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Characterising the behaviour of composite single lap bonded joints using digital image correlation
International Journal of Adhesion & Adhesives 40 (2013) 215–223
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Characterising the behaviour of composite single lap bonded joints using digital image correlation A.J. Comer n, K.B. Katnam, W.F. Stanley, T.M. Young Irish Centre for Composites Research (IComp), Materials and Surface Science Institute (MSSI), University of Limerick, Limerick, Ireland
a r t i c l e i n f o
abstract
Article history: Accepted 22 August 2012 Available online 28 August 2012
Three-dimensional and two-dimensional Digital Image Correlation (DIC) have been used to evaluate the evolution of deformation and strain in composite single lap bonded joints prior to failure. In general, composite components are increasingly being joined using structural adhesives for aerospace and other safety critical applications. Reliable design requires that the mechanical behaviour of composite bonded joints is well understood. In this respect, experimental tests are crucial to (a) characterise the deformation and strains induced under load and (b) develop and validate realistic numerical models. Although modern numerical models contain many degrees of freedom, only a few degrees of freedom are typically measured using conventional instrumentation such as strain gauges and extensometers. However, 3D DIC provides an opportunity to measure full-field deformations and surface strains. In the current study, 3D DIC was successfully used to measure full-field in-plane surface strains and out-ofplane surface deformations for composite single lap bonded joints (adherends manufactured from both fibre preimpregnated resin (pre-preg) and resin infused non-crimp-fabric (NCF)). Moreover, strategically located strain gauges were used to validate the strains measured by 3D DIC. Finally, 3D DIC measurements may be useful in detecting subcritical damage as shown in the case of the pre-preg joint. The specific location and magnitude of the maximum principal strain in the adhesive fillet region were determined using high magnification 2D DIC. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Digital Image Correlation Composites Epoxy adhesives Lap shear Stress analysis
1. Introduction Pre-preg composites consisting of carbon fibres preimpregnated with resin are traditionally used in applications where performance, material qualification and consistency are of paramount importance such as in the aerospace industry [1]. However, the high cost of pre-preg material and associated manufacturing process has seen an increase in the usage of resin infused non-crimp-fabric composites in aerospace structures [2,3]. Adhesively bonded non-crimp-fabric composites have significant potential for use in primary as well as secondary structural aerospace applications. With regard to joint configuration, the single lap joint is widely used to evaluate the bond quality in aerospace structures [4]. This joint configuration causes secondary bending to occur under tensile loading due to the eccentric load path inherent in the joint geometry. It is important to characterise the surface strains and out-of-plane deformation occurring in these joints to develop accurate numerical models for structural design and analysis purposes.
n
Corresponding author. Tel.: þ353 61 202253; fax: þ353 61 202944. E-mail address: [email protected] (A.J. Comer).
0143-7496/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijadhadh.2012.08.010
In the past, strain gauges [5–7], Moire´ interferometry [5] and photoelasticity [8] have been successfully used to characterise single lap joints. However, a number of issues may compromise strain gauge measurements, including (1) surface contact requirement, (2) bonding of strain-gauges (e.g. surface preparation, and misalignment), (3) single point information, and (4) transverse sensitivity of resistive strain gauges. The principal advantage of the 3D DIC system over conventional instrumentation is that it provides full-field strain and out-of-plane displacement information for hundreds of points for one test specimen [9]. For uniform strain fields, the results may be further averaged to provide a statistical mean. In general, DIC is an advanced, image based, noncontact, fullfield deformation measurement method capable of analysing materials under-going thermal, mechanical or variable environmental loading [10]. The method has been applied in many fields such as civil engineering [11,12], mechanical engineering [13], material science [14–16] and biomedical engineering [17,18]. In relation to materials testing, the technique involves tracking the movement of a naturally occurring or an applied surface pattern as load is applied to a specimen during a mechanical test. Full 3D surface measurements can be achieved with stereoscopic multicamera arrangements. The DIC technique has been described by several authors—see Pan et al. [19]; for example, a synopsis of the
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procedure is sufficient here. First, a series of digital images are acquired during specimen loading. The first ‘reference’ image is normally captured at zero load and corresponding zero strain. Post-acquisition, the area of interest is divided into discrete pixel blocks containing a minimum number of distinct surface features. Each subset should have a unique signature pattern. A correlation function based on the sum of the squared differences of the pixel grey values is minimised to determine the distortion of the signature patterns from image to image. Strain values are subsequently derived from the deformations often using a central difference scheme. Similar to conventional strain measurement techniques, experimental challenges are associated with the DIC technique. Haddadi and Belhabib [20] identified key sources of errors inherent in the DIC technique which include lighting, speckle pattern, subset size, grid pitch, data filtering and out-of-plane displacement (2D DIC). Speckle size in conjunction with the subset size was also found to influence the accuracy of measured displacements [21]. Lava et al. [22] stated that major attention should be given to the perpendicular alignment of the camera to the specimen surface (2D DIC). However, 3D stereo systems can largely compensate for oblique angle observation [22] and significant out-of-plane displacement [23]. Unfortunately, the accuracy and precision of 3D systems are typically not as good as those of a perpendicular 2D set-up [22], and the calibration procedure tends to be complicated. Tung and Shih [24] recently proposed a simplified 3D DIC system (using only one image capture device) to improve measurement precision. Distortion correction was cited as a key factor in improving measurement precision. The primary objective of this study was to investigate the use of the 3D Digital Image Correlation (DIC) technique to evaluate the inplane strain and out-of-plane deformation of single lap joints under quasi-static loading conditions. In general, composite laminates exhibit relatively low strains (o5%) at failure and consequently the application of DIC is challenging in terms of achieving good strain precision. The second objective was to evaluate the surface strains in the adhesive fillet region of a single lap joint and locate the maximum principal strain prior to failure of the bonded joints. As the thickness of adhesive bondlines is typically in the range of 100–1000 mm, experimental strain analysis of the adhesive bondline by means of conventional strain gauging was not possible. The use of high magnification 2D DIC for measuring bondline strains has not been extensively studied [25,26]. The current study focuses on the application of both 3D and 2D DIC to characterise composite single lap bonded joints manufactured from pre-preg and non-crimp-fabric laminates. Section 2 summarises the manufacture and testing of the composite single lap bonded joints. The experimental set-up, test procedure and the precision associated with the 3D DIC method is described in Section 3. Finally, the 3D DIC and 2D DIC high magnification results are presented and discussed in Section 4.
2. Materials and methods The manufacture, testing and static failure behaviour of the single lap joints presented in this section have been described by the authors in detail elsewhere [27]. The most important aspects are summarised in this section. The pre-preg (Hexcel HTA/6376) and NCF (Bi-directional (01/901) carbon fibre NCF, from Saertex) composite panels were bonded using a two-part research grade epoxy paste adhesive in a hot drape former (HDF2 from Laminating Technology) and cured at 80 1C for 4 h under 1 bar vacuum pressure. Single lap joints were then cut from the bonded panels using a wet diamond edged cutting wheel. Fig. 1 shows the final specimen dimensions which were in accordance with ASTM D 5868-01 [28].
Fig. 1. Composite single lap bonded joint with nominal dimensions in millimetre.
Table 1 Details of quasi-static tensile tests on single lap bonded joints. Composite Laminatea Number of tests Pre-preg NCF a
(01/901)4S (01/901)4
5 5
Failure load (kN)
Standard deviation
12.4 13.2
1.6 1.0
Surfaces were treated with O2 vacuum plasma.
X-ray microtomography (XMT) using a Phoenix X-ray nanotom (GE Sensing and Inspection Technologies) was employed to evaluate the void content in the adhesive bondline. A representative test specimen of each single lap bonded joint was scanned. The void content in the bondline of the pre-preg and NCF joints was 9.2% and 11.6% respectively at a voxel size of 16 mm. Quasi-static tensile tests were conducted on the pre-preg and NCF composite joints to determine the static strength at room temperature. The tests were performed at 0.01 mm/s cross-head displacement rate using a Dartec servo-hydraulic testing machine fitted with a 100 kN capacity load cell. Joint details and test results are given in Table 1.
3. Equipment and methodology: 2D and 3D DIC The experimental arrangement and methodology for the 3D and 2D DIC tests are detailed in this section. Representative prepreg and NCF composite single lap joint were selected from each batch (Table 1) for testing with 3D DIC. A representative NCF composite single lap joint was chosen for testing with high magnification 2D DIC. 3.1. Experimental arrangement: 3D DIC The 3D DIC apparatus consisted of (a) two Imager E-lite 2M cameras fitted with 50 mm lenses, (b) two gated white light sources and (c) a computer complete with Davis Strainmasters software (La Vision, GmbH). The 3D DIC experimental arrangement is shown in Fig. 2. It was possible to offset the hydraulic grips to accommodate the asymmetric nature of the single lap joint and to obviate the need to bond end tabs to the specimen. The charge coupled device (CCD) chips were 12 bit and had a spatial resolution of 1626 1236 pixels and a pixel size of 1.4 mm 1.4 mm. Each light source contained 12 LEDs in a linear configuration. The working distance of each camera from the specimen and the included angle between the cameras was approximately 500 mm and 801, respectively. Fig. 3 shows the composite single lap bonded joint in the tensile testing machine. The speckle required for the 3D DIC strain measurement is evident in the overlap region. Extensometers (Epsilon 3542) with a gauge length of 50 mm were employed to measure the local stiffness of the joint across the overlap. The global stiffness of the joint was determined using the crosshead displacement. Furthermore, the specimen was instrumented
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with a general purpose, 350 O strain gauge (Vishay) in a 3-wire quarter bridge configuration with a 1.0 V excitation source. The measured strain was an average of the area of the resistance grid (1.52 mm 1.27 mm). The gauge was orientated to record strain
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in the loading direction and was located out-side the overlap region at a distance of 35 mm from the bottom edge of the upper substrate. In Fig. 4, the coordinate system employed and the location of the strain gauge are schematically shown. The x-axis and z-axis are in the loading and out-of-plane directions, respectively.
3.2. Surface speckle
Fig. 2. (a) CCD camera with 50 mm lens, (b) composite single lap bonded joint speckled with acrylic paint, and (c) white light source.
Fig. 3. Single-lap-joint with speckled adherends, strain gauge and extensometers in the tensile testing machine.
Fig. 4. Coordinate system and axial strain gauge location.
The speckle patterns used on the 3D and 2D DIC test specimens are shown in Fig. 5. The objective was to ensure that each pixel subset contained a unique signature pattern which could be tracked by the pattern matching algorithm. Simonizs acrylic matt spray-paint from an aerosol container was used to generate the speckles on the adherends of the 3D DIC test specimens. The droplet size produced from the standard nozzle spraying at a distance of approximately 500 mm from the specimen was in the range of 220–440 mm. An airbrush (Badger model 200-3) precision spray gun was employed to generate a smaller diameter speckle for the high magnification 2D DIC test specimen. The resulting speckle diameters were in the range 48–72 mm. A 64 64 pixel subset size was chosen for both the 3D and 2D cases. This subset size ensured that speckles were sampled by at least a 3 3 pixel array and each subset contained a minimum of nine speckles thus minimising the possibility of peak locking. Fig. 5 also shows the subset size for the 3D case (2.816 mm) and the 2D case (0.256 mm). These were determined using the appropriate calibration factors (see Sections 3.4 and 3.6).
3.3. Focussing and illumination: 3D DIC The surface area to be digitally captured (field of view) was chosen to ensure that both the overlap region and the strain gauge were visible during the quasi-static test (i.e. from zero load to joint failure). Fig. 6(a) shows the overlap region, the applied speckle pattern and the strain gauge. The areas of interest (A1, A2 and A3) are also highlighted. Before calibrating the 3D DIC set-up, the focus for each camera was optimised for the areas of interest shown. Fig. 6(b) shows the illumination histogram for the area of interest A3. The normal distribution indicates that an optimum distribution of grey level intensities was achieved. The exposure of each camera was optimised to ensure 95% of the available dynamic range (the 12 bit E-lite 2M CCD camera has a dynamic range of 4096) was utilised. Camera exposure and light pulse width were 250 ms.
Fig. 5. Surface speckle patterns: (a) 64 64 pixel subset for the 3D DIC tests and (b) 64 64 pixel subset for the high magnification 2D DIC test.
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Fig. 6. (a) Areas of interest (A1 and A2 for 3D DIC validation) and (A3 for detailed strain analysis), and (b) illumination histogram over the dynamic range of the camera for area of interest, A3.
Fig. 7. CCD camera zoom-lens arrangement: (a) imager E-lite 2M camera, (b) 1X adaptor, and (c) 12 X Navitar zoom lens.
3.4. Calibration: 3D DIC The La Vision Strainmaster software was used to (a) simultaneously capture images from cameras 1 and 2 at a specified frequency (3 Hz) during mechanical loading, (b) generate mapping functions to correct for image distortions due to perspective projection and distortions inherent in the camera lens, (c) calibrate the images using a dual level calibration plate (calibration factor was 44 mm per pixel for both joints tested), (d) determine the surface height distribution, H(x,y) for each set of images (the surface height calculation uses the mapping functions in conjunction with a pattern matching correlation process to determine the three dimensional coordinates (x,y,z) of the surface of the test specimen), (e) determine 2D and subsequently 3D deformation and strain vectors using the mapping functions and the surface height distributions and finally; (f) extract deformation and strain data for the area of interest. 3.5. Experimental arrangement: 2D DIC A high magnification low distortion zoom lens (Navitar 6000) in conjunction with a digital camera (Imager E-lite 2M) was employed for the high magnification 2D DIC test (Fig. 7). An adaptor tube (1X) was fitted between the zoom lens (12X) and the camera. This arrangement resulted in a working distance of 86 mm with magnification and field of view ranges of (0.58– 7.00X) and (10.34–0.86 mm), respectively. Moreover, the depth of field range was between 1.39 mm and 0.05 mm. The 2D DIC high magnification arrangement was capable of capturing high resolution digital images of the adhesive fillet region in the x–z plane (Fig. 4). Bending about the z-axis was assumed to be negligible considering the section-modulus of the joint about this axis. 3.6. Focusing, illumination and calibration: 2D DIC The high magnification zoom lens arrangement necessitated the use of a high intensity light source (Dedolight DLH400D) with
a beam angle of 4.51 to illuminate the adhesive fillet region. An exposure time of 800 ms was specified for the CCD camera. Once sufficiently illuminated, the focus and magnification of the area of interest were optimised. Using a known dimension (the thickness of the composite laminate), the images were calibrated (4 mm/pixel) in the Strainmasters software. 3.7. Image processing parameters A multi-pass interrogation window scheme was selected to process the images. A 64 64 pixel interrogation window was chosen for both the 3D and 2D DIC analysis. Three passes were performed with a strong median filter to ensure spurious vectors were flagged and removed. Window deformation and adaptive shift routines were performed automatically by the software between passes. Deformation vectors were calculated relative to the first (undeformed state or zero load state) image. Relatively large deformations up to 732 pixels (1.4 mm for the 3D case) can be detected by the 64 64 pixel window. Given that the machine stroke at failure was less than 1.0 mm for both joint types, the 64 64 pixel window was adequate to detect the maximum deformation possible. The images for each test were processed using a window overlap of 50%, which, was a compromise between strain precision and spatial resolution. The correlation function chosen to process the images was a standard cyclic Fast Fourier Transform based algorithm, as given below: Cðdx,dyÞ ¼
x oX n,y o n x ¼ 0,y ¼ 0
I1 ðx,yÞI2 ðx þ dx,y þ dyÞ
n n odx,dy o 2 2
ð1Þ
In Eq. (1), I1 and I2 are the image intensities of the first and second interrogation windows. The two-dimensional array, C, gives the correlation strength for all integer displacements (dx, dy) between the two interrogation windows. The size of the interrogation window is denoted by n. Sub-pixel displacements were provided by a bi-cubic interpolation scheme. Vector fields were checked post-processing to ensure spurious vectors had not occurred.
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4. Results and discussion 4.1. 3D DIC strain precision This section discusses the strain precision or strain error associated with sub-pixel measurements made with the 3D DIC system. Strain precision is a statistical error and depends on the precision of the vectors and the vector spacing [10]. Good quality images and larger subset sizes ensure better sub-pixel resolution/ vector precision while increasing the vector spacing that maximises strain precision. However, spatial resolution diminishes as strain precision is optimised and thus a compromise is necessary. The strain precision associated with the strain vector calculation for the 3D DIC system is governed by [29]: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u pffiffiffi !2 u 2sv Strain error ¼ t þ ð0:0001EÞ2 ð2Þ g In Eq. (2), E is the strain magnitude, sv is the accuracy of the 3D vectors in pixels and g is twice the number of pixels between vectors. sv must be determined by experiment as it is dependent on a given experimental arrangement as well as the subset size chosen. It is clear that for small strains ( o5%), the strain error is dependent only on the precision of the 3D vectors and the number of pixels between vectors. Consequently, achieving accurate strain measurements in this strain domain is challenging due to the need to optimise sub-pixel resolution. Two methods were utilised to assess the strain error associated with the current 3D DIC measurements: (i) strain resolution test and (ii) strain gauge test. The objective of the strain resolution test was to evaluate the level of noise superimposed on the 3D DIC in-plane strain measurements. (The in-plane strains for composite laminates are typically relatively low and are consequently highly sensitive to noise on the strain measurement.) Any strain below the noise threshold are not resolvable. To this end, a one inch square, speckled composite sample was mounted on a translation stage complete with digital encoder and translated from 0 mm up to
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þ1 mm and back to 0 mm by increments between 1 mm and 100 mm. Images were captured via the 3D DIC system at each increment and the in-plane strain was subsequently calculated relative to the first image by the 3D DIC software using a 64 64 subset size with 50% overlap. By calculating the standard deviation of 100 strain measurements, it was found that the noise superimposed on the 3D DIC strain measurements was (with 95% probability) 750 microstrain. If relatively high strains are being measured, higher noise is tolerable. For example, Kuo et al. [14] determined that the strain resolution of their 2D DIC system was of the order of 230–310 microstrain. The strain gauge test directly compared the in-plane strain measurements from the strain gauges with the 3D strain measurement, as shown in Fig. 8. Images were captured via the 3D DIC system at a frequency of 3 Hz and the in-plane strain was subsequently calculated relative to the first image by the 3D DIC software using a 64 64 subset size with a 50% overlap consistent with the strain resolution test. The average DIC strain data was extracted from the areas of interest (A1 and A2, which were adjacent to the strain gauge as shown in Fig. 6a). A rectangle was selected in each area of interest where the length corresponded to the gauge length (1.52 mm) of the strain gauge and the width was three times the width of the strain gauge grid width (3 1.27 mm2). (It was assumed that tertiary or anticlastic type bending was negligible, which is a reasonable assumption since the specimens were only 25.4 mm wide.) Fig. 8 shows that the 3D DIC strain data is consistent with the strain gauge data over the full strain range to failure even though the strains recorded were relatively low ( o1500 microstrain) Secondly, rotation of the joint (i.e. secondary bending of composite adherends) caused compressive strains on the surface of the composite laminates at low load levels. This is more pronounced for the pre-preg joint compared to the NCF joint. However, as the axial load increased the tensile strains exceeded the compressive strains as shown in Fig. 8. Furthermore, the absolute error between the axial surface strains measured from the 3D DIC and the strain gauges (at 25%, 50%, 75% and 95% of the failure load) were within the strain error range (750 microstrain)
Fig. 8. Axial surface strain from 3D DIC and strain gauge versus tensile load.
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predicted by the strain resolution test. Fig. 8 also shows that the strains measured by 3D DIC in the case of the pre-preg joint deviated from the strain gauge data significantly for strains below 200 microstrain. This could be partly due to a discrepancy between the area selected for strain interrogation (3D DIC) and the actual location of the strain gauge, see Fig. 6(a). The relative strain error reflects the influence of the magnitude of the measured strain on the strain error. Minimal relative error was evident in the case of the pre-preg joint (6% error at 25% of failure). In the case of the NCF joint, the 3D DIC strain measurements were unreliable at 25% of failure as the measured strains were small (30 microstrain). As expected, agreement with the strain gauge improved as the magnitude of strain increased and thus good agreement was observed for both joints at loads greater than 50% of the failure load. Overall, it was concluded that strain gauges attached to the composite adherends complement 3D DIC strain measurements as they provide accurate baseline point measurements especially in regions of relatively low strains. 4.2. 3D DIC results and discussion Fig. 9 depicts full-field contour plots of (a) the strain in the loading direction and (b) the out-of-plane deformation of the prepreg joint just prior to failure. The overlap region consists of 15 9 vectors (m n) with a grid spacing of 1.4 mm. In Fig. 9(a), the black horizontal band indicates high compressive strains which correspond to the location of the adhesive fillet on the back-side of the single lap joint. Tensile strains are evident in the centre of the overlap region with the highest tensile strains occurring above the overlap region. The strain gauge was strategically located in the region where the highest tensile strains were obtained. Fig. 9(b) shows the magnitude of bending just before failure. The fact that the contour lines are not horizontal indicates that a degree of twisting has occurred under load. This would not be readily apparent with a point measurement technique. Fig. 10 shows the 3D DIC axial surface strain results for the pre-preg and NCF joints. Each DIC data point is an average of three vectors. Strain gauge point data is also shown. Good agreement was observed between the strain gauge results and the 3D DIC results at x¼ 35 mm for both joints. There is an obvious disparity between the strain profiles obtained for the two types of joints. The NCF joint exhibited a classic single lap joint surface strain
profile with compression at the gripped end of the overlap region. Furthermore, tensile surface strains occurred within the overlap region. The pre-preg joint did not exhibit tensile surface strains in the overlap region probably due to the presence of high compressive bending strains in this region which negated the surface tensile strains. More importantly, the location of the peak compressive strain shifted towards the centre of the overlap region as the applied load was increased from 50% of failure to 95% of failure. In fact, this shift occurred at approximately 72% of failure and was caused by the occurrence of significant subcritical damage in the overlap region. This damage caused a reduction in the load carrying capacity of the joint which was recorded by extensometers (fitted across the overlap region) during the quasistatic tensile test (Fig. 11). On the contrary, a similar phenomenon was not evident in the NCF joint (Fig. 11) and the location of the peak compressive strain only shifted marginally up to 95% of failure (Fig. 10). The out-of-plane deformation data extracted at specific load levels is shown in Fig. 12 (the bonded overlap region extends over the first 25.4 mm of the joint and the flexural rigidity (E I) is comparable for both specimens). Similar to the axial strain data, each data point is an average of three vectors. Considering the displacements at the extremities of the overlap region, neither joint exhibited perfect symmetry in bending even at 25% of failure. With regard to the pre-preg joint, the displacements at x¼25.4 mm particularly above 50% of failure were significantly greater than the displacements at x ¼0 mm. The excessive displacements above 70% of failure may partly be explained by the subcritical damage event mentioned earlier. With regard to the NCF joint, the asymmetric behaviour may be partly due to the twisting which was noted to occur in the joint (see Fig. 9). In summary, the asymmetric behaviour exhibited by both joints is likely to be caused by a combination of factors including (a) variation in the bondline thickness, (b) presence of manufacturing defects in the bondline, (c) void content, size and distribution in the adhesive, and (d) crack initiation in the bondline or laminate prior to failure. In conclusion, it is apparent that the 3D DIC technique has the potential to (a) assess the full-field behaviour of composite bonded joints and thus validate numerical models and (b) detect the onset of subcritical damage in the overlap region. Although, the single lap joints in the current study were manufactured to standard specimen dimensions [28], larger test specimens or higher resolution cameras would have allowed larger
Fig. 9. Contour plots of (a) axial surface strain and (b) the out-of-plane displacement of the NCF joint at 95% of the failure load (overlap region shown by dashed line).
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Fig. 10. The Axial surface strain profiles obtained from the 3D DIC tests on the pre-preg and NCF joints.
catastrophic failure of the bonded joint was 3.0%. This magnitude is consistent with the tensile failure strains obtained by tests on the bulk adhesive [30]. As shown in Fig. 13, large strains were induced at the inner corner of the laminate and protruded along the edge of the lower laminate. From the strain contours, it is thought that a crack initiated at the corner of the lower laminate and propagated unstably in two directions (a) into the bond-line and (b) along the edge of the laminate. It is important to note that a similar process possibly occurred simultaneously at the other fillet in the joint. Fig. 14 shows the crack path resulting from the strain concentration which occurred at the inner corner of the laminate. Away from the fillet region, the failure path was predominantly in the composite laminate [27]. In conclusion, it is apparent that high magnification 2D DIC has the potential to indicate (a) the location of strain concentration in the bondline and (b) the magnitude of strain at this location as a function of applied load. Consequently, this technique complements the global full-field characterisation provided by the 3D DIC technique.
5. Conclusions Fig. 11. Tensile load versus extensometer displacement for the pre-preg and NCF joints. Pre-preg joint exhibited a significant subcritical damage event (circled).
subset sizes to be chosen (e.g. 128 128). Higher strain precision without a reduction in spatial resolution would have been possible. 4.3. 2D DIC results and discussion A subset size of 256 mm 256 mm (64 634 pixel) was chosen to (a) sufficiently discretise the area of interest (adhesive fillet region) and (b) ensure that the subsets were larger than the largest voids present in the bondline. Subsets were overlapped by 50% to improve spatial resolution. Fig. 13 shows the maximum principal strain as a function of the applied load. The maximum principal strain just before
In this paper, the application of 3D Digital Image Correlation (DIC) and high magnification 2D DIC to evaluate the deformations and strains in composite single lap bonded joints under quasistatic tensile loading conditions was assessed. The main conclusions are as follows: 3D DIC was successfully used to generate full-field in-plane surface strain and out-of-plane surface deformation data for both pre-preg and non-crimp-fabric composite single lap bonded joints, which, could potentially be used to develop and accurately validate numerical models. Strain gauges, attached to the composite adherends at a region with a low strain gradient (i.e. away from the adhesive fillet) were used to measure axial strains in the composite adherends and to augment the DIC strain measurements. Good correlation between the 3D DIC and the strain gauge data was achieved for higher levels of strain. 3D DIC measurements (out-of-plane displacements and axial surface strain) may be useful in detecting subcritical damage as
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Fig. 12. Out-of-plane displacements from the 3D DIC tests on the pre-preg and NCF joints.
Fig. 13. Maximum principal strain at the corner of the adhesive fillet as a function of load level.
Fig. 14. The Crack path in the adhesive fillet resulting from the strain concentration.
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shown in the case of the pre-preg joint. The specific location and magnitude of the maximum principal strain in the adhesive fillet region were determined using high magnification 2D DIC. Furthermore, the maximum principal strain in the adhesive fillet at failure was found to be of the order of the failure strain obtained from bulk adhesive tests reported by the authors elsewhere [30].
Acknowledgements The authors would like to acknowledge (a) the Industrial Development Authority Ireland, and Enterprise Ireland for providing financial support to conduct the current research project STRICOM under Grant number CC/2008/1702A, (b) Dave Hollis, La Vision, UK, (c) SEAM at Waterford Institute of Technology for XMT scans, and (d) the individuals, Mr. Jeremy Dhote, Dr. Conor McCarthy, Prof. Noel O’Dowd, Dr. Denis O’Mahoney, and Mr. Adrian McEvoy at the Department of Mechanical, Aeronautical and Biomedical Engineering at the University of Limerick for their useful suggestions. References [1] Marsh G. Prepregs raw materials for high performance composites. Reinf Plast 2002;46(10):24–8. [2] Healey M, Johsen R. Noncrimp fabrics take off. Reinf Plast 2001;45(1). [3] Haberkern H. Tailor made reinforcements. Reinf Plast 2006;50(4):28–33. [4] Higgins A. Adhesive bonding of aircraft structures. Int J Adhes Adhes 2000;20:367–76. [5] Tsai MY, Morton J. An experimental investigation of nonlinear deformations in single lap joints. Mech Mater 1995;20(3):183–94. [6] Shenoy V, Ashcroft IA, Critchlow GW, Crocombe AD, Abdel Wahab MM. An investigation into the crack initiation and propagation behaviour of bonded single-lap joints using backface strain. Int J Adhes Adhes 2009;29(4):361–71. [7] Derewonko A, Godzimirski J, Kosiuczenko K, Niezgoda T, Kiczko A. Strength assessment of adhesive-bonded joints. Comput Mater Sci 2008;43(1):157–64. [8] Schroeder JA. Photoelastic stress analysis of bonded lap shear joints having thermoplastic adherends. J Adhes 1990;32(2–3). ˜ ski L, Dagher HJ, Thompson LD, Hess PE. [9] Lopez-Anido R, El-Chiti FW, Muszyn Composite material testing using a 3-D digital image correlation system, COMPOSITES 2004 convention and trade show American composites manufacturers association. Florida, USA: Tampa; 2004. [10] Sutton MA, Orteu JJ, Schreier H. Image correlation for deformation and shape measurements. New York: Springer; 2009. [11] Huang YH, Liu L, Sham FC, Chan YS, Ng SP. Optical strain gauge vs. traditional strain gauges for concrete elasticity modulus determination. Optik—Int J Light Electron Opt 2010;121(18):1635–41.
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[12] Corr D, Accardi M, Graham-Brady L, Shah S. Digital image correlation analysis of interfacial debonding properties and fracture behavior in concrete. Eng Fract Mech 2007;74(1–2):109–21. [13] Helfrick MN, Niezrecki C, Avitabile P, Schmidt Timothy. 3D digital image correlation methods for full-field vibration measurement. Mech Syst Signal Process 2011;25(3):917–27. [14] Kuo JC, Tung SH, Shih MH, Lu YY. Characterisation of indentation induced pattern using full field measurement. Strain 2010;46(3):277–82. [15] Catalanotti G, Camanho PP, Xavier J, Davila CG, Marques AT. Measurement of resistance curves in the longitudinal failure of composites using digital image correlation. Compos Sci Technol 2010;70:1986–93. [16] Wang ZY, Li HQ, Tong JW, Shen M, Aymerich F, Priolo P. Dual magnification digital image correlation based strain measurement in CFRP laminates with open hole. Compos Sci Technol 2008;68:1975–80. [17] Cheung W, Mahmud J, Evans S, Holt C, Snow M, Wang B, et al. T-9 evaluating the mechanical properties of a tendon graft, using digital image correlation (DIC) technique. J Biomech 2010;43(Suppl. 1):S63. [18] Thompson MS, Schell H, Lienau J, Duda GN. Digital image correlation: a technique for determining local mechanical conditions within early bone callus. Med Eng Phys 2007;29(7):820–3. [19] Pan B, Qian K, Xie H, Asundi A. Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol 2009;20:1–17. [20] Haddadi H, Belhabib S. Use of rigid-body motion for the investigation and estimation of the measurement errors related to digital image correlation technique. Opt Lasers Eng 2008;46(2):185–96. [21] Lecompte D, Smits A, Bossuyt S, Sol H, Vantomme J, Van Hemelrijck D, et al. Quality assessment of speckle patterns for digital image correlation. Opt Lasers Eng 2006;44(11):1132–45. [22] Lava P, Coppieters S, Wang Y, Van Houtte P, Debruyne D. Error estimation in measuring strain fields with DIC on planar sheet metal specimens with a non-perpendicular camera alignment. Opt Lasers Eng 2011;49(1):57–65. [23] Sutton MA, Yan JH, Tiwari V, Schreier HW, Orteu JJ. The effect of out-of-plane motion on 2D and 3D digital image correlation measurements. Opt Lasers Eng 2008;46(10):746–57. [24] Tung SH, Shih MH. Precision verification of a simplified three-dimensional DIC method. Opt Lasers Eng 2011;49(7). [25] Moutrille MP, Derrien K, Baptiste D, Balandraud X, Gre´diac M. Throughthickness strain field measurement in a composite/aluminium adhesive joint. Compos Part A: Appl Sci Manuf 2009;40(8):985–96. [26] Wang ZY, Wang L, Guo W, Deng H, Tong JW, Aymerich F. An investigation on strain/stress distribution around the overlap end of laminated composite single lap joints. Compos Struct 2009;89(4):589–95. [27] Katnam KB, Comer AJ, Stanley WF, Buggy M, Ellingboe AR, Young TM. Characterising pre-preg and non-crimp fabric composite single lap bonded joints. Int J Adhes Adhes 2011;31(7):679–86. [28] ASTM D 5868-01. Standard test method for lap shear adhesion for fiber reinforced plastic (FRP) bonding; Reapproved 2008. [29] DaVis Strainmaster 3DSoftware product manual, pdf number 1003017. ¨ Produced by LaVision GmbH. Gottingen; March 2009. [30] Katnam KB, Stevenson JPJ, Stanley WF, Buggy M, Young TM. Tensile strength of two-part epoxy paste adhesives: influence of mixing technique and microvoid formation. Int J Adhes Adhes 2011;31(7):666–73.
Contents lists available at SciVerse ScienceDirect
International Journal of Adhesion & Adhesives journal homepage: www.elsevier.com/locate/ijadhadh
Characterising the behaviour of composite single lap bonded joints using digital image correlation A.J. Comer n, K.B. Katnam, W.F. Stanley, T.M. Young Irish Centre for Composites Research (IComp), Materials and Surface Science Institute (MSSI), University of Limerick, Limerick, Ireland
a r t i c l e i n f o
abstract
Article history: Accepted 22 August 2012 Available online 28 August 2012
Three-dimensional and two-dimensional Digital Image Correlation (DIC) have been used to evaluate the evolution of deformation and strain in composite single lap bonded joints prior to failure. In general, composite components are increasingly being joined using structural adhesives for aerospace and other safety critical applications. Reliable design requires that the mechanical behaviour of composite bonded joints is well understood. In this respect, experimental tests are crucial to (a) characterise the deformation and strains induced under load and (b) develop and validate realistic numerical models. Although modern numerical models contain many degrees of freedom, only a few degrees of freedom are typically measured using conventional instrumentation such as strain gauges and extensometers. However, 3D DIC provides an opportunity to measure full-field deformations and surface strains. In the current study, 3D DIC was successfully used to measure full-field in-plane surface strains and out-ofplane surface deformations for composite single lap bonded joints (adherends manufactured from both fibre preimpregnated resin (pre-preg) and resin infused non-crimp-fabric (NCF)). Moreover, strategically located strain gauges were used to validate the strains measured by 3D DIC. Finally, 3D DIC measurements may be useful in detecting subcritical damage as shown in the case of the pre-preg joint. The specific location and magnitude of the maximum principal strain in the adhesive fillet region were determined using high magnification 2D DIC. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Digital Image Correlation Composites Epoxy adhesives Lap shear Stress analysis
1. Introduction Pre-preg composites consisting of carbon fibres preimpregnated with resin are traditionally used in applications where performance, material qualification and consistency are of paramount importance such as in the aerospace industry [1]. However, the high cost of pre-preg material and associated manufacturing process has seen an increase in the usage of resin infused non-crimp-fabric composites in aerospace structures [2,3]. Adhesively bonded non-crimp-fabric composites have significant potential for use in primary as well as secondary structural aerospace applications. With regard to joint configuration, the single lap joint is widely used to evaluate the bond quality in aerospace structures [4]. This joint configuration causes secondary bending to occur under tensile loading due to the eccentric load path inherent in the joint geometry. It is important to characterise the surface strains and out-of-plane deformation occurring in these joints to develop accurate numerical models for structural design and analysis purposes.
n
Corresponding author. Tel.: þ353 61 202253; fax: þ353 61 202944. E-mail address: [email protected] (A.J. Comer).
0143-7496/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijadhadh.2012.08.010
In the past, strain gauges [5–7], Moire´ interferometry [5] and photoelasticity [8] have been successfully used to characterise single lap joints. However, a number of issues may compromise strain gauge measurements, including (1) surface contact requirement, (2) bonding of strain-gauges (e.g. surface preparation, and misalignment), (3) single point information, and (4) transverse sensitivity of resistive strain gauges. The principal advantage of the 3D DIC system over conventional instrumentation is that it provides full-field strain and out-of-plane displacement information for hundreds of points for one test specimen [9]. For uniform strain fields, the results may be further averaged to provide a statistical mean. In general, DIC is an advanced, image based, noncontact, fullfield deformation measurement method capable of analysing materials under-going thermal, mechanical or variable environmental loading [10]. The method has been applied in many fields such as civil engineering [11,12], mechanical engineering [13], material science [14–16] and biomedical engineering [17,18]. In relation to materials testing, the technique involves tracking the movement of a naturally occurring or an applied surface pattern as load is applied to a specimen during a mechanical test. Full 3D surface measurements can be achieved with stereoscopic multicamera arrangements. The DIC technique has been described by several authors—see Pan et al. [19]; for example, a synopsis of the
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procedure is sufficient here. First, a series of digital images are acquired during specimen loading. The first ‘reference’ image is normally captured at zero load and corresponding zero strain. Post-acquisition, the area of interest is divided into discrete pixel blocks containing a minimum number of distinct surface features. Each subset should have a unique signature pattern. A correlation function based on the sum of the squared differences of the pixel grey values is minimised to determine the distortion of the signature patterns from image to image. Strain values are subsequently derived from the deformations often using a central difference scheme. Similar to conventional strain measurement techniques, experimental challenges are associated with the DIC technique. Haddadi and Belhabib [20] identified key sources of errors inherent in the DIC technique which include lighting, speckle pattern, subset size, grid pitch, data filtering and out-of-plane displacement (2D DIC). Speckle size in conjunction with the subset size was also found to influence the accuracy of measured displacements [21]. Lava et al. [22] stated that major attention should be given to the perpendicular alignment of the camera to the specimen surface (2D DIC). However, 3D stereo systems can largely compensate for oblique angle observation [22] and significant out-of-plane displacement [23]. Unfortunately, the accuracy and precision of 3D systems are typically not as good as those of a perpendicular 2D set-up [22], and the calibration procedure tends to be complicated. Tung and Shih [24] recently proposed a simplified 3D DIC system (using only one image capture device) to improve measurement precision. Distortion correction was cited as a key factor in improving measurement precision. The primary objective of this study was to investigate the use of the 3D Digital Image Correlation (DIC) technique to evaluate the inplane strain and out-of-plane deformation of single lap joints under quasi-static loading conditions. In general, composite laminates exhibit relatively low strains (o5%) at failure and consequently the application of DIC is challenging in terms of achieving good strain precision. The second objective was to evaluate the surface strains in the adhesive fillet region of a single lap joint and locate the maximum principal strain prior to failure of the bonded joints. As the thickness of adhesive bondlines is typically in the range of 100–1000 mm, experimental strain analysis of the adhesive bondline by means of conventional strain gauging was not possible. The use of high magnification 2D DIC for measuring bondline strains has not been extensively studied [25,26]. The current study focuses on the application of both 3D and 2D DIC to characterise composite single lap bonded joints manufactured from pre-preg and non-crimp-fabric laminates. Section 2 summarises the manufacture and testing of the composite single lap bonded joints. The experimental set-up, test procedure and the precision associated with the 3D DIC method is described in Section 3. Finally, the 3D DIC and 2D DIC high magnification results are presented and discussed in Section 4.
2. Materials and methods The manufacture, testing and static failure behaviour of the single lap joints presented in this section have been described by the authors in detail elsewhere [27]. The most important aspects are summarised in this section. The pre-preg (Hexcel HTA/6376) and NCF (Bi-directional (01/901) carbon fibre NCF, from Saertex) composite panels were bonded using a two-part research grade epoxy paste adhesive in a hot drape former (HDF2 from Laminating Technology) and cured at 80 1C for 4 h under 1 bar vacuum pressure. Single lap joints were then cut from the bonded panels using a wet diamond edged cutting wheel. Fig. 1 shows the final specimen dimensions which were in accordance with ASTM D 5868-01 [28].
Fig. 1. Composite single lap bonded joint with nominal dimensions in millimetre.
Table 1 Details of quasi-static tensile tests on single lap bonded joints. Composite Laminatea Number of tests Pre-preg NCF a
(01/901)4S (01/901)4
5 5
Failure load (kN)
Standard deviation
12.4 13.2
1.6 1.0
Surfaces were treated with O2 vacuum plasma.
X-ray microtomography (XMT) using a Phoenix X-ray nanotom (GE Sensing and Inspection Technologies) was employed to evaluate the void content in the adhesive bondline. A representative test specimen of each single lap bonded joint was scanned. The void content in the bondline of the pre-preg and NCF joints was 9.2% and 11.6% respectively at a voxel size of 16 mm. Quasi-static tensile tests were conducted on the pre-preg and NCF composite joints to determine the static strength at room temperature. The tests were performed at 0.01 mm/s cross-head displacement rate using a Dartec servo-hydraulic testing machine fitted with a 100 kN capacity load cell. Joint details and test results are given in Table 1.
3. Equipment and methodology: 2D and 3D DIC The experimental arrangement and methodology for the 3D and 2D DIC tests are detailed in this section. Representative prepreg and NCF composite single lap joint were selected from each batch (Table 1) for testing with 3D DIC. A representative NCF composite single lap joint was chosen for testing with high magnification 2D DIC. 3.1. Experimental arrangement: 3D DIC The 3D DIC apparatus consisted of (a) two Imager E-lite 2M cameras fitted with 50 mm lenses, (b) two gated white light sources and (c) a computer complete with Davis Strainmasters software (La Vision, GmbH). The 3D DIC experimental arrangement is shown in Fig. 2. It was possible to offset the hydraulic grips to accommodate the asymmetric nature of the single lap joint and to obviate the need to bond end tabs to the specimen. The charge coupled device (CCD) chips were 12 bit and had a spatial resolution of 1626 1236 pixels and a pixel size of 1.4 mm 1.4 mm. Each light source contained 12 LEDs in a linear configuration. The working distance of each camera from the specimen and the included angle between the cameras was approximately 500 mm and 801, respectively. Fig. 3 shows the composite single lap bonded joint in the tensile testing machine. The speckle required for the 3D DIC strain measurement is evident in the overlap region. Extensometers (Epsilon 3542) with a gauge length of 50 mm were employed to measure the local stiffness of the joint across the overlap. The global stiffness of the joint was determined using the crosshead displacement. Furthermore, the specimen was instrumented
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with a general purpose, 350 O strain gauge (Vishay) in a 3-wire quarter bridge configuration with a 1.0 V excitation source. The measured strain was an average of the area of the resistance grid (1.52 mm 1.27 mm). The gauge was orientated to record strain
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in the loading direction and was located out-side the overlap region at a distance of 35 mm from the bottom edge of the upper substrate. In Fig. 4, the coordinate system employed and the location of the strain gauge are schematically shown. The x-axis and z-axis are in the loading and out-of-plane directions, respectively.
3.2. Surface speckle
Fig. 2. (a) CCD camera with 50 mm lens, (b) composite single lap bonded joint speckled with acrylic paint, and (c) white light source.
Fig. 3. Single-lap-joint with speckled adherends, strain gauge and extensometers in the tensile testing machine.
Fig. 4. Coordinate system and axial strain gauge location.
The speckle patterns used on the 3D and 2D DIC test specimens are shown in Fig. 5. The objective was to ensure that each pixel subset contained a unique signature pattern which could be tracked by the pattern matching algorithm. Simonizs acrylic matt spray-paint from an aerosol container was used to generate the speckles on the adherends of the 3D DIC test specimens. The droplet size produced from the standard nozzle spraying at a distance of approximately 500 mm from the specimen was in the range of 220–440 mm. An airbrush (Badger model 200-3) precision spray gun was employed to generate a smaller diameter speckle for the high magnification 2D DIC test specimen. The resulting speckle diameters were in the range 48–72 mm. A 64 64 pixel subset size was chosen for both the 3D and 2D cases. This subset size ensured that speckles were sampled by at least a 3 3 pixel array and each subset contained a minimum of nine speckles thus minimising the possibility of peak locking. Fig. 5 also shows the subset size for the 3D case (2.816 mm) and the 2D case (0.256 mm). These were determined using the appropriate calibration factors (see Sections 3.4 and 3.6).
3.3. Focussing and illumination: 3D DIC The surface area to be digitally captured (field of view) was chosen to ensure that both the overlap region and the strain gauge were visible during the quasi-static test (i.e. from zero load to joint failure). Fig. 6(a) shows the overlap region, the applied speckle pattern and the strain gauge. The areas of interest (A1, A2 and A3) are also highlighted. Before calibrating the 3D DIC set-up, the focus for each camera was optimised for the areas of interest shown. Fig. 6(b) shows the illumination histogram for the area of interest A3. The normal distribution indicates that an optimum distribution of grey level intensities was achieved. The exposure of each camera was optimised to ensure 95% of the available dynamic range (the 12 bit E-lite 2M CCD camera has a dynamic range of 4096) was utilised. Camera exposure and light pulse width were 250 ms.
Fig. 5. Surface speckle patterns: (a) 64 64 pixel subset for the 3D DIC tests and (b) 64 64 pixel subset for the high magnification 2D DIC test.
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Fig. 6. (a) Areas of interest (A1 and A2 for 3D DIC validation) and (A3 for detailed strain analysis), and (b) illumination histogram over the dynamic range of the camera for area of interest, A3.
Fig. 7. CCD camera zoom-lens arrangement: (a) imager E-lite 2M camera, (b) 1X adaptor, and (c) 12 X Navitar zoom lens.
3.4. Calibration: 3D DIC The La Vision Strainmaster software was used to (a) simultaneously capture images from cameras 1 and 2 at a specified frequency (3 Hz) during mechanical loading, (b) generate mapping functions to correct for image distortions due to perspective projection and distortions inherent in the camera lens, (c) calibrate the images using a dual level calibration plate (calibration factor was 44 mm per pixel for both joints tested), (d) determine the surface height distribution, H(x,y) for each set of images (the surface height calculation uses the mapping functions in conjunction with a pattern matching correlation process to determine the three dimensional coordinates (x,y,z) of the surface of the test specimen), (e) determine 2D and subsequently 3D deformation and strain vectors using the mapping functions and the surface height distributions and finally; (f) extract deformation and strain data for the area of interest. 3.5. Experimental arrangement: 2D DIC A high magnification low distortion zoom lens (Navitar 6000) in conjunction with a digital camera (Imager E-lite 2M) was employed for the high magnification 2D DIC test (Fig. 7). An adaptor tube (1X) was fitted between the zoom lens (12X) and the camera. This arrangement resulted in a working distance of 86 mm with magnification and field of view ranges of (0.58– 7.00X) and (10.34–0.86 mm), respectively. Moreover, the depth of field range was between 1.39 mm and 0.05 mm. The 2D DIC high magnification arrangement was capable of capturing high resolution digital images of the adhesive fillet region in the x–z plane (Fig. 4). Bending about the z-axis was assumed to be negligible considering the section-modulus of the joint about this axis. 3.6. Focusing, illumination and calibration: 2D DIC The high magnification zoom lens arrangement necessitated the use of a high intensity light source (Dedolight DLH400D) with
a beam angle of 4.51 to illuminate the adhesive fillet region. An exposure time of 800 ms was specified for the CCD camera. Once sufficiently illuminated, the focus and magnification of the area of interest were optimised. Using a known dimension (the thickness of the composite laminate), the images were calibrated (4 mm/pixel) in the Strainmasters software. 3.7. Image processing parameters A multi-pass interrogation window scheme was selected to process the images. A 64 64 pixel interrogation window was chosen for both the 3D and 2D DIC analysis. Three passes were performed with a strong median filter to ensure spurious vectors were flagged and removed. Window deformation and adaptive shift routines were performed automatically by the software between passes. Deformation vectors were calculated relative to the first (undeformed state or zero load state) image. Relatively large deformations up to 732 pixels (1.4 mm for the 3D case) can be detected by the 64 64 pixel window. Given that the machine stroke at failure was less than 1.0 mm for both joint types, the 64 64 pixel window was adequate to detect the maximum deformation possible. The images for each test were processed using a window overlap of 50%, which, was a compromise between strain precision and spatial resolution. The correlation function chosen to process the images was a standard cyclic Fast Fourier Transform based algorithm, as given below: Cðdx,dyÞ ¼
x oX n,y o n x ¼ 0,y ¼ 0
I1 ðx,yÞI2 ðx þ dx,y þ dyÞ
n n odx,dy o 2 2
ð1Þ
In Eq. (1), I1 and I2 are the image intensities of the first and second interrogation windows. The two-dimensional array, C, gives the correlation strength for all integer displacements (dx, dy) between the two interrogation windows. The size of the interrogation window is denoted by n. Sub-pixel displacements were provided by a bi-cubic interpolation scheme. Vector fields were checked post-processing to ensure spurious vectors had not occurred.
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4. Results and discussion 4.1. 3D DIC strain precision This section discusses the strain precision or strain error associated with sub-pixel measurements made with the 3D DIC system. Strain precision is a statistical error and depends on the precision of the vectors and the vector spacing [10]. Good quality images and larger subset sizes ensure better sub-pixel resolution/ vector precision while increasing the vector spacing that maximises strain precision. However, spatial resolution diminishes as strain precision is optimised and thus a compromise is necessary. The strain precision associated with the strain vector calculation for the 3D DIC system is governed by [29]: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u pffiffiffi !2 u 2sv Strain error ¼ t þ ð0:0001EÞ2 ð2Þ g In Eq. (2), E is the strain magnitude, sv is the accuracy of the 3D vectors in pixels and g is twice the number of pixels between vectors. sv must be determined by experiment as it is dependent on a given experimental arrangement as well as the subset size chosen. It is clear that for small strains ( o5%), the strain error is dependent only on the precision of the 3D vectors and the number of pixels between vectors. Consequently, achieving accurate strain measurements in this strain domain is challenging due to the need to optimise sub-pixel resolution. Two methods were utilised to assess the strain error associated with the current 3D DIC measurements: (i) strain resolution test and (ii) strain gauge test. The objective of the strain resolution test was to evaluate the level of noise superimposed on the 3D DIC in-plane strain measurements. (The in-plane strains for composite laminates are typically relatively low and are consequently highly sensitive to noise on the strain measurement.) Any strain below the noise threshold are not resolvable. To this end, a one inch square, speckled composite sample was mounted on a translation stage complete with digital encoder and translated from 0 mm up to
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þ1 mm and back to 0 mm by increments between 1 mm and 100 mm. Images were captured via the 3D DIC system at each increment and the in-plane strain was subsequently calculated relative to the first image by the 3D DIC software using a 64 64 subset size with 50% overlap. By calculating the standard deviation of 100 strain measurements, it was found that the noise superimposed on the 3D DIC strain measurements was (with 95% probability) 750 microstrain. If relatively high strains are being measured, higher noise is tolerable. For example, Kuo et al. [14] determined that the strain resolution of their 2D DIC system was of the order of 230–310 microstrain. The strain gauge test directly compared the in-plane strain measurements from the strain gauges with the 3D strain measurement, as shown in Fig. 8. Images were captured via the 3D DIC system at a frequency of 3 Hz and the in-plane strain was subsequently calculated relative to the first image by the 3D DIC software using a 64 64 subset size with a 50% overlap consistent with the strain resolution test. The average DIC strain data was extracted from the areas of interest (A1 and A2, which were adjacent to the strain gauge as shown in Fig. 6a). A rectangle was selected in each area of interest where the length corresponded to the gauge length (1.52 mm) of the strain gauge and the width was three times the width of the strain gauge grid width (3 1.27 mm2). (It was assumed that tertiary or anticlastic type bending was negligible, which is a reasonable assumption since the specimens were only 25.4 mm wide.) Fig. 8 shows that the 3D DIC strain data is consistent with the strain gauge data over the full strain range to failure even though the strains recorded were relatively low ( o1500 microstrain) Secondly, rotation of the joint (i.e. secondary bending of composite adherends) caused compressive strains on the surface of the composite laminates at low load levels. This is more pronounced for the pre-preg joint compared to the NCF joint. However, as the axial load increased the tensile strains exceeded the compressive strains as shown in Fig. 8. Furthermore, the absolute error between the axial surface strains measured from the 3D DIC and the strain gauges (at 25%, 50%, 75% and 95% of the failure load) were within the strain error range (750 microstrain)
Fig. 8. Axial surface strain from 3D DIC and strain gauge versus tensile load.
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predicted by the strain resolution test. Fig. 8 also shows that the strains measured by 3D DIC in the case of the pre-preg joint deviated from the strain gauge data significantly for strains below 200 microstrain. This could be partly due to a discrepancy between the area selected for strain interrogation (3D DIC) and the actual location of the strain gauge, see Fig. 6(a). The relative strain error reflects the influence of the magnitude of the measured strain on the strain error. Minimal relative error was evident in the case of the pre-preg joint (6% error at 25% of failure). In the case of the NCF joint, the 3D DIC strain measurements were unreliable at 25% of failure as the measured strains were small (30 microstrain). As expected, agreement with the strain gauge improved as the magnitude of strain increased and thus good agreement was observed for both joints at loads greater than 50% of the failure load. Overall, it was concluded that strain gauges attached to the composite adherends complement 3D DIC strain measurements as they provide accurate baseline point measurements especially in regions of relatively low strains. 4.2. 3D DIC results and discussion Fig. 9 depicts full-field contour plots of (a) the strain in the loading direction and (b) the out-of-plane deformation of the prepreg joint just prior to failure. The overlap region consists of 15 9 vectors (m n) with a grid spacing of 1.4 mm. In Fig. 9(a), the black horizontal band indicates high compressive strains which correspond to the location of the adhesive fillet on the back-side of the single lap joint. Tensile strains are evident in the centre of the overlap region with the highest tensile strains occurring above the overlap region. The strain gauge was strategically located in the region where the highest tensile strains were obtained. Fig. 9(b) shows the magnitude of bending just before failure. The fact that the contour lines are not horizontal indicates that a degree of twisting has occurred under load. This would not be readily apparent with a point measurement technique. Fig. 10 shows the 3D DIC axial surface strain results for the pre-preg and NCF joints. Each DIC data point is an average of three vectors. Strain gauge point data is also shown. Good agreement was observed between the strain gauge results and the 3D DIC results at x¼ 35 mm for both joints. There is an obvious disparity between the strain profiles obtained for the two types of joints. The NCF joint exhibited a classic single lap joint surface strain
profile with compression at the gripped end of the overlap region. Furthermore, tensile surface strains occurred within the overlap region. The pre-preg joint did not exhibit tensile surface strains in the overlap region probably due to the presence of high compressive bending strains in this region which negated the surface tensile strains. More importantly, the location of the peak compressive strain shifted towards the centre of the overlap region as the applied load was increased from 50% of failure to 95% of failure. In fact, this shift occurred at approximately 72% of failure and was caused by the occurrence of significant subcritical damage in the overlap region. This damage caused a reduction in the load carrying capacity of the joint which was recorded by extensometers (fitted across the overlap region) during the quasistatic tensile test (Fig. 11). On the contrary, a similar phenomenon was not evident in the NCF joint (Fig. 11) and the location of the peak compressive strain only shifted marginally up to 95% of failure (Fig. 10). The out-of-plane deformation data extracted at specific load levels is shown in Fig. 12 (the bonded overlap region extends over the first 25.4 mm of the joint and the flexural rigidity (E I) is comparable for both specimens). Similar to the axial strain data, each data point is an average of three vectors. Considering the displacements at the extremities of the overlap region, neither joint exhibited perfect symmetry in bending even at 25% of failure. With regard to the pre-preg joint, the displacements at x¼25.4 mm particularly above 50% of failure were significantly greater than the displacements at x ¼0 mm. The excessive displacements above 70% of failure may partly be explained by the subcritical damage event mentioned earlier. With regard to the NCF joint, the asymmetric behaviour may be partly due to the twisting which was noted to occur in the joint (see Fig. 9). In summary, the asymmetric behaviour exhibited by both joints is likely to be caused by a combination of factors including (a) variation in the bondline thickness, (b) presence of manufacturing defects in the bondline, (c) void content, size and distribution in the adhesive, and (d) crack initiation in the bondline or laminate prior to failure. In conclusion, it is apparent that the 3D DIC technique has the potential to (a) assess the full-field behaviour of composite bonded joints and thus validate numerical models and (b) detect the onset of subcritical damage in the overlap region. Although, the single lap joints in the current study were manufactured to standard specimen dimensions [28], larger test specimens or higher resolution cameras would have allowed larger
Fig. 9. Contour plots of (a) axial surface strain and (b) the out-of-plane displacement of the NCF joint at 95% of the failure load (overlap region shown by dashed line).
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Fig. 10. The Axial surface strain profiles obtained from the 3D DIC tests on the pre-preg and NCF joints.
catastrophic failure of the bonded joint was 3.0%. This magnitude is consistent with the tensile failure strains obtained by tests on the bulk adhesive [30]. As shown in Fig. 13, large strains were induced at the inner corner of the laminate and protruded along the edge of the lower laminate. From the strain contours, it is thought that a crack initiated at the corner of the lower laminate and propagated unstably in two directions (a) into the bond-line and (b) along the edge of the laminate. It is important to note that a similar process possibly occurred simultaneously at the other fillet in the joint. Fig. 14 shows the crack path resulting from the strain concentration which occurred at the inner corner of the laminate. Away from the fillet region, the failure path was predominantly in the composite laminate [27]. In conclusion, it is apparent that high magnification 2D DIC has the potential to indicate (a) the location of strain concentration in the bondline and (b) the magnitude of strain at this location as a function of applied load. Consequently, this technique complements the global full-field characterisation provided by the 3D DIC technique.
5. Conclusions Fig. 11. Tensile load versus extensometer displacement for the pre-preg and NCF joints. Pre-preg joint exhibited a significant subcritical damage event (circled).
subset sizes to be chosen (e.g. 128 128). Higher strain precision without a reduction in spatial resolution would have been possible. 4.3. 2D DIC results and discussion A subset size of 256 mm 256 mm (64 634 pixel) was chosen to (a) sufficiently discretise the area of interest (adhesive fillet region) and (b) ensure that the subsets were larger than the largest voids present in the bondline. Subsets were overlapped by 50% to improve spatial resolution. Fig. 13 shows the maximum principal strain as a function of the applied load. The maximum principal strain just before
In this paper, the application of 3D Digital Image Correlation (DIC) and high magnification 2D DIC to evaluate the deformations and strains in composite single lap bonded joints under quasistatic tensile loading conditions was assessed. The main conclusions are as follows: 3D DIC was successfully used to generate full-field in-plane surface strain and out-of-plane surface deformation data for both pre-preg and non-crimp-fabric composite single lap bonded joints, which, could potentially be used to develop and accurately validate numerical models. Strain gauges, attached to the composite adherends at a region with a low strain gradient (i.e. away from the adhesive fillet) were used to measure axial strains in the composite adherends and to augment the DIC strain measurements. Good correlation between the 3D DIC and the strain gauge data was achieved for higher levels of strain. 3D DIC measurements (out-of-plane displacements and axial surface strain) may be useful in detecting subcritical damage as
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Fig. 12. Out-of-plane displacements from the 3D DIC tests on the pre-preg and NCF joints.
Fig. 13. Maximum principal strain at the corner of the adhesive fillet as a function of load level.
Fig. 14. The Crack path in the adhesive fillet resulting from the strain concentration.
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shown in the case of the pre-preg joint. The specific location and magnitude of the maximum principal strain in the adhesive fillet region were determined using high magnification 2D DIC. Furthermore, the maximum principal strain in the adhesive fillet at failure was found to be of the order of the failure strain obtained from bulk adhesive tests reported by the authors elsewhere [30].
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