Lifetime-based measurement of stress during cyclic elastic deformation using mechanoluminescence of SrAl2O4:Eu2+ Satoshi Someya,1,2,* Keiko Ishii,1,2 Tetsuo Munakata,1,2 and Masayuki Saeki3 1
National Institute of Advanced Industrial Science and Technology, 1-2-1 Namiki, Tsukuba, Ibaraki 3058564, Japan 2 School of Frontier Science, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba, 2778563, Japan 3 Department of Civil Enginnering, Tokyo University of Science, 2641, Yamasaki, Noda, Chiba 2788510, Japan * [email protected]
Abstract: The present study focused on the rise time and decay times of mechanoluminescence (ML) during cyclic elastic deformation of SrAl2O4:Eu2+. The time constants during compression and decompression, τup and τdown, respectively, did not change from the 2nd to the 5th cycle. Both τup and τdown were expressed by a linear function of the maximum load and the inverse of the loading rate. τup depended only on the loading time, whereas τdown was affected by the loading time and the rate of change of the strain energy. Measuring τdown may enable evaluation of the loading conditions even under cyclic loading and may enhance the practicality of a ML phosphor. ©2014 Optical Society of America OCIS codes: (040.0040) Detectors; (280.4788) Optical sensing and sensors; (280.5475) Pressure measurement; (260.3800) Luminescence.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
D. Olawale, T. Dickens, W. Sullivan, O. Okoli, J. Sobanjo, and B. Wang, “Progress in triboluminescence-based smart optical sensor system,” J. Lumin. 131(7), 1407–1418 (2011). C. Xu, T. Watanabe, M. Akiyama, and X. Zheng, “Direct view of stress distribution in solid by mechanoluminescence,” Appl. Phys. Lett. 74(17), 2414–2416 (1999). C. Xu, H. Yamada, X. Wang, and X. Zheng, “Strong elasticoluminescence from monoclinic-structure SrAl2O4,” Appl. Phys. Lett. 84(16), 3040–3042 (2004). Y. Jia, M. Yei, and W. Jia, “Stress-induced mechanoluminescence in SrAl2O4:Eu2+,Dy3+,” Opt. Mater. 28(8-9), 974–979 (2006). J. S. Kim, K. Kibble, Y. N. Kwon, and K. S. Sohn, “Rate-equation model for the loading-rate-dependent mechanoluminescence of SrAl2O4:Eu2+,Dy3+.,” Opt. Lett. 34(13), 1915–1917 (2009). M. R. Rahimi, G. J. Yun, G. L. Doll, and J. S. Choi, “Effects of persistent luminescence decay on mechanoluminescence phenomena of SrAl2O4:Eu2+, Dy3+ materials,” Opt. Lett. 38(20), 4134–4137 (2013). F. Clabau, X. Rocquefelte, S. Jobic, P. Deniard, M. Whangbo, A. Garcia, and T. Mercier, “On the phosphorescence mechanism in SrAl2O4:Eu2+ and its codoped derivatives,” Solid State Sci. 9(7), 608–612 (2007). V. K. Chandra and B. P. Chandra, “Dynamics of the mechanoluminescence induced by elastic deformation of persistent luminescent crystals,” J. Lumin. 132(3), 858–869 (2012). B. P. Chandra, V. D. Sonwane, B. K. Haldar, and S. Pandey, “Mechanoluminescence glow curves of rare-earth doped strontium aluminate phosphors,” Opt. Mater. 33(3), 444–451 (2011). B. P. Chandra, V. K. Chandra, and P. Jha, “Microscopic theory of elastic-mechanoluminescent smart materials,” Appl. Phys. Lett. 104(3), 031102 (2014). K. Sohn, S. Seo, Y. Kwon, and H. Park, “Direct observation of crack tip stress field using the mechanoluminescence of SrAl2O4:(Eu, Dy, Nd),” J. Am. Ceram. Soc. 85(3), 712–714 (2002). N. Terasaki, H. Yamada, and C. N. Xu, “Ultrasonic wave induced mechanoluminescence and its application for photocatalysis as ubiquitous light source,” Catal. Today 201, 203–208 (2013). S. Timilsina, K. H. Lee, I. Y. Jang, and J. S. Kim, “Mechanoluminescent determination of the mode I stress intensity factor in SrAl2O4:Eu2+,Dy3+,” Acta Mater. 61(19), 7197–7206 (2013). Y. Fujio, C. N. Xu, N. Terasaki, and N. Ueno, “Influence of organic solvent treatment on elasticoluminescent property of europium-doped strontium aluminates,” J. Lumin. 148, 89–93 (2014).
#212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21991
15. S. Someya, Y. Li, K. Ishii, and K. Okamoto, “Combined two-dimensional velocity and temperature measurements of natural convection using a high-speed camera and temperature sensitive particles,” Exp. Fluids 50(1), 65–73 (2011). 16. S. Someya, Y. Okura, T. Munakata, and K. Okamoto, “Instantaneous imaging 2D temperature in an engine cylinder in a frame combustion condition,” Int. J. Heat Mass Tran. 62, 382–390 (2013). 17. S. Someya, K. Ishii, M. Saeki, and T. Munakata, “Lifetime-based measurement of stress using mechanoluminescence of SrAl2O4:Eu2+.,” Opt. Lett. 38(7), 1095–1097 (2013).
1. Introduction Various organic and inorganic materials can emit mechanoluminescence (ML) due to factors such as stress, strain, friction and fracture [1]. Xu et al. [2, 3] developed a bright ML phosphor, SrAl2O4:Eu2+ (SAOE), which enables direct observation of the stress distribution. The ML intensity was three orders of magnitude higher than that of quartz [1]. The response characteristics [4–6], mechanisms [7–10], devices and applications [11–14] of ML have also been recently investigated. The ML intensity was found to increase proportionally with increasing applied stress [2]. The intensity was also related to the loading rate [5]. Intensity-based measurements for quantitative nondestructive evaluation require that the whole system be precisely controlled, because the intensity strongly depends not only on the stress, but also on factors such as the excitation power, SAOE concentration, and ambient light. However, to the best of the authors’ knowledge, all applications of SAOE thus far have adopted intensity-based sensing. The ML intensity was measured 5~10 min after 3~10 min of UV irradiation in order to maintain the initial excitation conditions. This results in an undesirable and unavoidable long stand-by time before each measurement. The intensity-based sensing doesn’t accept any change of stress condition during the stand-by time. This stand-by time limits the applicability of ML-based measurement techniques. The stress condition in many practical structures is not often stable. It is difficult to avoid undesirable stress and to have such stand-by time. Qualitative intensity-based measurements could be applied only for the first application of stress after the stand-by time, and could not measure a repetitive stress. Cyclic stress should be evaluated based on the other factors, except for the value of intensity. On the other hand, there have been many experimental studies on the lifetime of luminescence [15, 16]. The lifetime is typically not affected by the excitation power or by the concentration of the sensor material. Someya et al. [17] focused on transient ML behavior, i.e., the rise and decay time constants, during first application of elastic deformation. The measured rise and decay time constants were independent of concentration and excitation power. They were proportional to the applied loads and inversely proportional to the loading rates. These results indicate that measurements based on rise or decay time constants may decrease both the measurement uncertainty and stand-by time. However, it is still unknown whether ML and the lifetime-based measurement can be applied to a cyclic stress. There are few previous reports focused on the ML response under cyclic stress. Therefore, the present study focused on the ML rise and decay time constants during cyclic elastic deformation in order to enhance the applicability and the practicality of the ML. The effects of applied loads and loading rate to the rise and decay time constants were systematically investigated. 2. Experimental To evaluate the ML properties, a commercial SAOE powder (TAIKO-ML-1, Taiko Refractories Co., Ltd.) was mixed with an optical epoxy resin and used to form disks [2, 4] 30 mm in diameter and 7 mm thick. The mass fraction of SAOE was fixed at 10 wt%. The transient ML intensity was measured by a photomultiplier tube (H10721-01, Hamamatsu Photonics) and recorded using an oscilloscope (MSO2024B, Textronix Inc.). The entire experimental setup was shielded from ambient light to minimize its effect on the ML intensity measurements. The disks were exposed to 360-nm UV light at less than 100 mW for 1 min
#212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21992
ML intensity (PMT output) [V]
and aged in a dark room for 3 min to allow the luminescence to relax before loading. The initial ML intensity, i.e., the excitation power and the aging time, was fixed in the present experiments. Stress was applied to the sample by a materials testing machine (SVZ-200NB, Imada-ss Co.) which allowed control of the loading rate and maximum load. The maximum load and loading rate were varied from 400 to 900 N, from 117 to 365 N/s, respectively. Five cycles of loading were applied at intervals of three seconds. Three trials were performed under each set of experimental conditions. Nmax = 800[N]
1st Cycle 2nd Cycle 3rd Cycle 4th Cycle 5th Cycle
dN/dt = 240[N/s]
0.2
0.1
0 −5
0
5
Time[s]
Time constants of ML( τ)
Fig. 1. Transient intensity of ML under cyclic loading.
Cycle No. 1 2 3 2 4 5
τ up τ down
1
400
600
800
Maximum load[N]
Fig. 2. Relationship between Nmax and the time constants τup and τdown.
3. Results and discussion 3.1 ML response to the cyclic loading Figure 1 shows the instantaneous ML intensity and the applied load over five cycles. The initial ML intensity was subtracted from the raw data as background noise in Fig. 1. The intensity before and after each cycle was almost constant, and the intensity difference before and after each cycle was less than 0.003 V, a few percent of the total intensity. The time t was
#212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21993
defined as zero when the load was at its maximum, Nmax. In Fig. 1, the loading rate and maximum load were fixed at 240 N/s and 800 N, respectively. The peak intensity Imax of the first cycle has often been used in previous reports to evaluate the magnitude of the stress. Xu et al. [2] reported that the peak intensity in the first application of stress was linearly proportional to the magnitude of the applied load. It is seen that Imax decreased gradually during the cyclic loading in Fig. 1. Therefore the value of cyclic stress can’t be evaluated by the value of intensity at each cycle. The present study focused on the transient process. The luminescence intensity is usually expressed by an exponential function, Eq. (1), using a time constant, τ, which is a lifetime of trapped electrons [8, 9, 15–17]. We assumed that the ML rise and decay time constants during cyclic elastic deformation in Fig. 1 could be expressed by Eq. (1). The ML rise time constant, τup, and decay time constant, τdown, were individually calculated using the least squares method: I ( t ) = Ae − t τ + C
(1)
Here I(t) is the ML intensity at time t, and A and C are constants. Figure 2 shows the relationship between τup, τdown, and the peak value of the applied load Nmax at a fixed loading rate of 240 N/s under cyclic loading. The error bars represent the standard deviation, which are small especially after the second cycle. The dashed lines represent linear functions obtained using the least squares method. As shown in Fig. 2, both τup (open circles) and τdown (open triangles) in each cycle increased linearly with increasing Nmax. τup was shorter than τdown in all cases. This difference in time constants implies that the mechanisms operating during compression and decompression are different. The relationships between τup, τdown, and the peak value of the applied load almost never changed from the second cycle to the fifth cycle. However, the relationships between τup, τdown, and Nmax in the first cycle were different from those after the second cycle. The rate of change in τup also appears to be different between the first cycle and after the second cycle, while that of τdown looks to be nearly equal. Further studies are required to clarify the differences between the time constants τup and τdown during the first cycle and after the second cycle. 5
Time constants of ML( τ )
4 3
τ up τ down
Cycle No.1 2 3 4 5
2
1 0.9 0.8 0.7 0.6 0.5 100
200
Loading rate[N/s]
300
400
Fig. 3. Effect of loading rate on time constants τup and τdown.
The effect of the loading rate dN/dt on the rise and decay time constants under cyclic loading was also investigated, as shown in Fig. 3. Nmax was fixed at 800 N, and dN/dt was changed from 117 to 365 N/s. The dashed lines represent linear functions obtained using the least squares method. Both τup and τdown at each cycle in the different runs were found to be #212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21994
inversely proportional to dN/dt. τup was shorter than τdown in all cases. The relationships between τup, τdown, and the loading rate also remained nearly identical from the second cycle to the fifth cycle. However, the relationships between τup, τdown, and dN/dt in the first cycle were different from those after the second cycle. Once again, the rate of change in τup also appears to change after the second cycle, while that of τdown does not. These trends in τup and τdown were similar to those shown in Fig. 2. As shown in Figs. 2 and 3, the error bars for τup and τdown after the second cycle were smaller than those during the first cycle. Thus, the rise time constant τup and the decay time constant τdown may be useful for evaluating the peak load, even under cyclic loading, at least under a fixed loading rate. These values may also be useful for evaluating the loading rate given a fixed peak load, and may offer a lower degree of uncertainty than that associated with stress evaluation based on the value of intensity. The present paper focused on the transient intensity and the time constants τup and τdown during cyclic loading, resulting in the following relationship between the time constants and loading conditions:
τ up ,τ down ∝ N max ,1 ( dN dt )
(2)
Thus, measurements based on the time constants τup and τdown cannot only decrease the measurement uncertainty but can also remove the restriction of maximum intensity based measurements to the first loading after a required stand-by time. Measuring τup and τdown may enable evaluation of the loading conditions, even under cyclic loading. These relationships between τup, τdown, and the peak value of the applied load, the loading rate, during cyclic loading are firstly reported in this study and these may enhance the practicality of a ML phosphor. 3.2 Effect of the loading time Then, the effect of the loading time on the time constants were also investigated. From Eq. (2), τup and τdown can be represented as follows:
τ i = aτ
i
N max 1 + bτ i +c N +d ( dN dt ) ( dN dt ) τ i max τ i
(3)
Here, aτi, bτi, cτi, and dτi are constants dependent on the ML material and a test piece. The subscript i represents either up or down. Here, since the loading rate was not time dependent and was constant in each loading experiment, the product of Nmax and 1/dN/dt became the loading time Δt. Therefore, it is not clear whether the time constants τup and τdown depended on Nmax and dN/dt individually. There is a possibility that the time constants depended on the loading time (Nmax/(dN/dt)) only, regardless of the maximum load or loading rate, in other words, bτi and cτi might be both zero.
#212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21995
Peak intensity of ML, Imax [V]
0.2
Loading time 2s 2.5s 3s 3.5s
0.1 1 cycle 2 cycle 3 cycle 0
1
2
5 3 [ x 10 ]
Nmax dN/dt (Rate of change of strain energy,dE/dt )
Fig. 4. Relationship between Imax and the rate of change of strain energy under cyclic loading for various loading times.
Therefore, additional experiments were performed with varying loading times Δt = Nmax /(dN/dt). Figure 4 shows the maximum intensity Imax in the first three cycles, with loading times of 2.0 to 3.5 s. The loading time was controlled by changing Nmax and dN/dt from 235 to 900 N and from 117 to 363 N/s, respectively. The horizontal axis is the product of Nmax and dN/dt, which is related to the rate of change of the strain energy with time, dE/dt. The maximum intensity decreased as successive loading cycles were applied. There was no relationship between the maximum intensity and the loading time, at least in the range of 2.0– 3.5 s. Imax increased with increasing rate of change of the strain energy in each cycle. The dashed lines represent parabolic functions obtained using the least squares method, because the maximum intensity was proportional to both the maximum load and the loading rate. Thus, the peak intensity is found to be still proportional to Nmax and dN/dt during cyclic loading though the value decreases gradually in the sequential cycles and it is difficult to evaluate Nmax and dN/dt quantitatively during cyclic loading. τ up τ down
Time constants of ML( τ )
3
Loading time 3.5s 3s 2.5s 2s
2
1
0
1
2
5 3 [ x 10 ]
Nmax dN/dt (Rate of change of strain energy,dE/dt )
Fig. 5. Relationship between time constants and the rate of change of strain energy in the second cycle for various loading times.
#212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21996
Time constant of ML( τ )
1.2
1
0.8
2
2.5
3
Loading time [s]
3.5
Fig. 6. Relationship between the rising time constant τup and the loading time.
Figure 5 shows the relationship between the time constants after the second cycle and the rate of change of the strain energy, for loading times of 2.0 to 3.5 s. The time constant under compression τup depended only on the loading time Nmax / (dN/dt) and was independent of the rate of change of the strain energy. τup increased with increasing loading time, resulting in the increase of τup with increasing maximum load under fixed loading rate and the decrease of τup with increasing loading rate at the fixed maximum load. τup did not depend on the maximum load Nmax and the loading rate dN/dt separately. bτi and cτi in Eq. (3) were equal to zero. Therefore, the ML intensity during compression after the second cycle of loading can be represented by the following equation, Eq. (4). I ( t ) = Ae
( t ( Δt ⋅ a
τ up
+ dτ up
))
+C
(4)
Figure 6 summarizes the relationship between the loading time and the time constant τup. τup was expressed by a linear function of the loading time, and the coefficients aτup and dτup were calculated to be 0.37 and 0.006, respectively, in our experiments. dτup was nearly equal to zero and τup was almost proportional to the loading time. These empirical values also fit the experimental data shown as red dotted lines in Figs. 2 and 3. 3.3 Effect of the time rate of strain energy On the other hand, as shown in Fig. 5, τdown was strongly dependent on not only the loading time, but also on the rate of change of the strain energy. τdown decreased as the rate of change of the strain energy increased for each loading time, and with decreasing loading time at a fixed rate of change of the strain energy. The chain lines about τdown in Fig. 5 represent logarithmic functions, as given by Eq. (5), and were obtained using the least squares method for τdown at each loading time. y and x are constants. y increased and x decreased with increasing rate of change of the strain energy.
τ down = x ln ( N max ⋅ dN dt ) + y = x ln ( dE dt ) + y
(5)
Chandra and his group [8–10] discussed the mechanism of ML based on a decreasing trap depth of carriers due to the piezoelectric fields. Rahimi et al. [6] claimed that both the thermal energy and the piezoelectric fields affect the ML intensity. We speculate that there would be an excessive population of electrons in the excited state after the UV-excitation of ML materials, which would overflow as ML and photoluminescence during the first loading. Then, the electrons decay from the excited state to the ground state as ML due to piezoelectric
#212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21997
effects, almost without additional photoluminescent overflow, resulting in constant τup and τdown values after the second loading. However, there are few papers and experimental data of the transient ML intensity under cyclic loading. It is not easy to explain differences between the rise and decay time constants, and those between at first cycle and after second cycle. Further studies are required to clarify the mechanism of experimental facts found in the present paper. 4. Conclusion The conventional intensity-based sensing can’t be applicable to cyclic stress and needs the stand-by time to maintain the initial excitation condition. To overcome these problems and to investigate the applicability of ML to cyclic stress, the present paper focused on the transient intensity and the time constants τup and τdown during cyclic loading, resulting in the following relationship between the time constants and loading conditions: 1) The time constants τup and τdown are expressed by a linear function of the peak value of the applied load Nmax and the inverse of the loading rate dN/dt. 2) τup and τdown did not change from the second cycle to the fifth cycle. However, τup and τdown at the first cycle are different from those after the second cycle. 3) τup was decided only by the loading time, Nmax/(dN/dt), resulting in the linear function mentioned above. 4) τdown depended on not only the loading time. τdown under the fixed loading time depended on the time rate of strain energy, a function of Nmax × (dN/dt). Thus, the present study demonstrates that the transient mechanoluminescence during cyclic loading depends on the loading conditions, in a range from 400 to 900 N of the maximum applied load and from 117 to 365 N/s of loading rate. The peak intensity of ML in cyclic loadings are proportional to Nmax and dN/dt as same as those in the first loading reported in previous reports however none of them had previously summarized these properties in cyclic loading. Besides, the present paper first found that τup and τdown did not change from the 2nd to the 5th cycle. Both τup and τdown were expressed by a linear function of the maximum load and the inverse of the loading rate. τup depended only on the loading time, whereas τdown was affected by the loading time and the rate of change of the strain energy. Measuring τdown may make it possible to evaluate loading conditions under cyclic loading without the stand-by time and the precise control of initial conditions of measurement. It may overcome problems of the intensity-based sensing and enhance the practicality of the ML phosphors as a stress sensor material.
#212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21998
National Institute of Advanced Industrial Science and Technology, 1-2-1 Namiki, Tsukuba, Ibaraki 3058564, Japan 2 School of Frontier Science, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba, 2778563, Japan 3 Department of Civil Enginnering, Tokyo University of Science, 2641, Yamasaki, Noda, Chiba 2788510, Japan * [email protected]
Abstract: The present study focused on the rise time and decay times of mechanoluminescence (ML) during cyclic elastic deformation of SrAl2O4:Eu2+. The time constants during compression and decompression, τup and τdown, respectively, did not change from the 2nd to the 5th cycle. Both τup and τdown were expressed by a linear function of the maximum load and the inverse of the loading rate. τup depended only on the loading time, whereas τdown was affected by the loading time and the rate of change of the strain energy. Measuring τdown may enable evaluation of the loading conditions even under cyclic loading and may enhance the practicality of a ML phosphor. ©2014 Optical Society of America OCIS codes: (040.0040) Detectors; (280.4788) Optical sensing and sensors; (280.5475) Pressure measurement; (260.3800) Luminescence.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
D. Olawale, T. Dickens, W. Sullivan, O. Okoli, J. Sobanjo, and B. Wang, “Progress in triboluminescence-based smart optical sensor system,” J. Lumin. 131(7), 1407–1418 (2011). C. Xu, T. Watanabe, M. Akiyama, and X. Zheng, “Direct view of stress distribution in solid by mechanoluminescence,” Appl. Phys. Lett. 74(17), 2414–2416 (1999). C. Xu, H. Yamada, X. Wang, and X. Zheng, “Strong elasticoluminescence from monoclinic-structure SrAl2O4,” Appl. Phys. Lett. 84(16), 3040–3042 (2004). Y. Jia, M. Yei, and W. Jia, “Stress-induced mechanoluminescence in SrAl2O4:Eu2+,Dy3+,” Opt. Mater. 28(8-9), 974–979 (2006). J. S. Kim, K. Kibble, Y. N. Kwon, and K. S. Sohn, “Rate-equation model for the loading-rate-dependent mechanoluminescence of SrAl2O4:Eu2+,Dy3+.,” Opt. Lett. 34(13), 1915–1917 (2009). M. R. Rahimi, G. J. Yun, G. L. Doll, and J. S. Choi, “Effects of persistent luminescence decay on mechanoluminescence phenomena of SrAl2O4:Eu2+, Dy3+ materials,” Opt. Lett. 38(20), 4134–4137 (2013). F. Clabau, X. Rocquefelte, S. Jobic, P. Deniard, M. Whangbo, A. Garcia, and T. Mercier, “On the phosphorescence mechanism in SrAl2O4:Eu2+ and its codoped derivatives,” Solid State Sci. 9(7), 608–612 (2007). V. K. Chandra and B. P. Chandra, “Dynamics of the mechanoluminescence induced by elastic deformation of persistent luminescent crystals,” J. Lumin. 132(3), 858–869 (2012). B. P. Chandra, V. D. Sonwane, B. K. Haldar, and S. Pandey, “Mechanoluminescence glow curves of rare-earth doped strontium aluminate phosphors,” Opt. Mater. 33(3), 444–451 (2011). B. P. Chandra, V. K. Chandra, and P. Jha, “Microscopic theory of elastic-mechanoluminescent smart materials,” Appl. Phys. Lett. 104(3), 031102 (2014). K. Sohn, S. Seo, Y. Kwon, and H. Park, “Direct observation of crack tip stress field using the mechanoluminescence of SrAl2O4:(Eu, Dy, Nd),” J. Am. Ceram. Soc. 85(3), 712–714 (2002). N. Terasaki, H. Yamada, and C. N. Xu, “Ultrasonic wave induced mechanoluminescence and its application for photocatalysis as ubiquitous light source,” Catal. Today 201, 203–208 (2013). S. Timilsina, K. H. Lee, I. Y. Jang, and J. S. Kim, “Mechanoluminescent determination of the mode I stress intensity factor in SrAl2O4:Eu2+,Dy3+,” Acta Mater. 61(19), 7197–7206 (2013). Y. Fujio, C. N. Xu, N. Terasaki, and N. Ueno, “Influence of organic solvent treatment on elasticoluminescent property of europium-doped strontium aluminates,” J. Lumin. 148, 89–93 (2014).
#212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21991
15. S. Someya, Y. Li, K. Ishii, and K. Okamoto, “Combined two-dimensional velocity and temperature measurements of natural convection using a high-speed camera and temperature sensitive particles,” Exp. Fluids 50(1), 65–73 (2011). 16. S. Someya, Y. Okura, T. Munakata, and K. Okamoto, “Instantaneous imaging 2D temperature in an engine cylinder in a frame combustion condition,” Int. J. Heat Mass Tran. 62, 382–390 (2013). 17. S. Someya, K. Ishii, M. Saeki, and T. Munakata, “Lifetime-based measurement of stress using mechanoluminescence of SrAl2O4:Eu2+.,” Opt. Lett. 38(7), 1095–1097 (2013).
1. Introduction Various organic and inorganic materials can emit mechanoluminescence (ML) due to factors such as stress, strain, friction and fracture [1]. Xu et al. [2, 3] developed a bright ML phosphor, SrAl2O4:Eu2+ (SAOE), which enables direct observation of the stress distribution. The ML intensity was three orders of magnitude higher than that of quartz [1]. The response characteristics [4–6], mechanisms [7–10], devices and applications [11–14] of ML have also been recently investigated. The ML intensity was found to increase proportionally with increasing applied stress [2]. The intensity was also related to the loading rate [5]. Intensity-based measurements for quantitative nondestructive evaluation require that the whole system be precisely controlled, because the intensity strongly depends not only on the stress, but also on factors such as the excitation power, SAOE concentration, and ambient light. However, to the best of the authors’ knowledge, all applications of SAOE thus far have adopted intensity-based sensing. The ML intensity was measured 5~10 min after 3~10 min of UV irradiation in order to maintain the initial excitation conditions. This results in an undesirable and unavoidable long stand-by time before each measurement. The intensity-based sensing doesn’t accept any change of stress condition during the stand-by time. This stand-by time limits the applicability of ML-based measurement techniques. The stress condition in many practical structures is not often stable. It is difficult to avoid undesirable stress and to have such stand-by time. Qualitative intensity-based measurements could be applied only for the first application of stress after the stand-by time, and could not measure a repetitive stress. Cyclic stress should be evaluated based on the other factors, except for the value of intensity. On the other hand, there have been many experimental studies on the lifetime of luminescence [15, 16]. The lifetime is typically not affected by the excitation power or by the concentration of the sensor material. Someya et al. [17] focused on transient ML behavior, i.e., the rise and decay time constants, during first application of elastic deformation. The measured rise and decay time constants were independent of concentration and excitation power. They were proportional to the applied loads and inversely proportional to the loading rates. These results indicate that measurements based on rise or decay time constants may decrease both the measurement uncertainty and stand-by time. However, it is still unknown whether ML and the lifetime-based measurement can be applied to a cyclic stress. There are few previous reports focused on the ML response under cyclic stress. Therefore, the present study focused on the ML rise and decay time constants during cyclic elastic deformation in order to enhance the applicability and the practicality of the ML. The effects of applied loads and loading rate to the rise and decay time constants were systematically investigated. 2. Experimental To evaluate the ML properties, a commercial SAOE powder (TAIKO-ML-1, Taiko Refractories Co., Ltd.) was mixed with an optical epoxy resin and used to form disks [2, 4] 30 mm in diameter and 7 mm thick. The mass fraction of SAOE was fixed at 10 wt%. The transient ML intensity was measured by a photomultiplier tube (H10721-01, Hamamatsu Photonics) and recorded using an oscilloscope (MSO2024B, Textronix Inc.). The entire experimental setup was shielded from ambient light to minimize its effect on the ML intensity measurements. The disks were exposed to 360-nm UV light at less than 100 mW for 1 min
#212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21992
ML intensity (PMT output) [V]
and aged in a dark room for 3 min to allow the luminescence to relax before loading. The initial ML intensity, i.e., the excitation power and the aging time, was fixed in the present experiments. Stress was applied to the sample by a materials testing machine (SVZ-200NB, Imada-ss Co.) which allowed control of the loading rate and maximum load. The maximum load and loading rate were varied from 400 to 900 N, from 117 to 365 N/s, respectively. Five cycles of loading were applied at intervals of three seconds. Three trials were performed under each set of experimental conditions. Nmax = 800[N]
1st Cycle 2nd Cycle 3rd Cycle 4th Cycle 5th Cycle
dN/dt = 240[N/s]
0.2
0.1
0 −5
0
5
Time[s]
Time constants of ML( τ)
Fig. 1. Transient intensity of ML under cyclic loading.
Cycle No. 1 2 3 2 4 5
τ up τ down
1
400
600
800
Maximum load[N]
Fig. 2. Relationship between Nmax and the time constants τup and τdown.
3. Results and discussion 3.1 ML response to the cyclic loading Figure 1 shows the instantaneous ML intensity and the applied load over five cycles. The initial ML intensity was subtracted from the raw data as background noise in Fig. 1. The intensity before and after each cycle was almost constant, and the intensity difference before and after each cycle was less than 0.003 V, a few percent of the total intensity. The time t was
#212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21993
defined as zero when the load was at its maximum, Nmax. In Fig. 1, the loading rate and maximum load were fixed at 240 N/s and 800 N, respectively. The peak intensity Imax of the first cycle has often been used in previous reports to evaluate the magnitude of the stress. Xu et al. [2] reported that the peak intensity in the first application of stress was linearly proportional to the magnitude of the applied load. It is seen that Imax decreased gradually during the cyclic loading in Fig. 1. Therefore the value of cyclic stress can’t be evaluated by the value of intensity at each cycle. The present study focused on the transient process. The luminescence intensity is usually expressed by an exponential function, Eq. (1), using a time constant, τ, which is a lifetime of trapped electrons [8, 9, 15–17]. We assumed that the ML rise and decay time constants during cyclic elastic deformation in Fig. 1 could be expressed by Eq. (1). The ML rise time constant, τup, and decay time constant, τdown, were individually calculated using the least squares method: I ( t ) = Ae − t τ + C
(1)
Here I(t) is the ML intensity at time t, and A and C are constants. Figure 2 shows the relationship between τup, τdown, and the peak value of the applied load Nmax at a fixed loading rate of 240 N/s under cyclic loading. The error bars represent the standard deviation, which are small especially after the second cycle. The dashed lines represent linear functions obtained using the least squares method. As shown in Fig. 2, both τup (open circles) and τdown (open triangles) in each cycle increased linearly with increasing Nmax. τup was shorter than τdown in all cases. This difference in time constants implies that the mechanisms operating during compression and decompression are different. The relationships between τup, τdown, and the peak value of the applied load almost never changed from the second cycle to the fifth cycle. However, the relationships between τup, τdown, and Nmax in the first cycle were different from those after the second cycle. The rate of change in τup also appears to be different between the first cycle and after the second cycle, while that of τdown looks to be nearly equal. Further studies are required to clarify the differences between the time constants τup and τdown during the first cycle and after the second cycle. 5
Time constants of ML( τ )
4 3
τ up τ down
Cycle No.1 2 3 4 5
2
1 0.9 0.8 0.7 0.6 0.5 100
200
Loading rate[N/s]
300
400
Fig. 3. Effect of loading rate on time constants τup and τdown.
The effect of the loading rate dN/dt on the rise and decay time constants under cyclic loading was also investigated, as shown in Fig. 3. Nmax was fixed at 800 N, and dN/dt was changed from 117 to 365 N/s. The dashed lines represent linear functions obtained using the least squares method. Both τup and τdown at each cycle in the different runs were found to be #212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21994
inversely proportional to dN/dt. τup was shorter than τdown in all cases. The relationships between τup, τdown, and the loading rate also remained nearly identical from the second cycle to the fifth cycle. However, the relationships between τup, τdown, and dN/dt in the first cycle were different from those after the second cycle. Once again, the rate of change in τup also appears to change after the second cycle, while that of τdown does not. These trends in τup and τdown were similar to those shown in Fig. 2. As shown in Figs. 2 and 3, the error bars for τup and τdown after the second cycle were smaller than those during the first cycle. Thus, the rise time constant τup and the decay time constant τdown may be useful for evaluating the peak load, even under cyclic loading, at least under a fixed loading rate. These values may also be useful for evaluating the loading rate given a fixed peak load, and may offer a lower degree of uncertainty than that associated with stress evaluation based on the value of intensity. The present paper focused on the transient intensity and the time constants τup and τdown during cyclic loading, resulting in the following relationship between the time constants and loading conditions:
τ up ,τ down ∝ N max ,1 ( dN dt )
(2)
Thus, measurements based on the time constants τup and τdown cannot only decrease the measurement uncertainty but can also remove the restriction of maximum intensity based measurements to the first loading after a required stand-by time. Measuring τup and τdown may enable evaluation of the loading conditions, even under cyclic loading. These relationships between τup, τdown, and the peak value of the applied load, the loading rate, during cyclic loading are firstly reported in this study and these may enhance the practicality of a ML phosphor. 3.2 Effect of the loading time Then, the effect of the loading time on the time constants were also investigated. From Eq. (2), τup and τdown can be represented as follows:
τ i = aτ
i
N max 1 + bτ i +c N +d ( dN dt ) ( dN dt ) τ i max τ i
(3)
Here, aτi, bτi, cτi, and dτi are constants dependent on the ML material and a test piece. The subscript i represents either up or down. Here, since the loading rate was not time dependent and was constant in each loading experiment, the product of Nmax and 1/dN/dt became the loading time Δt. Therefore, it is not clear whether the time constants τup and τdown depended on Nmax and dN/dt individually. There is a possibility that the time constants depended on the loading time (Nmax/(dN/dt)) only, regardless of the maximum load or loading rate, in other words, bτi and cτi might be both zero.
#212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21995
Peak intensity of ML, Imax [V]
0.2
Loading time 2s 2.5s 3s 3.5s
0.1 1 cycle 2 cycle 3 cycle 0
1
2
5 3 [ x 10 ]
Nmax dN/dt (Rate of change of strain energy,dE/dt )
Fig. 4. Relationship between Imax and the rate of change of strain energy under cyclic loading for various loading times.
Therefore, additional experiments were performed with varying loading times Δt = Nmax /(dN/dt). Figure 4 shows the maximum intensity Imax in the first three cycles, with loading times of 2.0 to 3.5 s. The loading time was controlled by changing Nmax and dN/dt from 235 to 900 N and from 117 to 363 N/s, respectively. The horizontal axis is the product of Nmax and dN/dt, which is related to the rate of change of the strain energy with time, dE/dt. The maximum intensity decreased as successive loading cycles were applied. There was no relationship between the maximum intensity and the loading time, at least in the range of 2.0– 3.5 s. Imax increased with increasing rate of change of the strain energy in each cycle. The dashed lines represent parabolic functions obtained using the least squares method, because the maximum intensity was proportional to both the maximum load and the loading rate. Thus, the peak intensity is found to be still proportional to Nmax and dN/dt during cyclic loading though the value decreases gradually in the sequential cycles and it is difficult to evaluate Nmax and dN/dt quantitatively during cyclic loading. τ up τ down
Time constants of ML( τ )
3
Loading time 3.5s 3s 2.5s 2s
2
1
0
1
2
5 3 [ x 10 ]
Nmax dN/dt (Rate of change of strain energy,dE/dt )
Fig. 5. Relationship between time constants and the rate of change of strain energy in the second cycle for various loading times.
#212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21996
Time constant of ML( τ )
1.2
1
0.8
2
2.5
3
Loading time [s]
3.5
Fig. 6. Relationship between the rising time constant τup and the loading time.
Figure 5 shows the relationship between the time constants after the second cycle and the rate of change of the strain energy, for loading times of 2.0 to 3.5 s. The time constant under compression τup depended only on the loading time Nmax / (dN/dt) and was independent of the rate of change of the strain energy. τup increased with increasing loading time, resulting in the increase of τup with increasing maximum load under fixed loading rate and the decrease of τup with increasing loading rate at the fixed maximum load. τup did not depend on the maximum load Nmax and the loading rate dN/dt separately. bτi and cτi in Eq. (3) were equal to zero. Therefore, the ML intensity during compression after the second cycle of loading can be represented by the following equation, Eq. (4). I ( t ) = Ae
( t ( Δt ⋅ a
τ up
+ dτ up
))
+C
(4)
Figure 6 summarizes the relationship between the loading time and the time constant τup. τup was expressed by a linear function of the loading time, and the coefficients aτup and dτup were calculated to be 0.37 and 0.006, respectively, in our experiments. dτup was nearly equal to zero and τup was almost proportional to the loading time. These empirical values also fit the experimental data shown as red dotted lines in Figs. 2 and 3. 3.3 Effect of the time rate of strain energy On the other hand, as shown in Fig. 5, τdown was strongly dependent on not only the loading time, but also on the rate of change of the strain energy. τdown decreased as the rate of change of the strain energy increased for each loading time, and with decreasing loading time at a fixed rate of change of the strain energy. The chain lines about τdown in Fig. 5 represent logarithmic functions, as given by Eq. (5), and were obtained using the least squares method for τdown at each loading time. y and x are constants. y increased and x decreased with increasing rate of change of the strain energy.
τ down = x ln ( N max ⋅ dN dt ) + y = x ln ( dE dt ) + y
(5)
Chandra and his group [8–10] discussed the mechanism of ML based on a decreasing trap depth of carriers due to the piezoelectric fields. Rahimi et al. [6] claimed that both the thermal energy and the piezoelectric fields affect the ML intensity. We speculate that there would be an excessive population of electrons in the excited state after the UV-excitation of ML materials, which would overflow as ML and photoluminescence during the first loading. Then, the electrons decay from the excited state to the ground state as ML due to piezoelectric
#212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21997
effects, almost without additional photoluminescent overflow, resulting in constant τup and τdown values after the second loading. However, there are few papers and experimental data of the transient ML intensity under cyclic loading. It is not easy to explain differences between the rise and decay time constants, and those between at first cycle and after second cycle. Further studies are required to clarify the mechanism of experimental facts found in the present paper. 4. Conclusion The conventional intensity-based sensing can’t be applicable to cyclic stress and needs the stand-by time to maintain the initial excitation condition. To overcome these problems and to investigate the applicability of ML to cyclic stress, the present paper focused on the transient intensity and the time constants τup and τdown during cyclic loading, resulting in the following relationship between the time constants and loading conditions: 1) The time constants τup and τdown are expressed by a linear function of the peak value of the applied load Nmax and the inverse of the loading rate dN/dt. 2) τup and τdown did not change from the second cycle to the fifth cycle. However, τup and τdown at the first cycle are different from those after the second cycle. 3) τup was decided only by the loading time, Nmax/(dN/dt), resulting in the linear function mentioned above. 4) τdown depended on not only the loading time. τdown under the fixed loading time depended on the time rate of strain energy, a function of Nmax × (dN/dt). Thus, the present study demonstrates that the transient mechanoluminescence during cyclic loading depends on the loading conditions, in a range from 400 to 900 N of the maximum applied load and from 117 to 365 N/s of loading rate. The peak intensity of ML in cyclic loadings are proportional to Nmax and dN/dt as same as those in the first loading reported in previous reports however none of them had previously summarized these properties in cyclic loading. Besides, the present paper first found that τup and τdown did not change from the 2nd to the 5th cycle. Both τup and τdown were expressed by a linear function of the maximum load and the inverse of the loading rate. τup depended only on the loading time, whereas τdown was affected by the loading time and the rate of change of the strain energy. Measuring τdown may make it possible to evaluate loading conditions under cyclic loading without the stand-by time and the precise control of initial conditions of measurement. It may overcome problems of the intensity-based sensing and enhance the practicality of the ML phosphors as a stress sensor material.
#212495 - $15.00 USD Received 20 May 2014; revised 13 Jul 2014; accepted 13 Jul 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021991 | OPTICS EXPRESS 21998
