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Glass reinforced epoxy tubes subjected to indentation load: A study of scaling effects
Composite Structures 117 (2014) 433–444
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Composite Structures journal homepage: www.elsevier.com/locate/compstruct
Glass reinforced epoxy tubes subjected to indentation load: A study of scaling effects F. Hafeez ⇑, F. Almaskari The Petroleum Institute Abu Dhabi, United Arab Emirates
a r t i c l e
i n f o
Article history: Available online 2 July 2014 Keywords: Scaling Indentation Glass reinforced epoxy Filament wound tubes
a b s t r a c t Scaling effects in thin walled glass reinforced epoxy filament wound cylindrical tubes with [±55°] layup subjected to indentation load are presented in this work. Buckingham PI theorem is used to scale input and output parameters for four different scales (n = 1/4, 1/2, 3/4 and 1). Scaling laws are investigated for force, energy dissipation and damage propagation when tubes are resting on a flat surface. Damage propagation is captured with a video camera, by recording damage reflection on an upward facing mirror placed inside the tubes. The threshold force causing onset of delamination is identified and used for calculation of mode II energy release rate GIIC with already established relation between the two. The scaling laws have been found effective in estimating quite a few parameters, including force displacement, energy displacement relation and peak load. Damage growth is found to obey scaling law and it is presented with respect to force applied, energy dissipated, indentation displacement and time. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction A few of the basic barriers that are holding back composite materials in oil and gas industry include lack of data base for damage mechanism and in service integrity monitoring [1]. The behaviour of cylindrical or curved structural components made of composite materials under lateral loads have been studied for a past few decades but these have received less coverage as compared to relatively simpler geometries like plates and beams. For GRE tubes under lateral load, majority of the research is carried out to understand their behaviour under impact type loading [2– 13] where a few included results from static loading also. There are relatively less publications which only considered quasi static and indentation type loading on such geometries [14–17]. On the other hand there are only a few works that used a scaling technique to predict behaviour of filament wound pipes under solely impact type load, for example [11,18] where former considered thick GRE pipe and later used carbon reinforced epoxy cylinders. There is no study as such available on understanding if composite pipes subjected to indentation obey any scaling laws, at least in author’s knowledge. Tarfaoui et al. [11] presented scale and size effect in glass epoxy tubular structure under impact load where ⇑ Corresponding author. Address: Mechanical Engineering Department, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates. Tel.: +971 0 26075118. E-mail address: [email protected] (F. Hafeez). http://dx.doi.org/10.1016/j.compstruct.2014.06.021 0263-8223/Ó 2014 Elsevier Ltd. All rights reserved.
only two scales were used. Thick 10 and 31 layer [±55°] layup composite tubes were tested. This work successfully showed that response parameters like contact force and displacement could be estimated for a large structure by using small model tests. It was also concluded that scaling may not be very accurate for predicting damage magnitude, which was attributed to local material variation along thickness. Tarfaoui et al. [19] in another work presented residual strength of damaged thick glass epoxy tubes. The quasi static indentation test and impact tests were carried out. Authors observed that the static damage trend was similar to that of impact but it was smaller in magnitude. Also the damage shape which was in form of cones through the thickness was very similar for static and dynamic cases. Evans and Alderson [3–7] carried out series of tests on glass epoxy tubes and presented comprehensive results for static and impact testing. This work reported load displacement curves, damage photographs, residual properties and their correlation with impact damage. Authors identified some degree of equivalence between static and impact tests for load displacement relation. Quantification of damage revealed that the floor supported impact test fails with larger delamination areas, than floor supported static test. Hence the static test was used to predict performance over a range of impact energies and velocities. It was concluded that the only other parameter which affected the value of the load was pipe thickness. The effect of curvature was not cited in this work. Though effect of curvature was shown to affect the impact induced damage in composite laminates by other researchers [20]. This theoretical work proved that as the
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curvature increased, the maximum impact force became higher for the same impact velocity and the delaminated area widened. Frost and Cervenka [8] carried out overall assessment of glass reinforced filament wound pipes. They covered a wide range of performance criteria including impact performance and damage tolerance. This work was intended to understand failure mechanisms of pipes, to provide technical input into design guidelines for the oil and gas industry. The authors concluded that impact resistance of the pipe was directly proportional to the pipe flexibility. The ply delamination was related to mode II type energy release rate. It was also concluded that peak impact force caused specific damage however it was only applicable to specific pipe geometry. Christoforou and Swanson [21] studied the strength loss in composite cylinders under impact load. Pang and Kailasam [22] presented the effect of different parameters related to impact response of composite pipe including impacter geometry, velocity, mass and material. It was concluded that the impact response was sensitive to the fibre content. Doyum and Altay [9] compared the impact response of S glass and E glass reinforced epoxy tubes. Khalili et al. [23] used finite element modelling to understand low velocity impact behaviour of different geometries, including composite cylinder [18]. Khalid et al. [12] carried out experimental and finite element analysis of glass and carbon epoxy hybrid tubes subject to quasi static indentation load. Mustafa et al. [24] presented experimental results for laterally indented thin walled GRE tubes supported by a flat plate. The tube behaviour up to the failure was observed. Force, deflection and strain were measured at various indenter displacements. This work concluded that load deflection curve was sensitive to wall thickness. A change in wall thickness of 2.6% resulted in stiffness change of 7.5% [14]. It was suggested that the change in length or end constraints of tube may change the tube behaviour; but authors did not substantiate it with any experimental results. Soden et al. [16] compared the results from quasi static indentation with low speed impact on GRE tubes, and concluded that the behaviour of tubes was the same to a certain extent. Zou et al. [17] presented values of mode II type critical energy release rate of filament wound pipes by using lateral indentation tests. This work correlated dissipated energy with the delaminated area. Critical energy release rate was related to the thickness of the tubes, i.e. 5.5 mm thick tubes had higher energy release rate than 3 mm thick tubes. GIIC for former was 2.03 kJ m2 and for later it was 1.54 kJ m2. Corbett and Reid [15] studied failure of GRE pipes under quasi static and impact load and compared behaviour with that of steel tubes. Authors presented an interesting direct relation between delamination area and impact energy by curve fitting. It was a simple relation which only considered number of plies and surface area of delamination on the outer surface only. Davies and Zhang [25] used simple equation relating threshold force, causing instant delamination with mode II critical energy release rate. The authors argued that it may not be very accurate, however, its effectiveness and simplification made it worth considering as compared to relatively complex computational tools. The Purpose of this work is to study scaling effects in thin walled filament wound GRE pipes under quasi static indentation load. In this work, the authors carry out similitude study to find out relation in mechanical behaviour of scaled GRE pipe specimens subjected to indentation. There is no comparison available between mechanical properties of GRE tubes with those exhibited by smaller laboratory sized specimen. This study leads to build confidence on application of lab data to structural components in oil and gas industry including pipe lines. It should contribute to data base for damage mechanism as identified by [1] and mentioned at the beginning of this section. It has been reported in the literature that filament wound fibre reinforced tubes are susceptible to damage due to local lateral load [14]. Such local lateral
loading can be caused by accidental impact [17] for example a hand tool dropped on a pipe or accidental dropping of pipe itself. To substantiate this argument it was reported that half kg hammer dropped from a height of 1 m is equivalent of 5 J impact on a structural component [8]. Moreover such incidental low velocity impact can cause a reduction of 50% in residual tensile and compressive strength [6]. It has also been reported in the past that load displacement characteristic and appearance of damaged filament wound GRE specimens loaded quasi-statically and by drop weight impacts were similar. Experimental results reported in this work may be used to establish a scaling model to estimate damage caused by accidental impact on pipes. These results can be compared with damage in these specimens subjected to drop weight impact which authors are taking up as a separate work in the future. Generally, filament wound GRE tube stands as a good candidate for studying scaling effects as discussed by Davies and Petton [26]. Experiments carried out on a filament wound tube consider the properties of separately manufactured specimens, as compared to specimen cut from the full scale structure. Also the consistency of fibre distribution in filament winding is better than the other specimen preparation techniques, for example hand layup. 2. Similitude study Pintado and Morton [27] discussed the non dimensional relation between input and output parameters for a laminated beam under impact. Pintado and Morton represented maximum deflection during impact with d and expressed it as a function of input variables namely geometric variables, material properties and impact conditions.
d ¼ f ðL; w; h; E; m; q; v 0 ; E0 Þ L
ð1Þ
where L = Beam length. w = Beam width. h = beam thickness. E = Young’s modulus. m = Poisson’s ratio. q = Density. v0 = impact velocity. E0 = impact energy. Now for the purpose of current work if a tube is subjected to indentation load then above expression should be valid. Geometric variables of beam can be replaced with those of a cylinder and impact loading conditions should be replaced by indentation. Let L = Length of the tube. D = Internal diameter of the tube. t = Wall thickness of the tube. d = Indenter spherical diameter. d = Indentation displacement. v0 = Indentation speed. E0 = Energy absorbed. and the variables representing material properties remain same for the current work i.e. E = Young’s modulus.
m = Poisson’s ratio. q = Density.
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The expression for a laminated tube subjected to indentation load according to (1) becomes
d ¼ f ðL; D; t; E; m; q; v 0 ; E0 ; dÞ
ð2Þ
In order to reduce the number of dimensional variables Buckingham PI theorem is employed. L E and v0 are identified as dimensional variables and rest are non dimentionalized for similitude study. By adopting this methodology, for example see [28], following expression is obtained.
d D t qv 2 E0 d ¼f ; ; m; 0 ; 3 ; L L L E0 EL L
ð3Þ
3. Experimental set up 3.1. Specimens and material Glass reinforced epoxy samples used in this work are manufactured by the Future Pipe Industry UAE. These pipes are made of Diglycidyl ether of Bisphenol A and direct roving type E glass with filament wound industrial standard setup used by FPI industries for their commercial produce. Effective properties only in material direction are provided by the manufacture. These are longitudinal elastic modulus EZ = 10,500 MPa, Circumferential elastic modulus Eh = 20,500 MPa, Shear Modulus Gzh = 11,500 MPa and Poisson’s ratio vrh = 0.38. Four different types of scaled Specimen are obtained according to the dimensions listed in Table 1. These samples are delivered and stored carefully in air cushioned packing to ensure maximum protection against impact or damage during transportation and storage. The samples are manufactured without any liner to avoid any inconsistency. Such liner is usually incorporated as inner most resin rich thick layer. Average mass, volume and areal density of all samples are listed in Table 2 which also scale for different sizes. 3.2. The tensile test machine Indentation tests are carried out on MTS Alliance RF/150 tensile testing machine. Different parameters including force, displacement and time are recorded with the help of integrated MTSÒ software. The lower jaw holder of the tensile testing machine is completely removed so that the tubes can be placed on a completely flat surface. Indentation is carried out at desired speed by moving crosshead at constant downward speed. The scaled indentation speed results in identical indentation test time for all scales (see Fig. 1).
3.3. The indenters and the clamps All specimens are indented with spherical steel indenters of different but scaled spherical diameters. Hemispherical indenters are used in this study to produce large damage zone [22] and higher damage threshold load [29] as a worst case scenario. Also most of the studies carried out on GRE filament wound cylindrical geometries in the past used hemispherical indenter or impacter for example [14,24]. The four different indenters shown in Fig. 2 with hemispherical heads and threaded backs are made from mild steel. Spherical Indenter diameters along with indentation speeds for different scales are listed in Table 3. The relevant indenter for testing particular scale is loaded onto a circular bar with internal screw. This circular bar is held in the tensile machine grip attached to the cross head. This setup ensures convenient loading of different indenters into the griped circular bar and for keeping indentation point same for all the tests. Clamping strips are used to hold and position the tubes on the test machine bed. Clamping strip passes through the tube specimen and extends on each side outside the tube. Screws passing through slots at each end of the strip into the threaded hole of the test bed holds the specimen on the test bed firmly. It is similar to the flat plate specimen clamping technique suggested by ASTM standard [30] for clamping tubes in impact test. Four different metallic strips of scaled width 25, 50, 75 and 100 mm as shown in Fig. 3 are used for each scale (see Table 4). 3.4. Videography The video footage is captured for damage initiation and growth as the indentation load is applied on the sample tubes. It is achieved by placing a mirror inside the tube facing upwards just under the indenter. Mirror is mounted on a flexible probe gripped in a clamp stand. A video camera mounted on a tripod is positioned in such a way that reflection on the mirror is recorded while damage initiates and grows in the tube wall. Led lamp light is projected as a strong backlight throughout the tests on the external surface of the tubes for visibility of damage growth. 3.5. Non destructive testing 3.5.1. Measurement of damage size Image processing is used for measuring damage growth throughout the indentation test for each specimen. The terms delamination area and damage area are used for clarity and consistency purpose in this work. Former obviously means the sum of delamination areas across different layers and later refers to the
Table 1 Dimensions of the scaled specimens. Scale size N
Length (L) mm 500n
Diameter (D) mm 400n
No. of layers (N) 16n
Average wall thickness (t) mm 9n
L/D
D/t
1/4 1/2 3/4 1
125 250 375 500
100 200 300 400
4 8 12 16
2.25 4.5 6.75 9
1.25 1.25 1.25 1.25
44.44 44.44 44.44 44.44
Table 2 Mass, areal density and volume of scaled specimens. Scale size N
Sample mass n3 (kg)
Areal density n4 (kg/mm2)
Sample volume n3 (mm3)
Relative volume 64n3 (mm3)
1/4 1/2 3/4 1
0.16 1.279 4.314 10.27
0.359 5.752 29.120 92.035
86369.25 690954.03 2331969.86 5527632.27
1 8 27 64
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Fig. 1. GRE tubes for scale n = 1=4 , ½, 3=4 , and 1.
Fig. 3. Clamping Strips for scale n = 1=4 , ½, 3=4 and 1.
Fig. 2. Indenters for Scale n = 1=4 , ½, 3=4 , and 1.
Table 3 Indenter diameter, indentation speed and maximum indentation displacement for each scale. Scale size N
Indenter diameter 40n (mm)
Indentation speed 4n (mm/min)
Max. indentation 80n (mm)
1/4 1/2 3/4 1
10 20 30 40
1 2 3 4
20.00 40.00 60.00 80.00
size of the overall damaged section of tube wall. The damage area increases with respect to the load, indentation displacement and time. The images at the required time interval are extracted from the video. These were analysed with Adobe Photo Shop v 5.1 and damage area is measured with the inbuilt ‘‘Analysis’’ menu. A reference of known length is used to set the scale. This relates the number of pixels per unit area of the image. Once this relationship is established, outlined damage area is measured. Although this measurement neglects the effect of curvature because the damage area in the cylindrical wall is projected by a flat tilted mirror, however the effect of curvature is reduced as the indentation displacement increases. It increases the radius of curvature of the loaded surface. Also in this work, output parameters, including damage and delamination area are analysed comparatively hence effect of curvature, if any, is relative in all scales. 3.5.2. Measurement of delamination area Different authors tried to measure the total delamination area formed due to indentation by using different methods. For example
Table 4 Summary of parameters and scaling factors used. Parameter
Scaling factor
Tube diameter Average wall thickness Tube length Volume Areal density Indentation speed Indentation time Diameter of indenter Maximum indentation depth Clamp width Indentation force Energy Permanent deformation
n n n n3 n4 n 1 n n n n2 n3 n
Alderson and Evans [3] used non destructive back light and Zou et al. [17] used the destructive method where areas were measured by incremental grinding of the damage area and mapping of delamination area in every layer. A few very useful conclusions can be made from the work done by Zou et al. [17]. Delamination existed in all layers once delamination initiated, clearly marked by the initial load drop. It had delaminated areas of different sizes in every layer and had irregular shape and perimeter. The centre point of delamination in all layers was approximately point of indentation and delamination was spread in all directions in each layer. Delamination area overlaps in different layers. Keeping in mind these observations, processing of recorded video and images is found most effective in this current work. It is assumed that delamination in each layer has different tones of colour.
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Consider image in Fig. 4 which is reflected by a mirror placed inside the tube at indentation displacement = 24 mm, force = 4.98 kN, where the scale is n = 1/2 and image is taken at indentation time t = 12 min. This image presents overall damage area and it also highlights delamination in different layers. When this image is converted to 4 bit grayscale format shown in Fig. 5 subtle variations in grey tones enhance clarity on boundaries of different grey tones. When both images are compared side by side it is not difficult to outline the approximate boundaries of the delamination and measure the areas enclosed. The darkest grey spot is assumed as a delamination overlap in all layers. The area covered by pixels of the next darker grey tone is added on top of already measured darkest grey tone, to measure the area of the next bigger delamination area in the layer and so on. When all such areas for each layer are summed, it results in the total delamination area. Although this method results in approximate delamination growth rate but it is an effective and practical non destructive way. It is reliable than results from back light analysis carried out with the naked eye. There are number of short comings in this method. It is easier to use when the number of layers are only a few. As the number of layers grows, it becomes more challenging to analyse the images. Sometimes overlapping delamination areas pose difficulty in identification of delamination in every layer, particularly in the regions occupied by darker pixels. In that case, the sizes of such area have to be assumed and layers with missing clear outline of delamination are compensated by including equivalent areas in the total delamination. It can be identified by closely observing the images just before and after the image under analysis. A balanced back light projection is required otherwise the calculation of delamination area can be misleading. This method does not provide information as which layer has how much area of delamination but such information is not the aim of this work. As far as the area of delamination in every layer is calculated and the total delamination is evaluated, the delamination growth rate with respect to the input parameters can be calculated.
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Fig. 5. Grey scale of the same image shown in Fig. 4. This image format shows boundaries of different grey tones which are used to estimate delamination area in different layers.
4. Results and discussion 4.1. Force displacement curve The force displacement data for all specimens is obtained directly from the integrated MTSÒ software. The indentation test can be subdivided into three distinct phases for every specimen
Fig. 6. Specimen for scale n = 1 subjected to indentation.
Fig. 4. Damage in scale n = 1/2 at indentation time t = 12 min, force = 4.98 kN and indentation displacement = 24 mm.
as shown in Fig. 10. Small photos are added onto the plot to show state of the tube roughly at the given data points on the plot. Phase 1 can be related to the start of the test up to initiation of delamination, marked by first load drop clearly visible in all plots. During this phase each specimen behaves elastically [3]. In phase 2, force displacement relation has less steep gradient and damage grows continuously. Phase 3 basically consists of unloading path. Although the magnitude of force and indentation displacement is different but the trend and shape of the graph for each scale is very similar as compared in Fig. 11. The maximum indentation displacement for the biggest scale n = 1 is the highest and for the smallest scale n = 1/4 is lowest, essentially because of scaled maximum indentation displacement. Consequently peak force and force displacement gradients for both phase 1 and 2 are highest and lowest for n = 1 and n = 1/4 respectively. The unloading curve in all scales is smooth particularly as compared to their phase 2. The slope of unloading curve reduces as scale reduces however curves for all specimens converge to same graph near the end of
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Fig. 10. Typical force displacement plot labelled with three distinct phases.
Fig. 7. Specimen for n = 1/4 subjected to indentation.
Fig. 11. Force displacement curves for all specimens in same graph.
Fig. 8. Specimen for scale n = 1/2 and upward facing mirror reflecting the indentation growth.
Fig. 9. Specimen for scale n = 1/4 placed vertically after completion of indentation test. Damage on the inside of wall is visible.
unloading curve or origin of the plot. The indentation starts with deflection of the tube for the first few millimetres then the matrix crushing starts, however the force displacement relation remains linear. Sporadic Cracking noises are heard. The crushed matrix becomes visible if the internal wall surface is viewed. Then delamination initiates instantly and distinct load drop is observed in all scales, marking the end of phase 1. Continuous damage progression in the tube wall is observed with further indentation. Delamination growth at this stage is clearly visible particularly on the internal wall surface due to the strong back light on tube’s external surface. Louder and continuous cracking noises are heard throughout the loading cycle and cracks appear on the top surface of the tube. These cracks keep on growing for the rest of the loading path. Four shear cracks become distinctly visible on the top surface. These cracks start from the perimeter of the crushed area and grow outwards along the fibre direction. Cracking and fibre breakage noises become louder and frequent along with the growth of the delamination as the indentation continues. Further indentation makes the damage more complex as a mixture of all forms of damage including matrix cracks, interlaminar cracks, shear cracks, delamination and fibre breakage. Fibre bridging becomes clearer and a distinct rectangular area on the tube surface around indentation point becomes visible. The centre of this rectangular area is pushed downwards with four distinct shear cracks along the diag-
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onals of this rectangular area. Once the indenter reaches its maximum depth, it stops and starts moving upwards as unloading initiates, marking the end of phase 2 and beginning of phase 3. By now the cracking noise starts reducing and eventually become negligible as indenter moves towards its initial position. All specimens exhibit permanent deformation that is apparent from the unloading curve near the origin in Fig. 11. Though all specimens recover from most of their deflection, as the indentation test ends. 4.2. Scaled force displacement data Fig. 12 compares the scaled force vs scaled indentation displacement for all specimens, and shows that the force displacement behaviour scales quite well. There are lot of similarities including slope of initial gradient in the first phase, unload path and permanent deformation in each specimen. Scale 3/4 and 1 compare extraordinarily well and scale 1/4 and 1/2 are not as identical with the higher value of gradient in phase 2 and with peak load inversely proportional to the scale size. The consistency in scaled data for scale 3/4 and 1 has two distinct features. First the plots for these scales are more stable and secondly they have smaller gradient as compared to other two scales in phase 2. The stability of data is attributed to the size of indenter diameters. As indenter diameters for smaller scales is relatively close to the pattern unit of fibre net, they cause a change in local failure mode in upper ply resulting in unstable data relative to bigger scales. The closest example from the literature can be found in [31], where the authors made similar observation for sandwich structure with a top layer of woven carbon fibre reinforced epoxy. The reason for smaller gradient in phase 2 for bigger scales may also be related to relative size of the indenter to fibre net. For bigger scales it is observed that less force is required to cause same amount of damage (see Fig. 25) and delamination (see Fig. 30). It might be due to the fact that bigger size of indenter contributes towards more damage due to bigger contact area resulting in less force. As scale size reduces and consequently indenter diameter and contact area reduces, indenter causes local damage only. The indenter experiences more force from tube wall which has only localised and less damaged area as compared to bigger scales. This results in higher values of peak load and contributes to inconsistency of first half of scaled data for scale 1/4 and 1/2 in phase 3. Generally there is no previous data in literature to compare directly with this work, however current data is relatively stable and consistent as compared to other scaling studies, for example see [31], where data is compared
Fig. 12. Scaled force displacement curves for all scales compared on same graph.
for sandwich specimens subjected to indentation as well as impact type load. Similarly in [32], the authors studied impact behaviour of scaled FMLs and compared impact behaviour for four scales. Even in case of metals subjected to impact [33], the scaled force displacement data for different specimens exhibit certain inconsistency, however all such data collapse on same trend. The magnitude of variation in scaled data in Fig. 12 is of same order compared to these examples. The scaled data for initial gradient, Peak load and permanent deformation is listed in Table 5. The scaled slope of the initial gradients of all specimens is remarkably same and almost overlaps as shown in Fig. 12. End of phase 1 or first load drop occurs at higher force value for smaller scales (i.e. n = 1/4 and 1/2) as compared to bigger scales (n = 3/4 and 1). Gradients of phase 2 are highest for the smallest scale (n = 1/4) and lowest for (n = 1). This leads to the same observation for peak loads which are inversely proportional to the scale. Peak load at maximum displacement scales within the range of 4 kN. The gradients of scaled unloading curve is higher for smaller scales for at least first half of the unloading time, after which all unloading curves nearly converge on same graph. Smaller scales exhibit higher force value for the same displacement in the second half of unloading curve before intersecting Y axis of the graph, to exhibit permanent deformation. The permanent deformation scaling is not comparatively as good and Fig. 13 shows prediction of higher deformation in smaller scales i.e. n = 1/2 and n = 1/4. 4.3. Scaled energy displacement data The area under the force displacement loading curves obtained by trapezoid method is scaled and shown in Fig. 14. This estimation of energy dissipated by each specimen scales well. It can be argued that the force displacement curves presented in Figs. 11 and 12 are not exactly linear force displacement relations for complete loading and unloading paths, hence areas under the curves
Table 5 Scaled slope of the initial gradient (phase 1), peak load and permanent deformation for floor supported specimen. Scale
1/4
1/2
3/4
1
Slope Peak load (kN) Permanent Deformation (Dn) (mm) Normalised permanent deformation (Dn/D1)
628.80 29.78 7.48 1
653.40 27.63 7.34 0.98
608.40 25.20 6.13 0.82
635.70 25.48 5.90 0.79
Fig. 13. Permanent deformation normalised with respect to that of n = 1/4.
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Fig. 15. Damage initiation in a sample for scale n = 1/2.
Fig. 14. Scaled energy displacement curves for all scales compared on the same graph.
cannot be exact value of energy dissipated. However, scaled value of energy absorbed by the specimen is remarkably consistent corresponding to phase 1 of the force displacement curve after which the energy curves show diverging trends which reduces as the scale increases. Approximately above 30 mm of scaled indentation, smallest scale (n = 1/4) exhibit highest energy dissipation trend up to maximum indentation. Energy dissipation graphs for biggest scales (n = 1 and 3=4 ) are almost overlapping with lowest values as compared to other scales. 4.4. Scaled mode 2 energy release rate (GIIC) Davies and Zhang [25] presented an interesting relationship between (GIIC) mode 2 critical energy release rate and critical threshold force. In this relation, presented in Eq. (4), if one of these two parameters is known, other can be calculated.
Gc ¼
9P2c ð1 v 2 Þ 8p2 Et3
ð4Þ
where Gc is mode 2 critical energy release rate, Pc is the threshold force which initiates delamination, v is poisons ratio, t is thickness of the laminate and E is mean flexural modulus. Authors argued the usefulness of this simple relation over complex computational technique. Before applying this relation to the current work, it is evaluated for the work done by Zou et al. [17] where authors calculated energy release rate experimentally. Delamination is caused in 10 and 8 layer GRE tubes through indentation load. Energy absorbed to create delamination area is used to calculate average energy release rates of 2.03 kJ m2 and 1.54 kJ m2 for each set of 10 and 8 layered specimen respectively. Here if Eq. (4) is applied one can achieve GIIC values of 1.27 kJ m2 and 1.05 kJ m2 respectively which are not consistent with experimental results. Also these are average values which vary for different samples due to variation in delamination threshold load. Since value of the mean flexural modulus is not provided in [17] hence value of effective Young’s modulus is used instead for these calculations. Keeping in mind the effectiveness of this relation one can achieve conservative estimate of mode II energy release rate. In terms of applicability of this relation on the current work, threshold force can be measured to calculate GIIC. The video captured through mirror reflecting the damage growth from inside the specimens is very useful here to identify the threshold force. When the video is carefully watched the delamination initiation and growth can be easily identified
and exact threshold force can be obtained, corresponding to the time it initiates. Delamination initiation is shown in Fig. 15. By substituting this threshold force into Eq. (4), value for GIIC is calculated and results are presented in Table 6. Longitudinal elastic modulus provided by the manufacturer mentioned in an earlier section is used here for E in (4). GIIC value attained may not be accurate however it provides an estimation. These are quite similar for all scales except n = 1 which is approximately 30% higher as compared to the other scales. This suggests better performance against delamination by the biggest scale. It is worth mentioning that equation used here only involves thickness and ignores other geometric dimensions like curvature or length. 4.5. Damage growth rate w.r.t displacement, force and energy The damage area is plotted in relation to force applied, energy dissipated and time. Adobe Photoshop is used for image processing and damage area calculation. Its inbuilt ‘‘Analyses’’ menu which is meant to measure the area based on the number of pixels is utilised. The images of a scale n = 1/2 specimen at 6, 8, 10 and 12 min of indentation time are shown in Figs. 16–19. Damage area growth with respect to force, displacement, time and energy dissipated are presented in Figs. 20–23. Figs. 20 and 23 show damage area growth with respect to indentation displacement and time. Maximum indentation displacement is 4 cm and total test time is 40 min for this scale. Loading takes place in the first 20 min half and the specimen is unloaded in next half at same 2 mm/min speed. Fig. 23 presents
Table 6 Delamination initiation load and mode 2 energy release rate GIIC values. Scale
1/4
1/2
3/4
1
Scaled Delamination initiation Load (kN) GIIC [26]
19.20 0.86
13.65 0.87
11.28 0.89
11.26 1.18
Fig. 16. Damage at indentation displacement: 12 mm, force: 3.39 kN, energy dissipated: 22.48 J for scale n = 1/2 (t = 6 min).
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Fig. 17. Damage at indentation displacement: 16 mm force: 4.14 kN, energy dissipated: 37.55 J for scale n = 1/2 (t = 8 min).
Fig. 20. Damage growth with respect to indentation displacement for scale n = 1/2 during loading only.
Fig. 18. Damage at indentation displacement: 20 mm, force: 4.59 kN, energy dissipated: 55.14 J for scale n = 1/2 (t = 10 min).
Fig. 21. Damage growth with respect to force applied for scale n = 1/2 during loading only.
Fig. 19. Damage at indentation displacement: 24 mm, force: 4.98 kN, energy dissipated: 74.28 J for scale n = 1/2 (t = 12 min).
loading time up to maximum indentation depth. Both indentation displacement and time plots show similar trends as displacement speed is scaled. Damage prior to 5 min and 1 cm of indentation depth is mostly due to matrix crushing. After which, delamination initiates and damage growth rate increases. This rate further increases at around displacement of 1.8 cm and indentation time of 8 min. Similar behaviour is observed when damage area is plotted for force applied. As damage initiates just above 2 kN it continuously grows up till 4 kN, after which the gradient of the curve increases. Damage area and energy dissipation plot show similar trend with increase in damage growth rate around energy dissipation value of 0.05 kJ. It is interesting to see that when the damage area is scaled with a factor of n3 for all specimens it scales quite well. When plotted with respect to scaled indentation displacement and time, data for all scales collapse on the same graph. Since indentation speed and maximum indentation are scaled, both graphs are similar as
Fig. 22. Damage growth with respect to energy absorbed for scale n = 1/2 during loading only.
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Fig. 23. Damage growth with respect to indentation time for scale n = 1/2 during loading only.
Fig. 26. Scaled Damage area vs scaled energy for all scales. Scale factor for damage area is n3 and energy is n3.
Fig. 24. Scaled damage area vs indentation displacement for all scales. Scale factor for damage area is n3 and scale factor for displacement is n.
Fig. 27. Scaled Damage area vs time for all scales. Scale factor for damage area is n3 which is plotted with actual time as indentation speed is scaled.
specimen except n = 1. In specimen for n = 1/2 damage growth is consistent with other scales up to almost first half of the indentation depth and relatively smaller for the latter half. Similar trend can be seen in specimen for n = 3/4 where in later half of indentation depth the damage growth rate is the lowest amongst all scales. First half of the indentation depth is dominated by delamination after which it becomes a complex mixture of all types of damage. Shear cracks and layer splitting become dominant by the time indenter reaches maximum depth. The inconsistency in damage growth in the second half of indentation depth can be attributed to this complex damage where cracks particularly do not contribute much towards increase in the damage area. Generally the damage growth rate is similar in all scales with initial smaller growth rate increasing to higher gradient after scaled displacement approximately of 2.5 cm, as discussed in the previous section. 4.6. Scaled damage growth rate w.r.t displacement, force and energy Fig. 25. Scaled damage area vs scaled force for all scales. Scale factor for damage area is n3 and scale factor for force is n2.
shown in Figs. 24 and 27. The damage area in specimen for n = 1/4 and n = 1 coincide throughout indentation displacement and time however damage initiation is predicted to start early in all
The scaled damage area with respect to force applied is presented in Fig. 25. Damage area is scaled with factor of n3 and force is scaled with the factor of n2. Force data for all specimens is not scaled as well as that for time and there is a difference of around 5 kN between the smallest and the biggest scale. Damage initiates early in smaller scales as compared to n = 1 and generally scaled
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Fig. 28. Scaled delamination area vs indentation displacement for all scales. Scale factor for delamination area is n4 and scale factor for the displacement is n.
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Fig. 30. Scaled delamination area vs energy for all scales. Scale factor for delamination area is n4 and scale factor for the energy dissipated is n3.
Fig. 29. Scaled delamination area vs force applied for all scales. Scale factor for delamination area is n4 and scale factor for the force is n2.
Fig. 31. Scaled delamination area vs time for all scales. Scale factor for delamination area is n4 and time is not scaled as indentation speed is scaled.
force is higher in smaller scales. The graph of scaled damage area with respect to scaled energy dissipation is shown in Fig. 26. Here data for n = 1/4 and 1/2 scales well however the trend suggest relatively higher energy dissipation in them as compared to bigger scale n = 1. Plot for n = 3/4 coincides reasonably well with others for the first half of the indentation depth then it presents higher energy dissipation for smaller damage area.
with indentation depth and time. Specimen for scale n = 1/4 dissipated more energy for same delamination as compared to other scales. The same energy dissipation has produced highest delamination area in specimen for scale n = 3/4 in first half of the delamination depth and results of the second half for this specimen coincide well with scale for n = 1. The scaled energy dissipation to create delamination area is presented in Fig. 30. The general trend of data for all scales is similar to that of Fig. 29 which is due to the fact that energy values are obtained by area under force displacement graph. Specimen for scale n = 1/4 consumes the highest energy and data for rest of the scales obey scaling law quite well.
4.7. Scaled delamination rate w.r.t displacement, force and energy Image processing technique described in a previous section is employed to establish delamination growth rate and presented in Figs. 28–31. Delamination is scaled with factor n4 which is estimated by curve fitting. The scaled delamination areas with respect to indentation displacement and time are similar. Specimen for n = 1/2 scale exhibits highest delamination area for same indentation displacement and time particularly in the second half of indentation displacement. The scaled delamination area with respect to force for n = 1/4 shows the highest force values for the same delamination area as compared to that of the rest of the scales. Specimens for all other scales collapse quite well on the same trend for the whole of the indentation depth and the difference between force data reduces
5. Conclusions The effect of scaling are studied on GRE tubes subjected to quasi static indentation. Force displacement and energy displacement relation obey the scaling law quite well except for scales 1=4 and ½ as the data in Fig. 12 shows that the scale law for scales 3=4 and 1 are working well but not for the other scales. Force displacement consists of three phases for all scales. Force displacement gradient in initial elastic phase 1 scales remarkably very well. Phase 2 has lower force displacement gradients as compared to
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that of phase 1. This phase is relatively unstable due to damage growth but generally obeys the scaling law. The scaled phase 2 shows higher force values for smaller scales which reduces with scales and lower in two biggest scales i.e. n = 1 and 3/4. Unloading phase scales better in the second half of the unloading path closer to the end of the unloading cycle. Phase 3 is smooth as compared to phase 2. Energy displacement data collapse onto same graph when scaled particularly for the data corresponding to phase 1 of force displacement relation. The energy dissipated by the specimen for damage initiation growth is useful information for studying scaling effect on GRE tubes, subject to impact load which is being pursued by the authors as a future work. The damage area growth is calculated and presented with respect to displacement, force applied, energy dissipated and indentation time. Damage growth data collapses on the same graph when it is scaled with factor n3 and generally obeys scaling law with a few exceptions like force applied and energy dissipated is predicted higher for smaller scales. The delamination area is estimated with the help of image processing obtained with strong in situ back light. The non-destructive back lighting technique is improved with image processing to calculate the delamination area which collapses on the same graph when scaled with n4. Mode II critical energy release rate is measured with the help of delamination initiation force which is identified by post processing of videos captured for the tests. An already established relationship from available literature is used for this estimation. GIIC is around 0.85 kJ m2 for all scales except n = 1, for which it is 1.17 kJ m2. The thickness of the laminate is a major contributor here as it is the only geometric dimension considered in the formulation. It is concluded that this estimation is a conservative result based on rather simpler formulation. It can only be verified by destructive experimental results from the specimens indented up to phase I only, which is proposed by the authors as an extension of this work in the future. Acknowledgment Authors would like to acknowledge the financial support provided by the Petroleum Institute, Abu Dhabi under Grant for Project No. 12344. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.compstruct.2014. 06.021. References [1] Ochoa OO, Salama MM. Offshore composites: transition barriers to an enabling technology. Compos Sci Technol 2005;65(15–16):2588–96. [2] Tan TM, Sun CT. Use of statical indentation laws in the impact analysis of laminated composite plates. J Appl Mech 1985;52(1):6–12. [3] Alderson KL, Evans KE. Low velocity transverse impact of filament-wound pipes: Part 1. Damage due to static and impact loads. Compos Struct 1992;20(1):37–45.
[4] Alderson KL, Evans KE. Failure mechanisms during the transverse loading of filament-wound pipes under static and low velocity impact conditions. Composites 1992;23(3):167–73. [5] Alderson KL, Evans KE. Dynamic analysis of filament wound pipes undergoing low velocity transverse impact. Compos Sci Technol 1992;45(1):17–22. [6] Evans KE, Alderson KL. Low velocity transverse impact of filament-wound pipes: Part 2. Residual properties and correlations with impact damage. Compos Struct 1992;20(1):47–52. [7] Evans KE, Alderson KL, Marks PR. Modelling of the transverse loading of filament wound pipes. Comput Struct 1992;45(5–6):1089–95. [8] Frost SR, Cervenka A. Glass fibre-reinforced epoxy matrix filament-wound pipes for use in the oil industry. Compos Manuf 1994;5(2):73–81. [9] Doyum AB, Altay B. Low-velocity impact damage in glass fibre/epoxy cylindrical tubes. Mater Des 1997;18(3):131–5. [10] Gning PB, Tarfaoui M, Collombet F, Riou L, Davies P. Damage development in thick composite tubes under impact loading and influence on implosion pressure: experimental observations. Compos B Eng 2005;36(4):306–18. [11] Tarfaoui M, Gning PB, Davies P, Collombet F. Scale and size effects on dynamic response and damage of glass/epoxy tubular structures. J Compos Mater 2007;41(5):547–58. [12] Zuraida A, Khalid AA, Ismail AF. Performance of hybrid filament wound composite tubes subjected to quasi static indentation. Mater Des 2007;28(1):71–7. [13] Tarfaoui M, Gning PB, Hamitouche L. Dynamic response and damage modeling of glass/epoxy tubular structures: numerical investigation. Compos A Appl Sci Manuf 2008;39(1):1–12. [14] Li S, Soden PD, Reid SR, Hinton MJ. Indentation of laminated filament-wound composite tubes. Composites 1993;24(5):407–21. [15] Corbett GG, Reid SR. Failure of composite pipes under local loading with A hemispherically-tipped indenter. Int J Impact Eng 1994;15(4):465–90. [16] Curtis J, Hinton MJ, Li S, Reid SR, Soden PD. Damage, deformation and residual burst strength of filament-wound composite tubes subjected to impact or quasi-static indentation. Compos B Eng 2000;31(5):419–33. [17] Zou Z, Reid SR, Soden PD, Li S. Measurement of the critical energy release rate GIIC for filament wound GRP pipes. Compos A Appl Sci Manuf 2001;32(2):271–80. [18] Swanson SR, Smith NL, Qian Y. Analytical and experimental strain response in impact of composite cylinders. Compos Struct 1991;18(2):95–108. [19] Tarfaoui M, Gning PB, Collombet F. Residual strength of damaged glass/epoxy tubular structures. J Compos Mater 2007;41(18):2165–82. [20] Kim SJ, Goo NS, Kim TW. The effect of curvature on the dynamic response and impact-induced damage in composite laminates. Compos Sci Technol 1997;57(7):763–73. [21] Christoforou AP, Swanson SR. Strength loss in composite cylinders under impact. J Eng Mater Technol 1988;110(2):180–4. [22] Pang SS, Kailasam AA. A study of impact response of composite pipe. J Energy Resour Technol 1991;113(3):182–8. [23] Khalili SMR, Soroush M, Davar A, Rahmani O. Finite element modeling of lowvelocity impact on laminated composite plates and cylindrical shells. Compos Struct 2011;93(5):1363–75. [24] Mustafa B, Li S, Soden PD, Reid SR, Leech CM, Hinton MJ. Lateral indentation of filament wound GRP tubes. Int J Mech Sci 1992;34(6):443–57. [25] Davies GAO, Zhang X. Impact damage prediction in carbon composite structures. Int J Impact Eng 1995;16(1):149–70. [26] Davies P, Petton D. An experimental study of scale effects in marine composites. Compos A Appl Sci Manuf 1999;30(3):267–75. [27] Pintado P, Morton J. On the scaling of impact loaded composite beams. Compos Struct 1994;27(4):357–65. [28] White, F.M. Fluid mechanics, McGraw-Hill Higher Education; 2008. [29] Mitrevski T, Marshall IH, Thomson R, Jones R, Whittingham B. The effect of impactor shape on the impact response of composite laminates. Compos Struct 2005;67(2):139–48. [30] ASTM. Standard test method for determination of the impact resistance of thermoplastic pipe and fittings by means of a Tup (Falling Weight), vol. 44. West Conshohocken, PA; 2003, 2005. [31] Yang FJ, Hassan MZ, Cantwell WJ, Jones N. Scaling effects in the low velocity impact response of sandwich structures. Compos Struct 2013;99:97–104. [32] Carrillo JG, Cantwell WJ. Scaling effects in the low velocity impact response of fiber-metal laminates. J Reinforced Plast Compos 2008. [33] Wen H-M, Jones N. Experimental investigation of the scaling laws for metal plates struck by large masses. Int J Impact Eng 1993;13(3):485–505.
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Composite Structures journal homepage: www.elsevier.com/locate/compstruct
Glass reinforced epoxy tubes subjected to indentation load: A study of scaling effects F. Hafeez ⇑, F. Almaskari The Petroleum Institute Abu Dhabi, United Arab Emirates
a r t i c l e
i n f o
Article history: Available online 2 July 2014 Keywords: Scaling Indentation Glass reinforced epoxy Filament wound tubes
a b s t r a c t Scaling effects in thin walled glass reinforced epoxy filament wound cylindrical tubes with [±55°] layup subjected to indentation load are presented in this work. Buckingham PI theorem is used to scale input and output parameters for four different scales (n = 1/4, 1/2, 3/4 and 1). Scaling laws are investigated for force, energy dissipation and damage propagation when tubes are resting on a flat surface. Damage propagation is captured with a video camera, by recording damage reflection on an upward facing mirror placed inside the tubes. The threshold force causing onset of delamination is identified and used for calculation of mode II energy release rate GIIC with already established relation between the two. The scaling laws have been found effective in estimating quite a few parameters, including force displacement, energy displacement relation and peak load. Damage growth is found to obey scaling law and it is presented with respect to force applied, energy dissipated, indentation displacement and time. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction A few of the basic barriers that are holding back composite materials in oil and gas industry include lack of data base for damage mechanism and in service integrity monitoring [1]. The behaviour of cylindrical or curved structural components made of composite materials under lateral loads have been studied for a past few decades but these have received less coverage as compared to relatively simpler geometries like plates and beams. For GRE tubes under lateral load, majority of the research is carried out to understand their behaviour under impact type loading [2– 13] where a few included results from static loading also. There are relatively less publications which only considered quasi static and indentation type loading on such geometries [14–17]. On the other hand there are only a few works that used a scaling technique to predict behaviour of filament wound pipes under solely impact type load, for example [11,18] where former considered thick GRE pipe and later used carbon reinforced epoxy cylinders. There is no study as such available on understanding if composite pipes subjected to indentation obey any scaling laws, at least in author’s knowledge. Tarfaoui et al. [11] presented scale and size effect in glass epoxy tubular structure under impact load where ⇑ Corresponding author. Address: Mechanical Engineering Department, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates. Tel.: +971 0 26075118. E-mail address: [email protected] (F. Hafeez). http://dx.doi.org/10.1016/j.compstruct.2014.06.021 0263-8223/Ó 2014 Elsevier Ltd. All rights reserved.
only two scales were used. Thick 10 and 31 layer [±55°] layup composite tubes were tested. This work successfully showed that response parameters like contact force and displacement could be estimated for a large structure by using small model tests. It was also concluded that scaling may not be very accurate for predicting damage magnitude, which was attributed to local material variation along thickness. Tarfaoui et al. [19] in another work presented residual strength of damaged thick glass epoxy tubes. The quasi static indentation test and impact tests were carried out. Authors observed that the static damage trend was similar to that of impact but it was smaller in magnitude. Also the damage shape which was in form of cones through the thickness was very similar for static and dynamic cases. Evans and Alderson [3–7] carried out series of tests on glass epoxy tubes and presented comprehensive results for static and impact testing. This work reported load displacement curves, damage photographs, residual properties and their correlation with impact damage. Authors identified some degree of equivalence between static and impact tests for load displacement relation. Quantification of damage revealed that the floor supported impact test fails with larger delamination areas, than floor supported static test. Hence the static test was used to predict performance over a range of impact energies and velocities. It was concluded that the only other parameter which affected the value of the load was pipe thickness. The effect of curvature was not cited in this work. Though effect of curvature was shown to affect the impact induced damage in composite laminates by other researchers [20]. This theoretical work proved that as the
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curvature increased, the maximum impact force became higher for the same impact velocity and the delaminated area widened. Frost and Cervenka [8] carried out overall assessment of glass reinforced filament wound pipes. They covered a wide range of performance criteria including impact performance and damage tolerance. This work was intended to understand failure mechanisms of pipes, to provide technical input into design guidelines for the oil and gas industry. The authors concluded that impact resistance of the pipe was directly proportional to the pipe flexibility. The ply delamination was related to mode II type energy release rate. It was also concluded that peak impact force caused specific damage however it was only applicable to specific pipe geometry. Christoforou and Swanson [21] studied the strength loss in composite cylinders under impact load. Pang and Kailasam [22] presented the effect of different parameters related to impact response of composite pipe including impacter geometry, velocity, mass and material. It was concluded that the impact response was sensitive to the fibre content. Doyum and Altay [9] compared the impact response of S glass and E glass reinforced epoxy tubes. Khalili et al. [23] used finite element modelling to understand low velocity impact behaviour of different geometries, including composite cylinder [18]. Khalid et al. [12] carried out experimental and finite element analysis of glass and carbon epoxy hybrid tubes subject to quasi static indentation load. Mustafa et al. [24] presented experimental results for laterally indented thin walled GRE tubes supported by a flat plate. The tube behaviour up to the failure was observed. Force, deflection and strain were measured at various indenter displacements. This work concluded that load deflection curve was sensitive to wall thickness. A change in wall thickness of 2.6% resulted in stiffness change of 7.5% [14]. It was suggested that the change in length or end constraints of tube may change the tube behaviour; but authors did not substantiate it with any experimental results. Soden et al. [16] compared the results from quasi static indentation with low speed impact on GRE tubes, and concluded that the behaviour of tubes was the same to a certain extent. Zou et al. [17] presented values of mode II type critical energy release rate of filament wound pipes by using lateral indentation tests. This work correlated dissipated energy with the delaminated area. Critical energy release rate was related to the thickness of the tubes, i.e. 5.5 mm thick tubes had higher energy release rate than 3 mm thick tubes. GIIC for former was 2.03 kJ m2 and for later it was 1.54 kJ m2. Corbett and Reid [15] studied failure of GRE pipes under quasi static and impact load and compared behaviour with that of steel tubes. Authors presented an interesting direct relation between delamination area and impact energy by curve fitting. It was a simple relation which only considered number of plies and surface area of delamination on the outer surface only. Davies and Zhang [25] used simple equation relating threshold force, causing instant delamination with mode II critical energy release rate. The authors argued that it may not be very accurate, however, its effectiveness and simplification made it worth considering as compared to relatively complex computational tools. The Purpose of this work is to study scaling effects in thin walled filament wound GRE pipes under quasi static indentation load. In this work, the authors carry out similitude study to find out relation in mechanical behaviour of scaled GRE pipe specimens subjected to indentation. There is no comparison available between mechanical properties of GRE tubes with those exhibited by smaller laboratory sized specimen. This study leads to build confidence on application of lab data to structural components in oil and gas industry including pipe lines. It should contribute to data base for damage mechanism as identified by [1] and mentioned at the beginning of this section. It has been reported in the literature that filament wound fibre reinforced tubes are susceptible to damage due to local lateral load [14]. Such local lateral
loading can be caused by accidental impact [17] for example a hand tool dropped on a pipe or accidental dropping of pipe itself. To substantiate this argument it was reported that half kg hammer dropped from a height of 1 m is equivalent of 5 J impact on a structural component [8]. Moreover such incidental low velocity impact can cause a reduction of 50% in residual tensile and compressive strength [6]. It has also been reported in the past that load displacement characteristic and appearance of damaged filament wound GRE specimens loaded quasi-statically and by drop weight impacts were similar. Experimental results reported in this work may be used to establish a scaling model to estimate damage caused by accidental impact on pipes. These results can be compared with damage in these specimens subjected to drop weight impact which authors are taking up as a separate work in the future. Generally, filament wound GRE tube stands as a good candidate for studying scaling effects as discussed by Davies and Petton [26]. Experiments carried out on a filament wound tube consider the properties of separately manufactured specimens, as compared to specimen cut from the full scale structure. Also the consistency of fibre distribution in filament winding is better than the other specimen preparation techniques, for example hand layup. 2. Similitude study Pintado and Morton [27] discussed the non dimensional relation between input and output parameters for a laminated beam under impact. Pintado and Morton represented maximum deflection during impact with d and expressed it as a function of input variables namely geometric variables, material properties and impact conditions.
d ¼ f ðL; w; h; E; m; q; v 0 ; E0 Þ L
ð1Þ
where L = Beam length. w = Beam width. h = beam thickness. E = Young’s modulus. m = Poisson’s ratio. q = Density. v0 = impact velocity. E0 = impact energy. Now for the purpose of current work if a tube is subjected to indentation load then above expression should be valid. Geometric variables of beam can be replaced with those of a cylinder and impact loading conditions should be replaced by indentation. Let L = Length of the tube. D = Internal diameter of the tube. t = Wall thickness of the tube. d = Indenter spherical diameter. d = Indentation displacement. v0 = Indentation speed. E0 = Energy absorbed. and the variables representing material properties remain same for the current work i.e. E = Young’s modulus.
m = Poisson’s ratio. q = Density.
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The expression for a laminated tube subjected to indentation load according to (1) becomes
d ¼ f ðL; D; t; E; m; q; v 0 ; E0 ; dÞ
ð2Þ
In order to reduce the number of dimensional variables Buckingham PI theorem is employed. L E and v0 are identified as dimensional variables and rest are non dimentionalized for similitude study. By adopting this methodology, for example see [28], following expression is obtained.
d D t qv 2 E0 d ¼f ; ; m; 0 ; 3 ; L L L E0 EL L
ð3Þ
3. Experimental set up 3.1. Specimens and material Glass reinforced epoxy samples used in this work are manufactured by the Future Pipe Industry UAE. These pipes are made of Diglycidyl ether of Bisphenol A and direct roving type E glass with filament wound industrial standard setup used by FPI industries for their commercial produce. Effective properties only in material direction are provided by the manufacture. These are longitudinal elastic modulus EZ = 10,500 MPa, Circumferential elastic modulus Eh = 20,500 MPa, Shear Modulus Gzh = 11,500 MPa and Poisson’s ratio vrh = 0.38. Four different types of scaled Specimen are obtained according to the dimensions listed in Table 1. These samples are delivered and stored carefully in air cushioned packing to ensure maximum protection against impact or damage during transportation and storage. The samples are manufactured without any liner to avoid any inconsistency. Such liner is usually incorporated as inner most resin rich thick layer. Average mass, volume and areal density of all samples are listed in Table 2 which also scale for different sizes. 3.2. The tensile test machine Indentation tests are carried out on MTS Alliance RF/150 tensile testing machine. Different parameters including force, displacement and time are recorded with the help of integrated MTSÒ software. The lower jaw holder of the tensile testing machine is completely removed so that the tubes can be placed on a completely flat surface. Indentation is carried out at desired speed by moving crosshead at constant downward speed. The scaled indentation speed results in identical indentation test time for all scales (see Fig. 1).
3.3. The indenters and the clamps All specimens are indented with spherical steel indenters of different but scaled spherical diameters. Hemispherical indenters are used in this study to produce large damage zone [22] and higher damage threshold load [29] as a worst case scenario. Also most of the studies carried out on GRE filament wound cylindrical geometries in the past used hemispherical indenter or impacter for example [14,24]. The four different indenters shown in Fig. 2 with hemispherical heads and threaded backs are made from mild steel. Spherical Indenter diameters along with indentation speeds for different scales are listed in Table 3. The relevant indenter for testing particular scale is loaded onto a circular bar with internal screw. This circular bar is held in the tensile machine grip attached to the cross head. This setup ensures convenient loading of different indenters into the griped circular bar and for keeping indentation point same for all the tests. Clamping strips are used to hold and position the tubes on the test machine bed. Clamping strip passes through the tube specimen and extends on each side outside the tube. Screws passing through slots at each end of the strip into the threaded hole of the test bed holds the specimen on the test bed firmly. It is similar to the flat plate specimen clamping technique suggested by ASTM standard [30] for clamping tubes in impact test. Four different metallic strips of scaled width 25, 50, 75 and 100 mm as shown in Fig. 3 are used for each scale (see Table 4). 3.4. Videography The video footage is captured for damage initiation and growth as the indentation load is applied on the sample tubes. It is achieved by placing a mirror inside the tube facing upwards just under the indenter. Mirror is mounted on a flexible probe gripped in a clamp stand. A video camera mounted on a tripod is positioned in such a way that reflection on the mirror is recorded while damage initiates and grows in the tube wall. Led lamp light is projected as a strong backlight throughout the tests on the external surface of the tubes for visibility of damage growth. 3.5. Non destructive testing 3.5.1. Measurement of damage size Image processing is used for measuring damage growth throughout the indentation test for each specimen. The terms delamination area and damage area are used for clarity and consistency purpose in this work. Former obviously means the sum of delamination areas across different layers and later refers to the
Table 1 Dimensions of the scaled specimens. Scale size N
Length (L) mm 500n
Diameter (D) mm 400n
No. of layers (N) 16n
Average wall thickness (t) mm 9n
L/D
D/t
1/4 1/2 3/4 1
125 250 375 500
100 200 300 400
4 8 12 16
2.25 4.5 6.75 9
1.25 1.25 1.25 1.25
44.44 44.44 44.44 44.44
Table 2 Mass, areal density and volume of scaled specimens. Scale size N
Sample mass n3 (kg)
Areal density n4 (kg/mm2)
Sample volume n3 (mm3)
Relative volume 64n3 (mm3)
1/4 1/2 3/4 1
0.16 1.279 4.314 10.27
0.359 5.752 29.120 92.035
86369.25 690954.03 2331969.86 5527632.27
1 8 27 64
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Fig. 1. GRE tubes for scale n = 1=4 , ½, 3=4 , and 1.
Fig. 3. Clamping Strips for scale n = 1=4 , ½, 3=4 and 1.
Fig. 2. Indenters for Scale n = 1=4 , ½, 3=4 , and 1.
Table 3 Indenter diameter, indentation speed and maximum indentation displacement for each scale. Scale size N
Indenter diameter 40n (mm)
Indentation speed 4n (mm/min)
Max. indentation 80n (mm)
1/4 1/2 3/4 1
10 20 30 40
1 2 3 4
20.00 40.00 60.00 80.00
size of the overall damaged section of tube wall. The damage area increases with respect to the load, indentation displacement and time. The images at the required time interval are extracted from the video. These were analysed with Adobe Photo Shop v 5.1 and damage area is measured with the inbuilt ‘‘Analysis’’ menu. A reference of known length is used to set the scale. This relates the number of pixels per unit area of the image. Once this relationship is established, outlined damage area is measured. Although this measurement neglects the effect of curvature because the damage area in the cylindrical wall is projected by a flat tilted mirror, however the effect of curvature is reduced as the indentation displacement increases. It increases the radius of curvature of the loaded surface. Also in this work, output parameters, including damage and delamination area are analysed comparatively hence effect of curvature, if any, is relative in all scales. 3.5.2. Measurement of delamination area Different authors tried to measure the total delamination area formed due to indentation by using different methods. For example
Table 4 Summary of parameters and scaling factors used. Parameter
Scaling factor
Tube diameter Average wall thickness Tube length Volume Areal density Indentation speed Indentation time Diameter of indenter Maximum indentation depth Clamp width Indentation force Energy Permanent deformation
n n n n3 n4 n 1 n n n n2 n3 n
Alderson and Evans [3] used non destructive back light and Zou et al. [17] used the destructive method where areas were measured by incremental grinding of the damage area and mapping of delamination area in every layer. A few very useful conclusions can be made from the work done by Zou et al. [17]. Delamination existed in all layers once delamination initiated, clearly marked by the initial load drop. It had delaminated areas of different sizes in every layer and had irregular shape and perimeter. The centre point of delamination in all layers was approximately point of indentation and delamination was spread in all directions in each layer. Delamination area overlaps in different layers. Keeping in mind these observations, processing of recorded video and images is found most effective in this current work. It is assumed that delamination in each layer has different tones of colour.
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Consider image in Fig. 4 which is reflected by a mirror placed inside the tube at indentation displacement = 24 mm, force = 4.98 kN, where the scale is n = 1/2 and image is taken at indentation time t = 12 min. This image presents overall damage area and it also highlights delamination in different layers. When this image is converted to 4 bit grayscale format shown in Fig. 5 subtle variations in grey tones enhance clarity on boundaries of different grey tones. When both images are compared side by side it is not difficult to outline the approximate boundaries of the delamination and measure the areas enclosed. The darkest grey spot is assumed as a delamination overlap in all layers. The area covered by pixels of the next darker grey tone is added on top of already measured darkest grey tone, to measure the area of the next bigger delamination area in the layer and so on. When all such areas for each layer are summed, it results in the total delamination area. Although this method results in approximate delamination growth rate but it is an effective and practical non destructive way. It is reliable than results from back light analysis carried out with the naked eye. There are number of short comings in this method. It is easier to use when the number of layers are only a few. As the number of layers grows, it becomes more challenging to analyse the images. Sometimes overlapping delamination areas pose difficulty in identification of delamination in every layer, particularly in the regions occupied by darker pixels. In that case, the sizes of such area have to be assumed and layers with missing clear outline of delamination are compensated by including equivalent areas in the total delamination. It can be identified by closely observing the images just before and after the image under analysis. A balanced back light projection is required otherwise the calculation of delamination area can be misleading. This method does not provide information as which layer has how much area of delamination but such information is not the aim of this work. As far as the area of delamination in every layer is calculated and the total delamination is evaluated, the delamination growth rate with respect to the input parameters can be calculated.
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Fig. 5. Grey scale of the same image shown in Fig. 4. This image format shows boundaries of different grey tones which are used to estimate delamination area in different layers.
4. Results and discussion 4.1. Force displacement curve The force displacement data for all specimens is obtained directly from the integrated MTSÒ software. The indentation test can be subdivided into three distinct phases for every specimen
Fig. 6. Specimen for scale n = 1 subjected to indentation.
Fig. 4. Damage in scale n = 1/2 at indentation time t = 12 min, force = 4.98 kN and indentation displacement = 24 mm.
as shown in Fig. 10. Small photos are added onto the plot to show state of the tube roughly at the given data points on the plot. Phase 1 can be related to the start of the test up to initiation of delamination, marked by first load drop clearly visible in all plots. During this phase each specimen behaves elastically [3]. In phase 2, force displacement relation has less steep gradient and damage grows continuously. Phase 3 basically consists of unloading path. Although the magnitude of force and indentation displacement is different but the trend and shape of the graph for each scale is very similar as compared in Fig. 11. The maximum indentation displacement for the biggest scale n = 1 is the highest and for the smallest scale n = 1/4 is lowest, essentially because of scaled maximum indentation displacement. Consequently peak force and force displacement gradients for both phase 1 and 2 are highest and lowest for n = 1 and n = 1/4 respectively. The unloading curve in all scales is smooth particularly as compared to their phase 2. The slope of unloading curve reduces as scale reduces however curves for all specimens converge to same graph near the end of
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Fig. 10. Typical force displacement plot labelled with three distinct phases.
Fig. 7. Specimen for n = 1/4 subjected to indentation.
Fig. 11. Force displacement curves for all specimens in same graph.
Fig. 8. Specimen for scale n = 1/2 and upward facing mirror reflecting the indentation growth.
Fig. 9. Specimen for scale n = 1/4 placed vertically after completion of indentation test. Damage on the inside of wall is visible.
unloading curve or origin of the plot. The indentation starts with deflection of the tube for the first few millimetres then the matrix crushing starts, however the force displacement relation remains linear. Sporadic Cracking noises are heard. The crushed matrix becomes visible if the internal wall surface is viewed. Then delamination initiates instantly and distinct load drop is observed in all scales, marking the end of phase 1. Continuous damage progression in the tube wall is observed with further indentation. Delamination growth at this stage is clearly visible particularly on the internal wall surface due to the strong back light on tube’s external surface. Louder and continuous cracking noises are heard throughout the loading cycle and cracks appear on the top surface of the tube. These cracks keep on growing for the rest of the loading path. Four shear cracks become distinctly visible on the top surface. These cracks start from the perimeter of the crushed area and grow outwards along the fibre direction. Cracking and fibre breakage noises become louder and frequent along with the growth of the delamination as the indentation continues. Further indentation makes the damage more complex as a mixture of all forms of damage including matrix cracks, interlaminar cracks, shear cracks, delamination and fibre breakage. Fibre bridging becomes clearer and a distinct rectangular area on the tube surface around indentation point becomes visible. The centre of this rectangular area is pushed downwards with four distinct shear cracks along the diag-
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onals of this rectangular area. Once the indenter reaches its maximum depth, it stops and starts moving upwards as unloading initiates, marking the end of phase 2 and beginning of phase 3. By now the cracking noise starts reducing and eventually become negligible as indenter moves towards its initial position. All specimens exhibit permanent deformation that is apparent from the unloading curve near the origin in Fig. 11. Though all specimens recover from most of their deflection, as the indentation test ends. 4.2. Scaled force displacement data Fig. 12 compares the scaled force vs scaled indentation displacement for all specimens, and shows that the force displacement behaviour scales quite well. There are lot of similarities including slope of initial gradient in the first phase, unload path and permanent deformation in each specimen. Scale 3/4 and 1 compare extraordinarily well and scale 1/4 and 1/2 are not as identical with the higher value of gradient in phase 2 and with peak load inversely proportional to the scale size. The consistency in scaled data for scale 3/4 and 1 has two distinct features. First the plots for these scales are more stable and secondly they have smaller gradient as compared to other two scales in phase 2. The stability of data is attributed to the size of indenter diameters. As indenter diameters for smaller scales is relatively close to the pattern unit of fibre net, they cause a change in local failure mode in upper ply resulting in unstable data relative to bigger scales. The closest example from the literature can be found in [31], where the authors made similar observation for sandwich structure with a top layer of woven carbon fibre reinforced epoxy. The reason for smaller gradient in phase 2 for bigger scales may also be related to relative size of the indenter to fibre net. For bigger scales it is observed that less force is required to cause same amount of damage (see Fig. 25) and delamination (see Fig. 30). It might be due to the fact that bigger size of indenter contributes towards more damage due to bigger contact area resulting in less force. As scale size reduces and consequently indenter diameter and contact area reduces, indenter causes local damage only. The indenter experiences more force from tube wall which has only localised and less damaged area as compared to bigger scales. This results in higher values of peak load and contributes to inconsistency of first half of scaled data for scale 1/4 and 1/2 in phase 3. Generally there is no previous data in literature to compare directly with this work, however current data is relatively stable and consistent as compared to other scaling studies, for example see [31], where data is compared
Fig. 12. Scaled force displacement curves for all scales compared on same graph.
for sandwich specimens subjected to indentation as well as impact type load. Similarly in [32], the authors studied impact behaviour of scaled FMLs and compared impact behaviour for four scales. Even in case of metals subjected to impact [33], the scaled force displacement data for different specimens exhibit certain inconsistency, however all such data collapse on same trend. The magnitude of variation in scaled data in Fig. 12 is of same order compared to these examples. The scaled data for initial gradient, Peak load and permanent deformation is listed in Table 5. The scaled slope of the initial gradients of all specimens is remarkably same and almost overlaps as shown in Fig. 12. End of phase 1 or first load drop occurs at higher force value for smaller scales (i.e. n = 1/4 and 1/2) as compared to bigger scales (n = 3/4 and 1). Gradients of phase 2 are highest for the smallest scale (n = 1/4) and lowest for (n = 1). This leads to the same observation for peak loads which are inversely proportional to the scale. Peak load at maximum displacement scales within the range of 4 kN. The gradients of scaled unloading curve is higher for smaller scales for at least first half of the unloading time, after which all unloading curves nearly converge on same graph. Smaller scales exhibit higher force value for the same displacement in the second half of unloading curve before intersecting Y axis of the graph, to exhibit permanent deformation. The permanent deformation scaling is not comparatively as good and Fig. 13 shows prediction of higher deformation in smaller scales i.e. n = 1/2 and n = 1/4. 4.3. Scaled energy displacement data The area under the force displacement loading curves obtained by trapezoid method is scaled and shown in Fig. 14. This estimation of energy dissipated by each specimen scales well. It can be argued that the force displacement curves presented in Figs. 11 and 12 are not exactly linear force displacement relations for complete loading and unloading paths, hence areas under the curves
Table 5 Scaled slope of the initial gradient (phase 1), peak load and permanent deformation for floor supported specimen. Scale
1/4
1/2
3/4
1
Slope Peak load (kN) Permanent Deformation (Dn) (mm) Normalised permanent deformation (Dn/D1)
628.80 29.78 7.48 1
653.40 27.63 7.34 0.98
608.40 25.20 6.13 0.82
635.70 25.48 5.90 0.79
Fig. 13. Permanent deformation normalised with respect to that of n = 1/4.
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Fig. 15. Damage initiation in a sample for scale n = 1/2.
Fig. 14. Scaled energy displacement curves for all scales compared on the same graph.
cannot be exact value of energy dissipated. However, scaled value of energy absorbed by the specimen is remarkably consistent corresponding to phase 1 of the force displacement curve after which the energy curves show diverging trends which reduces as the scale increases. Approximately above 30 mm of scaled indentation, smallest scale (n = 1/4) exhibit highest energy dissipation trend up to maximum indentation. Energy dissipation graphs for biggest scales (n = 1 and 3=4 ) are almost overlapping with lowest values as compared to other scales. 4.4. Scaled mode 2 energy release rate (GIIC) Davies and Zhang [25] presented an interesting relationship between (GIIC) mode 2 critical energy release rate and critical threshold force. In this relation, presented in Eq. (4), if one of these two parameters is known, other can be calculated.
Gc ¼
9P2c ð1 v 2 Þ 8p2 Et3
ð4Þ
where Gc is mode 2 critical energy release rate, Pc is the threshold force which initiates delamination, v is poisons ratio, t is thickness of the laminate and E is mean flexural modulus. Authors argued the usefulness of this simple relation over complex computational technique. Before applying this relation to the current work, it is evaluated for the work done by Zou et al. [17] where authors calculated energy release rate experimentally. Delamination is caused in 10 and 8 layer GRE tubes through indentation load. Energy absorbed to create delamination area is used to calculate average energy release rates of 2.03 kJ m2 and 1.54 kJ m2 for each set of 10 and 8 layered specimen respectively. Here if Eq. (4) is applied one can achieve GIIC values of 1.27 kJ m2 and 1.05 kJ m2 respectively which are not consistent with experimental results. Also these are average values which vary for different samples due to variation in delamination threshold load. Since value of the mean flexural modulus is not provided in [17] hence value of effective Young’s modulus is used instead for these calculations. Keeping in mind the effectiveness of this relation one can achieve conservative estimate of mode II energy release rate. In terms of applicability of this relation on the current work, threshold force can be measured to calculate GIIC. The video captured through mirror reflecting the damage growth from inside the specimens is very useful here to identify the threshold force. When the video is carefully watched the delamination initiation and growth can be easily identified
and exact threshold force can be obtained, corresponding to the time it initiates. Delamination initiation is shown in Fig. 15. By substituting this threshold force into Eq. (4), value for GIIC is calculated and results are presented in Table 6. Longitudinal elastic modulus provided by the manufacturer mentioned in an earlier section is used here for E in (4). GIIC value attained may not be accurate however it provides an estimation. These are quite similar for all scales except n = 1 which is approximately 30% higher as compared to the other scales. This suggests better performance against delamination by the biggest scale. It is worth mentioning that equation used here only involves thickness and ignores other geometric dimensions like curvature or length. 4.5. Damage growth rate w.r.t displacement, force and energy The damage area is plotted in relation to force applied, energy dissipated and time. Adobe Photoshop is used for image processing and damage area calculation. Its inbuilt ‘‘Analyses’’ menu which is meant to measure the area based on the number of pixels is utilised. The images of a scale n = 1/2 specimen at 6, 8, 10 and 12 min of indentation time are shown in Figs. 16–19. Damage area growth with respect to force, displacement, time and energy dissipated are presented in Figs. 20–23. Figs. 20 and 23 show damage area growth with respect to indentation displacement and time. Maximum indentation displacement is 4 cm and total test time is 40 min for this scale. Loading takes place in the first 20 min half and the specimen is unloaded in next half at same 2 mm/min speed. Fig. 23 presents
Table 6 Delamination initiation load and mode 2 energy release rate GIIC values. Scale
1/4
1/2
3/4
1
Scaled Delamination initiation Load (kN) GIIC [26]
19.20 0.86
13.65 0.87
11.28 0.89
11.26 1.18
Fig. 16. Damage at indentation displacement: 12 mm, force: 3.39 kN, energy dissipated: 22.48 J for scale n = 1/2 (t = 6 min).
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Fig. 17. Damage at indentation displacement: 16 mm force: 4.14 kN, energy dissipated: 37.55 J for scale n = 1/2 (t = 8 min).
Fig. 20. Damage growth with respect to indentation displacement for scale n = 1/2 during loading only.
Fig. 18. Damage at indentation displacement: 20 mm, force: 4.59 kN, energy dissipated: 55.14 J for scale n = 1/2 (t = 10 min).
Fig. 21. Damage growth with respect to force applied for scale n = 1/2 during loading only.
Fig. 19. Damage at indentation displacement: 24 mm, force: 4.98 kN, energy dissipated: 74.28 J for scale n = 1/2 (t = 12 min).
loading time up to maximum indentation depth. Both indentation displacement and time plots show similar trends as displacement speed is scaled. Damage prior to 5 min and 1 cm of indentation depth is mostly due to matrix crushing. After which, delamination initiates and damage growth rate increases. This rate further increases at around displacement of 1.8 cm and indentation time of 8 min. Similar behaviour is observed when damage area is plotted for force applied. As damage initiates just above 2 kN it continuously grows up till 4 kN, after which the gradient of the curve increases. Damage area and energy dissipation plot show similar trend with increase in damage growth rate around energy dissipation value of 0.05 kJ. It is interesting to see that when the damage area is scaled with a factor of n3 for all specimens it scales quite well. When plotted with respect to scaled indentation displacement and time, data for all scales collapse on the same graph. Since indentation speed and maximum indentation are scaled, both graphs are similar as
Fig. 22. Damage growth with respect to energy absorbed for scale n = 1/2 during loading only.
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Fig. 23. Damage growth with respect to indentation time for scale n = 1/2 during loading only.
Fig. 26. Scaled Damage area vs scaled energy for all scales. Scale factor for damage area is n3 and energy is n3.
Fig. 24. Scaled damage area vs indentation displacement for all scales. Scale factor for damage area is n3 and scale factor for displacement is n.
Fig. 27. Scaled Damage area vs time for all scales. Scale factor for damage area is n3 which is plotted with actual time as indentation speed is scaled.
specimen except n = 1. In specimen for n = 1/2 damage growth is consistent with other scales up to almost first half of the indentation depth and relatively smaller for the latter half. Similar trend can be seen in specimen for n = 3/4 where in later half of indentation depth the damage growth rate is the lowest amongst all scales. First half of the indentation depth is dominated by delamination after which it becomes a complex mixture of all types of damage. Shear cracks and layer splitting become dominant by the time indenter reaches maximum depth. The inconsistency in damage growth in the second half of indentation depth can be attributed to this complex damage where cracks particularly do not contribute much towards increase in the damage area. Generally the damage growth rate is similar in all scales with initial smaller growth rate increasing to higher gradient after scaled displacement approximately of 2.5 cm, as discussed in the previous section. 4.6. Scaled damage growth rate w.r.t displacement, force and energy Fig. 25. Scaled damage area vs scaled force for all scales. Scale factor for damage area is n3 and scale factor for force is n2.
shown in Figs. 24 and 27. The damage area in specimen for n = 1/4 and n = 1 coincide throughout indentation displacement and time however damage initiation is predicted to start early in all
The scaled damage area with respect to force applied is presented in Fig. 25. Damage area is scaled with factor of n3 and force is scaled with the factor of n2. Force data for all specimens is not scaled as well as that for time and there is a difference of around 5 kN between the smallest and the biggest scale. Damage initiates early in smaller scales as compared to n = 1 and generally scaled
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Fig. 28. Scaled delamination area vs indentation displacement for all scales. Scale factor for delamination area is n4 and scale factor for the displacement is n.
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Fig. 30. Scaled delamination area vs energy for all scales. Scale factor for delamination area is n4 and scale factor for the energy dissipated is n3.
Fig. 29. Scaled delamination area vs force applied for all scales. Scale factor for delamination area is n4 and scale factor for the force is n2.
Fig. 31. Scaled delamination area vs time for all scales. Scale factor for delamination area is n4 and time is not scaled as indentation speed is scaled.
force is higher in smaller scales. The graph of scaled damage area with respect to scaled energy dissipation is shown in Fig. 26. Here data for n = 1/4 and 1/2 scales well however the trend suggest relatively higher energy dissipation in them as compared to bigger scale n = 1. Plot for n = 3/4 coincides reasonably well with others for the first half of the indentation depth then it presents higher energy dissipation for smaller damage area.
with indentation depth and time. Specimen for scale n = 1/4 dissipated more energy for same delamination as compared to other scales. The same energy dissipation has produced highest delamination area in specimen for scale n = 3/4 in first half of the delamination depth and results of the second half for this specimen coincide well with scale for n = 1. The scaled energy dissipation to create delamination area is presented in Fig. 30. The general trend of data for all scales is similar to that of Fig. 29 which is due to the fact that energy values are obtained by area under force displacement graph. Specimen for scale n = 1/4 consumes the highest energy and data for rest of the scales obey scaling law quite well.
4.7. Scaled delamination rate w.r.t displacement, force and energy Image processing technique described in a previous section is employed to establish delamination growth rate and presented in Figs. 28–31. Delamination is scaled with factor n4 which is estimated by curve fitting. The scaled delamination areas with respect to indentation displacement and time are similar. Specimen for n = 1/2 scale exhibits highest delamination area for same indentation displacement and time particularly in the second half of indentation displacement. The scaled delamination area with respect to force for n = 1/4 shows the highest force values for the same delamination area as compared to that of the rest of the scales. Specimens for all other scales collapse quite well on the same trend for the whole of the indentation depth and the difference between force data reduces
5. Conclusions The effect of scaling are studied on GRE tubes subjected to quasi static indentation. Force displacement and energy displacement relation obey the scaling law quite well except for scales 1=4 and ½ as the data in Fig. 12 shows that the scale law for scales 3=4 and 1 are working well but not for the other scales. Force displacement consists of three phases for all scales. Force displacement gradient in initial elastic phase 1 scales remarkably very well. Phase 2 has lower force displacement gradients as compared to
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that of phase 1. This phase is relatively unstable due to damage growth but generally obeys the scaling law. The scaled phase 2 shows higher force values for smaller scales which reduces with scales and lower in two biggest scales i.e. n = 1 and 3/4. Unloading phase scales better in the second half of the unloading path closer to the end of the unloading cycle. Phase 3 is smooth as compared to phase 2. Energy displacement data collapse onto same graph when scaled particularly for the data corresponding to phase 1 of force displacement relation. The energy dissipated by the specimen for damage initiation growth is useful information for studying scaling effect on GRE tubes, subject to impact load which is being pursued by the authors as a future work. The damage area growth is calculated and presented with respect to displacement, force applied, energy dissipated and indentation time. Damage growth data collapses on the same graph when it is scaled with factor n3 and generally obeys scaling law with a few exceptions like force applied and energy dissipated is predicted higher for smaller scales. The delamination area is estimated with the help of image processing obtained with strong in situ back light. The non-destructive back lighting technique is improved with image processing to calculate the delamination area which collapses on the same graph when scaled with n4. Mode II critical energy release rate is measured with the help of delamination initiation force which is identified by post processing of videos captured for the tests. An already established relationship from available literature is used for this estimation. GIIC is around 0.85 kJ m2 for all scales except n = 1, for which it is 1.17 kJ m2. The thickness of the laminate is a major contributor here as it is the only geometric dimension considered in the formulation. It is concluded that this estimation is a conservative result based on rather simpler formulation. It can only be verified by destructive experimental results from the specimens indented up to phase I only, which is proposed by the authors as an extension of this work in the future. Acknowledgment Authors would like to acknowledge the financial support provided by the Petroleum Institute, Abu Dhabi under Grant for Project No. 12344. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.compstruct.2014. 06.021. References [1] Ochoa OO, Salama MM. Offshore composites: transition barriers to an enabling technology. Compos Sci Technol 2005;65(15–16):2588–96. [2] Tan TM, Sun CT. Use of statical indentation laws in the impact analysis of laminated composite plates. J Appl Mech 1985;52(1):6–12. [3] Alderson KL, Evans KE. Low velocity transverse impact of filament-wound pipes: Part 1. Damage due to static and impact loads. Compos Struct 1992;20(1):37–45.
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