Quantitative full-field strain measurements by SAOED (SrAl₂O₄:Eu²⁺,Dy³⁺) mechanoluminescent materials

In order to manufacture ML sensing films, commercial SAOED particles (LumiNova G-300, United Mineral & Chemical Corporation) were mixed with an optical epoxy resin (West System 105/206). Several factors determine characteristics of transient changes of the ML emission from a thin ML sensing film. These factors can be classified into two categories; (1) manufacturing factors (i.e. materials concentration ratio, ML film thickness, epoxy matrix, etc and (2) experimental factors (i.e. effects of the PL, stress rate, and photoexcitation) [19]. In this paper, the manufacturing factors were fixed by selecting a constant mass concentration ratio of epoxy to ML powder (1:1) and by choosing 0.03 inch (0.762 mm) thickness for the ML film. The ML film was fabricated by the doctor blade method and then the cut ML sensing film was coated on the test specimens by using a commercial adhesive (M-Bond 200 from micro-measurements). The doctor blade method is an efficient way to manufacture thin films with a constant thickness [23]. The thickness can be precisely adjusted by the scale of the doctor blade. By using a flat glass plate, the gap between the blade and the glass plate remains constant.

Before carrying out each of the tests, the ML sensing film was consistently photo-excited by a 60 W broadband light source having wavelength range of 400–1000 nm for 2 min to assure it is fully saturated with the same photoexcitation power. Following full saturations of the films, they were aged for a fixed time in the stress-free state to minimize the effect of stress-free PL decay on the ML emission and to obtain higher ML sensitivity. Therefore, ML sensing films attached on the specimens were aged in the dark place for exactly 7 min before the onset of the loading. A charge-couple device (CCD) camera (AVT MANTA G-0.33B) with a consistent setting of gain factor and a fixed exposure time (100 ms) was positioned around 25 cm in the direction normal to the surface of ML sensing films to photograph the ML emission during the loading process. The images were captured at 10 fps (frames per second) and the ML light intensity was read from the captured images. An Instron Material Tester machine with a capacity of 200 kips is synchronized to the image acquisition by the CCD camera so that onset point of loading is matched with the first image. Figure 1 illustrates the schematic experimental test setup and configuration. While capturing the images, ambient light was completely blocked to minimize undesirable influences of the environmental lights on experimental results. The test in the daylight could be difficult due to weak ML light intensity and effects of transient environmental light. However, a dark chamber can be used to make light condition same to the lab environment.

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The first reference test method needs multiple uniaxial tensile tests of standard dog-bone specimens with ML sensing film coated at various strain rates and loadings. One restraint is that the ML sensing films must be prepared through consistent manufacturing process and bonded securely on the specimen throughout the tests. In this case, the ML intensities are averaged over the pixels within the gauge section since the specimen is under constant stress state. The corresponding constant uniaxial strain can be computed from the axial displacement and Poisson ratio of the substrate material. The average light intensity corresponding to the stress on the ML film is calculated by dividing the area integration of ML light intensity in gray level by the area of the region of the interest in pixels. These data are synchronized with the load step data to obtain ML light intensity-force (i.e. stress) curves. The maximum load is limited in a way that the aluminum specimen remains within linear elastic range during the tests since it is intended to measure strains within elastic range of the substrate material. An advantage of the first method is that it can directly measure both strains and corresponding ML intensity, which are deemed as true values. However, it requires more times and labors due to needs for multiple tests.

The second reference test method is to conduct test with a specimen that show a non-uniform strain distribution. An advantage of the second method is that it can generate strain distributions showing a wide range of strains and strain rates even with a single test. Thus, it can save times and labors compared to the first method. Nevertheless, it would not be easy to measure full-field strain distributions within the zone of interests by conventional sensors like strain gauges. Therefore, the best option is to use strains predicted by three-dimensional FEA that is verified by experimental tests. Non-uniform strain states can be easily generated by design of specimens with complex geometries. In this paper, I-beam for four-point bending test was selected to produce non-uniform strain states since stresses on the web between loading point and supports are highly non-uniform. Generally, non-uniform strain states around loading points or notches are generated due to stress concentrations. However, it is worth noting that any irregular shapes of specimens can be used to produce non-uniform strain states.

The ML light intensity is a scalar value whereas strains are a tensor. Thus, on a basis of a hypothesis that the ML emission process is most effectively triggered by movement of dislocations within SAOED crystals, the effective strain is determined to be measured from ML light intensity. In metallic materials, dislocations result in yielding and plastic deformation. Obviously, it was evidenced that deviatoric stresses in the ML film are more effective for stimulating the ML process of trap-releasing and recombination with emission centers than hydrostatic or mean stress [24]. The effective strain is analogous to the von Mises stress, which is compared to uniaxial yield stress in the yield criteria of metal plasticity. The von Mises stress corresponds to a certain multiaxial stress state. Analogously, a certain state under multiaxial strains yields an effective strain to be matched with a ML light intensity. The effective strain is a scalar value defined as follows [25]

$$\begin{eqnarray}&&{\varepsilon }_{{\rm{eff}}}=\displaystyle \frac{2}{3}\sqrt{\displaystyle \frac{1}{2}\left[{({\varepsilon }_{11}-{\varepsilon }_{22})}^{2}+{({\varepsilon }_{22}-{\varepsilon }_{33})}^{2}+{({\varepsilon }_{33}-{\varepsilon }_{11})}^{2}+\displaystyle \frac{3}{2}({\gamma }_{12}^{2}+{\gamma }_{23}^{2}+{\gamma }_{31}^{2})\right]},\end{eqnarray} \tag{ 1 }$$

where ${\varepsilon }_{{\rm{eff}}}$ is the effective strain, ${\varepsilon }_{11},$ ${\varepsilon }_{22}$ , and ${\varepsilon }_{33}$ are the normal strain components, and ${\gamma }_{12},$ ${\gamma }_{23},$ and ${\gamma }_{13}$ are the engineering shear strain components. For the first reference test under a uniaxial tensile stress state, the effective stress becomes

$$\begin{eqnarray}&&{\varepsilon }_{{\rm{eff}}}=\displaystyle \frac{2}{3}{\varepsilon }_{11}(1+\nu ),\end{eqnarray} \tag{ 2 }$$

where $\nu$ is Poisson ratio (0.33) of the aluminum material (Aluminum Alloy 6061). The ML light intensity is mapped to this effective strain by a calibration model to be proposed in the following subsections. Although it is challenging to achieve perfect isotropy within ML sensing film, it is assumed that ML sensing film shows isotropic material properties.

For the second reference test method, a three-dimensional FE model is used to extract effective strains since stresses can be highly inhomogeneous. Therefore, equation (1) is used for computing effective strains from FEA results.

In order to create the ML calibration model which predicts the full-field strain values, a series of comprehensive experimental tension tests were conducted on a standard aluminum dog-bone specimen. The test database was prepared under various conditions by varying the loading rates (0.1, 0.2, 0.3, and 0.4 mm s⁻¹) after the stress free PL decay time of 7 min Loads were linearly applied up to 15 kN and each test was repeated three times to minimize the experimental error. After carrying out image processing in MATLAB, an average value of ML light intensity was calculated for each frame over the gauge section on the film. Having a fixed frame rate at 10 fps (frame per second), ML light intensity versus time can be drawn for each time step (0.1 s).

The incremental values of step time $({\rm{\Delta }}t),$ change of the ML light intensity $({\rm{\Delta }}{\rm{LI}}),$ a state variable $({\rm{\Delta }}\eta ),$ and the effective strain from previous step $({\varepsilon }_{{\rm{eff}}(n-1)})$ are incorporated into the multi-gene genetic programming (MGGP) toolbox [26, 27] to develop a calibration equation of the change of effective strain $({\varepsilon }_{{\rm{eff}}})$ in each time step. The genetic programming (GP) is a widely known evolutionary algorithm that can produce encoded symbolic mathematical expressions from a large training data base. Its backbone algorithm is similar to genetic algorithm that searches for the best individual through cross-over and mutation events. MGGP is a variant of GP which produces a symbolic expression as a weighted linear combination of the outputs from a number of GP individual trees [27]. For each model, the linear coefficients are derived from the training data base using ordinary least square methods. It is known that MGGP's symbolic regression is more accurate and efficient than the GP [27]. More details can be referred to [27].

The general form of the calibration model can be shown as follows

$$\begin{eqnarray}&&{\rm{\Delta }}{\varepsilon }_{{\rm{eff}}(n)}=f({\rm{\Delta }}{t}_{(n)},{{\rm{\Delta }}{\rm{LI}}}_{(n)},{\rm{\Delta }}{\eta }_{(n)},{\varepsilon }_{{\rm{eff}}(n-1)})\end{eqnarray} \tag{ 3 }$$

in which ${\rm{\Delta }}{\varepsilon }_{{\rm{eff}}(n)}$ is the change of the effective strain at step $n;$ ${\rm{\Delta }}{t}_{(n)}$ is the time increment at step $n;$ ${\rm{\Delta }}{{\rm{LI}}}_{(n)}$ is the change of the ML light intensity at step $n;$ ${\rm{\Delta }}{\eta }_{(n)}={\varepsilon }_{{\rm{eff}}(n-1)}{{\rm{\Delta }}\mathrm{LI}}_{(n)},$ and ${\varepsilon }_{{\rm{eff}}(n-1)}$ is the effective strain at step (n − 1). ${\rm{\Delta }}\eta$ is used in the calibration model to improve the accuracy of the model [28]. For each loading case, the incorporated input data were prepared corresponding to five different step time increments, ∆t = 0.1, 0.2, 0.3, 0.4 and 0.5 s.

A final calibration model equation for the change of the effective strain at step $n,$ was obtained as follows

$$\begin{eqnarray}&&{\rm{\Delta }}{\varepsilon }_{{\rm{e}}{\rm{f}}{\rm{f}}(n)}={C}_{1}({\rm{\Delta }}{t}_{(n)}+\,\mathrm{log}| {{\rm{\Delta }}\mathrm{LI}}_{(n)}+{\varepsilon }_{{\rm{eff}}(n-1)}| \\ &&\quad \quad \quad \,\,\,-(\mathrm{log}| {\varepsilon }_{{\rm{eff}}(n-1)}| )+{C}_{2}({{\rm{\Delta }}\mathrm{LI}}_{(n)}+\,\mathrm{log}| {\rm{\Delta }}{t}_{(n)}| )\\ &&\quad \quad \quad \,\,\,+{C}_{3}({\varepsilon }_{{\rm{eff}}(n-1)}-{\rm{\Delta }}{\eta }_{(n)}-\,\mathrm{log}| {\rm{\Delta }}{\eta }_{(n)}| )+{C}_{4},\end{eqnarray} \tag{ 4 }$$

where $| \cdot |$ indicates an absolute value; $\mathrm{log}$ indicates the natural log; ${C}_{1},$ ${C}_{2},$ ${C}_{3},$ and ${C}_{4}$ are the model constants and calibrated as ${C}_{1}=0.1,$ ${C}_{2}=0.0859,$ ${C}_{3}=0.014\,08,$ and ${C}_{4}=0.1719$ for present cases. No physical meanings are assigned to the model constants. The effective strain in each time step can be obtained by accumulation of the changes of the effective strain value of the previous time steps. This proposed model can measure only monotonically increasing effective strains. Although the proposed approach can be attempted to cyclic or dynamic loadings, the topic is out of the scope for this paper.

In this section, a calibration model from the second reference test approach was proposed. It was obtained from a four-point loading test of I-beam. In the test, a ML sensing film was attached on the one-side web of the beam between a loading point and a support as shown in figure 2. Since in this area, in-plane shear stress is dominant and the range of strains and strain rates are vastly wide, the ML light intensities from this area were used for developing a calibration model. The loading was applied linearly up to 150 kN.

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A calibration model was developed based on the ML light intensities at 600 arbitrary pixel points on the film and corresponding FE effective strains. The ML light intensities were captured from CCD camera during the loading test and the effective strains were calculated from FEA. Figure 3 shows a view of the three-dimensional FE model of the I-beam used to extract the effective strains.

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To verify the FE model, a strain gauge (Vishay Micro-Measurements SR-4 model WK-06-062AP-350) was installed on the bottom flange of the mid span. The material properties of the FE model were adjusted to elastic modulus 69 000 MPa and Poisson ratio 0.33 until the longitudinal strain by FE simulation matched to the experimental strain value from the strain gauge at the same location. Table 1 summarizes the strains obtained at the highest load (150 kN). In addition, ML light intensities from selected pixel points are regressed to reduce noises from experimental measurements.

Unlike the calibration model from the uniaxial tensile test, using this test provides different strain rates in one test due to inhomogeneous strain distribution over the area. The strain rates used in the development were between 0.0003 and 0.0021 s⁻¹ and the in-plane shear strains used in the development were between 0.000 08 and 0.0037 s⁻¹.

The incremental values of step time $({\rm{\Delta }}t),$ change of the ML light intensity $({\rm{\Delta }}{\rm{LI}}),$ the state variable $({\rm{\Delta }}\eta ),$ and the effective strain from previous step $({\varepsilon }_{{\rm{eff}}(n-1)})$ were also incorporated into the MGGP toolbox [26] to develop a calibration equation for the change of effective strain $({\varepsilon }_{{\rm{eff}}})$ in each time step. The variables are the same as those of the model from the uniaxial tensile reference test. Also the data were prepared with five different time increments, ${\rm{\Delta }}t=\mathrm{0.1,0.2},$ 0.3, 0.4 and 0.5 s.

The final calibration model equation for the change of the effective strain at step $n,$ was obtained as follows

$$\begin{eqnarray}&&{\rm{\Delta }}{\varepsilon }_{{\rm{eff}}(n)}=\,{C}_{1}(| (\mathrm{log}| {\rm{\Delta }}{{\rm{LI}}}_{(n)}-{\rm{\Delta }}t+{C}_{5}| )| )\\ &&\quad \quad \quad \quad +{C}_{2}| {\rm{\Delta }}t+{\rm{\Delta }}t\cdot {\varepsilon }_{{\rm{eff}}(n-1)}+{C}_{6}| \\ &&\quad \quad \quad \quad +{C}_{3}({\rm{\Delta }}t+{\rm{\Delta }}t\cdot {\rm{\Delta }}{{\rm{LI}}}_{(n)}+{\rm{\Delta }}t.{\varepsilon }_{{\rm{eff}}(n-1)}\\ &&\quad \quad \quad \quad .({\rm{\Delta }}{\eta }_{(n)}+{C}_{7}))+{C}_{4},\end{eqnarray} \tag{ 5 }$$

where ${C}_{1},$ ${C}_{2},$ ${C}_{3},$ ${C}_{4},$ ${C}_{5},$ ${C}_{6}$ and ${C}_{7}$ are the model constants and calibrated as ${C}_{1}=0.019\,67,$ ${C}_{2}=0.045\,17,$ ${C}_{3}=0.002\,216,$ ${C}_{4}=-0.4093,$ ${C}_{5}=5.034,$ ${C}_{6}=8.33,$ ${C}_{7}=8.33$ for the current case.

Figure 4 shows plots of comparisons for the true experimental effective strains and measured effective strain versus relative ML light intensity for different loading rates. The results are presented in five different time step increments for each test. These figures demonstrate that the calibration model can accurately relate the measured ML light intensities to the effective strains at various strain rates and time increments. These results also show that the model accuracy is not very sensitive to different step time increments; however, relatively larger errors were observed at time step 0.1 s than other time step increments. The reason for more errors at time step 0.1 s can be found from the nature of the proposed equation in a recurrence form and the prepared data. The original raw ML light intensities were obtained at 10 fps (i.e. ${\rm{\Delta }}t=0.1{\rm{s}})$ that includes large noises whereas data at other time step sizes were prepared after removing the noises. Another reason is an effect of error accumulations from previous time steps. More number of time steps make more errors accumulated from effective strains predicted at previous steps. These errors also seem to be decreasing as the loading rate increases. According to results from figure 4, the minimum and maximum strains from the reference tests were 0.0001 and 0.0032, respectively. Also the minimum and maximum strain rates were 0.0007 and 0.0025 s⁻¹, respectively.

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In order to validate the calibration model from the uniaxial tensile reference test, thin ML sensing films were applied on a dog-bone specimen with an open-hole specimen. The full-field effective strain values from the proposed calibration model were compared with FE simulation results. The ML films used in the test were so manufactured that the thickness and concentration ratio are as close to the ML film used in the reference tests as possible. The camera setting and conditions for photoexcitation and PL decay time were also kept so that they are as close to those of reference tests as possible.

5.1.1. Uniaxial tensile test of aluminum dog-bone specimen with an open-hole

A uniaxial tensile test was conducted using a dog-bone aluminum specimen with an open-hole. The tensile load was applied linearly up to 45 kN with the loading rate = 0.4 mm s⁻¹. According to FE simulation, areas around the hole in the aluminum specimen are yielded due to stress concentration when the load exceeds 6 kN. Since the calibration model was developed for the specimens within linear elastic range, it is reasonable to compare effective strains from ML and FEA for the loads less than 6 kN. The time increments and the change of the ML light intensity for each step time were recorded through image processing. Effective strains were measured at each pixel by equation (4). The effective strain for each pixel in each step time was obtained by accumulation of the changes of the effective strain values of the previous step times. Figure 5 demonstrates the distribution of the full-field effective strain values at three different loading levels (1.78, 3.57 and 5.35 kN) measured by the calibration model. Also, the effective strain values calculated from the FE simulation (ABQUS 6.13-2) results are presented in figure 5. According to the figure, the present calibration model measured the effective strain with a reasonable accuracy and the results are validated with acceptable accuracy. Maximum strain in figures 5 and 6 is 0.0027, which is within the strain range (0.0001–0.0032) from reference tests. However, the max strain rate was 0.003 s⁻¹, which is slightly over the max strain rate (0.0025 s⁻¹) from reference tests.

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As it can be seen in figure 5, the distribution of the effective strain from ML sensor is not perfectly symmetric and the area in the right hand side shows higher strain values. The imperfection in specimen set-up in-between the tester machine's grips yielded non-symmetric distribution of the effective strain values on the specimen. The realistic distribution of effective strain values is a considerable advantage of the ML sensor over the FEA since the uncertainty in boundary conditions, material properties, and manufacturing imperfection are the main concerns in standard FE simulations.

The effective strains in the vicinity of the open-hole by the ML sensor and FE simulation are presented with error percentage distribution at different loading levels in figure 6. The error percentages of the calibration model were obtained by simply subtracting the pixel-by-pixel ML effective strains from FE effective strains and dividing the differences by FE effective strains. According to the error percentage figures, the error of the ML sensor decreases by increasing the loading levels. However, it is worth noting that FE results are assumed to be true reference values.

To verify the calibration model from the non-uniform strain reference test (i.e. the model in section 4.2), the ML effective strains were compared to the effective strains from FEA as shown in figure 7. As described in section 4.2, the calibration model was determined by using test and simulation data from the side span. The results in figure 7 verify that the calibration model has a capability of reproducing the effective strains from the measured ML light intensity. According to results in figure 7, the minimum and maximum strains were 0.0001 and 0.0033, respectively. Also, the minimum and maximum strain rates were 0.000 34 s⁻¹ and 0.0021 s⁻¹, respectively.

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Results in figure 7(c) show small errors in the majority of the film area. However, larger errors are particularly shown in two specific areas where the effective strains are too high or too low. The reason for errors in the low strain areas is because the ML sensing film has an inherent material limitation, which is not sensitive enough to react to low strain rates and low strains. The ML light intensity data were selectively collected. Most of data points are from areas with moderate strain level and less data points with high strain level. This makes the calibration model biased to the moderate strain level and causes higher error percentage in the area with high level of strains.

To validate the model's capability of measuring effective strains, thin ML film were applied on two aluminum specimens (1) mid span of the I-beam under four-point load and (2) a standard specimen for pure shear test [29]. The full-field effective strain values from the proposed calibration model were also compared with FE simulation results (ABAQUS 6.13-2) for both tests.

5.2.1. Four-point bending test of the aluminum I-beam

The purpose of this test is to validate measurements of full-field effective strains under typical bending stress states by the proposed calibration model. One side of the web along the center span of an I-beam was coated with a thin ML sensing film with four inches width and three inches height as shown in figure 8. Strain gauges (WK-06-062AP-350) were also installed on the top of the upper flange and on the bottom of the lower flanges for verifying a FE model to be used for comparisons. Table 2 indicates strains on the top and the bottom flanges of the I beam from the FE analysis are acceptably close to ones from the real test. A four-point bending test was conducted by applying the load up to 180 kN so that the I-beam remained in linear elastic range with the maximum loading. Figure 8 displays the experimental test set-up

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The distributed effective strain from the FE simulation and ML sensor using the calibration model are presented in figure 9. The error percentages of the results are also shown in figure 9 at different loading levels. According to the results, it can be seen that the errors are reduced as the loading levels increase. It can also be concluded that the calibration model for ML sensor can measure the effective strain at higher strain levels with less errors. Along the neural axis, errors are very high since the strains and strain rates along the neutral axis are extremely small and thus out of the range of the reference strain data. Maximum strain in figure 9 was 0.0017, which is below the maximum strain (0.0033) from the reference test. Also the maximum strain rate in figure 9 was 0.0011 s⁻¹, which is below the maximum strain rate (0.0021 s⁻¹) from the reference test. Assuming that the effective strains from the FE simulation are true, other possible sources of the errors include differences in test conditions (e.g. environmental light, temperature, etc), differences in dispersions of ML particles in the resin, thickness and concentration of ML sensing films, delamination and/or microcracks in the adhesive, and errors in the camera sensor. If all of these error sources are sufficiently minimized, the strains from ML sensors can be considered true values.

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Figure 10 demonstrates the correlation between the effective strains from the ML sensor and the effective strains from the FE simulation results of the aluminum I-beam specimen at three different loading levels. It should be noted that only the results from the bottom of the film (0 < y < 25.4 mm) and from the top of the film (50.8 < y < 76.2 mm) are presented in the figure because of large errors along the neutral axis. As it can be seen in the figures, the correlation becomes close to one and also the accuracy of the ML sensor improves as the applied load increases. It indicates that the proposed ML strain sensing method can measure strains within the range of strains and strain rates collected from reference test.

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5.2.2. Pure shear test of an aluminum alloy specimen

In the second validation test, a standard pure shear test was performed on aluminum alloy (6061), following the ASTM standard B 831-05 [29]. Slotted single shear test fixture was used to mount the specimen to the Instron testing machine (Model No. 5569). Load was applied linearly up to 1540 N with the loading rate of 0.3 mm s⁻¹. The calibration model was used to measure distributed effective strains at three different loading levels (770, 1150, and 1540 N). Also, a FE model of the specimen was developed by using commercial software (ABQUS 6.13-2) to numerically calculate the effective strain values under the same loading conditions. Figure 11 shows the black and white raw images along with distributed effective strains from FE simulations and ML sensor. The step time between the raw images was 0.1 s. As expected, the high stress concentration accrued around the notch and the effective strains increase as increasing the loading level. The lower and higher bounds of the color bar were fixed in all figures in order to have accurate comparisons of the FE simulation and ML sensor results.

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Figure 12 displays the distributions of the effective strain results by the ML sensor and FE simulation in the zoomed-in region of interest around the notch. The error percentages of the ML sensor at different loading levels are also depicted in figure 12 for the cropped area. According to the figure, ML sensor can acceptably measure the full-field effective strain for the region with the high shear stress concentration. Maximum strain in figures 11 and 12 is 0.002, which is within the range of strain (0.0001–0.0033) from the non-uniform strain reference test. However, the strain rate was 0.0035 s⁻¹, which is greater than the max strain rate (0.0021 s⁻¹) from the reference test.

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The applied load on the pure shear specimen versus averaged values of the effective strain from the ML sensor and FE simulation for the cropped region (see figure 12) is plotted in figure 13. The figure shows that the average value of the effective strain from ML sensor and FE simulation increase linearly by increasing the load level and the difference between them increases slightly at higher strain levels.

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According to results from validation tests, errors were observed from comparing effective strains for ML sensor models and FEA. The sources for these errors could be listed as following:

• The measured effective strains are based on raw ML light intensities that may contain errors from environmental ambient light and camera noise.
• ML light emission is known to vary by temperature changes. Thus, the errors may be slightly influenced by changes of temperature. However, all the tests in this paper were conducted at room temperature. So, the temperature effect would be minimal.
• ML sensing film used in the reference tests could have concentrations and quality of dispersions of ML particles in the epoxy resin which are different from the ML sensing films used in validation experimental tests.
• ML sensing films used in the reference tests could have different thickness from those used in validation experimental tests due to different level of shrinkage and precipitation of ML particles after cured.
• Adhesive is the connector element between specimen and ML film. Every crack, micro-crack or bonding failure in the structure of adhesive could disconnect ML film from the specimen and cause differences between effective strain from ML and effective strain from FE.

Therefore, it is important to note that for an ML sensing film with a different thickness, concentration ratio or test conditions, the parameters of the proposed model may need to be recalibrated with new test data.