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A thermographic technique for in-plane thermal diffusivity measurement of electroplated coatings
Optics and Laser Technology 113 (2019) 338–344
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A thermographic technique for in-plane thermal diffusivity measurement of electroplated coatings
T
⁎
S. Genna , N. Ucciardello Department of Enterprise Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy CIRTIBS Research Centre, University of Naples Federico II, P.le Tecchio 80, 80125 Naples, Italy
H I GH L IG H T S
procedure was developed for the in-plane thermal diffusivity. • AThethermographic is effective for the in-plane thermal diffusivity of thin coatings. • The technique • coating allows an increase of about 45% in thermal diffusivity of the aluminium.
A R T I C LE I N FO
A B S T R A C T
Keywords: Laser Thermal analysis Thermography Copper Aluminium alloy
In the present work, a thermographic procedure is developed and tested with the aim to determine the in-plane thermal diffusivities of electroplated coatings with different thickness on an aluminium alloy (AA6082). For the tests, a single pulse of a diode laser source was adopted to generate a thermal contrast on the specimen’s surface. An infrared camera was adopted to acquire the surface gradient temperature and a MATLAB algorithm was developed to calculate the thermal diffusivity. In order to study the influence of the laser parameters set on the technique, two different laser pulses were adopted to heat the specimens; moreover, the influence of the starting acquiring time by IR camera was also evaluated. From the results, the technique is demonstrated to be effective for the in-plane thermal diffusivity measurement of thin coatings and, within the investigated parameters window, to be not affected by the checked parameters.
1. Introduction Nowadays, heat dissipation represents a critical issue in many technological fields; for example, in many electronic devices and systems, the specific thermal power to be dissipated is very high, because the surfaces for the heat exchange are very small. As a matter, the cooling performances cannot achieve the required ones, because of the limited thermal conductivity of the adopted materials [1]. Thus, new materials characterized by higher thermal conductivity are needed to be developed [2]; in last years, a lot of studies were conducted to use the excellent mechanical and thermal properties of nanoscale carbon materials: carbon nanotubes (CNT) [3,4], graphene [5,6] or graphite nanoplatelets (GNP) [7] and nanodiamonds [8,9] were adopted as filler of metal matrix composites (MMC) by different techniques [10–14]. Accordingly, the knowledge of the thermal conductivity of these new materials is crucial; since the thermal conductivity measurement require the knowledge of the heat flux (difficult and unreliable
⁎
measurement), it is generally preferred to experimentally evaluate the thermal diffusivity (α) and to obtain the thermal conductivity (k) by the well-known relation:
k = αρCp
(1)
where ρ and Cp represent the density and the specific heat capacity, respectively. For the measurement of the thermal diffusivity, a lot of techniques are proposed and discussed in the literature [15–23]; the most adopted one is the flash method [24–27]. In this technique, a short laser pulse, or flash xenon lamp, heats the front face of the sample while its rear temperature surface is acquired and analyzed. The technique was adopted in [26], where an infrared camera was used to acquire the rear temperature of an AISI 304 stainless steel sheet and the resulting inplane thermal diffusivity value was calculated; these values were successfully compared with the literature one and the obtained ones by the thermal wave interferometry. In [27] the technique was applied in one side configuration: a Nd:Yag pulsed laser was adopted to heat the
Corresponding author at: Via del Politecnico 1, 00133 Rome, Italy. E-mail address: [email protected] (S. Genna).
https://doi.org/10.1016/j.optlastec.2019.01.004 Received 9 October 2018; Received in revised form 16 November 2018; Accepted 7 January 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 113 (2019) 338–344
S. Genna, N. Ucciardello
2
surface while an infrared camera acquired the heated surface, for 1 s at 150 Hz, after the laser pulse. The tests were performed on 4 different materials and on AISI 304 as a reference sample. The obtained values were compared to the obtained one by the classical flash method. In [28] the technique was applied to semitransparent materials (glasses, metallic oxides and cardboard). The flash method has the advantage that consists in a very simple set-up, as compared to the lock-in infrared thermography, that needs synchronization between the laser source and the infrared camera. In [29], for example, a diode laser source (980 nm in wavelength) and the infrared camera were connected to the lock-in synchronization box, that allowed controlling the image capturing and the laser pulse at a certain frequency. From the results, the lock-in thermography approach resulted in good accordance with literature data. In this work, a simple thermographic technique for in-plane thermal diffusivity measurement of electroplated coatings on an aluminium alloy (AA6082) is developed and presented. According to this technique, the heating source and the temperature monitoring are located on the same surface, this allows the measuring of the thermal characteristics on the specimens surfaces, making it particularly suitable for thermal measurements of thin coatings and, in all the application where the rear surface is not accessible for the measuring. For the experiments, five coatings thickness (5, 10, 20, 50 and 100 µm) were electroplated on the aluminium and tested. In the technique, a diode laser source, 975 nm in wavelength, was adopted to induce a thermal contrast on the specimens’ surface. An infrared camera, with a frame rate of 200 Hz, was adopted to acquire the surface gradient temperature and a MATLAB algorithm was developed to calculate the thermal diffusivity. In order to study the influence of the laser parameters set on the technique, two different laser pulses were adopted to heat the specimens; moreover, the influence of the starting acquiring time by IR camera was evaluated. From the results, the technique is demonstrated to be effective for the in-plane thermal diffusivity measurement of thin coatings and, within the investigated parameters window, to be not affected by the checked parameters. Moreover, compared to the uncoated aluminium, the electroplated coatings allow increasing the inplane thermal diffusivity to about 45%.
F (0, t ) = −k
T (r , 0, t ) =
∞
2Q ε
π 3t
exp ⎛− ⎝ n =−∞
∑
⎜
2 [(n − 1)/ L]2 1 ⎞ ⎞·exp ⎛− 2r 2 2 αt R + 8αt ⎠ ⎝ R + 8αt ⎠ ⎟
⎜
⎟
(4) A possible solution to solve the Eq. (4) (i.e. obtaining the temperature as a function of the coordinate r and of the time) is the technique known as ‘Space resolved method’: with the auxilium of the thermographic analysis, the spatial profile along a line passing through the irradiated center spot can be experimentally traced and it can be approximated by a Gaussian equation, as the following: 2
− 2r 1 1 e R2 + 8αt 2 2π R + 8αt
(5)
where the b parameter is given by:
b=
R2 + 8αt
(6)
By this way, the Eq. (4) can be experimentally approximated by the Eq. (5). By squaring Eq. (6), the thermal diffusivity can be calculated as (7)
α = m/8 where m is the slope of the best fitting line (b − t) [16,24,26]. 2
3. Materials and methods 3.1. Coatings preparation 6082-aluminium sheet was chosen as substrate for the electrodeposition process. All the aluminium samples were obtained from the same plate (2 mm in thickness) and manufactured with the same dimensions (40 × 20 mm2). The surface preparation was carried out using a sandblasting machine, which exploits tiny corundum spheres, at high pressure, on the sample surface. The surface preparation was led using grain 80 (180–212 μm) as particle size of the sand, 6 bars for the pressure and 8 s as time of execution of the process, according to [30]. This treatment enables to easily remove the oxide layer that is formed on the aluminium surface, which is the cause of an imperfect and irregular coating, and varying the surface roughness profile that affects the electrodeposition process. Since the rate at which the oxide layer is regenerated is particularly high, the electrodeposition was realized immediately after the sandblasting process. For the process of copper plating, a copper sulfate-based solution was used as acidic electrolytic bath. The sacrificial anode used for the entire process was composed of two copper plates (70 × 35 × 1.5 mm3) connected to each other. In order to maintain the same distance between the electrodes, a specimen holder was designed and build by additive manufacturing (XFAB2000 by DWS), and immersed into the solution, as schematically reported in Fig. 2. The anode was thus also designed to make easily accessible that part of the aluminium sample, which is always above the free surface of the solution, because connected to the terminal of the current generator. The electrolytic bath used was an acidic bath consisted of: 1.25 M CuSO4, 0.61 M H2SO4 and Cl− 50 ppm [31,32]. The baths were kept in agitation by a magnetic agitator, located inside the electrolytic cell. The agitation was set at 3 rpm. According to the Faraday’s law, the current density was set (0.069 A/cm2) and the time of process was changed (t = 3.24, 6.48, 12.97, 32.44 e 64. 89 s) to obtain, respectively, copper thicknesses of 5, 10, 20, 50 and 100 μm. In Fig. 3 the SEM images of cross section of two copper coating
When a Gaussian heat source (with radius R) irradiates an infinite plate (L in thickness), as reported in Fig. 1, neglecting the heat losses, the following equation can be written in cylindrical coordinates:
1 ∂ T (r , z , t ) = 0 α ∂t
(3)
where Q is the total amount of heating energy and δ is the Dirac function. The solution of Eq. (3) can be approximated as follow, according to [26]:
2. Theoretical background
∇2 T 2 (r , z , t ) −
∂ 2Q −2 r 2 T (r , 0, t ) = e R δ (t ) ∂z πR2
(2)
The heat flux on the specimen surface (z = 0) is:
Fig. 1. Schematic of the coordinate system. 339
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Fig. 4. SEM image: typical morphology of surface coatings.
In order to assess the effect of the laser power (P) and the pulse duration (D) on the technique, the measure was repeated with two different laser pulses (P = 20 W, D = 0.05 s and P = 50 W, D = 0.5 s). Secondly, in order to study the influence of the starting acquiring time (i.e. the time beyond which the temperature profiles were extracted and fitted), two different measurements were performed on an AISI316 sample, with two different starting time (0.01 s and 1 s after peak temperature). In Fig. 7 the typical temporal plot in the center of a sample is reported; from the picture, the peak temperature is clearly visible, and it corresponds to the switching-off of the laser radiation. Finally, the thermal diffusivity measurements were performed on the electroplated coatings of an aluminium alloy (AA6082). The measurement was also conducted on the uncoated aluminium to quantify the increase in the diffusivity due to the coatings. For all the tests the samples’ dimensions were fixed (20 × 40 mm2). Before the tests, all the samples surfaces exposed to the laser radiation were black painted, with the aim to uniform the absorption coefficient and to increase the emissivity.
Fig. 2. Schematic of setup for copper plating.
(5 µm and 10 µm) are reported; Fig. 4 depicts the typical morphology of surface coatings. 3.2. Experimental procedure The thermal diffusivity was measured in air at room temperature in one side configuration, i.e. with the heating and the temperature monitoring on the same surface, according to [27]. The experimental set-up adopted is reported in Fig. 5: the center of each sample surface was heated by a single laser pulse of a diode laser, with a beam diameter of about 5 mm. By this way, a thermal contrast on the specimens’ surface was induced. The main laser source characteristics are shown in Table 1. An infrared camera (A655SC by FLIR), with a spectral range of 7.5–14.0 µm, was placed near the samples (300 mm from the surface) to acquire the samples superficial temperature during all the tests. The IR camera was equipped with a lens of 24.6 mm in focal length and the images were captured at the resolution of 640 × 120 pixel, with a frame rate of 200 Hz. The main infrared camera characteristics are shown in Table 2. After the acquisition, the temperature profiles along the line passing through the center of the heated spot (L1 line showed in Fig. 5) were extracted for each acquired frame. A MATLAB algorithm was developed to fit the temperature profiles by Gaussian equation; then, the b2 parameter of each equation was calculated and plotted against the time. In Fig. 6 the flow chart of the algorithm is shown. The thermal diffusivity was calculated from Eq. (6), i.e. ⅛ of the slope of linear regression passing across the couples (b2 − t), according to [16,24,26]. Firstly, the measurement of the diffusivity was performed on a pure copper reference sample, with the aim to check the experimental setup.
4. Results and discussion In Fig. 8 the temperature profile along line passing through the center of the heat spot (Fig. 5) is reported in the case of the pure copper sample, after 1 frame from the peak temperature (corresponding to t = 0.01 s) for the lower laser pulse (P = 20 W, D = 0.05 s). The dots represent the experimental data (acquired by the IR camera), while the line is the best fitting curve, found by the MATLAB algorithm. By the knowledge of the equation of the fitting curve, it is possible to calculate the b2 parameter; in Fig. 9a and b the fitting plots for 20 frames after the peak are reported for the lower and the higher laser pulse, respectively. As can be inferred, the adoption of a higher laser pulse allows reaching, as expected, higher peak temperature (60 °C instead of 30 °C). In Fig. 10 the variation of b2 parameter is plotted against the time for both the adopted pulses; from the diagram, a good coefficient
Fig. 3. SEM images of cross section: nominal thickness (a) 5 µm; (b) 10 µm. 340
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Fig. 5. Experimental set-up for the thermal diffusivity measuring. Table 1 Laser source characteristics. Characteristics
Symbol
Value
Unit
Emission centroid wavelength Emission Linewidth Maximum power Output fibre core diameter Output beam diameter Beam Parameter Product
λ Δλ P
975 ± 5 6 200 200 ≅5 22
[nm] [nm] [W] [μm] [mm] [mm × mrad]
BPP
Table 2 IR camera characteristics. Characteristics
Symbol
Value
Unit
Thermal sensitivity Field of view Focal length Spatial resolution Spectral range Focal Plane Array
NETD FOV – IFOV – FPA
< 0.05 25 × 19 24.6 0.68 7.5–14.0 uncooled
[°C] [deg] [mm] [mrad] [µm] –
of determination is observable for both the pulses; in addition, the slopes of the two lines, corresponding to the linear regression for the calculation of the thermal diffusivity, just differs of 0.5%; thus, the laser pulse, within the adopted values, does not significantly affect the thermal diffusivity measurement. The measured thermal diffusivity (α ≈ 100 mm2 s−1, with a standard deviation equal to 12) is slightly lower than the literature value [33]; it is worth noting that no information on plate manufacturing (i.e. cold worked, annealed,…) is given, this can lead to deviations from the literature value. About the study of the influence of the starting acquiring time, two different measurements were performed on an AISI316 sample, with two different frames after peak temperature, corresponding to the switching-off of the laser radiation: the second frame after the peak temperature (corresponding to 0.01 s) and the two-hundredth one (corresponding to 1 s). The choice of such material was due to its poor thermal characteristics (low thermal diffusivity); this means that the readability of the thermal contrast by the IR camera is good for a relatively long time, allowing testing the procedure up to 1 s after the peak time. On the other hand, these thermal characteristics suggest testing the material with the lower laser pulse (P = 20 W, D = 0.05 s). Following the same procedure adopted in the case of the pure copper, it was possible to obtain the fitting plots and the variation of b2 parameter for both the starting times (reported in Fig. 11 and Fig. 12, respectively). As can be inferred, the coefficient of determination of Fig. 12 is very high (R2 = 0.9997), this means that b2 parameter has a linear trend with the time for both the cases, and, therefore, the measurement of the
Fig. 6. Flow chart of the MATLAB algorithm.
thermal diffusivity is not affected by the starting acquiring time (within the tested values). As a matter of fact, depending on the type of material to be tested, the measurement must be carried out in such a time as to have good thermal contrast on the surface of the sample. If the material has good thermal characteristics (like the copper), the starting time should be as short as possible (to have a good thermal contrast of the specimen surface); on the contrary, in the case of a material with poor thermal characteristics, the measure can start after a relatively long time. The 341
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Fig. 7. Typical temporal plot of center of the irradiated area. Fig. 10. b2 parameter versus time for pure copper for different laser pulses.
On the bases of the aforementioned considerations, the diffusivity measurement of the uncoated aluminium (AA6068) was performed with the higher laser pulse (P = 50 W, D = 0.5 s) and the lower starting time (t = 0.01 s). The results are reported in Fig. 13a and b, where the Gaussian fitting plots and b2 parameter versus time are reported, respectively. From the results, the thermal diffusivity resulted: α ≈ 60 mm2 s−1. Following the same procedure, the thermal diffusivity was measured also for the coated aluminium samples; the results are reported in Fig. 14; for more clarity, the value of the uncoated aluminium is also reported (i.e. thickness = 0). In order to assess the influence of the coating thickness on the thermal diffusivity, the one-way ANOVA (Analysis of Variance) was adopted, with a confidence level of 95% (α = 0.05). From the analysis, the p-value of 0.957 was found; thus, the coating thickness does not statistically affect the in-plane thermal diffusivity. Thus, the adoption of the coating allows an increase of about 45% in the in-plane thermal diffusivity as referred to the uncoated aluminium. Referred to the pure copper, the in-plane thermal diffusivity of the electroplated coating is just lower of 15%. This is a great advantage because the electroplated coating allows adopting the aluminium instead of the pure copper, for example, in some electronic devices.
Fig. 8. Pure copper sample: temperature profile along line passing through the center of the heat spot after the peak temperature (t = 0.01 s) for the lower laser pulse (P = 20 W, D = 0.05 s): the dots represent the experimental data (acquired by the IR camera), the line is the fitting plot.
same considerations can be done in the case of the pulse laser setting: the power and duration have to be set in a way as to not heat all the sample, but only to induce a thermal gradient that can be easily detected by the infrared camera.
5. Conclusions A thermographic procedure, based on the single laser pulse heating,
Fig. 9. Pure copper sample: fitting plots for 20 frames from second frame after the peak temperature (t = 0.01 s) for different laser pulses: (a) P = 20 W, D = 0.05 s, (b) P = 50 W, D = 0.5 s. 342
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Fig. 11. AISI316 sample: Gaussian fitting plots for 20 frames for the same laser pulse (P = 20 W, D = 0.05 s) with different starting acquiring time: (a) t = 0.01 s, (b) t = 1 s after the peak temperature.
Fig. 14. Thermal diffusivity of AA6082 samples (P = 50 W, D = 0.5 s) for different coatings thickness. Fig. 12. AISI316 sample: b2 parameter versus time at the same laser pulse (P = 20 W, D = 0.05 s) with different starting acquiring time: t = 0.01 s and t = 1 s after the peak temperature.
• •
to measure the in-plane thermal diffusivity was presented and discussed. From the results, within the investigated parameters window, the main findings are:
• the
•
technique is effective for the in-plane thermal diffusivity
measurement of different metals (pure copper, AISI316 and aluminium alloy 6082) and of thin electroplated coatings; the coating thickness does not statistically affect the in-plane thermal diffusivity; the adoption of the electroplated coating (even only 5 µm) allows an increase of about 45% in the in-plane thermal diffusivity, as referred to the uncoated aluminium; the in-plane diffusivity of the coated aluminium is just lower than
Fig. 13. AA6082 sample (P = 50 W, D = 0.5 s): (a) Gaussian fitting plots and (b) b2 parameter versus time. 343
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15% of the pure copper one;
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• the technique can be adopted to characterize cooling systems for
electronic devices with the coating on just one side; alternatively, in all the application where the rear surface is not accessible for the measuring.
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Full length article
A thermographic technique for in-plane thermal diffusivity measurement of electroplated coatings
T
⁎
S. Genna , N. Ucciardello Department of Enterprise Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy CIRTIBS Research Centre, University of Naples Federico II, P.le Tecchio 80, 80125 Naples, Italy
H I GH L IG H T S
procedure was developed for the in-plane thermal diffusivity. • AThethermographic is effective for the in-plane thermal diffusivity of thin coatings. • The technique • coating allows an increase of about 45% in thermal diffusivity of the aluminium.
A R T I C LE I N FO
A B S T R A C T
Keywords: Laser Thermal analysis Thermography Copper Aluminium alloy
In the present work, a thermographic procedure is developed and tested with the aim to determine the in-plane thermal diffusivities of electroplated coatings with different thickness on an aluminium alloy (AA6082). For the tests, a single pulse of a diode laser source was adopted to generate a thermal contrast on the specimen’s surface. An infrared camera was adopted to acquire the surface gradient temperature and a MATLAB algorithm was developed to calculate the thermal diffusivity. In order to study the influence of the laser parameters set on the technique, two different laser pulses were adopted to heat the specimens; moreover, the influence of the starting acquiring time by IR camera was also evaluated. From the results, the technique is demonstrated to be effective for the in-plane thermal diffusivity measurement of thin coatings and, within the investigated parameters window, to be not affected by the checked parameters.
1. Introduction Nowadays, heat dissipation represents a critical issue in many technological fields; for example, in many electronic devices and systems, the specific thermal power to be dissipated is very high, because the surfaces for the heat exchange are very small. As a matter, the cooling performances cannot achieve the required ones, because of the limited thermal conductivity of the adopted materials [1]. Thus, new materials characterized by higher thermal conductivity are needed to be developed [2]; in last years, a lot of studies were conducted to use the excellent mechanical and thermal properties of nanoscale carbon materials: carbon nanotubes (CNT) [3,4], graphene [5,6] or graphite nanoplatelets (GNP) [7] and nanodiamonds [8,9] were adopted as filler of metal matrix composites (MMC) by different techniques [10–14]. Accordingly, the knowledge of the thermal conductivity of these new materials is crucial; since the thermal conductivity measurement require the knowledge of the heat flux (difficult and unreliable
⁎
measurement), it is generally preferred to experimentally evaluate the thermal diffusivity (α) and to obtain the thermal conductivity (k) by the well-known relation:
k = αρCp
(1)
where ρ and Cp represent the density and the specific heat capacity, respectively. For the measurement of the thermal diffusivity, a lot of techniques are proposed and discussed in the literature [15–23]; the most adopted one is the flash method [24–27]. In this technique, a short laser pulse, or flash xenon lamp, heats the front face of the sample while its rear temperature surface is acquired and analyzed. The technique was adopted in [26], where an infrared camera was used to acquire the rear temperature of an AISI 304 stainless steel sheet and the resulting inplane thermal diffusivity value was calculated; these values were successfully compared with the literature one and the obtained ones by the thermal wave interferometry. In [27] the technique was applied in one side configuration: a Nd:Yag pulsed laser was adopted to heat the
Corresponding author at: Via del Politecnico 1, 00133 Rome, Italy. E-mail address: [email protected] (S. Genna).
https://doi.org/10.1016/j.optlastec.2019.01.004 Received 9 October 2018; Received in revised form 16 November 2018; Accepted 7 January 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
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2
surface while an infrared camera acquired the heated surface, for 1 s at 150 Hz, after the laser pulse. The tests were performed on 4 different materials and on AISI 304 as a reference sample. The obtained values were compared to the obtained one by the classical flash method. In [28] the technique was applied to semitransparent materials (glasses, metallic oxides and cardboard). The flash method has the advantage that consists in a very simple set-up, as compared to the lock-in infrared thermography, that needs synchronization between the laser source and the infrared camera. In [29], for example, a diode laser source (980 nm in wavelength) and the infrared camera were connected to the lock-in synchronization box, that allowed controlling the image capturing and the laser pulse at a certain frequency. From the results, the lock-in thermography approach resulted in good accordance with literature data. In this work, a simple thermographic technique for in-plane thermal diffusivity measurement of electroplated coatings on an aluminium alloy (AA6082) is developed and presented. According to this technique, the heating source and the temperature monitoring are located on the same surface, this allows the measuring of the thermal characteristics on the specimens surfaces, making it particularly suitable for thermal measurements of thin coatings and, in all the application where the rear surface is not accessible for the measuring. For the experiments, five coatings thickness (5, 10, 20, 50 and 100 µm) were electroplated on the aluminium and tested. In the technique, a diode laser source, 975 nm in wavelength, was adopted to induce a thermal contrast on the specimens’ surface. An infrared camera, with a frame rate of 200 Hz, was adopted to acquire the surface gradient temperature and a MATLAB algorithm was developed to calculate the thermal diffusivity. In order to study the influence of the laser parameters set on the technique, two different laser pulses were adopted to heat the specimens; moreover, the influence of the starting acquiring time by IR camera was evaluated. From the results, the technique is demonstrated to be effective for the in-plane thermal diffusivity measurement of thin coatings and, within the investigated parameters window, to be not affected by the checked parameters. Moreover, compared to the uncoated aluminium, the electroplated coatings allow increasing the inplane thermal diffusivity to about 45%.
F (0, t ) = −k
T (r , 0, t ) =
∞
2Q ε
π 3t
exp ⎛− ⎝ n =−∞
∑
⎜
2 [(n − 1)/ L]2 1 ⎞ ⎞·exp ⎛− 2r 2 2 αt R + 8αt ⎠ ⎝ R + 8αt ⎠ ⎟
⎜
⎟
(4) A possible solution to solve the Eq. (4) (i.e. obtaining the temperature as a function of the coordinate r and of the time) is the technique known as ‘Space resolved method’: with the auxilium of the thermographic analysis, the spatial profile along a line passing through the irradiated center spot can be experimentally traced and it can be approximated by a Gaussian equation, as the following: 2
− 2r 1 1 e R2 + 8αt 2 2π R + 8αt
(5)
where the b parameter is given by:
b=
R2 + 8αt
(6)
By this way, the Eq. (4) can be experimentally approximated by the Eq. (5). By squaring Eq. (6), the thermal diffusivity can be calculated as (7)
α = m/8 where m is the slope of the best fitting line (b − t) [16,24,26]. 2
3. Materials and methods 3.1. Coatings preparation 6082-aluminium sheet was chosen as substrate for the electrodeposition process. All the aluminium samples were obtained from the same plate (2 mm in thickness) and manufactured with the same dimensions (40 × 20 mm2). The surface preparation was carried out using a sandblasting machine, which exploits tiny corundum spheres, at high pressure, on the sample surface. The surface preparation was led using grain 80 (180–212 μm) as particle size of the sand, 6 bars for the pressure and 8 s as time of execution of the process, according to [30]. This treatment enables to easily remove the oxide layer that is formed on the aluminium surface, which is the cause of an imperfect and irregular coating, and varying the surface roughness profile that affects the electrodeposition process. Since the rate at which the oxide layer is regenerated is particularly high, the electrodeposition was realized immediately after the sandblasting process. For the process of copper plating, a copper sulfate-based solution was used as acidic electrolytic bath. The sacrificial anode used for the entire process was composed of two copper plates (70 × 35 × 1.5 mm3) connected to each other. In order to maintain the same distance between the electrodes, a specimen holder was designed and build by additive manufacturing (XFAB2000 by DWS), and immersed into the solution, as schematically reported in Fig. 2. The anode was thus also designed to make easily accessible that part of the aluminium sample, which is always above the free surface of the solution, because connected to the terminal of the current generator. The electrolytic bath used was an acidic bath consisted of: 1.25 M CuSO4, 0.61 M H2SO4 and Cl− 50 ppm [31,32]. The baths were kept in agitation by a magnetic agitator, located inside the electrolytic cell. The agitation was set at 3 rpm. According to the Faraday’s law, the current density was set (0.069 A/cm2) and the time of process was changed (t = 3.24, 6.48, 12.97, 32.44 e 64. 89 s) to obtain, respectively, copper thicknesses of 5, 10, 20, 50 and 100 μm. In Fig. 3 the SEM images of cross section of two copper coating
When a Gaussian heat source (with radius R) irradiates an infinite plate (L in thickness), as reported in Fig. 1, neglecting the heat losses, the following equation can be written in cylindrical coordinates:
1 ∂ T (r , z , t ) = 0 α ∂t
(3)
where Q is the total amount of heating energy and δ is the Dirac function. The solution of Eq. (3) can be approximated as follow, according to [26]:
2. Theoretical background
∇2 T 2 (r , z , t ) −
∂ 2Q −2 r 2 T (r , 0, t ) = e R δ (t ) ∂z πR2
(2)
The heat flux on the specimen surface (z = 0) is:
Fig. 1. Schematic of the coordinate system. 339
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Fig. 4. SEM image: typical morphology of surface coatings.
In order to assess the effect of the laser power (P) and the pulse duration (D) on the technique, the measure was repeated with two different laser pulses (P = 20 W, D = 0.05 s and P = 50 W, D = 0.5 s). Secondly, in order to study the influence of the starting acquiring time (i.e. the time beyond which the temperature profiles were extracted and fitted), two different measurements were performed on an AISI316 sample, with two different starting time (0.01 s and 1 s after peak temperature). In Fig. 7 the typical temporal plot in the center of a sample is reported; from the picture, the peak temperature is clearly visible, and it corresponds to the switching-off of the laser radiation. Finally, the thermal diffusivity measurements were performed on the electroplated coatings of an aluminium alloy (AA6082). The measurement was also conducted on the uncoated aluminium to quantify the increase in the diffusivity due to the coatings. For all the tests the samples’ dimensions were fixed (20 × 40 mm2). Before the tests, all the samples surfaces exposed to the laser radiation were black painted, with the aim to uniform the absorption coefficient and to increase the emissivity.
Fig. 2. Schematic of setup for copper plating.
(5 µm and 10 µm) are reported; Fig. 4 depicts the typical morphology of surface coatings. 3.2. Experimental procedure The thermal diffusivity was measured in air at room temperature in one side configuration, i.e. with the heating and the temperature monitoring on the same surface, according to [27]. The experimental set-up adopted is reported in Fig. 5: the center of each sample surface was heated by a single laser pulse of a diode laser, with a beam diameter of about 5 mm. By this way, a thermal contrast on the specimens’ surface was induced. The main laser source characteristics are shown in Table 1. An infrared camera (A655SC by FLIR), with a spectral range of 7.5–14.0 µm, was placed near the samples (300 mm from the surface) to acquire the samples superficial temperature during all the tests. The IR camera was equipped with a lens of 24.6 mm in focal length and the images were captured at the resolution of 640 × 120 pixel, with a frame rate of 200 Hz. The main infrared camera characteristics are shown in Table 2. After the acquisition, the temperature profiles along the line passing through the center of the heated spot (L1 line showed in Fig. 5) were extracted for each acquired frame. A MATLAB algorithm was developed to fit the temperature profiles by Gaussian equation; then, the b2 parameter of each equation was calculated and plotted against the time. In Fig. 6 the flow chart of the algorithm is shown. The thermal diffusivity was calculated from Eq. (6), i.e. ⅛ of the slope of linear regression passing across the couples (b2 − t), according to [16,24,26]. Firstly, the measurement of the diffusivity was performed on a pure copper reference sample, with the aim to check the experimental setup.
4. Results and discussion In Fig. 8 the temperature profile along line passing through the center of the heat spot (Fig. 5) is reported in the case of the pure copper sample, after 1 frame from the peak temperature (corresponding to t = 0.01 s) for the lower laser pulse (P = 20 W, D = 0.05 s). The dots represent the experimental data (acquired by the IR camera), while the line is the best fitting curve, found by the MATLAB algorithm. By the knowledge of the equation of the fitting curve, it is possible to calculate the b2 parameter; in Fig. 9a and b the fitting plots for 20 frames after the peak are reported for the lower and the higher laser pulse, respectively. As can be inferred, the adoption of a higher laser pulse allows reaching, as expected, higher peak temperature (60 °C instead of 30 °C). In Fig. 10 the variation of b2 parameter is plotted against the time for both the adopted pulses; from the diagram, a good coefficient
Fig. 3. SEM images of cross section: nominal thickness (a) 5 µm; (b) 10 µm. 340
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Fig. 5. Experimental set-up for the thermal diffusivity measuring. Table 1 Laser source characteristics. Characteristics
Symbol
Value
Unit
Emission centroid wavelength Emission Linewidth Maximum power Output fibre core diameter Output beam diameter Beam Parameter Product
λ Δλ P
975 ± 5 6 200 200 ≅5 22
[nm] [nm] [W] [μm] [mm] [mm × mrad]
BPP
Table 2 IR camera characteristics. Characteristics
Symbol
Value
Unit
Thermal sensitivity Field of view Focal length Spatial resolution Spectral range Focal Plane Array
NETD FOV – IFOV – FPA
< 0.05 25 × 19 24.6 0.68 7.5–14.0 uncooled
[°C] [deg] [mm] [mrad] [µm] –
of determination is observable for both the pulses; in addition, the slopes of the two lines, corresponding to the linear regression for the calculation of the thermal diffusivity, just differs of 0.5%; thus, the laser pulse, within the adopted values, does not significantly affect the thermal diffusivity measurement. The measured thermal diffusivity (α ≈ 100 mm2 s−1, with a standard deviation equal to 12) is slightly lower than the literature value [33]; it is worth noting that no information on plate manufacturing (i.e. cold worked, annealed,…) is given, this can lead to deviations from the literature value. About the study of the influence of the starting acquiring time, two different measurements were performed on an AISI316 sample, with two different frames after peak temperature, corresponding to the switching-off of the laser radiation: the second frame after the peak temperature (corresponding to 0.01 s) and the two-hundredth one (corresponding to 1 s). The choice of such material was due to its poor thermal characteristics (low thermal diffusivity); this means that the readability of the thermal contrast by the IR camera is good for a relatively long time, allowing testing the procedure up to 1 s after the peak time. On the other hand, these thermal characteristics suggest testing the material with the lower laser pulse (P = 20 W, D = 0.05 s). Following the same procedure adopted in the case of the pure copper, it was possible to obtain the fitting plots and the variation of b2 parameter for both the starting times (reported in Fig. 11 and Fig. 12, respectively). As can be inferred, the coefficient of determination of Fig. 12 is very high (R2 = 0.9997), this means that b2 parameter has a linear trend with the time for both the cases, and, therefore, the measurement of the
Fig. 6. Flow chart of the MATLAB algorithm.
thermal diffusivity is not affected by the starting acquiring time (within the tested values). As a matter of fact, depending on the type of material to be tested, the measurement must be carried out in such a time as to have good thermal contrast on the surface of the sample. If the material has good thermal characteristics (like the copper), the starting time should be as short as possible (to have a good thermal contrast of the specimen surface); on the contrary, in the case of a material with poor thermal characteristics, the measure can start after a relatively long time. The 341
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Fig. 7. Typical temporal plot of center of the irradiated area. Fig. 10. b2 parameter versus time for pure copper for different laser pulses.
On the bases of the aforementioned considerations, the diffusivity measurement of the uncoated aluminium (AA6068) was performed with the higher laser pulse (P = 50 W, D = 0.5 s) and the lower starting time (t = 0.01 s). The results are reported in Fig. 13a and b, where the Gaussian fitting plots and b2 parameter versus time are reported, respectively. From the results, the thermal diffusivity resulted: α ≈ 60 mm2 s−1. Following the same procedure, the thermal diffusivity was measured also for the coated aluminium samples; the results are reported in Fig. 14; for more clarity, the value of the uncoated aluminium is also reported (i.e. thickness = 0). In order to assess the influence of the coating thickness on the thermal diffusivity, the one-way ANOVA (Analysis of Variance) was adopted, with a confidence level of 95% (α = 0.05). From the analysis, the p-value of 0.957 was found; thus, the coating thickness does not statistically affect the in-plane thermal diffusivity. Thus, the adoption of the coating allows an increase of about 45% in the in-plane thermal diffusivity as referred to the uncoated aluminium. Referred to the pure copper, the in-plane thermal diffusivity of the electroplated coating is just lower of 15%. This is a great advantage because the electroplated coating allows adopting the aluminium instead of the pure copper, for example, in some electronic devices.
Fig. 8. Pure copper sample: temperature profile along line passing through the center of the heat spot after the peak temperature (t = 0.01 s) for the lower laser pulse (P = 20 W, D = 0.05 s): the dots represent the experimental data (acquired by the IR camera), the line is the fitting plot.
same considerations can be done in the case of the pulse laser setting: the power and duration have to be set in a way as to not heat all the sample, but only to induce a thermal gradient that can be easily detected by the infrared camera.
5. Conclusions A thermographic procedure, based on the single laser pulse heating,
Fig. 9. Pure copper sample: fitting plots for 20 frames from second frame after the peak temperature (t = 0.01 s) for different laser pulses: (a) P = 20 W, D = 0.05 s, (b) P = 50 W, D = 0.5 s. 342
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Fig. 11. AISI316 sample: Gaussian fitting plots for 20 frames for the same laser pulse (P = 20 W, D = 0.05 s) with different starting acquiring time: (a) t = 0.01 s, (b) t = 1 s after the peak temperature.
Fig. 14. Thermal diffusivity of AA6082 samples (P = 50 W, D = 0.5 s) for different coatings thickness. Fig. 12. AISI316 sample: b2 parameter versus time at the same laser pulse (P = 20 W, D = 0.05 s) with different starting acquiring time: t = 0.01 s and t = 1 s after the peak temperature.
• •
to measure the in-plane thermal diffusivity was presented and discussed. From the results, within the investigated parameters window, the main findings are:
• the
•
technique is effective for the in-plane thermal diffusivity
measurement of different metals (pure copper, AISI316 and aluminium alloy 6082) and of thin electroplated coatings; the coating thickness does not statistically affect the in-plane thermal diffusivity; the adoption of the electroplated coating (even only 5 µm) allows an increase of about 45% in the in-plane thermal diffusivity, as referred to the uncoated aluminium; the in-plane diffusivity of the coated aluminium is just lower than
Fig. 13. AA6082 sample (P = 50 W, D = 0.5 s): (a) Gaussian fitting plots and (b) b2 parameter versus time. 343
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15% of the pure copper one;
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• the technique can be adopted to characterize cooling systems for
electronic devices with the coating on just one side; alternatively, in all the application where the rear surface is not accessible for the measuring.
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