Experimental analysis of transverse impact loading on composite cylinders

Accepted Manuscript Experimental analysis of transverse impact loading on composite cylinders Marcelo Leite Ribeiro, Dirk Vandepitte, Volnei Tita PII: DOI: Reference:

S0263-8223(15)00634-0 http://dx.doi.org/10.1016/j.compstruct.2015.07.088 COST 6669

To appear in:

Composite Structures

Please cite this article as: Ribeiro, M.L., Vandepitte, D., Tita, V., Experimental analysis of transverse impact loading on composite cylinders, Composite Structures (2015), doi: http://dx.doi.org/10.1016/j.compstruct.2015.07.088

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EXPERIMENTAL ANALYSIS OF TRANSVERSE IMPACT LOADING ON COMPOSITE CYLINDERS Marcelo Leite Ribeiro 1, Dirk Vandepitte2 and Volnei Tita1* 1

Department of Aeronautical Engineering, São Carlos School of Engineering, University of São Paulo, São Carlos, Brazil 2 Department of Mechanical Engineering - PMA division, KU Leuven, Leuven, Belgium

Abstract

The present study consists on experimental analyses of composite cylinders made by filament winding process, which are under transverse impact loading. The results are shown and discussed considering the influence of the stacking sequence as well as the total thickness of the cylinders. Thus, the results are normalized regarding the stiffness of each cylinder, and there are discussions based on identified damages, different graphics (force, displacement and strain vs. time), energy balance between impactor and coupons, as well as elastic and dissipated energy ratios and response delays for different strain gauges positions on the cylinders. Finally, guidelines for designing composite cylinders are presented considering the aspects addressed by the experimental analyses.

Keywords: experimental analysis; filament wound cylinders; transverse impact loading; impact damage.

*

Corresponding author: Phone +55 16 3373-8612; Fax +55 16 3373-9590. E-mail address: [email protected] (Volnei Tita)

1

INTRODUCTION

The usage of composite materials in aeronautical industry has increased considerably in the last decades, even in large civil aircrafts, where high stiffness and low weight are driving factors [1]. In terms of the structural shapes and component functionality, the intrinsic anisotropy of components allows achieving an optimal material performance. This characteristic is very strategic for the development of pressurized fuselages made of composite materials. By one side, design guidelines for composite vessels were established more than 40 years ago, and it is recommended to apply high safety factors in order to avoid failure, mainly for pressurized vessels. By other side, criteria for designing composite vessels, tubes or cylinders under transverse impact loadings are not established yet. And, scientific investigations in this field (e.g. [2]) can provide important contributions for helping the development of more safety products. Considering several causes of failure, impact loading damage is a special category, mainly for composite structures. Despite high strength in fiber direction, out-of-plane loads, for example transverse impact loads due to dropped tool, can cause relevant damages in composite materials. Thus, composite structures are generally more susceptible to impact damage than similar metallic ones. Impact loads can cause internal damages in composite laminates, which are usually not detected by visual inspection, because the damage is very small, e.g. matrix cracking, delamination and/or fiber breakage. However, this internal damage can produce a severe reduction of the strength [3], affecting the structural response. In addition, the initial kinetic energy of the impactor is an important parameter, as well as the mass and the impact velocity. As reported at the literature [3], a small mass with high velocity produces a different damage pattern than a large mass with low velocity, even if both impactors hit the target (composite structures) with equal kinetic energy. Normally, for low velocity impact, the damage starts with matrix cracking, which evolves to delaminations in interface of plies with different orientations. Hence, comparing metallic to composite structures, transverse impact loadings can cause not only more complex damage process, but also more complicated damage detection analyses [4]. Therefore, it is very strategic the investigation of transverse impact loadings on composite structures, mainly with curved geometry. Regarding the literature, it is possible to find many testing standards for flat composite coupons (tensile, compression, shear, bending, fatigue, impact, etc), such as the standards

ASTM D7136 [5] for composite and ASTM D5628 [6] for rigid plastics, which provide guidelines to perform the impact test on flat coupons. Moreover, several researchers have investigated impact problems on flat composite plates [7-11]. However, there are few scientific contributions about impact on curved composite structures [4, 12] compared to flat ones. And, there is no standard for impact on curved composite coupons. Hence, there is a reduced number of data, results and discussion about transverse impact on curved composite structures at the literature. In addition, it is not common to find guidelines for designing composite cylinders under transverse impact loadings, which can normally occur in service. Considering the scenario pointed above, in the present work, experimental analyses of transverse impact tests are carried out for carbon fiber filament wound cylinders. The results are shown and discussed regarding the influence of the stacking sequence as well as the total thickness of the cylinders, which are different due to the fiber orientations in the manufacturing process. Thus, the results are normalized regarding the stiffness of each cylinder. Finally, based on experimental results for three different lay-ups of the cylinders and two levels of energy, guidelines for designing composite cylinders are presented considering transverse impact loadings.

2

COMPOSITE CYLINDERS UNDER TRANSVERSE IMPACT TESTING

Filament winding was the manufacturing process used to produce composite cylinders with 150mm of length and 81mm of inner diameter (Figure 1). Table 1 shows three different layups for the composite cylinders, which were identified as type A with 3.49 mm thickness; type B with 3.25 mm thickness and type C with 3.54 mm thickness. For all types of cylinders, the value of thickness was calculated based on the average of all nominally identical specimens. It is observed that the total thickness is different for each type of cylinder. In fact, due to the filament winding process, the ply thicknesses depend on the fiber orientation as shown in Table 2. Therefore, even the cylinder has the same number of plies; the total thickness can be different, if the stacking sequences are not the same. One reason is the application of the same tension in the carbon fiber for all fiber orientations during the filament winding process. Another reason may be the difference of the temperature distribution along the coupon during the cure process. The problem is that for designing composite cylinders under transverse impact loadings, it is necessary to consider not only the stacking sequence, but also the total thickness as well as the thickness of each ply. Hence, in

the present work, the results for the three different types of cylinders are shown considering those effects, i.e. they are normalized by the respective cylinder stiffness. The transverse impact tests were carried out by using a drop tower apparatus. The displacement of the impactor were acquired using a light detector placed at the bottom of the drop tower apparatus (Figure 2), which measures the intensity of a Light Emitting Diode (LED) with 37kHz frequency, mounted on the impactor frame (Figure 3). Once the LED is stabilized (constant intensity), the distance measured by the light detector is proportional to ~ 1/ d 2 , where d is the distance between the LED and the light detector. The displacement is

set “zero” at the top point of the cylinder, when the impactor tough the specimen (Figure 3). Thus, the displacement measurements include the cylinder lateral compression and the coupon dart indentation, which is the result of elastic and inelastic strains, such as dent mark phenomenon. In fact, the drop tower apparatus consists of two guiding bars to guide the falling weight during the test (Figure 3(a)). These guiding bars limit the impact height to 1.8m. The cylinders were placed at the base of the tower (Figure 3(a) and (b)). The tests were performed using an aluminum round impactor head with a diameter of 16 mm. The round head avoids penetration into the coupon. According to the data recorder, it only saves the data for the first impact, not saving information due to the impactor rebouncing. A piezoelectric crystal, placed between the impactor head and impactor frame, was used as load cell for impact force acquisition (Figure 3(b)). In this work, the cylindrical coupons are positioned on a flat surface for impact test under energy level equal to 8.4 J (Figure 3(b)) and, in a “V-block” base, for impact test under energy level equal to 31 J (Figure 3(c)). The load cell was plugged to KistlerTM amplifier (model 5007), which has 11 bit data acquisition system with three channels for input data and sampling frequency set to 20 kHz. The strain measurements were performed by using HBM amplifier with 50 kHz sampling frequency capacity. The software was set to record samples with 20 kHz frequency and sample size equal to 64,000 points. The force measurements threshold was 50 N, and the displacement measurements started for the falling frame equal to 50 mm away from the coupon. The impact test equipment provides the information of force, displacement and time when the impactor and coupon interact during the impact event. Besides, bidirectional strain gauges were placed in two different points on the cylinders as shown by Figure 4. The strain gauges “1” (Figure 4) were placed as closer as possible to the impact region. The strain gauges “2” (Figure 4) were placed at the middle of cylinder axial distance in order to measure hoop and axial strains. It is worth to mention that strain gauges data were only available for one value

of impact energy (8.4 J). Finally, the nomenclature used to indicate the strain gauge position and the measured strain direction is shown by Figure 5.

3

EXPERIMENTAL ANALYSES

The experimental tests were carried out for two energy levels (8.4 J and 31 J) and three different lay-ups as shown by Table 3. It is important to highlight that for each impact test, it was analyzed in details different graphics: impact test force vs. time history; displacement vs. time history, strain vs. time history as well as the transferred energy. This procedure of analysis is quite important, because damage initiation can be detected in the force vs. time history, when a sudden force drop occurs due to stiffness reduction caused by damage growth. For example, it is possible to identify the delamination threshold by the first sudden force drop [13]. However, matrix cracking, which is the first type of damage due to impact loading, does not almost affect the laminate stiffness. Therefore, it is necessary to evaluate in details the other graphics.

3.1 Results for Cylinder Type A Figure 6 shows the force vs. time and displacement vs. time for 8.4 J impact tests on type A

cylinders (Table 1). For this cylinder type and energy level, it was performed four tests, but only two of them had presented good results. Figure 6 shows that the force histories or displacement histories are nearly identical for both coupons. The impact duration was around 15 ms, and the maximum displacement was around -6.7 mm (Table 4). The responses for 8.4 J impact tests on type A cylinders (Figure 6 and Figure 7) show that the force increases quickly close to 5.17 ms and then a sudden force drop occurs. The strain gauge SG 1 90 (Figure 7) for the same period of time (regardless a very small delay of 0.3 ms in the beginning of the impact event) had a similar behavior. Thus, the strain gauge shows a smoother curve and the strain drop was not so pronounced compared to the force drop. Also, the strain value is around minus 0.3% for the first force trough (at 5.9 ms). After that, in Figure 6, the force increases again and a new sudden drop occurs. Few milliseconds after (at 6.5 ms), the force starts to increase again, and the force peak reaches its maximum value

(about 1400 N). The strain gauge did not account for this peak. It is remarkable that the maximum registered force value (around 6.8 ms) did not correspond to neither the maximum displacement point (around 9.5 ms), nor the maximum strain as shown by the Figure 6. In fact, the maximum strain corresponds to the maximum displacement (from 9.3 ms to 9.9 ms) as shown by Figure 6 and Figure 7. This result is especially interesting for this energy level once damage or delaminations was not detected by C-Scan or visual inspections (Figure 13(a)). On the other hand, a linear elastic finite element simulation for the impact on cylinder for this energy level showed same behavior. And, this result will be discussed further in this work. A similar behavior of force peaks and valleys was presented by Minak et al. [12]. And, these peaks and valleys may indicate the initialization of delamination between several layers. After damage initiation, the delamination propagation can cause further oscillations in the force vs. time history, as observed by Schoeppner and Abrate [13] on flat coupons. It is possible to observe some differences of the strain measurements between coupons 1 and 3 in Figure 7. Most of those differences were due to small position errors of the coupon on the base of drop-tower, so the impactor did not hit the coupons exactly on the same place. Moreover, strains gauges locations were not exactly the same for each coupons. To improve the understanding of the results, the bending stiffness in axial and hoop direction was calculated for each cylinder type (A, B and C) using eq. (3) and eq. (4) [16].

Daxial

Ex h3  12(1  x  x )

(3)

E h3 12(1  x  x )

(4)

Dhoop 

Where Ex  1 a11 , E  1 a22 ,  x   a12 a11 ,   x   a12 a22 (for symmetric laminates [17]) and h is the total laminate thickness. The terms aij are the components of laminate compliance matrix. Table 4 shows the results for bending stiffness for the three cylinders layups. Regarding the axial direction, as expected, type A has the lowest stiffness. On the other hand, type A is the most stiffness in hoop direction. Also, the type A axial bending stiffness is only

20% of its hoop bending stiffness and this difference is not so pronounced for the other cylinders layups. Thus, type A cylinders have less stiffness to deform in axial direction and, in this direction, the response is driven by the epoxy matrix behavior. Table 5 summarizes the results for force, displacement and strain for type A cylinders under

impact energy equal to 8.4 J. This table also shows the force, displacement and strain results normalized by the type A hoop stiffness. Analyzing the response of all strain gauges in Figure 8, a small delay of 1.6 ms (regarding the normalized hoop stiffness value, 3.19x10-6 ms/Nmm) in the strain gauges “1” and “2” response is observed. This delay corresponds to the time that the stress wave takes to reach the strain gauge “2”. SG 2 0 did not measure any strain in the axial direction (Figure 4). For the other coupon, the measured strains behave in similar way. Another important parameter, which can be used in the analysis, is the amount of the energy transferred from the impactor to the coupon during the impact event, i.e. the impact energy is converted to elastic energy and to dissipated energy or absorbed energy (depending on the adopted reference). Tita et al. [7] performed these calculations for composite flat panels. In the present work, the authors have used the energy transferred ( Et ) from the impactor to the composite cylinders as shown by eq. (1). mv 2 m  v  t   Et  0  2 2

2

(1)

Where v  t  is the impactor speed at t ( t  0 ), m is the total impact mass (impactor, frame impactor and load cell) and v0 is the speed at the impact onset. The impactor speed can be obtained by using eq. (2). vt  t   v0 

t

1 Fexp dt m 0

(2)

Where Fexp is the measured experimental force. The first part of the time scale on Figure 9, from 4.5 ms until 9.0 ms, shows how the kinetic energy was transferred from the impactor to the coupon. The kinetic energy transfer occurs with same slope for all the coupons. The second part of the time scale, from 9.0 ms until the

end, shows the dissipated energy by the cylinder because of the failure mechanisms and the elastic energy, which is represented by the elastic vibrations. Thus, one part of the dissipated energy by the coupon is related to structural damping. Another part of the dissipated energy is related to the damage process (Figure 9) as matrix cracking, fiber breakage, delaminations and other failure mechanisms. For example, in the cylinder type A, a small dent mark is observed on the coupon like an indentation (inelastic deformation). As composite materials damping is the result of several sources such as matrix viscoelastic or microplastic (mainly under compression loads), relative fiber and matrix slippage and stacking sequence, which affects the laminate damping [14]. Besides, it is important to notice that a great range of frequencies are excited during impact tests, as Greif and Hebert [15] shown, the variation of laminate damping with frequency in which higher frequency leads to higher damping values. However, further experimental investigations would be required to testify those hypotheses. Although Figure 9 provides an estimation of the energy that the cylinder can absorb, it is not possible to evaluate neither the value of the energy used to trigger any damage process, nor the value dissipated by structural damping. It is further remarkable that damage in the impacted region was not detected by C-Scan analysis. Thus, it is concluded that the size of the damage in the cylinders type A is very small (e.g. matrix micro-cracks), considering 8.4 J of impact energy level. Table 6 shows the ratio between the elastic energy (transferred back to the impactor) and

dissipated energy (unrecoverable). Considering the lay-up [90 / 60 / 60 / 90 / 60 / 60 / 90]S (type A cylinders), impact energy level and impactor type, the elastic energy is around 130% of the dissipated energy for the coupon 1. The ratio between elastic energy (E e) and dissipated energy (Ed) is also calculated for coupons 2 and 3. Therefore, the average value for the elastic energy is around 1.33% of the dissipated energy (Table 6). In order to investigate the influence of the impact energy level, additional mass was attached on the impactor frame (Figure 3(a)) and the initial impactor height was increased, as well. This combination of mass and height leads to a potential energy around 31 J (the exact value is 30.65 J).

For type A cylinders under 31 J impact energy, the force vs. time and displacement vs. time results are shown in Figure 10. The graphics show that the repetitions produce almost identical results. The 31 J impact tests on Type A cylinders ( Figure 10) show that the force increases quickly close to 5.2 ms and then a sudden force drop occurs. After that, the force increases again and a new sudden drop occurs. The maximum force peaks (around 2500 N) occur from 7 ms to 7.5 ms for all coupons. Just after this interval, the force drops again. The maximum force peak happens around 0.0078 s and the maximum displacement at 11.1 ms (response delay of 3.3 ms). This trend repeats close to 8.7 ms of the impact event. A similar behavior was presented by Minak et al. [12]. This part of peaks and valleys may be an indication of the initialization of delaminations between several layers. After this period of time (from 4.7 ms to 8.7 ms), the delamination propagation can causes further oscillations in the force vs. time history, as observed by Schoppner and Abrate [13] for flat coupons. Also, Figure 10 shows that the maximum force level does not occur in the first peak and that the maximum force value does not occur in the same time of the maximum displacement. This same behavior was already observed for 8.4 J impact tests. Figure 11 shows the amount of energy that is transferred from the impactor to the coupons.

When compared to the type A coupons tested at 8.4 J, in this case (at 31 J), there is a different behavior, because during the initial phase, when the impactor loses part of the kinetic energy, the slope of the curve changes. Thus, first, the slope decreases at 23.8 J (8.19 ms) and, after (at 26 J), the slope increases again (Figure 11) to a value closer to the first slope. It is important to mention that this increase in the slope did not mean that the cylinder becomes stiffer, but how the rate of transferred energy increases. The rate of transferred energy decreases between 8 and 9 ms (Figure 11). This period of time corresponds to a force drop (Figure 10) after that (from 9 ms) the force increases again almost to the same level as before 8 ms. This corresponds to the new increase in the rate of energy. This phenomenon occurs because the impact energy level produces a lot of damage in the coupons. For example, matrix cracking and delaminations were visible as well as fiber failures, which were detected only near the impact area (Figure 12). The impactor also produces a small dent mark on the coupon (inelastic deformation). Table 7 shows the maximum peak force value for each coupon, the maximum displacement,

as well as those results normalized by the hoop stiffness. As observed in the 8.4 J impact

tests, there is no correlation between the maximum measured forces and the maximum displacement for the 31 J impact tests. The ratio between elastic energy and dissipated energy is around 0.98 (Table 8). Thus, for type A cylinders (31 J), more energy was dissipated than restored to the impactor. The main sources of unrecoverable energy consist not only on the failure mechanisms discussed earlier, but also on the material damping, e.g. viscoelastic behavior of the epoxy matrix and as mentioned before, composite damping is very complex and is highly dependent of the laminate layup [14] and frequency [15, 18]. Furthermore, the inelastic strains in the impact region (dent marks, Figure 12) also have an important effect on the impact response. The force vs. displacement diagrams showed several difficulties to extract some useful information due to its high noise pattern, for that reasons those graphics are not presented in this work.

3.2 Results for Cylinder Type B This section presents the results for type B cylinders. Figure 13(a) shows the C-Scan images of the axial line on the 8.4 J impacted region of type B cylinder, which has no indication of damage. The force vs. time history for type B cylinders (Figure 13 (b)) under 8.4 J impact energy shows a similar behavior as for type A cylinders under 8.4 J impact tests. This behavior indicates that the peaks and valleys are not really related to delaminations and to damage propagation. The effect of boundary conditions and the cylindrical geometry is pronounced compared to flat plates. Oscillations in the force vs. time may be caused by two sources: (1) the impactor excites the natural modes of the structure (impactor ringing); (2) the coupon reacts with flexural vibrations [5]. Apart of delaminations, the oscillatory behavior may also be explained by the wave propagation across the cylindrical structure and the cylinder modal vibrations. Figure 14 shows force vs. time history of a finite element simulation for type B cylinders

under 8.4 J impact test with no damage. The finite element analysis was carried out using ABAQUSTM/explicit. The composite cylinder was modeled using 4 node homogeneous reduced integration elements (S4R) and the steel base was modeled using a 4 node homogenous hexahedron elements. For the impactor, a 3 node discrete rigid element was used. The ABAQUSTM general contact algorithm regarding hard contact normal behavior was

used to model the interactions between the cylinder and the base as well as for the cylinder and the impactor head. More details about the finite element analyses can be found at Ribeiro et al. [19]. This simulation did not include any damage model and progressive failure analysis, i.e. there is only elastic response. The oscillatory behavior observed in the response of the structure is not related to any kind of damage. Moreover, the finite element simulations show that there is a response delay provided by the base (reaction force) compared to the input force provided by the impactor (Figure 14). When the impactor just hit the cylinder, the input force increases very fast, but there is no reaction in the support (base) yet. After 0.6 ms, the reaction force in the base increases, but the force in the impactor decreases. The next force peak of the impactor corresponds to a decrease of the base reaction force. This trend repeats until 3.0 ms of the impact event, after this time, there are no clear correlations. It indicates that there is a delay of the response between the support reaction and the impactor. The explanation of this effect is the velocity of the wave propagation from the impact point to the base. Laron et al. [20] showed the effect of the dynamic stress concentration due to boundary reflections and that the maximum and minimum hoop stress increases with the increases in fiber angle. Figure 15 shows the force vs. time and displacement vs. time for type B cylinders under 8.4 J

impact. The repetitions produced nearly identical results. The trend of peaks and valleys is similar to type A cylinder, but for type B cylinders the maximum peak force occurs closer to the maximum displacement data (around 0.6 ms) than type A cylinders (around 2.6 ms). The strain vs. time and force vs. time are shown in Figure 16. For cylinder type B under 8.4 J impact energy level, the maximum force and maximum displacement occur almost in the same point, as well as for the minimum strain (response delay around 0.48 ms) as shown by the Figure 16. Table 9 summarizes the results for force, displacement, strain, which are normalized by the

type B hoop direction stiffness for type B cylinders under 8.4 J of impact. The maximum displacement and the minimum strain are larger than the values presented by type A cylinders, as well as for the normalized force, displacement and strains. The force and displacement differences between type A and B cylinders are small (Table 9), on the other hand, when using the normalized values, those differences were increased. As observed for type A, the average response delay between strain gauge “1” and “2” for type B (8.4J) is around 1.5 ms (Figure 17). Table 10 shows the response delay between strain

gauge “1” and “2” for type B cylinders under 8.4 J impact test as well as those values normalized by the hoop stiffness. In this case, it was not possible to measure the delay for coupon 3. The average delay between the response of strain gauge “1” and “2” for type B are around 1.5 ms or 5.6 10-6 ms/Nmm for normalized value. Thus, the response delay for type B cylinders (under 8.4 J impact test) is 8% faster than type A cylinders (under 8.4 J impact test), but type B cylinders are less thick than type A cylinders, thus the stress wave has a smaller path to run in order to reach the strain gauge. On the other hand, type A cylinders have the normalized value almost 70% smaller than type B cylinders. Considering Figure 18, the impactor transfers its kinetic energy to the coupon in a single slope curve as observed for type A cylinder coupons. The differences between type A and type B cylinders are shown in the end of the impact event, once type B cylinders showed very small dissipated energy (Table 11). The elastic energy is around 7 (seven) times the dissipated energy (Table 11) for type B cylinders. Almost all energy is restored to the impactor and the impact does not cause any significant damage, confirming the measurements performed by C-scan analysis (Figure 13(a)). For type B cylinders, the results of 31 J impact tests (force vs. time and displacement vs. time) are shown in Figure 19. All experimental data show a good repeatability of the tests. At a same high level of impact energy, type A cylinders and type B cylinders show a similar pattern of peaks and valleys. However, the force peak intensity is higher for cylinder type B, due to the lay-up and the differences in the thickness of each layer. Delaminations, matrix damage and indentation marks (inelastic deformation) are detected for type B cylinders under 31 J impact tests, as well. Figure 19 shows that the maximum force peak value occurs around 6.7 ms and the maximum displacement occurs at 11.2 ms, which represents a response delay of 4.5 ms. This delay is caused not only by the damage process, but also by the lateral compression and dart indentation. Depends on the impact energy level, these three phenomena can be combined or not. Table 12 shows that the standard deviation for the displacement measurements is small. However, from 12.7 ms, it is observed that the displacement measurements start to diverge. For the force values, the standard deviation is 19.1% of the average value. Thus there is a considerable dispersion in the maximum peak value measurement. However, regarding the force history for all coupons, they are rather close. Again, there is no correlation between the

maximum measured force and displacement, and Table 12 also shows the normalized values for this test. Considering the energy balance between the impactor and the coupons for type B cylinders under 31 J impact tests, the impactor transfers its kinetic energy to the coupons in a bilinear way as shown by Figure 20. This behavior is different compared to type A cylinders (31 J). Regarding the restored energy, cylinder configuration B dissipates 77 % (in average) of the elastic energy (Table 13) Delaminations are observed between several plies (Figure 21) in some coupons. As expected, the delaminations occur between plies with different orientations [3] and extend from the impacted area to the free edges of the cylinder. Cylinder configuration B dissipates 25 % less energy than type A cylinders ( Table 13). Also, type B cylinders, for this impact condition, restore more energy than they dissipate.

3.3 Results for Cylinder Type C Figure 22 shows the force vs. time and displacement vs. time for type C cylinders under 8.4 J

impact test. In this case, as for type B 8.4 J impact test, the maximum force occurs almost at the same point (response delay of 0.4 ms). It is important to notice that even when there is no damage, it is possible to observe some delay between the maximum force peak and maximum displacement. As commented earlier, other phenomena can occur such as lateral compression and/or dart indentation. Also, the test results for all coupons show good repeatability. Figure 23 shows the strain vs. time and force vs. time results for type C cylinders under 8.4 J

impact. Unfortunately, only the strain-gauge data for coupons 1 and 3 were recorded. Maximum force peak occurs close to the minimum strain with a small response delay of 0.4ms. Table 14 shows the maximum force, maximum displacement and minimum strain values for the type C cylinders under 8.4 J impact, as well as the normalized values. Figure 24 shows the measured strains for type C cylinders (8.4 J). The delay of the response

between strain gauge “1” and “2” is around 1.6 ms (Figure 24) Table 15 shows the response delay between strain gauge “1” and “2” for all type C cylinders under 8.4 J impact, as well as the normalized values. Type C delay is similar to type A delay, also type A and type C cylinders have a similar wall thickness. On the other hand, the normalized delays show smaller values for type A than for type C.

As observed for type A and B cylinders under 8.4 J impact, the impactor transfers its kinetic energy in a constant slope line as shown by Figure 25. As identified for type B, type C cylinders restored almost all energy, once the elastic energy is around 10 times the dissipated energy (Table 16). Thus it is possible to consider that all energy was restored to the impactor and the impact did not cause any considerable damage, confirming the results obtained by Cscan analysis. Figure 26 shows the force vs. time and displacement vs. time results for type C cylinders under 31 J impact test. The same evaluation for type A and B cylinders is applicable for those cylinders. Besides, this configuration reaches the highest value of force peak over all cylinders type. Delaminations, matrix damage and indentation marks (inelastic deformation) are also detected for type C cylinders. Table 17 summarizes the results for coupons type C under 31 J impact. In this case, the

displacement standard deviation is 3.1%. Hence, this is the highest value, considering all cylinder responses. Also, the force standard deviation is 11.0% of the average value. Again, there is no correlation between maximum force and displacement, and Table 17 also shows the normalized values. Considering the energy balance between the impactor and the type C cylinders under 31 J impact tests, the impactor transfers its kinetic energy to the coupons in a bilinear way ( Figure 27). This behavior was identified for type B cylinders, but not for type A. The maximum

force peak occurs at 6.8 ms, the maximum displacement occurs at 11.7 ms and a response delay of 5.0 ms is observed. Regarding the restored energy, this cylinder configuration dissipates 77 % of the elastic energy (Table 18). This result is almost the same as evaluated for the type B configuration. As observed for the 31 J impact tests, the behavior of the kinetic energy balance (Figure 27) shows a pattern, which confirms the influence of the damage process on the energy transfer from the coupon to the impactor.

3.4 Comparison of Results The type C cylinders present higher load peaks (Table 19 and Table 20) than other cylinder types. However, for 8.4 J impact tests, the average values of forces were close to each other over all cylinder types. Regarding the hoop stiffness, normalized values for 8.4 J show that type A cylinders have the lowest value for normalized force (higher hoop stiffnes) and type B

and type C have almost the same normalized forces. On the other hand, for axial stiffness, type A cylinders have the highest normalized force value (lower axial stiffness), and type C have the lowest one due to the highest axial stiffness. Table 20 shows the values of the maximum load peak and the differences between type A and

the others. This table shows that for same impact energy, type C cylinders have an average force 40.7% higher than type A cylinders. And, type B cylinders have an average force 13.6% higher than type A. These differences did not occur for 8.4 J impact tests. Table 20 also shows the normalized results for 31 J impact test. Regarding the hoop stiffness, as type A cylinders have the highest hoop stiffness, the normalized force are the smallest one, and for this energy level, there is a significant difference for type B and C normalized force (22.3%). Despite the significant difference for type B and C normalized hoop stiffness force, for normalized axial stiffness, the difference between type B and C are considerable small (6.6%). As expected, type A cylinders have the highest normalized forces, regarding axial stiffness. The type B cylinders present the highest displacement values, in terms of absolute and normalized displacement for hoop and axial stiffness (Table 21 and Table 23). Also, type B cylinders are thinner than others. Thus, all comments addressed for Type A cylinders are also valid for Type C cylinders. Average results were rather close for both under 8.4 J and 31 J impact tests, but for normalized values (considering hoop and axial stiffness), the results differences are more pronounced. Hence, type B cylinders have the highest hoop stiffness normalized displacement; nevertheless it is not observed the same behavior for the axial stiffness normalized displacement under 8.4 J impact tests. Regarding 31 J impact tests normalized results, it is observed that type B cylinders have the highest normalized displacement considering both stiffness (hoop and axial). Additionally, the difference between type B and C are more significant regarding the axial stiffness (26%). And type A normalized results are significantly different than for the others considering both normalized stiffness (hoop and axial) displacement (Table 23). The strain data, test results and normalized values, are show in Table 22. The test results show the smallest absolute values for type A. By the other side, type C shows the highest absolute ones due to the lowest number of fibers in 90º direction. Regarding the hoop stiffness normalized results, type C and type B show similar results and both are significantly

higher than type A. For axial stiffness normalized value, type A also shows the highest values. Regarding the damaged area, type A cylinders are more damaged than others, mostly in the internal surface. The other cylinders types do not show damage in the internal surface. Delaminations, matrix damage and indentation marks are also detected for type C cylinders. The response delay in type A cylinders has the lowest value and type C produces the highest one. Type A has the lay-up with fiber angles close to 90o, which are stiffer for hoop stress than type B and C. Besides, type C has only two layers with 90o, which means that it is less stiff for hoop stress. Therefore, the stress wave propagates faster in type A than type B and C in the hoop direction. Table 24 shows the average delay value between the strain gauges “1” and “2” for cylinders type A, B and C. This table also shows the normalized results. The delay between the different cylinders types are more related to the layup thickness, once type A and C shows almost the same delay and they have almost the same thickness. Moreover, type B shows the smallest delay, and type B cylinders are thinner. Additionally all strain gauges are attached on 90º ply. On the other hand, the normalized values show a different scenario, type B presents the highest value, not so different from type C, but type A shows very small value. Considering the average values of elastic to dissipated energy ratio for 8.4 J impact for all cylinders types (Table 25), the difference between type B, C and type A is very significant. Type B and C cylinders restore almost all energy to the impactor with almost no damage. On the other hand, type A cylinders restore much less energy due to internal damage process, which was not detected by the C-scan analysis. Finally, there is a comparison between the average values of elastic dissipated energy ratio for 31 J impact tests (Table 26). The difference between type B, C and A is not so pronounced as shown by 8.4 J impact test. Under 31 J energy level, type B and C cylinders restore more energy to the impactor than they dissipate, and type A cylinders restore less energy to the impactor. All cylinder types show several failure mechanisms after the impact under 31 J.

4

CONCLUSIONS

As expected, the results of impact tests on a set of cylinders show that the stacking sequence is a very important parameter for cylinder impact behavior. Type A cylinders have different behavior than type B or C for the two energy level tested. Type A cylinders lay-up have the most significant difference regarding the bending stiffness in axial and hoop direction. On the other hand, for type B and C lay-ups, this difference is not so pronounced. Thus, type A cylinders have the hoop direction response driven by fibers, but axial direction response driven by the matrix. Type A cylinders under 8.4 J impact test had shown a similar response as for high energy impact tests, i.e. the delay among the maximum force peak and the maximum displacement and the relative amount of absorbed energy. On the other hand, C-scan and visual inspection did not detect any damage. Cylinders type B and C did not dissipate a considerable amount of energy for 8.4 J impact test, and the delay between the maximum force value and maximum displacement (or minimum strain) was small and much lower than for type A cylinders. Thus, the maximum force and displacement occur almost in the same time and this is the expected behavior for the undamaged structure. Additionally, the normalized values for force and displacement showed the same behavior, i.e. the normalized values between type B and C are similar and both are different from type A results. The delay between the strain gauge responses have shown to be more related to the layup thickness than for other parameter. It is reasonable as for all cylinders types, the strain gauges are attached on a 90º ply. Considering the 31 J impact test, all coupons showed several damage types, as delaminations, matrix cracking and dent mark. Also, for all types, the off-set between the maximum force and maximum displacement is considerable. Therefore, this delay can be also regards as a damage indicator, once it was not detected for the elastic response obtained from 8.4 J impact tests (cylinders type B and C). Furthermore, for 31 J impact energy, the kinetic energy were transferred from the impactor to the cylinders in at least two slope curves, this change of slope indicates that a more severe type of damage takes place. It is important to highlight that this behavior were not detected for all cylinders types under 8.4 J impact test. For those cases, the impact energy was transferred to the cylinders in one slope curve. Regarding the displacements, which are the

result of lateral cylinder displacement and dart indentation, they were very similar for all types, considering both tested energy level. Regarding the normalized force results, there are differences between all cylinders types, but the differences are more considerable between type C and B when compared to type A. This is also valid for the impactor displacement. The effect of layup on composite cylinders impact behavior has been shown and some design guidelines could be extracted from those results. For example, if the impact strength is desired, it would be more effective to have a layup similar to type B and C cylinder. By the other side, if it is desirable to absorb more impact energy, it is better to use a layup similar to type A, which can absorb much more impact energy than the other layups and still have almost no damaged for relative low energy level. Finally, normalized values present a valuable way to design composite cylinders as they can highlight some particularities, which are not possible to detect using only test data. For example, the normalized force for 8.4 J are similar for type B and C, but rather different for type A. Moreover, regarding the force test results, there are not noticeable difference between the cylinders types, but the type A cylinder showed very different behavior than others.

5

ACKNOWLEDGEMENTS

The authors are grateful for the support from CTM (Navy Technological Center – Brazil), São Paulo Research Foundation (FAPESP process number: 2009/00544-5), National Council of Research (CNPq process numbers: 135652/2009-0 and 208137/2012-2), FAPEMIG for partially funding the present research work through the INCT-EIE, AFOSR and US-Army (Grant/Contract Number: FA9550-10-1-0011) as well as Arenberg Doctoral School for the university cooperation and financial support.

6

REFERENCES

[1] K.V. Williams, R. Vaziri and A. Poursartip, "A physically based continuum damage mechanics model for thin laminated composite structures", International Journal of Solids and Structures, vol. 40, n. 9, pp. 2267-2300, 2003.

[2] S. Kobayashi and M. Kawahara, "Effects of stacking thickness on the damage behavior in CFRP composite cylinders subjected to out-of-plane loading", Composites Part A: Applied Science and Manufacturing, vol. 43, n. 1, pp. 231-237, 2012. [3] S. Abrate, Impact on composite structures, Cambridge University Press, 1998. [4] L. Ballère, P. Viot, J.-L. Lataillade, L. Guillaumat and S. Cloutet, "Damage tolerance of impacted curved panels", International Journal of Impact Engineering, vol. 36, n. 2, pp. 243-253, 2009. [5] ASTM D7139, Standard Test Method for Measuring the Damage Resistance of a Fiber-Reinforced Polymer Matrix Composite to a Drop-Weight Impact Event, 2007. [6] ASTM D5628, Standard Test Method for Impact Resistance of Flat, Rigid Plastic Specimens by Means of a Falling Dart (Tup or Falling Mass), 2007. [7] V. Tita, J. Carvalho and D. Vandepitte, "Failure analysis of low velocity impact on thin composite laminates: Experimental and numerical approaches", Composite Structures, vol. 83, n. 4, pp. 413428, 2008. [8] S. Abrate, "Modeling of impacts on composite structures", Composite Structures, vol. 51, n. 2, pp. 129-138, 2001. [9] A.P. Christoforou and A.S. Yigit, "Scaling of low-velocity impact response in composite structures", Composite Structures, vol. 91, n. 3, pp. 358-365, 2009. [10] C. Menna, D. Asprone, G. Caprino, V. Lopresto and A. Prota, "Numerical simulation of impact tests on GFRP composite laminates", International Journal of Impact Engineering, vol. 38, n. 8, pp. 677-685, 2011. [11] M. Quaresimin, M. Ricotta, L. Martello and S. Mian, "Energy absorption in composite laminates under impact loading", Composites Part B: Engineering, vol. 44, n. 1, pp. 133-140, 2013. [12] G. Minak, S. Abrate, D. Ghelli, R. Panciroli and A. Zucchelli, "Residual torsional strength after impact of CFRP tubes", Composites Part B: Engineering, vol. 41, n. 8, pp. 637-645, 2010. [13] G. Schoeppner and S. Abrate, “Delamination threshold loads for low velocity impact on composite laminates”, Composites Part A: Applied Science and Manufacturing, vol. 31, n. 9, pp. 903-915, 2000. [14] V. Tita, J. Carvalho and J. Lirani, “A procedure to estimate the dynamic damped behavior of fiber reinforced composite beams submitted to flexural vibrations”, Materials Research, vol. 4, n. 4, 315-321, 2001.

[15] R. Greif and B. Hebert, “Experimental techniques for dynamics characterization of composite materials”, Advances in Experimental Mechanics and Biometrics-ASME, vol. 29, pp. 83-97, 1992. [16] J.R. Vinson and R.L. Sierakowski, “The behavior of structures composed of composite materials”, Martinus Nijhoff Publishers, 1987. [17] C.T. Herakovich, Mechanics of fibrous composites, John Wiley & Sons, 1997. [18] K. Koo and I. Lee, “Dynamic behavior of thick composite beams”, Journal of reinforced plastics and composites, vol 14, pp. 196-210, 1995. [19] M.L. Ribeiro, T. Martins, R.A. Angélico, D. Vandepitte and V. Tita, “Progressive failure analysis of low energy impact on carbon fiber filament winding cylinders”, Proceedings of 10th World Congress on Computational Mechanics (X WCCM), 2012.

EXPERIMENTAL ANALYSIS OF TRANSVERSE IMPACT LOADING ON COMPOSITE CYLINDERS Marcelo Leite Ribeiro 1, Dirk Vandepitte2 and Volnei Tita1* 1

Department of Aeronautical Engineering, São Carlos School of Engineering, University of São Paulo, São Carlos, Brazil 2 Department of Mechanical Engineering - PMA division, KU Leuven, Leuven, Belgium

FIGURES

Figure 1: Cylinder manufactured by filament winding process

Figure 2: Displacement measurement principle for the impact tests.

(b)

(a)

(c)

Figure 3: (a) Drop tower apparatus, (b) Test coupon placed at the drop tower base (8.4 J tests); (c) Test schema using V-block at the base (31 J tests)

Figure 4: Strain gauges position on cylindrical coupons.

Figure 5: Strain gauge nomenclature.

Figure 6: Type A (8.4 J) - force vs. time and displacement vs. time.

Figure 7: Type A (8.4 J) force vs. time and strain vs. time for strain gauge 1 90.

Figure 8: Type A - strains for coupon 1.

Figure 9: Kinetic energy balance between impactor and type A coupons for 8.4 J impact test.

Figure 10: Type A (31 J) - force vs. time and displacement vs. time.

Figure 11: Kinetic energy balance between impactor and type A coupons for 31 J impact test.

Figure 12: 31 J impacted area for type A cylinder.

(a)

(b)

Figure 13: Type B cylinders (8.4 J impact energy): (a) C-Scan image; (b) force vs. time.

Figure 14: Force vs. time history measured in the impactor and in the base for type B cylinders - 8.4J impact energy.

Figure 15: Type B (8.4 J) - force vs. time and displacement vs. time.

Figure 16: Type B (8.4 J) - force vs. time and strain vs. time.

Figure 17: Type B - strains for coupon 1.

Figure 18: Kinetic energy balance between impactor and type B coupons for 8.4 J impact test.

Figure 19: Type B (31 J) - force vs. time and displacement vs. time.

Figure 20: Kinetic energy balance between impactor and type B coupons for 31 J impact test.

Figure 21: Delamination in the cylinder free edge – type B cylinder (31 J).

Figure 22: Type C (8.4 J) - force vs. time and displacement vs. time.

Figure 23: Type C (8.4 J) - force vs. time and strain vs. time.

Figure 24: Type C coupon 3 strains

Figure 25: Kinetic energy balance between impactor and type C coupons for 8.4 J impact.

Figure 26: Type C (31 J) - force vs. time and displacement vs. time

Figure 27: Kinetic energy balance between impactor and type C coupons for 31 J impact.

Table 1. Cylinder lay-ups and average thickness. Identification Type A Type B Type C

Lay-up

Thickness [mm] 3.49

[90 / 60 / 60 / 90 / 60 / 60 / 90]S [90 / 30 / 30 / 90 / 30 / 30 / 90]S [90 / 30 / 30 / 60 / 60 / 30 / 30]S

3.25 3.54

Table 2. Ply thicknesses for each cylinder type. Type A Orientation

Type B Thickness [mm]

Orientatio n

Type C Thickness [mm]

Orientatio n

Thickness [mm]

90°(*)

0.29

90°(*)

0.28

90°(*)

0.25

60°

0.29

30°

0.245

30°

0.25

-60°

0.29

-30°

0.245

-30°

0.25

90°

0.25

90°

0.24

60°

0.26

60°

0.25

30°

0.245

-60°

0.26

-60°

0.25

-30°

0.245

30°

0.25

90°

0.25

90°

0.205

-30°

0.25

90°

0.25

90°

0.205

-30°

0.25

-60°

0.25

-30°

0.245

30°

0.25

60°

0.25

30°

0.245

-60°

0.26

90°

0.25

90°

0.24

60°

0.26

-60°

0.23

-30°

0.225

-30°

0.25

60°

0.23

30°

0.225

30°

0.25

90°(**)

0.17

90°(**)

0.16

90°(**)

0.21

Average

0.249

Average

0.232

Average

0.249

per layer (*) outer layer; (**) inner layer.

per layer

per layer

Table 3. Experimental tests. Cylinder type Type A Type B Type C

Number of tests at 8.4 J 4 4 4

Number of tests at 31 J 4 4 4

Table 4. Axial and radial (hoop direction) bending stiffness. Difference Cylinder Type

[Nmm]

Type A Type B Type C

104500 228010 301420

Daxial

Difference

DTypei  DType A DTtype A

Dhoop

100

[Nmm]

118% 188%

DTypei  DType A DTtype A

509920 276750 298090

100

46% 42%

Table 5. Maximum force, displacement and strain for type A cylinders (8.4 J).

Coupon 1 3 Average

Max. Maximum force force peak/Dhoop peak [N] [1/mm] 1430.7 0.0028 1396.5 0.0027 1413.6 0.0028

Maximum Maximum displacement displacement/Dhoop [mm] [1/N] 7.0 7.5 7.2

1.37E-05 1.47E-05 1.42E-05

Minimum Minimum strain strain/Dhoop [%] [1/Nmm] -0.805 -0.854 -0.829

Table 6. Ratio between elastic energy (Ee) and dissipated energy (Ed) – Type A cylinders. Coupon 1 3 Average

Ee/Ed 1.34 1.32 1.33

-1.58E-06 -1.67E-06 -1.63E-06

Table 7. Results summary for type A cylinders (31 J).

Coupon

2388.9 2319.3 2563.5 2270.5 2385.6

Maximum force peak/Dhoop [1/mm] 0.0047 0.0045 0.0050 0.0045 0.0047

128.2

0.0003

Maximum force peak [N]

1 2 3 4 Avarage Standard Deviation

16.0 16.2 16.3 16.3 16.2

Maximum displacement/Dhoop [1/N] 3.14E-05 3.18E-05 3.20E-05 3.20E-05 3.18E-05

0.2

2.77E-07

Maximum displacement [mm]

Table 8. Ratio between elastic energy (Ee) and dissipated energy (Ed) – Type A cylinders (31 J). Coupon 1 2 3 4 Average

Ee/Ed 0.84 1.11 0.97 0.97 0.98

Table 9. Maximum force, displacement and strain for type B cylinders (8.4 J).

Coupon 1 2 4 Average Standard Deviation

Max. Maximum Maximum Maximum force force displacement displacement/Dhoop peak/Dhoop peak [N] [mm] [1/N] [1/mm] 1342.8 0.0049 7.4 2.67E-05 1333.0 0.0048 7.6 2.75E-05 1228.0 0.0044 8.0 2.89E-05 1301.3 0.0047 7.7 2.77E-05 63.6

0.0002

0.3

Minimum strain [%]

1.10E-06

Table 10. Delay between strain gauge “1” and “2” – Type B cylinders (8.4 J). Coupon

Delay [ms]

1 2 4 Average

1.5 1.6 1.5 1.5

Delay/Dhoop [ms/Nmm] 5.42E-06 5.78E-06 5.42E-06 5.54E-06

Minimum strain/Dhoop [1/Nmm]

-1.031 -1.025 -1.010 -1.022

-3.73E-06 -3.70E-06 -3.65E-06 -3.69E-06

0.018

3.91E-08

Table 11. Ratio between elastic energy (Ee) and dissipated energy (Ed) – Type B cylinders (8.4 J). Coupon 1 2 4 Average

Ee/Ed 6.64 6.01 6.59 6.41

Table 12. Results summary for type B cylinders (31 J).

Coupon 1 2 3 4 Avarage Standard Deviation

Maximum force peak [N] 2319.3 2441.4 2612.3 3466.8 2710.0

Maximum force peak/Dhoop [1/mm] 0.0084 0.0088 0.0094 0.0125 0.0098

518.7

0.0019

16.4 16.4 16.6 16.2 16.4

Maximum displacement/Dhoop [1/N] 5.93E-05 5.93E-05 6.00E-05 5.85E-05 5.93E-05

0.1

5.90E-07

Maximum displacement [mm]

Table 13. Ratio between elastic energy (Ee) and dissipated energy (Ed) – Type B cylinders (31 J). Coupon 1 2 3 4 Average

Ee/Ed 1.30 1.33 1.23 1.44 1.30

Table 14. Maximum force, displacement and strain for type C cylinders (8.4 J).

Coupon 1 2 3 4 Average Standard Deviation

Max. Maximum Maximum force force displacement peak/Dhoop peak [N] [mm] [1/mm] 1401.4 0.0047 7.1 1335.4 0.0045 7.2 1411.1 0.0047 7.6 1462.4 0.0049 7.6 1402.6 0.0047 7.4 52.2

0.0002

Minimum Maximum Minimum strain/Dhoop displacement/Dhoop strain [1/Nmm] [1/N] [%]

0.3

2.38E-05 2.42E-05 2.55E-05 2.55E-05 2.47E-05

-1.009 -1.205 -1.107

-3.38E-06 -4.04E-06 -3.71E-06

8.82E-07

-

-

Table 15. Delay between strain gauge “1” and “2” – Type C cylinders (8.4 J). Coupon

Delay [ms]

1 2 3 4 Average

1.6 1.6 1.5 1.7 1.6

Delay/Dhoop [ms/Nmm] 5.37E-06 5.37E-06 5.03E-06 5.70E-06 5.37E-06

Table 16. Ratio between elastic energy (Ea) and dissipated energy (Ed) – Type C cylinders (8.4 J). Coupon 1 2 3 4 Average

Ee/Ed 10.84 6.59 8.21 15.69 10.33

Table 17. Maximum force and displacement for type C cylinders (31 J).

Coupon 1 2 3 4 Avarage Standard Deviation

Maximum force peak [N] 3393.6 3808.6 2905.3 3320.3 3356.95

Maximum force peak/Dhoop [1/mm] 0.0114 0.0128 0.0097 0.0111 0.0113

369.98

0.0012

15.5 15.8 15.9 16.7 15.98

Maximum displacement/Dhoop [1/N] 5.20E-05 5.30E-05 5.33E-05 5.60E-05 5.36E-05

0.51

1.72E-06

Maximum displacement [mm]

Table 18. Ratio between elastic energy (Ea) and dissipated energy (Ed) – Type C (31 J). Coupon 1 2 3 4 Average

Ee/Ea 1.76 1.05 1.18 1.46 1.30

Table 19. Maximum force peak (8.4 J). Difference

Cylinder Type

Maximu m peak load [N]

VTypei  VType A

Type A Type B Type C

1368.4 1301.7 1402.6

-4.90% 2.50%

VTtype A

Maximum 100 force peak/Dhoop [1/mm] 0.0028 0.0047 0.0047

Difference

VTypei  VType A VTtype A 69.61% 69.73%

Maximum 100 force peak/Daxial [1/mm] 0.0135 0.0057 0.0047

Difference

VTypei  VType A VTtype A 57.81% 65.60%

100

Table 20. Maximum force peak (31 J). Difference

Cylinder Type

Maximum peak load [N]

VTypei  VType A

Type A Type B Type C

2385.6 2710.0 3356.9

13.60% 40.72%

VTtype A

Maximum 100 force peak/Dhoop [1/mm]

Difference

VTypei  VType A VTtype A

0.0047 0.0098 0.0113

Difference

Maximum 100 force peak/Daxial [1/mm]

109.31% 140.72%

VTypei  VType A VTtype A

0.0228 0.0119 0.0111

100

47.94% 51.21%

Table 21. Maximum displacement (absolute values) for 8.4 J. Difference

Cylinder Type

Maximum displacement [mm]

VTypei  VType A

Type A Type B Type C

7.2 7.7 7.4

6.94% 2.78%

VTtype A

Difference

VTypei  VType A

Maximum 100 displacement/ Dhoop [1/N]

VTtype A

1.42E-05 2.77E-05 2.47E-05

94.84% 74.01%

Difference

Maximum displacement/ 100 Daxial [1/N]

VTypei  VType A

6.94E-05 3.36E-05 2.45E-05

51.53% 64.73%

VTtype A

100

Table 22. Minimum strain (strain gauge “1” – 90o) for 8.4 J. Difference

Cylinder Type

Minimum strain [%]

Type A Type B Type C

-0.761 -1.022 -1.107

VTypei  VType A VTtype A 34.30% 45.47%

Difference

Minimum 100 strain/Dhoop [1/Nmm] -1.63E-06 -3.69E-06 -3.71E-06

VTypei  VType A VTtype A 127.01% 128.29%

Difference

Minimum 100 strain/Daxial [1/Nmm] -7.94E-06 -4.48E-06 -3.67E-06

VTypei  VType A VTtype A 43.53% 53.73%

100

Table 23. Maximum displacement (absolute values) for 31 J. Difference Cylinder Type

Maximum displacement [mm]

VTypei  VType A

Type A Type B Type C

16.2 16.4 16.0

1.23% 1.23%

VTtype A

Difference Maximum

VTypei  VType A

Dhoop [1/N]

VTtype A

100 displacement/ 3.18E-05 5.93E-05 5.36E-05

Difference Maximum

VTypei  VType A

Daxial [1/N]

VTtype A

1.55E-04 7.19E-05 5.30E-05

53.60% 65.81%

displacement/ 100

86.53% 68.69%

100

Table 24. Delay between strain gauges for 8.4 J.

Cylinder Type

Delay [ms]

Type A Type B Type C

1.63 1.50 1.60

Difference

Difference

Difference

VTypei  VType A Delay/D hoop 100 [ms/Nmm] VTtype A

VTypei  VType A Delay/D axial 100 [ms/Nmm] VTtype A

VTypei  VType A

7.98% 1.84%

3.20E-06 5.42E-06 5.37E-06

69.56% 67.91%

1.56E-05 6.58E-06 5.31E-06

Table 25. Energy ratio for 8.4 J. Difference Cylinder Type

Ee/Ed

VTypei  VType A VTtype A

Type A Type B Type C

1.51 6.98 10.33

100

362.2% 584.1%

Table 26. Energy ratio for 31 J. Difference Cylinder Type

Ee/Ed

VTypei  VType A VTtype A

Type A Type B Type C

0.98 1.30 1.30

32.6% 32.6%

100

VTtype A

57.82% 65.97%

100