Abstract
The mechanical contact during material mechanical damage evaluation with electromechanical impedance technique was investigated, and the influencing factors, such as the times of in situ contact, contact stress, and area, were studied. The resonance frequency shift Δf of electrical impedance signature was regarded as the damage identification index. Results show that the influence of mechanical contact on damage evaluation could not be neglected. With increasing times of in situ contact, the characteristic resonant peak shifted leftward gradually due to the resulted superficial indentations, and the Δf value was in the order of 10−2–10−1 kHz for each mechanical clamping. The evolution direction of the resonance peak with contact stress was reversed, and the Δf value was about 10−1–100 kHz. The order was equal or even more serious against that of the early-stage mechanical damage. The relationship between the Δf value and the contact area, however, was elusive because of the combined effects of indentation damage and the compressive stress. Simulation experiments were conducted accordingly, and the abnormality was discussed. The quantitative results were compared between the steel and the Al alloy, and the variation with material property was demonstrated. Effective precautions to avoid the influence of mechanical contact were proposed.
Introduction
In virtue of the piezoelectric effect, the electromechanical impedance (EMI) technique, which couples the electrical impedance to reflect the mechanical impedance of the host structure, has been developed to be an important structural health monitoring method. With the low cost, small dimensions, and various forms, piezoelectric transducers are ideal for the damage monitoring of vital engineering structures and components (Ayres et al., 1998; Park et al., 2000). The high-frequency band information provided by piezoelectric transducers makes them sensitive to the tiny damage in the near field, which is really a new way for early-stage mechanical damage evaluation of materials. Although many other methods have been developed, such as scanning/transmission electron microscope (Haque and Saif, 2002), eddy current (Morozov et al., 2010), and in situ characterization could be realized, the damage information is relatively local. It is not easy to get a global view of the testing sample in one time. Nevertheless, the sensing region of the EMI technique is really superior. For only one small lead zirconate titanate (PZT) patch, the region is in the scale of meter for metallic structure. The integration of PZT array in particular makes it possible to realize the online monitoring of structures with large volumes and complicated shapes (Park et al., 2000).
The material mechanical damage behavior evaluated by EMI technique has been reported by several researchers (Giurgiutiu et al., 1999; Lim and Soh, 2010, 2011; Palomino, 2011; Park et al., 2010; Sevostianov et al., 2010; Zagrai et al., 2009). Aluminum alloys were widely used because of its high availability and the low price. Giurgiutiu et al. (1999) discovered that an initial decrease of the structural stiffness (∼20%) in a spot-welded joint corresponded with a ∼40% increase of a damage index, root-mean-square deviation (RMSD). Further researches demonstrated that the reduction of strength and the local Young’s modulus in a fatigued sample was correlated with the resonance frequency shift Δf (Sevostianov et al., 2010). The initiation and propagation of the fatigue crack have also been monitored. The two damage indexes, Δf and RMSD, were successfully incorporated to qualitatively distinguish the fatigue stage and quantitatively evaluate the damage extent (Giurgiutiu et al., 1999; Li et al., 2012; Zagrai et al., 2009). Other methods, such as linear elastic fracture mechanics (LEFM) (Lim and Soh, 2010) and statistical model (Palomino et al., 2011), were also introduced to estimate the fatigue life or the stress state.
Nevertheless, because of the intrinsic sensitivity characteristic of the EMI method for the integral damage, some potential problems eventually become visible. It is well known that contact mechanical tests are commonly performed in laboratories to study the damage behavior of materials. Parts contacting with the fixtures would inevitably produce some superficial indentations, scratches, and so on (Giurgiutiu et al., 1999; Li et al., 2012; Lim and Soh, 2010, 2011, 2012; Luo et al., 2013; Palomino et al., 2011; Park et al., 2010; Zagrai et al., 2009). The damage level is the same or even more serious against that of the early-stage material we concerned about. For other methods, the sensing ability is so limited that only the area interested could be examined while the contact parts with fixtures are ignored. For EMI method, however, damages resulted from the mechanical contact and the corresponding evaluation results should be carefully treated. In fact, influences of mechanical clamping on damage evaluation have been considered where possible in previous work (Li et al., 2012; Luo et al., 2013). However, the results were really a primary trial, and many relevant factors have not been studied in detail. In this work, the influences of mechanical contact on damage evaluation were comprehensively investigated from the perspective of the times of in situ contact, the contact stress, and the contact area. Specially designed experiments were conducted to clarify interaction effects of superficial indentations and the clamping stress. The damage was quantitatively analyzed by dint of Δf index extracted from impedance signatures.
Experimental procedures
Two kinds of engineering materials, austenitic stainless steel (ASS) and rolled aluminum alloy, were selected here. Tensile samples with approximately 3 mm thickness plates were mainly used, and the dimensions are shown in Figure 1(a). The two sides with large cross-sectional area were designed for the clamping of hydraulic grips. All the samples were carefully ground, and some were even polished with the 1.5 µm diamond paste for morphology observation. PZT sensors with the size of 10 × 10 × 1 mm3 were bonded to the surface with superglue. The specific location was in the part with a large cross-sectional area and about 15 mm away from the nearer fringe. A small notch with the size of 3 × 2 × 0.2 mm3 was prefabricated in the middle of the parallel part in order to minimize the strain around the adhesion between the PZT and the host structure. The bottom electrode of the PZT plate was extended to the top surface, so these two electrodes could be accessible with the soldering method. Compression tests were also conducted to study the influence of the compressive stress. The specimen is shown in Figure 1(b), of which the surface was also ground and polished. The location of PZT was the same as that in Figure 1(a). Small grooves were specially fabricated on both the top and the bottom surfaces, which created a delimitation between the mechanical loading part and the impedance testing one. The details will be discussed in the following section.
Schematic illustration of PZT sensors and specimens used in mechanical testing: (a) tensile specimen and (b) compression specimen.
The mechanical and EMI testing instruments are shown in Figure 2. Mechanical contact was realized by hydraulic clamping with the SHIMADZU hydraulic servo fatigue test system. Load control accuracy was higher than 0.3%. The detailed arrangement was the same as the tensile test, as shown in Figure 2(a). The upper side was clamped continuously, and the bottom clamping was adjusted to realize different contact parameters. The most important difference from a tensile test is that the sample was only compressed by the hydraulic fixture but without any axial stress. The clamping force could be modified with the hydraulic loading pressure, although the value could not be obtained directly. The clamping couples are shown in Figure 2(b) where many aligned micro-bumps could be observed. Electrical impedance signatures were examined by the impedance analyzer WK6500B, as shown in Figure 2(c). The excitation voltage on the PZT patch was 1 V, and the impedance measurement accuracy was higher than ∼0.05%. The influence of clamping and some related factors like indentations are concerned about, so all the impedance testing results were obtained online with the samples being clamped (or compressed in the compression tests). The morphology of indentations was observed by JSM-5600LV scanning electron microscopy (SEM), which could provide a reference for the impedance and mechanical analyses.
Experimental equipments for mechanical and impedance testing: (a) hydraulic fixture, (b) details of clamping part, and (c) impedance analyzer.
Results and discussion
Fluctuations of reference impedance spectrum
The selection of the reference spectrum (baseline) is critical for the quantitative damage evaluation with the EMI method. Therefore, how to obtain a reliable reference electrical impedance signature becomes important. In contact mechanical testing, repeated clamping is generally inevitable because the alignment, the clamping position, and some other factors related to the clamping force are commonly needed to be modified several times. During this procedure, two questions are still not clear: (1) whether the electrical impedance spectrum varies with the manual operation and (2) what is the extent compared with that of the early-stage material damage. Here, an intact ASS sample was used, and the evolution of the electrical impedance with the number of repeated clamping was recorded. Before the impedance testing, trial and error method was used to determine the appropriate testing frequency band. The frequency range of 10–500 kHz was scanned, and the spectrum in the range of 25–65 kHz is presented in Figure 3. The number of sampling points in each band was 801, and the frequency interval was 50 Hz. Detailed selection discipline has been discussed previously (Luo et al., 2013) and is omitted here. It was observed that the main resonant peak in the electrical impedance signature of the 1st clamping was located around 50 kHz, and the amplitude was higher than 10,000 Ω. When the sample was clamped again, the 2nd clamping signature, which is more clearly shown in Figure 3(b), presented a 0.3 kHz shift to the left from 51.44 kHz and the amplitude decreased to some extent. Like the operations in usual mechanical testing, a series of adjustments of the alignment, the clamping position, and the clamping force were performed. As a result, the impedance amplitude of the 6th clamping increased against that of the 2nd and the peak frequency shifted rightward to 51.78 kHz, which is totally different from the situation above. We know that the resonant frequency, as an intrinsic parameter of the structural dynamics, is widely accepted as a critical damage evaluation index. Although the value might vary with the shape, dimension, material property, and testing frequency band, the results of our and others’ experiments have all demonstrated that the Δf value corresponding to the early-stage damage of a dog-bone sample was about 10−1 kHz (Li et al., 2012; Palomino et al., 2011; Zagrai et al., 2009). For the ASS sample used in previous work, the sub-millimeter crack damage and a plastic deformation zone around the pre-notch resulted a 0.2–0.3 kHz peak frequency decrease (Luo et al., 2013). The result in Figure 3 thus strongly demonstrates that the impedance evolution during mechanical contact procedure cannot be ignored, and it would confuse the judgment of the early-stage material damage evaluation. The surface morphology of the ASS specimen after the mechanical contact was studied and that of the 3rd clamping was presented in Figure 4. Diamond-shaped indentations were observed, the scale of which was about several hundred micrometers. Owing to the displacement control error and the different hydraulic levels, the positions and depths of indentations varied a little from each other. The details of the edge between two indentations indicated by the arrow in Figure 4(a) are shown in Figure 4(b). Extrusions with obvious plastic deformation were observed. It is indubitable that mechanical contacts have damaged the surface and the level deteriorates with increasing clamping times, which would theoretically result in the loss of structural resonant frequency. While for the 6th clamping, the root cause of the abnormal shift direction is still ambiguous. It could confirm that mechanical contact could not be simply treated as indentations. Consequently, the detailed factors are analyzed in the following sections.
Electrical impedance spectra of ASS specimen under different mechanical clamping: (a) frequency band, 25–65 kHz, and (b) enlarged view of typical resonant peak.
Surface morphology of ASS specimen after 3rd mechanical clamping: (a) indentations and (b) details of edge part in (a).
Influencing factors of the mechanical contact
According to the practical mechanical testing, the influencing factors of the mechanical contact could be studied from three aspects: the times of in situ contact, the contact stress, and the contact area. The contact couples were confined to steel/ASS and steel/Al, as shown in the apparatus of Figure 2(a). The surface finish of the testing samples and the block couple were similar under each testing condition. So it will not be discussed here. The evolutions of characteristic resonant frequencies of ASS and Al specimens are presented in Figures 5 and 6, respectively. A wide frequency band was usually scanned in advance to ensure the fairness of the overall judgment on the shift direction of resonant peaks in Figure 5(a). It is clear that with increasing times of in situ contact, that is, mechanical clamping, as depicted in Figure 5(a), the resonant peak shifted leftward gradually. After the 2nd clamping, Δf was about 0.1 kHz. When it increased to 5th clamping, the peak frequency was about 51.96 kHz, with a continuous decrease.
Electrical impedance spectra of ASS specimen under different contact parameters: (a) times of in situ contact, (b) contact stress (the values such as 3 MPa indicate the loading hydraulic levels), and (c) contact area.
Electrical impedance spectra of Al specimen under different contact parameters: (a) times of in situ contact, (b) contact stress, and (c) contact area.
In the case of the contact stress, three different hydraulic levels (3, 6, and 9 MPa) were conducted, and the electrical impedance spectra were shown in Figure 5(b). The specimen was being clamped all the time, and the hydraulic level was loaded in sequence. Although detailed contact force/stress value could not be reflected directly, it is not difficult to conclude that the force would increase proportionally as to the structure of the mechanical clamping part depicted in Figure 2(b). When the level increased from 3 to 6 MPa, the resonant peak 80.3 kHz shifted to the right about 0.98 kHz. It is different from that of in situ contact from the aspect of either the shift direction or the amount. A further loading result also demonstrated this point. In the case of hydraulic level at 9 MPa, the peak showed a continuous 0.72 kHz horizontal shift. With a continuous increment of 3 MPa, the enhancement of Δf value, however, is obviously smaller than the former ones.
Contact area is also an important parameter usually encountered during the practical mechanical testing. The corresponding electrical impedance spectra are shown in Figure 5(c). Displacement control was used, and the clamping area increased with ∼100 mm2 for each step. It was observed that the evolution of the resonant peak was not monodirectional. It first shifted rightward to a great extent and then to the opposite direction. Compared with the above results, the extent was relatively large, in the order of several kilohertz. This indicates that the influence of the contact area is quite abnormal and really a great concern.
Due to the particularity of the casting microstructure of ASS specimen, the mechanical property would present some nonuniformity. The impedance results might be influenced. To verify the preliminary results above and compare with others’, similar experiments were conducted with rolled aluminum alloy shown in Figure 6. The basic evolution of electrical impedance spectra was similar. The resonant frequency decreased with the increasing in situ contact times (Figure 6(a)) but increased with the contact stress (Figure 6(b)). For that of contact area shown in Figure 6(c), the spectra also showed an abnormal transition. The quantitative summary is given in Figure 7. The three states under each loading parameter are corresponding to I, II, and III, respectively. The left shift of the resonant peak was specified as negative and the right as positive. It is observed that the evolution of loading sequence was different. The shift amount of contact area was much larger, of which the biggest value was about 6.03 kHz. The smallest value, however, was only about −0.07 kHz to that of ASS under the first in situ contact. While the influence of material properties depended on the specified testing condition. In the case of contact times, although the state III of ASS corresponded to the 5th clamping, the Δf value was only −0.3 kHz, which was much smaller than that of Al, −0.43 kHz (1st clamping) and −0.97 kHz (3rd clamping). This demonstrates that the stiffness loss of Al with lower material hardness caused by the superficial damage was severer. Consequently, it is urgent that appropriate modifications should be performed on the published damage–impedance relationship based on Al alloy (Giurgiutiu et al., 1999; Lim and Soh, 2010, 2011, 2012; Palomino et al., 2011; Park et al., 2010; Zagrai et al., 2009). The contact stress results of the two testing materials were roughly equivalent. The reason might be that the number of indentations was nearly constant with the variation of compressive stress but without any change of clamping position. The results of the contact area are really perplexing. When the state I transformed to II, the Δf value of ASS was as large as 6.03 kHz and that of Al reached even 3.37 kHz. With a continuous increment, the change of ASS and Al was 5.40 and 8.63 kHz, respectively, to the left. One question is that whether there was any relationship with the loading procedure. During the experiment, the hydraulic levels of both materials were set at 3 MPa, and the clamping areas of the two materials under each step were kept the same. In other words, the clamping area started from about 100 mm2 and increased with 100 mm2 in each stage. Although the initial value was mainly controlled by manual operation, the following were realized by displacement control of the testing system. The error was smaller than 50 µm. So the experimental process is reasonable and the accuracy is satisfactory. The above abnormal impedance evolution might result from the waxing and waning of some controversy factors, and we will discuss it further in the following sections.
Mechanical contact: superficial damage and compressive stress
In order to obtain a higher friction coefficient between the testing sample and the grips, rough surface of contact parts is preferred. Consequently, superficial damage such as indentations becomes the main form during mechanical testing. Because of the online monitoring in this study, the compressive stress occurs simultaneously. So the influence of the mechanical contact on the impedance spectra should not be simply treated as a superficial damage. To clarify the effects of the two factors, simulation experiments were conducted. Artificial indentations, marks of steel nail, were used to simulate the superficial damage of the Al specimen. The morphology and the impedance evolution with the mark number are presented in Figures 8 and 9, respectively. The mark showed a crater shape, of which the margin deformed obviously. Compared with those in Figure 3, the diameter was about four times larger. It is indubitable that the damage became more and more serious. With the elevation of the mark point number from 0 to 14, the resonant peaks shifted to the left to about 0.1 kHz, which is in the same degree of one additional in situ clamping of the Al sample.
Morphology of artificial nail mark on the surface of Al specimen.
Evolution of characteristic resonant peak with nail mark number of Al specimen.
For a relatively large specimen in a common compression test, it is not easy to avoid indentations because of the small jigs. Especially owing to the attached brittle PZT plate, how to perform mechanical loading without any damage to PZT/structure bonding is therefore quite difficult. Here, an Al sample was specially designed, and the sketch is shown in Figure 1(b). The compressed part was the brick body with a dimension of 5 × 10 × 3 mm3. A pair of concave arcs was fabricated on the upper and lower surfaces between the compression and the PZT part. Two steel blocks with a 15 × 15 mm2 section were used as the jigs and placed on or under the surface of the compression part. The brick was covered totally but without any contact with the impedance part. The jig surfaces were carefully ground and polished in order to reduce the simultaneous superficial damage as much as possible. Impedance testing was conducted during the mechanical intervals with the compressive stress being held. The nominal stress–strain curve and impedance results are presented in Figure 10. Six stress levels were determined, and the colors were in accordance with impedance signatures. An impedance signature under the condition of 20 MPa, of which only the 136.4 kHz resonant peak was shown in Figure 10(b), was regarded as a reference. When the loading continued to 60 and 120 MPa, the resonant peak shifted rightward and the impedance amplitude increased. The quantitative results are summarized in Figure 10(c). For 120 MPa, the value of Δf was about 0.3 kHz. In the previous research, the influence of tensile stress on impedance evolution has been studied (Luo et al., 2013). For a 3-mm-thick ASS plate, the maximum frequency shift in elastic stage (≤300 MPa) was smaller than 0.1 kHz. Similar results were also obtained with Al alloy (Luo et al., 2012). This indicates that vertical compressive stress has a more obvious effect on the impedance testing against the axial tensile stress. This is consistent with that of the contact stress in Figures 5(b) and 6(b). In Figure 10(a), it is observed that the specimen transited from elastic to plastic deformation in the range of 120–140 MPa. With a continuous loading, the sample deformed plastically and the flow stress maintained a relatively large ratio to the nominal strain, until the end, 240 MPa. In the case of 160 MPa, the corresponding Δf value was 0.43 kHz. When the stress increased to 200 and 240 MPa, the resonant frequency achieved the maximum value and then decreased. The values are presented in Figure 10(c) as 0.5 and 0.47 kHz, respectively. The nominal plastic strain was about 0.55%. It suggests that some microcracks had generated in the region of higher stress concentration, and the mechanical damage is serious. Macroscopic observation also confirmed this point. Theoretically, the resonant frequency of testing specimen would present a continuous decrement during the plastic deformation, reflecting a loss of the structural stiffness. Combined with the elastic result, the result proposed here is that the stiffening effect of compressive stress is more dominant under the stress levels below 200 MPa. Although the plastic damage has been existing from the beginning of the elastic–plastic transformation and growing more seriously, the potential decreasing amount of resonant frequency is too small to counteract that of the compressive stress.
Compression test of rolling Al specimen: (a) nominal stress–strain curve, (b) electrical impedance spectra, and (c) quantitative resonant frequency shift of 136.4 kHz.
Impedance evolution under stresses
The influence of stress on the evolution of EMI signature was considered from the perspective of the boundary condition by Park et al. (2000). Subsequently, in situ stresses in structure members such as the beam and the plate were investigated by Abé et al. (2001) and Ong et al. (2002). Shifts in the natural frequencies of the structures were observed in the presence of stresses. A more detailed and thorough discussion was given by Annamdas et al. (2007) and Lim and Soh (2012). For a uniform axially loaded thin beam, the extensional vibration is not affected by any static axial load acting in the same direction theoretically. The mth natural frequency, Ω m , which is only for the transverse mode, is given as (Lim and Soh, 2012)
where ρ, A,
This indicates that an axial tensile stress will lead to an increase in a natural frequency and a compressive stress will cause a reduction. It is obviously inconsistent with the results in Figures 5 to 7, where the Δf value under compressive stress was about 1–2 kHz. Similar contradiction was also encountered by Annamdas et al. (2007) and Lim and Soh (2012). After a series of experimental, analytical, and numerical studies on a one-dimensional (1D) beam with the fixed boundary condition, they attributed that to the boundary stiffening effect of mechanical loading on the admittance signatures. The fixed ends, that is, clamping here, built stresses in the specimen and then interacted with the wave propagation generated from the PZT transducer. In other words, the fixed–fixed condition either counteracts the negative effect resulted from the compressive stress or strengthens the positive effect of the tensile stress and finally promotes the increasing of the resonant frequencies. Because of the difference of the loading and clamping profile, the stiffening mechanism varies with each other, commonly surface shear stress in the tensile test and surface compressive stress in compression. While from the perspective of the mechanical contact, the clamping and especially the simulation compression shown in Figure 1(b) yield more local compressive stress for the whole sample. So the Δf versus stress in Figure 10(c) presents a more gently increasing relationship than that in Figure 12 of Lim and Soh (2012). The value, however, was larger than the previous elastic tensile results, which were smaller than 0.1 kHz (Luo et al., 2012, 2013). This shows that the influence of compressive stress on the shift of the resonant frequency is more remarkable. It is worth mentioning that only the axial and transverse modes of vibration were considered here. The evolution of other vibration modes such as thickness and width needs to be further studied.
Back to the contact area results discussed in section “Impedance evolution under stresses,” the horizontal clamping force imposed by block couple was kept constant under the same hydraulic level based on the jig structure depicted in Figure 2(b). The contact stress, however, would decrease along with the increasing contact area. The surface of the sample was also damaged more seriously in the form of indentations. These two factors both brought a reduction of the resonant frequencies. Simultaneously, it was observed that the length of the beam between the two fixed boundaries was shortened during this procedure. As to equation (1), it will enhance the value of the natural frequency Ω m . It is reasonably deduced that the resonant frequency will also increase. Consequently, the quantitative impedance evolution of ASS and Al specimens with contact area in Figure 7 is a reflection of the waxing and waning among the above three factors. We know that quantitative analytical calculations are more persuasive to interpret the results in Figure 7. It is a pity that we could not get the frequency loss resulted merely from indentations and the exact compressive stress value. Whether any other factors had functioned during this procedure is not quite clear. In any case, contact area is of great influence on the selection of the reference impedance signature, and any ignorance will mislead the material or structural damage evaluation.
Precautions against the influence of mechanical contacts
According to the results and discussion presented above, the precautions against the influence of mechanical contacts on the reference impedance signature selection are proposed here. To realize the online damage evaluation, the ultimate contact state during the clamping adjustment in advance of the mechanical testing, for example, tensile and fatigue, is recommended to be selected as the reference state, while the impedance signature could be the baseline for the following examinations. Any operations, including re-clamping and modification on the contact stress and contact area, which break the established contact state would bring about a mendacious report and, therefore, are not suggested. Nevertheless, it is easy to avoid re-clamping operations but difficult to stabilize the superficial damage during the mechanical testing process. How to minimize the influence of indentations which might evolve dynamically is a challenge we have to confront. According to the mechanical behavior of ductile metals, we know that the plastic flow stress is higher than that of elastic stress in a common wide strain range. So a superficial plastic deformation of the clamping part ahead might stabilize the indentations during the online damage evaluation. In our experiments, pre-clamping several or dozens of times with relatively higher contact force was found to be effective to obtain a good reference impedance spectrum. So it is recommended to the future damage evaluation with the EMI method.
Conclusion
Influences of mechanical contact on material mechanical damage evaluation with the EMI technique were investigated from three aspects, the times of in situ contact, contact area, and force. The important results are summarized as follows:
Along with the change of the three influencing factors, the shift direction and magnitude of the resonance peak in electrical impedance signature became different from each other. With increasing times of in situ contact, the resonant frequency decreased gradually in the order of 10−2–10−1 kHz for each clamping with hydraulic fixtures and reversed to about 10−1–100 kHz with the increasing hydraulic level of clamping. The relationship between Δf and the contact area, however, was a little abnormal.
Because of the combined effects of the online examination, the special compression specimen was designed, and the simulation experiments were conducted to clarify the respective effect of the indentation damage and the compressive stress. The loss of structural stiffness caused by indentations was confirmed, and the quantitative frequency shift with the compressive stress was obtained. Approximately linear strengthening effect in elastic stage was consistent with that of the clamping under different hydraulic levels. Results of clamping area might be attributed to the balance of indentations, the compressive stress, and the beam length between the two fixed boundaries.
The Δf evolution of the ASS and the Al alloy in this study demonstrated that the impedance response to mechanical contact had a strong dependence on the material property. Hard and strong ASS was less sensitive to environmental loads than soft and ductile Al alloy. The order of impedance change, however, was equal or even more serious against that of the early-stage mechanical damage of the testing structure. Consequently, the influence of the mechanical contact on an actual damage evaluation with the EMI technique should be taken into serious consideration. Repeated clamping which led to a residual plastic deformation was found to be effective precautions to avoid the possible influence on the damage evaluation.
Footnotes
Declaration of conflicting interests
The authors declare that there is no conflict of interest.
Funding
This study received financial support from the National Basic Research Program of China (grant no. 2009CB724305) and the Fundamental Research Funds for the Central Universities of China (grant no. DUT11RC (3)69).