves and thermoelastic waves in the sample. The thermal waves are attenuated, and the thermoelastic waves are detected by the PZT (thickness of 0.1 mm and diameter of 18.2 mm) and converted to an electric signal. An oscilloscope records the signal, and a computer deals with the experimental data and fitting procedure. All measurements were done at room temperature. 3.1 System Verification For verifying the effectiveness of the thermal-diffusivity determination by the TD PAPE technique, two standard samples of copper and nickel were studied. The samples are made in disk form, with a diameter of 17 mm and thicknesses of 2.00 mm and 1.98 mm, respectively. The TD PAPE experimental data and the best fitted curves are shown in Fig. 2a, and the fitted thermal-diffusivity values are shown in Table 1. The modulation frequencies are chosen to be 31 Hz for the copper measurement and 29 Hz for nickel, which satisfy the thermally thick conditions for all the samples. From Fig. 2a and Table 1, it can be seen that the measured thermal diffusivities of copper and nickel are 114 mm2 ·s−1 and 22.6 mm2 ·s−1 , respectively; the relative errors are 1.3 % and 2.2 %, respectively. The error sources may be as follows: (1) the simplified model neglects the influence of the PZT on the sample vibration; (2) the TD signal tends to be influenced by the stability of the optical and electrical systems; and (3) the high frequency TD PAPE component is low, leading to the amplitude and phase errors. However, the variances [13] are very small, and the relative errors are within 3 %, which means that the TD PAPE technique is effective for the determination of the thermal diffusivity.

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Int J Thermophys Table 1 Thermal diffusivities of copper, nickel, and CLF-1 steel Sample

Measured (mm2 ·s−1 )

Reference (mm2 ·s−1 )

Relative error (%)

Var [14]

Copper

114

115.5 [15]

1.3

0.0026

Nickel

22.6

23.1 [15]

2.2

0.0015

CLF-1

8.2

–

–

0.0013

3.2 Measurement for RAFM Steel The thermal diffusivity of CLF-1 steel was measured with the TD PAPE system. The sample is made in disk form, with a diameter of 17 mm and thickness of 1.98 mm. The TD PAPE experimental data and the best fitting curves are shown in Fig. 2b, and the fitted thermal diffusivity is shown in Table 1. The modulation frequency is chosen to be 31 Hz, which satisfies the thermally thick condition for the sample. The thermal diffusivity of CLF-1 was measured to be 8.2 mm2 ·s−1 . Comparing the result with that obtained by the FD PAPE technique [12], the measurement results are consistent with each other, which indicates that the TD PAPE technique is effective for the determination of thermal diffusivity of CLF-1. The thermal diffusivity of ordinary steels range from 3 mm2 ·s−1 to 14 mm2 ·s−1 , depending on the contents of other elements in the material. So, the heat-dissipation ability of CLF-1 is at a medium level among the ordinary steel materials.

4 Conclusion Based on the simplified PAPE model, the TD PAPE method is setup, and the thermal diffusivity of CLF-1 is measured; therefore, several conclusions can be obtained. (1) The TD PAPE theoretical model is developed, and the analytical expression of the TD signal for the modulation frequency and material parameters is obtained. (2) The measurement method and the corresponding experimental system of the thermal diffusivity determination by the TD PAPE method are setup, by which the copper and nickel samples are measured. The relative error is within 3 %. (3) Using the TD PAPE technique, the thermal diffusivity of the RAFM steel CLF-1 was estimated to be 8.2 mm2 ·s−1 , which is at a medium level among ordinary steel materials. The results show that the TD PAPE technique provides an effective, fast, simple, and low-cost way to investigate the thermophysical properties of fusion reactor structural materials. Acknowledgments This work was supported by the Fundamental Research Funds for the Central Universities of China (Nos. ZYGX2012Z006 and E022050205), the Sichuan Province Youth Foundation (No. 2011JQ0025) and the National Science Foundation of China (Nos. 50506006, 61379013, and 61107078).

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