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Measurement of the energy release rate of compressive failure in composites by combining infrared thermography and digital image correlation
Composites Part A 122 (2019) 59–66
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Measurement of the energy release rate of compressive failure in composites by combining infrared thermography and digital image correlation
T
Yanan Yuana, , Shen Wangb ⁎
a b
School of Civil Engineering, Wuhan University, Wuhan 430000, China Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
ARTICLE INFO
ABSTRACT
Keywords: Composites Energy release rate Infrared thermography Digital image correlation
The compressive behavior of composites after low velocity impact is one of the most important characteristics that should be taken into consideration when evaluating the damage tolerance of composite structures. In this paper, a novel experimental method combining infrared thermography and digital image correlation has been proposed to measure the energy release rate of composites under the compression-after-impact test. This method was chosen to avoid the error caused by the thermal stability assumption in the traditional methods that are used. First, a theoretical framework was developed and the formula for the energy release rate was established. Then, the calculation procedure has been described in detail with the combination of the temperature information from infrared thermography and the displacement information from the digital image correlation. Finally, an experimental case has been presented and by comparing the new method with the traditional methods, the accuracy of this proposed method has been validated.
1. Introduction Advanced composite materials are a new type of material that first arose in the 1960 s. They have many beneficial properties, such as high specific strength, high specific stiffness, customizable performance, corrosion resistance and integral forming [1–3], and they have been widely used in modern engineering fields [4,5]. An important achievement in the field of composites it that the proportion of composite materials that have been used in the structure of an aircraft has exceeded 50% for the first time in recent years [6]. However, low-speed impact damage, which can be caused by a wide range of environmental factors, such as the impact of a tool being dropped, runway debris and hail, still seriously threaten the strength of composite structures. Although there may be no obvious marks on the impact surface, these low-speed impacts can cause internal damage, and may further result in a sharp decline in the residual strength [7]. Therefore, the compressive behavior of composite structures after a low-speed impact is one of the most serious concerns that must be considered when evaluating the damage tolerance of composite structures. Sun and Hallett [8]investigated the key driving mechanisms and damage evolution of the compressive failure of laminated composites by 3D Digital Image Correlation (DIC) under compression after impact and indentation (CAI) tests. In fact, the compression-after-impact (CAI) process for composite structures is complicated. Matrix cracking, ⁎
delamination, surface indentation and fiber breakage etc. are involved during the low-speed impact and compressive process. Besides, kinkband damage mode is also found during the compressive process using both experimental [9] and numerical [10] methods. Actually, the previous studies on the damage tolerance of composite structures were mainly focused on the prediction of the residual compressive strength, i.e., the ratio of the compressive strength of the structure before and after an impact, or after an in-plane and/or edge impact. Papanicolaou and Stavropoulos [11] proposed a model to predict the residual compressive strength of composites. Hosur et al. [12] summarized the compression-after-impact tests of T300/914 laminates for different impact energies, and proposed a mathematical relationship between the impact energy and the residual compressive strength of the composites. Rhead et al. [13] proposed a semi-analytical fracture mechanics model to predict the residual compressive strength of a composite’s stiffeners after an edge impact. Recently, Koo et al. [14] established the correlation between the depth of the surface pits caused by an impact and the composite’s residual compressive strength. Ostre et al. [15] fixed the bottom edge of composite laminates using a specific clamp to simulate the boundary conditions of T-type stiffened plates under compression, and finally, they found that compression damage to the fibres was the fundamental factor that determined compression failure and governed the residual compressive strength of a composite after an edge impact. It is well known that when a crack propagates or a material breaks,
Corresponding author. E-mail address: [email protected] (Y. Yuan).
https://doi.org/10.1016/j.compositesa.2019.04.022 Received 12 January 2019; Received in revised form 6 April 2019; Accepted 17 April 2019 Available online 18 April 2019 1359-835X/ © 2019 Elsevier Ltd. All rights reserved.
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part of the mechanical energy is converted to heat, which increases the temperature field near a crack or a defect. The quantitative relationship between the temperature field and the fracture properties of the material has been developed in the literature [16]. From an experimental point of view, Infrared thermography (IRT) is a non-contact technology that can be used to measure the temperature field of a sample, and it has the advantages of a wide measuring range [17], high measurement speed [18], high frame rate of acquisition [19] and good accuracy. Infrared thermography has been used to measure the temperature field in a wide range of applications, including materials characterization [20], the fracture process [21,22], fatigue behavior [23,24], damage propagation [25], adhesion science [26], defect detection [27], and is involved in a broad range of materials and structures, such as woven composites [28], aerospace or aircraft carbon fiber reinforced polymer (CFRP) composites [4,10,29], carbon-carbon composites [30], and sandwich structures [31]. In addition, infrared thermography (active infrared thermography [22,30] and passive infrared thermography [21]) has also been used to measure the fracture properties of composite materials. Bhalla et al. [32], investigated the temperature field ahead of a stable, Mode I, growing crack in a ductile material that was imaged using an infrared camera and the thermal images were analyzed to compute the energy flux in the crack, and a good match was achieved with the simulation results. Diaz et al. [33] presented an improvement in the methodology for monitoring fatigue crack growth and inferring the stress intensity factor from the thermoelastic data from a sample. Recently, Vieille et al. [34] compared the residual compressive strength and behavior of conventional thermosetting epoxy and high-performance thermoplastic epoxy based laminates, that were initially subjected to low velocity impacts, using the Infrared thermography technique. Lisle [16,28] et al. presented a new procedure, based on the estimation of heat source fields, to calculate the energy release rate that is associated with transverse weft cracking in a thin woven composite laminate under static tension. Infrared thermography technology calculates the exothermic heat of a composite during the process of being damaged by capturing the temperature field of the composite. The information that can be obtained by infrared technology is very limited (only the temperature field changes). In order to obtain more information about the process of damage to composites, recently some researchers have tried to combine infrared technology with other technologies such as the digital image correlation (DIC) method, X-ray tomography, ultrasonics and Markov chains to obtain more information about the fracture parameters of composites. Goidescu et al. [35] investigated the damage to CFRP composites using full-field measurement techniques by combining digital image stereo-correlation, infrared thermography and X-ray tomography. Image stereo-correlation and infrared thermography can be used in live recording during on-axis and off-axis tensile tests. X-ray tomography allows for a post-failure analysis of the degradation patterns within the laminate’s volume to be carried out. In order to evaluate the overall delamination of composites under impact load in a reliable way, Meola et al. [36] adopted two techniques (infrared thermography and ultrasonics) to establish a nondestructive evaluation method of carbon fibre reinforced composites. Wei et al. [37] proposed a stochastic fatigue damage method for composite materials, based on Markov chains and infrared thermography. With the development of new technologies, more and more combined methods have been proposed to solve complex measurement problems. In general, Infrared thermography is an effective method that can be used to evaluate the fracture toughness or energy release rate of composites when damage occurs. However, most of the existing studies have been based on the assumption of thermal stability. In fact, it should be noted that the heat released in the fracture process is very intense, and it takes a certain amount of time to achieve a stable state. Thus, the assumption of thermal stability may introduce errors. Furthermore, the shape of the temperature field and the
deformation of the specimen during compression were not considered in the previous research. In order to break through the limitation of the thermal stability assumption, a more general method has been proposed in this paper to measure the energy release rate of composite materials, which has combined infrared thermography with digital image correlation technology, and this method has been experimentally verified. The main novelty of the present work has been the proposal of a novel experimental method combining infrared thermography and digital image correlation to measure the energy release rate of a composite during the compression-after-impact test. This method was chosen to avoid the error that is caused by the thermal stability assumption in the traditional methods that are used for this process. In fact the method that has been proposed is more suitable for the non-thermal stability process and can directly characterize the strain energy release rate in the process of the crack growth of composite materials. 2. Experimental tests The experiments carried out in this paper were conducted according to the ASTM (American Society for Testing and Materials) D7136 standard [38] (for the case of a drop-weight impact event) and ASTM D7137 standard [39] (for the case of a compressive test after an impact). T300/QY8911 with a stacking sequence of [0 /90 /45 / 45 ]4s was chosen as the model composite material, and the specimen had dimensions of 150mm × 100mm × 4mm . In order to verify the method that has been proposed, 12 specimens were prepared as shown in Fig. 1. The impact load was applied to the center of the specimen by a 2.7 Kg weight that was dropped from a height of 0.8 m. The compression speed was 2 mm/min. The density of the material is = 1578kg /m3 and the specific heat of the material is C = 862J / kg . A complementary metal oxide semiconductor (CMOS) camera (DH-SV1421Gx) and an infrared thermal imager were positioned on the same side of the sample during the compression testing process, and set at the same frame rate to achieve synchronous image acquisition. The infrared thermal imager that was used was the FLIR T650, and it has a temperature field measurement accuracy of 0.1 °C within 150 °C. Speckles were sprayed onto the specimen’s surface, the speckled images and the surface’s temperature field were recorded by the CMOS camera and the infrared thermal imager, respectively. The details of the compression experiment have been shown in Fig. 1, including the experimental setup, the specimen and the force-displacement curve for the compression process of the specimen. The compression experiment was carried out until the specimen was destroyed. The compression-after-impact (CAI) process of testing a composite is very complicated and the fracture process is accompanied with either tension or compression, which will cause the large deformation of the materials. Therefore, the position of the corresponding points in the different images will change during the fracture process. In the experiment, it was found that the displacements of the corresponding points in the different images could be as much as several millimeters. These displacements can cause significant errors and therefore cannot be ignored. Furthermore, it was also found that the local deformation in the vicinity of the crack occurred during crack propagation, so the displacements of these corresponding points could not be considered as rigid body displacement, which meant that each pixel had a different displacement in the temperature images. In order to correct the displacements of these corresponding points in the different images, the digital image correlation method was used and combined with the infrared thermography technique. Fig. 2 shows the infrared temperature images of the composite during the crack propagation process in the compression-after-impact test. It could be seen that there were two typical heat-related stages during the propagation of the crack, i.e., heat generation and heat transfer. The heat generation originated from the energy release during the crack initiation, in which the released energy was directly transmitted to the material and caused the temperature to rise in the 60
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Fig. 1. The compression experiment. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
material near the tip of the crack. The heat generation process was almost synchronous with the crack propagation, and occurred in a short period of time. When the local temperature rose, the temperature field changed to a non-equilibrium state and the heat gradually transferred from the higher temperature region to the lower temperature region. The heat transfer process was relatively slow; it began at the start of the heat generation process and continued after the crack propagation had finished. During the heat generation process, the temperature field had a large gradient, in which the high temperature region was narrow and the edge was clear. At this time the temperature field was unstable; as the heat transfer process proceeded, the temperature field became less intense with a smaller gradient, and the edges became blurred. Finally, the whole temperature field reached a state of equilibrium. During the compression experiment, the surface temperature field of the specimen hardly changed before the initiation of the crack and after the heat transfer stabilized. The temperature field only changed dramatically during a short period during the crack initiation and propagation. It can be clearly seen from Fig. 2 that two cracks occurred in the specimen during compression. The speckled images of the specimen corresponding to the thermal images in Fig. 2 are shown in Fig. 3. Before the digital image correlation
was applied to the speckled images, the calculation area first needed to be selected. The first step was to select the calculation area on the thermal image, which needed to be large enough to cover the whole crack during the propagation process. The next step was to select the calculation area on the speckled images, which needed to be large enough to cover the calculation area on the thermal image. After this the digital image correlation method was used to calculate the displacement field of the speckled image, which is shown in Fig. 4. Through comparison of Fig. 2 and Fig. 3, it could be clearly seen that the bulge in the material occurred after the crack propagation. The bulge was found in image 7, and the crack propagation process was displayed during images 2–6. According to the experimental results of the temperature field and the displacement field, the average fracture toughness of the CFRP composites during the CAI test could be evaluated by the thermo-mechanical theoretical model which has been explained in the next section. 3. Theoretical framework During crack propagation, part of the potential energy of the material is irreversibly released, most of which is transformed into heat
Fig. 2. The temperature field of the specimen during the crack propagation process. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 61
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Fig. 3. The speckled images of the specimen corresponding to the thermal images. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
[18], while the rest of the irreversibly released energy is consumed in modifying the molecular structure of the material. Following the definition in the literature [15], the parameter has been introduced here to denote the proportion of the irreversible mechanical energy that is transformed into heat. For different materials, the transformation efficiency is different. For example, the value of can be up to 70∼100% for metallic materials [19] and 50∼90% for polymers [20]. Assuming the ratio of is uniformly distributed throughout the as shown in Fig. 5, and the specific free surface calculation area energy is much smaller than the total energy released, the energy release rate G can be expressed as [16]:
G=
Wdiss ·dS
dissipated during time dt , respectively. As shown in Fig. 2, the heat generation process is relatively intense, and the heat transfer process is relatively slow. Therefore, it can be assumed that the temperature fields shown in Fig. 2 (1–6) are dominated by the heat generation process, and the heat transfer process is negligible, which contains heat transfer from the material to the external environment and other parts of the material. Therefore the energy that is converted into heat and released by the fracturing of the material changes the temperature field of the material near the crack tip, that is, this part of the energy is converted into the internal energy of the material itself. By employing a two-dimensional (2D) model, in which the crack extends throughout the thickness of the material, and given that the temperature field is evenly distributed in the direction of the thickness of the material, the heat energy converted into Wdiss can be written as:
(1)
where dS and Wdiss are the crack growth area and the thermal energy
Fig. 4. The displacement field of the speckled images. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 62
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Fig. 6. The flowchart for the process of correcting the thermal images. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. The full field thermal image and the calculation area. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Wdiss =
m
c Ti dm =
cd Ti ds
dS
obtained. The flowchart for the process of correcting the thermal images with the DIC method has been given in Fig. 6. By calculating the images of the different crack propagation stages or the different cracks of the same specimen, multiple energy release rates could be calculated, and the measurement accuracy of the energy release rate could be further improved by taking an average of these values.
(2)
where c is the specific heat of the material, d is the thickness of the specimen, is the density of the material, and Ti is the temperature change of each point in the crack propagation area dS during the compression. Fig. 5 has shown the full field temperature image caught by the Infrared thermal imager and the square frame of the four zones were chosen as the calculation area. The speckle was sprayed onto the surface of the specimen before the experiment to obtain speckled images to calculate the displacement fields. As the infrared thermal imager was not integrated with the CMOS camera, there were rigid body displacements and zoom coefficients to account for between the thermal images and the speckled images. In order to eliminate the influence of the rigid body displacements and the zoom coefficients, the area in the speckled image corresponding to the calculation area in the thermal image needed to be first ascertained by some feature points in the image, such as the corner of the specimen. Then the digital image correlation method was applied to calculate the displacement field of the speckled images captured before and after deformation. The integral of Eq. (2) can be obtained by subtracting the temperature fields before and after the fracture processes. More specifically since the temperature field was outputted in the form of a digital image, which is in essence a matrix, the integral could be discretized and expressed by summation, then the energy release rate can be written as:
cd
A key step in evaluating the energy release rate was to choose the calculation area of the thermal image corresponding to the speckled image using the feature points, as shown in Fig. 7. Taking the left crack (Zone 1) as an example, the calculation process was carried out as follows: Firstly, the position of the four bolts in the speckled image and the temperature image were read, and the linear relationship between the coordinates of the two images was calculated. Then, the coordinates of the four corners of the calculation area in the thermal image were read, and by putting these coordinates into the linear relationship, the corresponding area in the speckled image could be found, and the corresponding displacement field was then extracted. The next step was to calculate the zoom coefficient, from Eq. (4), between the speckled image and the thermal image. The zoom coefficient could be calculated by reading the heights of the specimen in the speckled image and the thermal image, which were 1636 pixels and 307 pixels, respectively. As a result, the zoom coefficient could be calculated as k = 307/1636 = 0.188. In this way, the displacement of each pixel in the temperature image calculation area could be calculated. Finally, for each pixel of the calculation area in the thermal images, the correction process was carried out using Eq. (5). These four steps were then repeated in the calculation area in the entire deformed temperature field, that is, the left crack in Fig. 2(2–12), the correction process was then carried out, which has been shown in Fig. 8. In this experiment, it was difficult to observe the propagation of the cracks, and almost all parts of the cracks occurred at the same time. Therefore, it was impossible to calculate the energy release rate at the different stages of crack propagation, therefore only the calculation of the energy release rate of multiple cracks can be used to improve the measurement accuracy. For a crack, the energy release rate can be calculated from two images, one taken before crack initiation and one taken after crack propagation. Therefore, it was necessary to find the end point of crack propagation. Fig. 2(1) was considered as the state before crack initiation, because the image had no obvious thermal characteristics. When the crack occurred, the surface temperature rose locally, and the summation value in Eq. (3) increased. When the difference of this value between the two images was less than 5%, the
s T n
G=
4. Results and analysis
(3)
· dS
where s represents the actual area corresponding to a pixel. According to the displacement of each pixel in the speckled image, the displacement of each pixel in the thermal image could be calculated by: (4)
u = ku, v = kv
where u , v are the displacements of the speckled images, u , v are the displacements of the thermal image, and k is the zoom coefficient. Finally, the Fourier transform phase shift method was used to correct the displacement of each pixel in the thermal image, i.e.:
f =F
1
[F (f )·e2
(v + u )
·e
]
2i
(5)
where F represents the Fourier transform and f represents the value for each pixel in the thermal image. Then, using Eq. (3) to calculate the difference between the temperature field before deformation and the corrected temperature field after deformation, the energy release rate of the material could be 63
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Fig. 7. The process of finding the calculation area of the temperature in the speckled image. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. The temperature field of the left crack after correction. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
64
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almost all material systems. The only differences are the mechanical/ thermodynamic properties of the material and the damage modes which may change the temperature field and the heat transformation efficiency. However the key mechanism is constant for different material systems. In spite of the difficulties in estimating the β coefficient, the energy release rate measured by this new method in this paper, was also relatively consistent with those found in a previous study on a similar material. For example, the energy release rate of the material T700GC/ M21 carbon/epoxy [16] was measured as 32.6 KN/m, and it was measured as 34–39 KN/m for the T800/924C carbon-epoxy laminates in the literature [2].
Table 1 Summation from Eq. (3) of the thermal image calculation area. State Zone Zone Zone Zone Zone Zone
n
1: 1: 2: 2: 3: 3:
s T (mm2 ·K )
by by by by by by
IR&DIC IR only IR&DIC IR only IR&DIC IR only
1
2
3
4
5
6
7
8
0 0 0 0 0 0
78.0 74.9 8.2 7.8 0.5 0.5
281.1 264.4 79.3 76.3 4.9 5.3
318.9 307.5 136.4 131.3 7.7 8.7
340.1 335.1 178.4 173.2 9.2 10.6
353.7 352.9 208.8 204.6 9.4 11.3
357.4 362.6 209.5 238.9 9.5 11.5
357.9 389.9 248.2 274.2 — —
Table 2 The material and its experimental parameters.
5. Conclusion
Density
1578kg /m3
Specific heat
862J /kg· K 0.5 0.9 0.465mm 150mm × 100mm × 4mm
[15–16] Pixel length Specimen size
Through the combination of the digital image correlation method and infrared thermography, a new method for measuring the energy release rate of composite materials during the compression-after-impact experiment has been proposed in this paper. A theoretical framework was developed as a guide for the experimental procedure, and the calculation process of the method has been described in detail. The main conclusions that were drawn were as follows:
Table 3 Values of the parameters of the heat sources for the three zones. Test
Zone no.
n
s T
(mm2 ·K ) CAI
1 2 3
389.9 237.6 13.6
by IR
n
s T (mm2 ·K ) by
S (mm2)
IR&DICs 357.9 209.5 9.5
193.7 108.5 5.8
G (N/mm) by IR&DIC
(1) In the compression-after-impact experiment, it was found that the energy conversion and the deformation of the material were coupled. The influence of the deformation field on the temperature field should be corrected during the calculation process. (2) This new method that combined the infrared thermography technique and the digital image correlation method was well suited for measuring the energy release rate of composite materials for the compression-after-impact test. (3) The error in measuring the energy release rate of composites using this new method was 5%, which could be further reduced by calculating the energy release rate using the images of different crack propagation stages, different cracks in the same specimen or through the use of a high speed camera with a high resolution.
11.1–20.1 11.7–21.0 9.9–17.9
crack was considered to have finished occurring and no more internal energy was being produced. Table 1 has listed the calculation results for the left side crack both with DIC correction and without DIC correction. In the process of the experiment and data processing, the purpose of the DIC method was to obtain the temperature field of the same region at different times, so as to subtract the temperature field and calculate the amount of heat released. In the process of loading, deformation often leads to local deformation of the temperature field. If DIC technology is not used and the pixel matrix is directly subtracted, the measurement of the release of heat will be erroneous and will have difficulty converging. Therefore, it is thought that the convergent heat released in the specified crack region could be measured by considering the displacement and temperature field information of DIC, which is the key to solving the fracture toughness of composites. As can be seen from Table 1, the data showed good convergence after the DIC correction, which removed the error caused by the compression deformation. According to the convergence results, Fig. 2(6) was considered as the end point of crack propagation. By using the material and experimental parameters provided in Table 2, the energy release rate could be calculated for the left hand crack in this experiment and has been shown in Table 3. In addition, it should be pointed out that the experimental results shown in this paper, including the thermal images or the images from the DIC results, are only about one typical example because other similar experimental results have already been obtained. The values of the parameters of the heat sources for the four zones and the calculated values for the fracture toughness of the CFRP during the CAI tests have been listed in Table 3. For the right hand crack (Zone 2) in this experiment, and using the same calculation process, the other energy release rate could be calculated as G = 11.7 21.0KN / m . This result indicated that the error between the different cracks in the same specimen was only 5%, which has proven the accuracy and reliability of this new method that has been introduced in this paper. The method that has been proposed in this paper can be applied to many material systems with more than one composite laminate configuration. In fact, the fracture process and the heat generation process can be found in
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Composites Part A journal homepage: www.elsevier.com/locate/compositesa
Measurement of the energy release rate of compressive failure in composites by combining infrared thermography and digital image correlation
T
Yanan Yuana, , Shen Wangb ⁎
a b
School of Civil Engineering, Wuhan University, Wuhan 430000, China Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
ARTICLE INFO
ABSTRACT
Keywords: Composites Energy release rate Infrared thermography Digital image correlation
The compressive behavior of composites after low velocity impact is one of the most important characteristics that should be taken into consideration when evaluating the damage tolerance of composite structures. In this paper, a novel experimental method combining infrared thermography and digital image correlation has been proposed to measure the energy release rate of composites under the compression-after-impact test. This method was chosen to avoid the error caused by the thermal stability assumption in the traditional methods that are used. First, a theoretical framework was developed and the formula for the energy release rate was established. Then, the calculation procedure has been described in detail with the combination of the temperature information from infrared thermography and the displacement information from the digital image correlation. Finally, an experimental case has been presented and by comparing the new method with the traditional methods, the accuracy of this proposed method has been validated.
1. Introduction Advanced composite materials are a new type of material that first arose in the 1960 s. They have many beneficial properties, such as high specific strength, high specific stiffness, customizable performance, corrosion resistance and integral forming [1–3], and they have been widely used in modern engineering fields [4,5]. An important achievement in the field of composites it that the proportion of composite materials that have been used in the structure of an aircraft has exceeded 50% for the first time in recent years [6]. However, low-speed impact damage, which can be caused by a wide range of environmental factors, such as the impact of a tool being dropped, runway debris and hail, still seriously threaten the strength of composite structures. Although there may be no obvious marks on the impact surface, these low-speed impacts can cause internal damage, and may further result in a sharp decline in the residual strength [7]. Therefore, the compressive behavior of composite structures after a low-speed impact is one of the most serious concerns that must be considered when evaluating the damage tolerance of composite structures. Sun and Hallett [8]investigated the key driving mechanisms and damage evolution of the compressive failure of laminated composites by 3D Digital Image Correlation (DIC) under compression after impact and indentation (CAI) tests. In fact, the compression-after-impact (CAI) process for composite structures is complicated. Matrix cracking, ⁎
delamination, surface indentation and fiber breakage etc. are involved during the low-speed impact and compressive process. Besides, kinkband damage mode is also found during the compressive process using both experimental [9] and numerical [10] methods. Actually, the previous studies on the damage tolerance of composite structures were mainly focused on the prediction of the residual compressive strength, i.e., the ratio of the compressive strength of the structure before and after an impact, or after an in-plane and/or edge impact. Papanicolaou and Stavropoulos [11] proposed a model to predict the residual compressive strength of composites. Hosur et al. [12] summarized the compression-after-impact tests of T300/914 laminates for different impact energies, and proposed a mathematical relationship between the impact energy and the residual compressive strength of the composites. Rhead et al. [13] proposed a semi-analytical fracture mechanics model to predict the residual compressive strength of a composite’s stiffeners after an edge impact. Recently, Koo et al. [14] established the correlation between the depth of the surface pits caused by an impact and the composite’s residual compressive strength. Ostre et al. [15] fixed the bottom edge of composite laminates using a specific clamp to simulate the boundary conditions of T-type stiffened plates under compression, and finally, they found that compression damage to the fibres was the fundamental factor that determined compression failure and governed the residual compressive strength of a composite after an edge impact. It is well known that when a crack propagates or a material breaks,
Corresponding author. E-mail address: [email protected] (Y. Yuan).
https://doi.org/10.1016/j.compositesa.2019.04.022 Received 12 January 2019; Received in revised form 6 April 2019; Accepted 17 April 2019 Available online 18 April 2019 1359-835X/ © 2019 Elsevier Ltd. All rights reserved.
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part of the mechanical energy is converted to heat, which increases the temperature field near a crack or a defect. The quantitative relationship between the temperature field and the fracture properties of the material has been developed in the literature [16]. From an experimental point of view, Infrared thermography (IRT) is a non-contact technology that can be used to measure the temperature field of a sample, and it has the advantages of a wide measuring range [17], high measurement speed [18], high frame rate of acquisition [19] and good accuracy. Infrared thermography has been used to measure the temperature field in a wide range of applications, including materials characterization [20], the fracture process [21,22], fatigue behavior [23,24], damage propagation [25], adhesion science [26], defect detection [27], and is involved in a broad range of materials and structures, such as woven composites [28], aerospace or aircraft carbon fiber reinforced polymer (CFRP) composites [4,10,29], carbon-carbon composites [30], and sandwich structures [31]. In addition, infrared thermography (active infrared thermography [22,30] and passive infrared thermography [21]) has also been used to measure the fracture properties of composite materials. Bhalla et al. [32], investigated the temperature field ahead of a stable, Mode I, growing crack in a ductile material that was imaged using an infrared camera and the thermal images were analyzed to compute the energy flux in the crack, and a good match was achieved with the simulation results. Diaz et al. [33] presented an improvement in the methodology for monitoring fatigue crack growth and inferring the stress intensity factor from the thermoelastic data from a sample. Recently, Vieille et al. [34] compared the residual compressive strength and behavior of conventional thermosetting epoxy and high-performance thermoplastic epoxy based laminates, that were initially subjected to low velocity impacts, using the Infrared thermography technique. Lisle [16,28] et al. presented a new procedure, based on the estimation of heat source fields, to calculate the energy release rate that is associated with transverse weft cracking in a thin woven composite laminate under static tension. Infrared thermography technology calculates the exothermic heat of a composite during the process of being damaged by capturing the temperature field of the composite. The information that can be obtained by infrared technology is very limited (only the temperature field changes). In order to obtain more information about the process of damage to composites, recently some researchers have tried to combine infrared technology with other technologies such as the digital image correlation (DIC) method, X-ray tomography, ultrasonics and Markov chains to obtain more information about the fracture parameters of composites. Goidescu et al. [35] investigated the damage to CFRP composites using full-field measurement techniques by combining digital image stereo-correlation, infrared thermography and X-ray tomography. Image stereo-correlation and infrared thermography can be used in live recording during on-axis and off-axis tensile tests. X-ray tomography allows for a post-failure analysis of the degradation patterns within the laminate’s volume to be carried out. In order to evaluate the overall delamination of composites under impact load in a reliable way, Meola et al. [36] adopted two techniques (infrared thermography and ultrasonics) to establish a nondestructive evaluation method of carbon fibre reinforced composites. Wei et al. [37] proposed a stochastic fatigue damage method for composite materials, based on Markov chains and infrared thermography. With the development of new technologies, more and more combined methods have been proposed to solve complex measurement problems. In general, Infrared thermography is an effective method that can be used to evaluate the fracture toughness or energy release rate of composites when damage occurs. However, most of the existing studies have been based on the assumption of thermal stability. In fact, it should be noted that the heat released in the fracture process is very intense, and it takes a certain amount of time to achieve a stable state. Thus, the assumption of thermal stability may introduce errors. Furthermore, the shape of the temperature field and the
deformation of the specimen during compression were not considered in the previous research. In order to break through the limitation of the thermal stability assumption, a more general method has been proposed in this paper to measure the energy release rate of composite materials, which has combined infrared thermography with digital image correlation technology, and this method has been experimentally verified. The main novelty of the present work has been the proposal of a novel experimental method combining infrared thermography and digital image correlation to measure the energy release rate of a composite during the compression-after-impact test. This method was chosen to avoid the error that is caused by the thermal stability assumption in the traditional methods that are used for this process. In fact the method that has been proposed is more suitable for the non-thermal stability process and can directly characterize the strain energy release rate in the process of the crack growth of composite materials. 2. Experimental tests The experiments carried out in this paper were conducted according to the ASTM (American Society for Testing and Materials) D7136 standard [38] (for the case of a drop-weight impact event) and ASTM D7137 standard [39] (for the case of a compressive test after an impact). T300/QY8911 with a stacking sequence of [0 /90 /45 / 45 ]4s was chosen as the model composite material, and the specimen had dimensions of 150mm × 100mm × 4mm . In order to verify the method that has been proposed, 12 specimens were prepared as shown in Fig. 1. The impact load was applied to the center of the specimen by a 2.7 Kg weight that was dropped from a height of 0.8 m. The compression speed was 2 mm/min. The density of the material is = 1578kg /m3 and the specific heat of the material is C = 862J / kg . A complementary metal oxide semiconductor (CMOS) camera (DH-SV1421Gx) and an infrared thermal imager were positioned on the same side of the sample during the compression testing process, and set at the same frame rate to achieve synchronous image acquisition. The infrared thermal imager that was used was the FLIR T650, and it has a temperature field measurement accuracy of 0.1 °C within 150 °C. Speckles were sprayed onto the specimen’s surface, the speckled images and the surface’s temperature field were recorded by the CMOS camera and the infrared thermal imager, respectively. The details of the compression experiment have been shown in Fig. 1, including the experimental setup, the specimen and the force-displacement curve for the compression process of the specimen. The compression experiment was carried out until the specimen was destroyed. The compression-after-impact (CAI) process of testing a composite is very complicated and the fracture process is accompanied with either tension or compression, which will cause the large deformation of the materials. Therefore, the position of the corresponding points in the different images will change during the fracture process. In the experiment, it was found that the displacements of the corresponding points in the different images could be as much as several millimeters. These displacements can cause significant errors and therefore cannot be ignored. Furthermore, it was also found that the local deformation in the vicinity of the crack occurred during crack propagation, so the displacements of these corresponding points could not be considered as rigid body displacement, which meant that each pixel had a different displacement in the temperature images. In order to correct the displacements of these corresponding points in the different images, the digital image correlation method was used and combined with the infrared thermography technique. Fig. 2 shows the infrared temperature images of the composite during the crack propagation process in the compression-after-impact test. It could be seen that there were two typical heat-related stages during the propagation of the crack, i.e., heat generation and heat transfer. The heat generation originated from the energy release during the crack initiation, in which the released energy was directly transmitted to the material and caused the temperature to rise in the 60
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Fig. 1. The compression experiment. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
material near the tip of the crack. The heat generation process was almost synchronous with the crack propagation, and occurred in a short period of time. When the local temperature rose, the temperature field changed to a non-equilibrium state and the heat gradually transferred from the higher temperature region to the lower temperature region. The heat transfer process was relatively slow; it began at the start of the heat generation process and continued after the crack propagation had finished. During the heat generation process, the temperature field had a large gradient, in which the high temperature region was narrow and the edge was clear. At this time the temperature field was unstable; as the heat transfer process proceeded, the temperature field became less intense with a smaller gradient, and the edges became blurred. Finally, the whole temperature field reached a state of equilibrium. During the compression experiment, the surface temperature field of the specimen hardly changed before the initiation of the crack and after the heat transfer stabilized. The temperature field only changed dramatically during a short period during the crack initiation and propagation. It can be clearly seen from Fig. 2 that two cracks occurred in the specimen during compression. The speckled images of the specimen corresponding to the thermal images in Fig. 2 are shown in Fig. 3. Before the digital image correlation
was applied to the speckled images, the calculation area first needed to be selected. The first step was to select the calculation area on the thermal image, which needed to be large enough to cover the whole crack during the propagation process. The next step was to select the calculation area on the speckled images, which needed to be large enough to cover the calculation area on the thermal image. After this the digital image correlation method was used to calculate the displacement field of the speckled image, which is shown in Fig. 4. Through comparison of Fig. 2 and Fig. 3, it could be clearly seen that the bulge in the material occurred after the crack propagation. The bulge was found in image 7, and the crack propagation process was displayed during images 2–6. According to the experimental results of the temperature field and the displacement field, the average fracture toughness of the CFRP composites during the CAI test could be evaluated by the thermo-mechanical theoretical model which has been explained in the next section. 3. Theoretical framework During crack propagation, part of the potential energy of the material is irreversibly released, most of which is transformed into heat
Fig. 2. The temperature field of the specimen during the crack propagation process. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 61
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Fig. 3. The speckled images of the specimen corresponding to the thermal images. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
[18], while the rest of the irreversibly released energy is consumed in modifying the molecular structure of the material. Following the definition in the literature [15], the parameter has been introduced here to denote the proportion of the irreversible mechanical energy that is transformed into heat. For different materials, the transformation efficiency is different. For example, the value of can be up to 70∼100% for metallic materials [19] and 50∼90% for polymers [20]. Assuming the ratio of is uniformly distributed throughout the as shown in Fig. 5, and the specific free surface calculation area energy is much smaller than the total energy released, the energy release rate G can be expressed as [16]:
G=
Wdiss ·dS
dissipated during time dt , respectively. As shown in Fig. 2, the heat generation process is relatively intense, and the heat transfer process is relatively slow. Therefore, it can be assumed that the temperature fields shown in Fig. 2 (1–6) are dominated by the heat generation process, and the heat transfer process is negligible, which contains heat transfer from the material to the external environment and other parts of the material. Therefore the energy that is converted into heat and released by the fracturing of the material changes the temperature field of the material near the crack tip, that is, this part of the energy is converted into the internal energy of the material itself. By employing a two-dimensional (2D) model, in which the crack extends throughout the thickness of the material, and given that the temperature field is evenly distributed in the direction of the thickness of the material, the heat energy converted into Wdiss can be written as:
(1)
where dS and Wdiss are the crack growth area and the thermal energy
Fig. 4. The displacement field of the speckled images. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 62
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Fig. 6. The flowchart for the process of correcting the thermal images. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. The full field thermal image and the calculation area. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Wdiss =
m
c Ti dm =
cd Ti ds
dS
obtained. The flowchart for the process of correcting the thermal images with the DIC method has been given in Fig. 6. By calculating the images of the different crack propagation stages or the different cracks of the same specimen, multiple energy release rates could be calculated, and the measurement accuracy of the energy release rate could be further improved by taking an average of these values.
(2)
where c is the specific heat of the material, d is the thickness of the specimen, is the density of the material, and Ti is the temperature change of each point in the crack propagation area dS during the compression. Fig. 5 has shown the full field temperature image caught by the Infrared thermal imager and the square frame of the four zones were chosen as the calculation area. The speckle was sprayed onto the surface of the specimen before the experiment to obtain speckled images to calculate the displacement fields. As the infrared thermal imager was not integrated with the CMOS camera, there were rigid body displacements and zoom coefficients to account for between the thermal images and the speckled images. In order to eliminate the influence of the rigid body displacements and the zoom coefficients, the area in the speckled image corresponding to the calculation area in the thermal image needed to be first ascertained by some feature points in the image, such as the corner of the specimen. Then the digital image correlation method was applied to calculate the displacement field of the speckled images captured before and after deformation. The integral of Eq. (2) can be obtained by subtracting the temperature fields before and after the fracture processes. More specifically since the temperature field was outputted in the form of a digital image, which is in essence a matrix, the integral could be discretized and expressed by summation, then the energy release rate can be written as:
cd
A key step in evaluating the energy release rate was to choose the calculation area of the thermal image corresponding to the speckled image using the feature points, as shown in Fig. 7. Taking the left crack (Zone 1) as an example, the calculation process was carried out as follows: Firstly, the position of the four bolts in the speckled image and the temperature image were read, and the linear relationship between the coordinates of the two images was calculated. Then, the coordinates of the four corners of the calculation area in the thermal image were read, and by putting these coordinates into the linear relationship, the corresponding area in the speckled image could be found, and the corresponding displacement field was then extracted. The next step was to calculate the zoom coefficient, from Eq. (4), between the speckled image and the thermal image. The zoom coefficient could be calculated by reading the heights of the specimen in the speckled image and the thermal image, which were 1636 pixels and 307 pixels, respectively. As a result, the zoom coefficient could be calculated as k = 307/1636 = 0.188. In this way, the displacement of each pixel in the temperature image calculation area could be calculated. Finally, for each pixel of the calculation area in the thermal images, the correction process was carried out using Eq. (5). These four steps were then repeated in the calculation area in the entire deformed temperature field, that is, the left crack in Fig. 2(2–12), the correction process was then carried out, which has been shown in Fig. 8. In this experiment, it was difficult to observe the propagation of the cracks, and almost all parts of the cracks occurred at the same time. Therefore, it was impossible to calculate the energy release rate at the different stages of crack propagation, therefore only the calculation of the energy release rate of multiple cracks can be used to improve the measurement accuracy. For a crack, the energy release rate can be calculated from two images, one taken before crack initiation and one taken after crack propagation. Therefore, it was necessary to find the end point of crack propagation. Fig. 2(1) was considered as the state before crack initiation, because the image had no obvious thermal characteristics. When the crack occurred, the surface temperature rose locally, and the summation value in Eq. (3) increased. When the difference of this value between the two images was less than 5%, the
s T n
G=
4. Results and analysis
(3)
· dS
where s represents the actual area corresponding to a pixel. According to the displacement of each pixel in the speckled image, the displacement of each pixel in the thermal image could be calculated by: (4)
u = ku, v = kv
where u , v are the displacements of the speckled images, u , v are the displacements of the thermal image, and k is the zoom coefficient. Finally, the Fourier transform phase shift method was used to correct the displacement of each pixel in the thermal image, i.e.:
f =F
1
[F (f )·e2
(v + u )
·e
]
2i
(5)
where F represents the Fourier transform and f represents the value for each pixel in the thermal image. Then, using Eq. (3) to calculate the difference between the temperature field before deformation and the corrected temperature field after deformation, the energy release rate of the material could be 63
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Fig. 7. The process of finding the calculation area of the temperature in the speckled image. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. The temperature field of the left crack after correction. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
64
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almost all material systems. The only differences are the mechanical/ thermodynamic properties of the material and the damage modes which may change the temperature field and the heat transformation efficiency. However the key mechanism is constant for different material systems. In spite of the difficulties in estimating the β coefficient, the energy release rate measured by this new method in this paper, was also relatively consistent with those found in a previous study on a similar material. For example, the energy release rate of the material T700GC/ M21 carbon/epoxy [16] was measured as 32.6 KN/m, and it was measured as 34–39 KN/m for the T800/924C carbon-epoxy laminates in the literature [2].
Table 1 Summation from Eq. (3) of the thermal image calculation area. State Zone Zone Zone Zone Zone Zone
n
1: 1: 2: 2: 3: 3:
s T (mm2 ·K )
by by by by by by
IR&DIC IR only IR&DIC IR only IR&DIC IR only
1
2
3
4
5
6
7
8
0 0 0 0 0 0
78.0 74.9 8.2 7.8 0.5 0.5
281.1 264.4 79.3 76.3 4.9 5.3
318.9 307.5 136.4 131.3 7.7 8.7
340.1 335.1 178.4 173.2 9.2 10.6
353.7 352.9 208.8 204.6 9.4 11.3
357.4 362.6 209.5 238.9 9.5 11.5
357.9 389.9 248.2 274.2 — —
Table 2 The material and its experimental parameters.
5. Conclusion
Density
1578kg /m3
Specific heat
862J /kg· K 0.5 0.9 0.465mm 150mm × 100mm × 4mm
[15–16] Pixel length Specimen size
Through the combination of the digital image correlation method and infrared thermography, a new method for measuring the energy release rate of composite materials during the compression-after-impact experiment has been proposed in this paper. A theoretical framework was developed as a guide for the experimental procedure, and the calculation process of the method has been described in detail. The main conclusions that were drawn were as follows:
Table 3 Values of the parameters of the heat sources for the three zones. Test
Zone no.
n
s T
(mm2 ·K ) CAI
1 2 3
389.9 237.6 13.6
by IR
n
s T (mm2 ·K ) by
S (mm2)
IR&DICs 357.9 209.5 9.5
193.7 108.5 5.8
G (N/mm) by IR&DIC
(1) In the compression-after-impact experiment, it was found that the energy conversion and the deformation of the material were coupled. The influence of the deformation field on the temperature field should be corrected during the calculation process. (2) This new method that combined the infrared thermography technique and the digital image correlation method was well suited for measuring the energy release rate of composite materials for the compression-after-impact test. (3) The error in measuring the energy release rate of composites using this new method was 5%, which could be further reduced by calculating the energy release rate using the images of different crack propagation stages, different cracks in the same specimen or through the use of a high speed camera with a high resolution.
11.1–20.1 11.7–21.0 9.9–17.9
crack was considered to have finished occurring and no more internal energy was being produced. Table 1 has listed the calculation results for the left side crack both with DIC correction and without DIC correction. In the process of the experiment and data processing, the purpose of the DIC method was to obtain the temperature field of the same region at different times, so as to subtract the temperature field and calculate the amount of heat released. In the process of loading, deformation often leads to local deformation of the temperature field. If DIC technology is not used and the pixel matrix is directly subtracted, the measurement of the release of heat will be erroneous and will have difficulty converging. Therefore, it is thought that the convergent heat released in the specified crack region could be measured by considering the displacement and temperature field information of DIC, which is the key to solving the fracture toughness of composites. As can be seen from Table 1, the data showed good convergence after the DIC correction, which removed the error caused by the compression deformation. According to the convergence results, Fig. 2(6) was considered as the end point of crack propagation. By using the material and experimental parameters provided in Table 2, the energy release rate could be calculated for the left hand crack in this experiment and has been shown in Table 3. In addition, it should be pointed out that the experimental results shown in this paper, including the thermal images or the images from the DIC results, are only about one typical example because other similar experimental results have already been obtained. The values of the parameters of the heat sources for the four zones and the calculated values for the fracture toughness of the CFRP during the CAI tests have been listed in Table 3. For the right hand crack (Zone 2) in this experiment, and using the same calculation process, the other energy release rate could be calculated as G = 11.7 21.0KN / m . This result indicated that the error between the different cracks in the same specimen was only 5%, which has proven the accuracy and reliability of this new method that has been introduced in this paper. The method that has been proposed in this paper can be applied to many material systems with more than one composite laminate configuration. In fact, the fracture process and the heat generation process can be found in
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