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Split Hopkinson pressure bar testing of 3D woven composites
Composites Science and Technology 71 (2011) 1196–1208
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Split Hopkinson pressure bar testing of 3D woven composites M. Pankow a, A. Salvi a, A.M. Waas a,⇑, C.F. Yen b, S. Ghiorse b a b
Composite Structures Laboratory, Department of Aerospace Engineering, University of Michigan, 1320 Beal Street, Ann Arbor, MI 48109-2140, USA Army Research Laboratories, Aberdeen Proving Ground, MD, USA
a r t i c l e
i n f o
Article history: Received 23 November 2010 Received in revised form 1 March 2011 Accepted 24 March 2011 Available online 2 April 2011 Keywords: B: Impact behaviour E: Braiding B: Mechanical properties A: Textile composites B: Delamination B: Plastic Deformation
a b s t r a c t Results from a series of split Hopkinson pressure bar (SHPB) tests on 3D woven tetxile composites (3DWC) are presented. These tests were done to determine the rate dependent compression response of 3DWC. Three different configurations of the 3DWC, corresponding to compression response in the plane of the material and through-the-thickness direction (out-of-plane) were studied. The rate dependent responses were compared against quasi-static test results and it was found that 3DWC showed an increase in strength in all three directions studied, however, accompanied by a transition in the failure mechanism. The in-plane orientations showed the largest increase in (about 100%) strength at the elevated rates of loading. A follow-on paper provides finite element based results that correspond to the experimental results presented here. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Early uses of laminated composite materials revealed that delamination was one of the major failure mechanisms of the material [1]. In order to prevent this mode of failure from occurring, different types of through-the-thickness reinforcement have been introduced. One such technique is 3D weaving, where fiber tows are woven together in a complex 3D architecture to create one preform [2]. 3DWC materials are relatively new and investigations to characterize the deformation response of the material, other than simple quasi-static mechanical tests, are ongoing [3]. New applications of the material have lead to considering complex loading scenarios in-service, which include periods of high rates of loading. Historically, the split Hopkinson pressure bar method [4], has been used in conjunction with homogeneous and isotropic materials to obtain information on the effect of strain rate on yield strength, for example in metals. In the present study, the SHPB test is adopted to examine the deformation response of 3DWC when subjected to high strain rates. Since the fiber tows (that consists of fibers and matrix) and the SC15 polymer matrix are the basic constituents of the 3DWC, separate studies have been carried out to obtain the high rate response of these constituent materials [5]. SHPB testing of 2D in-plane woven S-2 glass fiber with SC-15 matrix composites has been shown to exhibit a rate dependency [6]. Additionally, studies of off-axis layered composites have been ⇑ Corresponding author. Tel.: +1 734 764 8227; fax: +1 734 763 0578. E-mail address: [email protected] (A.M. Waas). 0266-3538/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2011.03.017
reported in [7]. SHPB testing of 3DWC has also been done previously [8,9], although in these studies the authors simply assume equilibrium in the specimen, even though a constant strain rate is not achieved during the test duration. Other researchers have examined the tensile rate dependent properties of woven composites showing and explaining the rate-dependent behavior due to the reinforcement [10]. A modified Hopkinson bar has been used to perform high strain rate punch shear tests [11], showing the rate dependency of the 3DWC. In this paper, results from compression SHPB testing of 3DWC are reported along with quasi-static test results for comparison purposes. High speed Digital image correlation (DIC), a full field strain measurement technique, has been used to determine the strain history on the side surface of the specimens that have a rectangular cross-section. These measurements are used to verify the accuracy of the measurements and to also determine the nature of equilibrium (or lack thereof) during the time period in which data is obtained. The SHPB measurements are also analyzed in a traditional manner to determine the ‘‘effective’’ properties of the 3DWC material. In order to better understand the experimental results presented here, a follow-on paper discusses the results from a finite element model that uses micromechanics to examine the composite response and how it is influenced by the tow architecture and the constituent material properties [12]. 2. SHPB method The SHPB test procedure has been developed and refined over several decades, starting with pioneering work by Kolsky [13].
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Most routine SHPB tests are based on a 1D wave propagation analysis in a solid as described in [5]. The results obtained from such an analysis of the experimental data are used to obtain the effective stress–strain curve of the material as obtained from strain gauge data. These results are also validated using DIC techniques to better understand the full field strain field and interpret the inferred results since, traditionally, SHPB testing is carried out for homogeneous monolithic materials. In the present study, DIC measurements were taken on all of the samples during deformation to determine the effective strain field of the samples. This aspect is very important since it shows the ‘‘synthesis’’ of the strain signal that is recorded through the strain gages in the incident and transmitted bars, due to a highly complex stress and strain field that is present in a non-homogeneous 3DWC sample. Fig. 1 shows the specimen as it would be situated between the two bars. It is necessary that the specimen is perfectly flat between the two bars otherwise there will be poor transmission of the stress waves, at the interfaces between the incident bar, the 3DWC specimen, and the transmission bar. The samples were ground flat using a precision surface grinder.The strain rate was changed in the samples through a combination of changing the length of the pulse shapers and through changing the velocity of the impact bar. Material properties for the bars are provided in Table 1, and bar lengths and dimensions are given in Table 2. To record and capture digital images at high rates, a Photron SA.5 camera was used. A sequence of raw images captured in a SHPB test will be presented in a later section. 3. DIC data interpretation The DIC data was used to not only synthesize the strain gage measurements, but also for further information on failure mechanisms and strain field non-uniformity. Preliminary tests showed that the spatially averaged strain in the sample agreed well with the strain measured from strain gauges in the bars. When the two measurements are plotted as a function of time, the two results show good agreement, however the results diverge at a certain point, see Fig. 2. The DIC results show that the strain reaches a critical value, however the strain gauges continue to predict ‘‘strain’’. From the DIC images, it is seen that the inferred measurement (from strain gages) often produces more strain than measured in the specimen, therefore the DIC data was used to determine where to truncate the data points that are used to
Table 1 Physical properties of incident and transmitted bars. Material
440C stainless steel
Density
Kg 7620 m 3 220 GPa 1965 MPa 580
Young’s modulus Ultimate tensile strength Brinell hardness
Table 2 Length of bars.
Bar diameter Incident bar length Transmitted bar length Striker bar length
Small bar
Big bar
12.7 mm 1.83 m 1.22 m 0.30 m
38.1 mm 2.438 m 1.527 m 0.457 m
construct an effective stress–strain relation, derived from the strain gauge responses. The reason for ‘‘more’’ strain production in the bars is due to the fact that this is an inferred measurement. The strain recorded in the bars is based on the integral of the reflected signal. Therefore such a measurement is insensitive to failure occurring within the specimen volume. Additionally, when the strain field in the specimen becomes highly localized due to failure, the specimen will soften and continue to compress, however, strain relaxation in other areas of the specimen leads to a net decrease in the DIC data. Strain relaxation cannot occur in the 1D wave analysis since a negative reflected signal would need to occur. The ARAMIS DIC software was used with a facet size of 17 pixels and a step size of 1 pixel for image processing. Additionally, it should be noted that the large variation in strain is due to the matrix and fiber tows within the 3DWC undergoing different strain histories. These differences are related to the different wave speeds within each constituent. 4. Material The material studied here is a 6% Z-fiber reinforced architecture. The Z-fiber reinforced architecture consists of a system of warp and weft fibers (in the remainder of this paper, the word fiber and fiber tow are interchangeably used to refer to a fiber tow). Fig. 3a shows
Fig. 1. SHPB setup showing the placement of the specimen in the apparatus. The specimen is held between the two bars. The specimen shown here is not one of the specimens tested as the one shown here is round and the ones tested were square.
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RUC Warp tow Weft tow
Fig. 2. Comparison of strain gauge and DIC data obtained from a typical SHPB test.
Length
Thickness
(mm)
(in.)
(mm)
(in.)
(mm)
(in.)
6.80 2.71 3.11
0.2676 0.1065 0.1225
8.03 8.03 6.80
0.3162 0.3162 0.2676
6.35 0.63 0.60
0.2500 0.0248 0.0235
fraction of Z-fibers (as a percentage of all fibers) used in the binding process. Fig. 3b shows the actual architecture from the 6% Z-fiber material along with details of the path followed by the Z-fibers. 6% of the fibers are used as binding while the remaining is split between the warp and weft directions. The warp and weft layers are essentially layers of unidirectional fiber tow bundles that act like a laminate. The Z-fiber bundle moves from the top row to the bottom. The tow will pass under two rows of weft fibers and then move to the top where it will pass over two rows of weft fibers. This alternating process creates a bridging of the weak matrix layers. The thickness of the material is approximately 6.35 mm in a cured state. The overall fiber volume fraction is 46% for the composite. General dimensions of the individual fiber two bundles have been presented in Table 3, which identifies each tow and the volume that it would occupy. 4.1. Fabrication The panels were made using a Vacuum Assisted Resin Transfer Mold (VARTM) system. VARTM is a derived process from the Resin Transfer Mold Process (RTM). The main difference between the two is that in VARTM, a vacuum bag replaces one half of the mold and the matrix is then drawn through the material to ensure proper impregnation of the fibers through the assistance of a vacuum suction on the resin flow [14]. There are many benefits to this process some of which include, shorter mold time, lower tooling costs, reduced volatile emissions, lower injection pressures, and the ability to do much larger structures [15]. The VARTM process was performed at the Army Research Laboratories (ARL), Aberdeen proving ground, MD. 4.2. SC-15 material The material used as resin to infuse the panels was SC-15 epoxy, a thermoset polymer. SC-15 is a low-viscosity two-phase toughened epoxy resin system consisting of part A (resin mixture of diglycidylether epoxy toughener) and part B (hardener mixture of cycloaliphaic amine poluoxylalkylamine) [16]. Due to the low viscosity of the material it was a good choice for the VARTM process because it was able to flow well under vacuum to completely impregnate the material. 5. Experimental results Hopkinson bar testing was carried out in both in-plane orientations, warp and weft, with a third direction being tested
Fig. 3. Details of Z-fiber architectures. (a) The Z-fiber path path is shown in yellow and represents the course that the Z-fiber follows during the weaving process. (b) Details of 6% Z-fiber architecture. (c) Details of the RUC in the material.
a schematic of this, with the weft fibers denoted by red and the warp fibers represented as blue. The yellow fiber representing the Z-fiber binds all of these layers together. The 6% refers to the
Fig. 4. Through-the-thickness compression specimen, post failure image showing side view.
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Fig. 5. Through-the-thickness stress–strain and strain rate-strain plots obtained from SHPB tests of small specimens.
Fig. 6. _ vs. R: Strain rate dependency of SC-15, where R ¼ rr0 .
through-the-thickness. Each of the orientations were subjected to four separate strain rates. Failure was observed in all of the orientations producing stress–strain responses until failure. The throughthe-thickness test results will be examined first. 5.1. SHPB testing through-the-thickness One of the more critical aspects of this study was the throughthe-thickness response of the 3DWC material, since this is related to how the material will respond to a distributed pressure pulse loading over a small surface area. Additionally the information about how the material would fail either from shear banding or delamination was also of interest. A quasi-static test, using a standard laboratory testing frame, was also performed to characterize the through-the-thickness compressive response of the material. This test was performed to determine a baseline response of the material to understand differ-
ences induced by different loading rates. The effective quasi-static stress–strain response will be used later on in many of the comparisons. The test was run at a rate of 0.01 mm/s (0.0004 in/s) on specimens identical to that used in the SHPB testing. The specimen dimensions are, 15.8 mm (0.622 in.) by 15.5 mm (0.611 in.) and 5.95 mm (0.234 in.) thick. The specimens contain about 4–8 repeat unit cells of the nearly periodic woven architecture. The material failed through individual fiber tow delamination and matrix failure in compression as shown in Fig. 4. It can be seen that the matrix and fiber tows have separated apart in all of the layers, which can be characterized as delamination of the fiber tows. The matrix material has plastically deformed while the fiber tow bundles remain somewhat intact. Some tow bundles have failed due to the large strains. The outline of the tows can clearly be seen in the matrix material that is separating. Following quasi-static testing, SHPB tests were performed. Through-the-thickness tests were performed using bars with a diameter of 38.1 mm. The larger bar was needed to ensure that all of the unit cells were loaded equally. The incident bar was 2.438 m long and the transmitted bar was 1.524 m in length. The striker bar was 0.457 m long. The raw strain gauge signals from the SHPB can be seen in Fig. 5c. The effective through-the-thickness stress–strain response can be seen in Fig. 5. The plot shows the material response subjected to four different constant strain rates of 750, 1000, 1500, 1750 strain per second, which were all achieved through different methods of pulse shaping. The stress– strain response had nearly identical results. The data does not suggest any form of rate dependent behavior in the material at these rates. All of the specimens had a maximum stress of about 600 MPa and a maximum strain of about 7.5%. The small amount of variation seen is within experimental scatter. However, it is noted that there is an increase in strength in comparison with the quasi-static compression strength. This increase is from
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Fig. 7. The high speed image sequence taken of the through-the-thickness test.
500 MPa at 6.5% strain to 600 MPa at 7.5% strain. This increase is attributed to the rate dependent properties of the matrix material. The results show an absence of rate dependent modulus behavior (stress–strain response) at low straining rates (up to 1750 per second), but an increase in the failure strength, showing a rate dependent strength response. Fig. 6 shows the rate-dependent behavior of the pure SC-15 matrix material. These results were obtained from SHPB tests using a 12.7 mm diameter bar and samples were prepared as described in [5]. The rate dependent failure results are presented here. More details can be found in reference [17], which describes these experiments in more detail and shows that the modulus of the material is rate independent. The plot shows an increase in yield stress as a function of loading rate. Note that ro is a reference (static) yield stress, while r is the current yield stress corresponding to the strain rate being considered. Beyond a strain rate of about 3000 per second it is seen that R, the yield stress ratio, approaches a fairly constant value suggesting that for strain rates larger than this, the matrix would be less sensitive to strain rate, based on the theoretical fit. Thus, when 3DWC are examined using the SHPB, rate dependency can be expected at strain rates corresponding to matrix strain rates of 0–3000 per second. Although the bulk of the material is under 1750 per second at the highest rate, the matrix material could be experiencing much higher strain rates. The failure mode of 3DWC material contains a shear band forming in the specimen. Fig. 7 shows the raw image files. It can be seen that in the later images, there is indication of material failure and out of plane deformation causing blurred images. This blurring can lead to image non-correlation in the DIC analysis. Fig. 8 shows the full field strain data as a function of time. In the later DIC images, the formation of a localized dark blue band of high strain, which
can be seen in subfigure o, indicates the failure path, in this case corresponding to a shear band failure. The band corresponds to the shear plane that is formed in the specimen. In the subsequent images one can see the shear band consolidate. The different strain contours are directly related to the different layers of fiber tows that occur in the material. Due to material mismatch, the wave speed in the fiber tows and the matrix material are different, causing the strain to build differently in different constituents. Image O and P are the points corresponding to where failure is occurring. Theoretically, from the SHPB bar data, strain corresponding to these points would not be accurate anymore. They are just later points in the test, but do not correlate with the stress–strain curve, since the material has failed catastrophically. Therefore they have been removed from the stress–strain response plot. The line contour plot shows the strain evolution history, with the corresponding times shown on the right hand side of the figure. It can be seen that, initially, the strain distribution shows a fairly uniform spatially periodic build-up that corresponds to the different fiber tows. With increasing time, the initiation of strain localization (image (h)) results in a subsequent evolution that corresponds to pronounced non-uniformity (images (i) and (j)) . In these latter images, the correlation drops on the left hand side due to some motion blur.The strain amplitudes are quite large (in excess of 6%), indicating failure within this band. The surface oriented at ninety degrees to the shear band shows a different phenomenon. Fig. 9 shows this opposite face as the specimen deforms. This surface again does not show a constant strain, but rather distinct bands corresponding to locations where the matrix and fibers exist in the different layers. Since the shear band occurs in the plane that is ninety degrees to this face, failure on this specimen will appear as a separation of layers which can be
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Fig. 8. The evolution of
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x obtained from DIC in a through-the-thickness SHPB test. Stress–strain relationship is shown in Fig. 7 along with loading diagram.
seen in sub-image k. The right most layer has separated, and this is where the shear band is exiting the sample. This shear failure follows closely the textile tow architecture of the material, as can be seen in Figs. 10 and 11. These images of a specimen after SHPB testing shows some of the different constituents in the architecture. The shear band that formed followed many of the different warp and weft fiber tows in the material. Often the individual tows will remain intact except where they have sheared across and the matrix will be turned into ‘‘powder’’ from the coalescence of matrix micro-cracks. Fiber tow bundles near the edges of the material will often fail earlier by shearing out before ultimate failure of the specimen. This type of shear banding failure leads to a significant loss in load carrying capacity. The compression response of the 6% Z-fiber reinforced material offers insight into the rate-dependent behavior of the 3DWC material and shows a transition in failure mode with an increase in loading rate. As the material is stressed at higher rates it does not fail by delamination as noticed in the static test, but rather through a shear band formation. This transition in failure mode is important to note. The transition is likely due to the rate dependent yield stress of the matrix. At low rates, delamination is preferred since this mode of failure leads to a larger dissipation and is initiated by matrix cracking occurring at the free edges due to mismatch in properties between the tows and the matrix, and because shear banding is controlled by the matrix inelasticity. At higher rates, the rate of increase of yield strength appears to be less than the rate of increase of matrix cracking strain (strength). Thus, shear banding is the preferred mode of failure at higher rates. This
transition is important in understanding how to design 3DWC structures. 5.2. In-plane loading The in-plane quasi-static compression response of the material was also investigated. The test was run at a rate of 0.01 mm/s (0.0004 in/s) using an identical specimen to that used in the SHPB tests. The specimens measured 12.7 mm (0.500 in.) by 12.7 mm (0.500 in.) and 6.60 mm (0.260 in.) thick. The results show that the weft direction has a higher initial modulus while the warp direction is able to sustain a higher failure load. The material failed by delamination between the layers in the center with kink bands forming on the outer layers of the material, occurring in both the warp and weft directions, as shown in Fig. 12. The stress–strain responses for each of these orientations are shown in Fig. 13. The strain to failure was approximately 1%, for both in-plane directions. Additional tests were performed to determine if there was any variation in load with respect to size of the specimen. Larger panels were tested with a size of 152.4 mm (6 in.) by 101.6 mm (4 in.) with a thickness of 12.7 mm (0.50 in.). These panels were tested in compression with a fixture that has anti-buckling guides. The material was tested in two configurations, one with a uniform panel and one with a reduced cross section to promote failure in the test section. The stress–strain responses with a comparison with the corresponding response from a smaller sample size is shown in Fig. 14. The material response had very similar characteristics. The material failed in the weft direction at approximately
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Fig. 9. The evolution of
x obtained from DIC in a through-the-thickness SHPB test, viewed at 90° to the face corresponding to results presented in Fig. 8.
Fig. 10. Failed 6% Z-fiber specimen after through-the-thickness compression test. It should be noted that this specimen suffered catastrophic damage and not all of the surface can be seen.
250 MPa and at about 200 MPa in the warp direction. The failure strain was approximately 1% for both orientations. The failure mode was, again, kink band formation, as shown in Fig. 15. The in-plane SHPB tests were performed on a smaller diameter bar, 12.7 mm (0.5 in.), where specimens were cut into squares of
dimensions 12.7 mm (0.50 in.) by 12.7 mm (0.50 in.) and 6.60 mm (0.260 in.). The specimens were kept as large as possible to ensure that there were approximately four repeat unit cells present in each of the specimens. The dimensions of the specimens were matched to the 12.7 mm (0.50 in.) incident and transmitted bars. The warp direction was tested first, and four separate strain rates were achieved. The raw strain gauge signals from a test can be seen in Fig. 16c. An interesting phenomenon in the response was observed. In all of the in-plane tests, the strain rate would reach a peak of about 0.5% strain and then begin decreasing. In examining the strain gauge signals from the bars, the reason for this occurrence becomes clear. The incident wave is essentially a square wave while the transmitted wave is similar to a linearly increasing wave. Initially, the separation between the two gauges is large causing a high strain rate, but as the transmitted bar value approaches the square wave value it causes the strain rate to decrease. This is due to the fact that a wave is propagating through a highly non-homogeneous material. The waves enter the specimen cleanly, but due to the complex microstructure of the 3DWC, internal reflections cause wave interactions. This result is consistent with every in-plane SHPB test. The difficult part is determining what strain rate the response actually occurs at. In a typical SHPB test the rate will be fairly constant until failure. However with these materials the strain rate is not constant. There is typically a maximum seen and then a decrease until failure. The maximum strain rate achieved will be reported and used to discriminate between different cases.
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Fig. 11. Failed 6% Z-fiber specimen after through-the-thickness compression test indicating the fiber tow shear failure.
Fig. 12. Failed in-plane specimens for the warp and weft directions. The failure mechanism corresponds to kink band formation in the tows.
Fig. 13. Static compression test results for 6% Z-fiber reinforced composite material.
Fig. 14. Static compression test results for 6% Z-fiber reinforced composite material.
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Fig. 15. Weft specimen failed in kink band formation.
The warp direction results can be seen in Fig. 16, which clearly shows the decrease in strain rate as the specimen deforms further.
The figure also contains a static compression test for comparison. The SHPB experimental responses clearly follow the same material modulus (based on averaged stress and strain values) as the static test case. Additionally, the strength of the material increases with strain rate. The quasi-static test showed failure in the material at 275 MPa, while the SHPB testing revealed a maximum stress of 375–450 MPa. There is clearly a strain rate dependence of the material strength, with an increase in strength as a function of strain rate. Additionally, as the strain rate increases, the samples were able to undergo larger strains before failure. Since the material had the same modulus this result is expected. The DIC time history is shown in Fig. 17. The plots show that the material does not experience a uniform strain. The strain field shows areas of elevated and localized concentrations. The onset of failure corresponds to one end of the specimen initiating failure, and releasing the built-up internal strain energy. The data in Fig. 17 shows that the right end has failed, while the left end returns to near zero strain. The failure seen in the DIC data corresponds to delamination of the individual tows. There were no kink bands formed. This result is consistent with the longer specimens initially tested. In the quasi-static test, the specimen failed through kink band formation which initiates delamination. Thus, here a clear transition in failure mode from kink banding at low rates to only delamination at higher rates is observed. Notice that in these in-plane tests, while the fiber tows are directly compressed axially, they are free to move out-of-plane, since there is no lateral confinement. Thus, end ‘‘brooming’’ or splitting which is controlled by the mode-I fracture toughness of the matrix dominates because the tow kinking, which is controlled by the matrix yield strength is now elevated due to the increased matrix yield strength at elevated rates. The competition between splitting and fiber kinking has
Fig. 16. Stress–strain, and strain rate–strain plots for small specimens subjected to compression in the Warp direction.
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Fig. 17.
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x DIC time history in the warp direction.
been addressed before in Yerramalli and Waas [18]. To get an actual failure mode of a panel one would need to perform the same
Fig. 18. Failed in-plane specimens for the warp direction. The failure mode transitions from kink band formation and delamination, to delamination only at higher rates of loading.
tests with lateral confinement at the end to prevent tow failure from occurring. This would likely result in a much higher strength and strain in the sample. Fig. 18 shows a comparison of the two failed specimens, it is evident that there are different failure mechanisms corresponding to the different loading rates. At higher rates, since the matrix shows elevated yield strength, the kink band mode of failure appears to be suppressed in favor of the splitting which is controlled by the fracture toughness. It is also interesting to note that the result for in-plane response is reversed from that observed in the through-the-thickness case. In that case, delamination occurred at low rates (controlled by matrix cracking strain, or strength of the matrix) and shear banding at elevated rates (controlled by the matrix yield strength). In those tests, the weft and warp fiber tows are not directly loaded so failure modes that involve fiber tow axial failure, such as fiber tow kinking, see Song et al. [19] is absent. The warp direction shows a significant strain rate dependency, in both the maximum stress, but also in the failure mode. The kink bands associated with the static test disappear and only delamination is seen to occur in the specimens. This is because of the
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Fig. 19. Stress–strain and strain rate–strain plots for small specimens subjected to compression in the weft direction.
elevated yield stress of the matrix at higher rates which pushes the stress to initiate the kink banding to higher values. The weft direction had very similar results and trends. The raw strain gauge signals from a test can be seen in Fig. 19c. Fig. 19 shows the correlations obtained experimentally. These results show that there seems to be a rate dependency in the material once again. There is not as much dependency in the maximum strain, but rather in the load achieved. The result also shows a quasi-static compression test for comparison, which again shows that the modulus is not affected by strain rate. The weft directions response has similar trends to that of the warp direction, however the failure strength has increased from 250 MPa to 500 MPa and the strain has increased from 1% to 2% as a function of loading rate. While these results are very similar to the results seen in the warp direction, the strength has doubled. This is a very significant increase due to the rate dependency of the material. The DIC time history is shown in Fig. 20. The specimen is observed to be not in equilibrium, however there is less deviation in the warp and weft direction responses compared to the through-the-thickness direction response. It appears that the in-plane responses are closer to strain equilibrium than the through-the-thickness direction response. There are some strain concentrations near the end, and this is the location of failure in the specimen. Failure relieves the strain energy of the specimen, relaxing much of the strain in the un-failed region except near the actual failure site, where permanent deformation has occurred. The observed failure modes and mechanisms in the weft specimens were identical to the warp specimens. Delaminations occurred in the material causing the different tows to separate
from the matrix. Fig. 21 shows a comparison of the static and higher rate failure modes. The transition in failure mode from kink band dominated to delamination dominated observed in the warp direction is also noticed in the weft direction. All of the SHPB testing revealed a transition in failure mode as a function of loading rate, principally controlled by the rate-dependent behavior of the matrix. 6. Conclusions The SHPB tests provided a means for evaluating the rate dependence of the through-the-thickness and in-plane compression response of 3D 6% Z-fiber woven composite. Through-the-thickness testing revealed information about the rate dependent parameters and a transition in failure mode at higher rates. Architecture dependent strains were noticed in the DIC results, showing distinct bands where tows and matrix existed in regimes of different strain states. The in-plane results revealed similar trends to the through-thethickness results, however a large difference in measured values was observed. The in-plane, elevated rate strength of the material nearly doubled when compared to the quasi-static strength. The material had a clear transition in failure mode dominated by kink band formation at low rates to delamination at much higher rates. The in-plane compression response showed the largest rate dependent properties. The non-constant decreasing strain rate is unique to the 3DWC as well, due to the complex architecture causing interaction of waves between constituents within the specimen. Further, the failure mode transition from delamination to shear banding observed in the through-the-thickness testing was reversed for the warp and weft in-plane responses. This was
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Fig. 20.
x DIC time history in the weft direction.
Fig. 21. Failed in-plane specimens in the weft direction. The failure mode transitions from kink band formation to delamination at higher rates of loading.
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explained by examining the load bearing role of fiber tows in conjunction with the rate dependent response of the matrix. These experimental results are currently being used to develop a computational model in a follow-on paper [12], for predicting high rate 3DWC response, as reported in [20] Acknowledgement The authors would like to thank the Army Research Laboratories, Aberdeen proving ground, for their continued financial support. References [1] Wang S, Zahlan N, Suemasu H. Compressive stability of delaminated random short-fiber composites, part ii-experimental and analytical results. J Compos Mater 1985;19:317–33. [2] Stobbe D, Mohamed M. 3d woven composites: cost and performance viabiliity in comercial applications. in: 48th international SAMPE symposium, SAMPE; 2003. [3] Donadon M, Falzon B, Iannucci L, Hodgkinson J. A 3-d micromechanical model for predicting the elastic behaviour of woven laminates. Compos Sci Technol 2007;67:2467–77. [4] Garry III GT, ASM handbooks online. vol. 8, ASM International; 2004. [1985, Ch. High Strain Rate Testing]. [5] Pankow M, Attard C, Waas A. Specimen size and shape effect in split Hopkinson pressure bar testing. J Strain Anal Eng Des 2009;44(8):689–98. [6] Song B, Chen W, Werrasooriya T. Quasi-static and dynamic compressive behaviors of a s-2 glass/sc15 composite. J Compos Mater 2003;37(19): 1723–43.
[7] Ninan L, Tsai J, Sun C. Use of split Hopkinson pressure bar for testing off-axis composites. Int J Impact Eng 2001;25:291–313. [8] Sun B, Hu H, Gu B. Compressive behavior of multi-axial multi-layer warp knitted (mmwk) fabric composite and various strain rates. Compos Struct 2007;78:84–90. [9] Sun B, Gu B. High strain rate behavior of 4-step 3d braided composites under compressive failure. J Mater Sci 2007;42:2463–70. [10] Sun B, Liu F, Gu B. Influence of the strain rate on the uniaxial tensile behavior of 4-step 3d braided composites. Composites: Part A 2005;36:1477–85. [11] Sun B, Gu B. Shear behavior of 3d orthogonal woven fabric composites under high strain rates. J Reinf Plast Compos 2006;25:1833–45. [12] Pankow M, Waas A, Yen C, Ghiorse S. Modeling of 3d woven composites under dynamic loading conditions, University of Michigan, Aerospace Engineering Report; 2011. [13] Gama B, Lopatnikov SK, Gillespie Jr J. Hopkinson bar experimental technique: a critical review. Appl Mech Rev 2004;57(4);223–50. [14] Song X. Vacuum assisted resin transfer modling (vartm): Model development and verification. Ph.d. dissertation, Virginia Polytechnic Institute and State University; April 2003. [15] Chen R, Dong C, Liang Z, Zhang C, Wang B. Flow modeling and simulation for vacuum assisted resin transfer molding process with the equivalent premeability method. Polym Compos 2004;25(2):146–64. [16] Zhou Y, Pervin F, Biswas M, Rangari V, Jeelani S. Fabrication and characterization of montmorillonite clay-filled sc-15 epoxy. Mater Lett 2006;60:869–73. [17] Pankow M, Waas A, Yen C, Ghiorse S. Shock loading of 3d woven composites: a validated finite element investigation. Compos Struct 2011;93:1347–62. [18] Yerramalli C, Waas A. A non-dimensional number to classify composite compressive failure. J Appl Mech 2004;71:402–8. [19] Song et al. Compression response strength and post-peak response of an axial fiber reinforced tow. Int J Mech Sci 2009;51(7):491–9. [20] Pankow M. The deformation response of 3d woven composites subjected to high rates of loading. Ph.d. dissertation, The University of Michigan; May 2010.
Contents lists available at ScienceDirect
Composites Science and Technology journal homepage: www.elsevier.com/locate/compscitech
Split Hopkinson pressure bar testing of 3D woven composites M. Pankow a, A. Salvi a, A.M. Waas a,⇑, C.F. Yen b, S. Ghiorse b a b
Composite Structures Laboratory, Department of Aerospace Engineering, University of Michigan, 1320 Beal Street, Ann Arbor, MI 48109-2140, USA Army Research Laboratories, Aberdeen Proving Ground, MD, USA
a r t i c l e
i n f o
Article history: Received 23 November 2010 Received in revised form 1 March 2011 Accepted 24 March 2011 Available online 2 April 2011 Keywords: B: Impact behaviour E: Braiding B: Mechanical properties A: Textile composites B: Delamination B: Plastic Deformation
a b s t r a c t Results from a series of split Hopkinson pressure bar (SHPB) tests on 3D woven tetxile composites (3DWC) are presented. These tests were done to determine the rate dependent compression response of 3DWC. Three different configurations of the 3DWC, corresponding to compression response in the plane of the material and through-the-thickness direction (out-of-plane) were studied. The rate dependent responses were compared against quasi-static test results and it was found that 3DWC showed an increase in strength in all three directions studied, however, accompanied by a transition in the failure mechanism. The in-plane orientations showed the largest increase in (about 100%) strength at the elevated rates of loading. A follow-on paper provides finite element based results that correspond to the experimental results presented here. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Early uses of laminated composite materials revealed that delamination was one of the major failure mechanisms of the material [1]. In order to prevent this mode of failure from occurring, different types of through-the-thickness reinforcement have been introduced. One such technique is 3D weaving, where fiber tows are woven together in a complex 3D architecture to create one preform [2]. 3DWC materials are relatively new and investigations to characterize the deformation response of the material, other than simple quasi-static mechanical tests, are ongoing [3]. New applications of the material have lead to considering complex loading scenarios in-service, which include periods of high rates of loading. Historically, the split Hopkinson pressure bar method [4], has been used in conjunction with homogeneous and isotropic materials to obtain information on the effect of strain rate on yield strength, for example in metals. In the present study, the SHPB test is adopted to examine the deformation response of 3DWC when subjected to high strain rates. Since the fiber tows (that consists of fibers and matrix) and the SC15 polymer matrix are the basic constituents of the 3DWC, separate studies have been carried out to obtain the high rate response of these constituent materials [5]. SHPB testing of 2D in-plane woven S-2 glass fiber with SC-15 matrix composites has been shown to exhibit a rate dependency [6]. Additionally, studies of off-axis layered composites have been ⇑ Corresponding author. Tel.: +1 734 764 8227; fax: +1 734 763 0578. E-mail address: [email protected] (A.M. Waas). 0266-3538/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2011.03.017
reported in [7]. SHPB testing of 3DWC has also been done previously [8,9], although in these studies the authors simply assume equilibrium in the specimen, even though a constant strain rate is not achieved during the test duration. Other researchers have examined the tensile rate dependent properties of woven composites showing and explaining the rate-dependent behavior due to the reinforcement [10]. A modified Hopkinson bar has been used to perform high strain rate punch shear tests [11], showing the rate dependency of the 3DWC. In this paper, results from compression SHPB testing of 3DWC are reported along with quasi-static test results for comparison purposes. High speed Digital image correlation (DIC), a full field strain measurement technique, has been used to determine the strain history on the side surface of the specimens that have a rectangular cross-section. These measurements are used to verify the accuracy of the measurements and to also determine the nature of equilibrium (or lack thereof) during the time period in which data is obtained. The SHPB measurements are also analyzed in a traditional manner to determine the ‘‘effective’’ properties of the 3DWC material. In order to better understand the experimental results presented here, a follow-on paper discusses the results from a finite element model that uses micromechanics to examine the composite response and how it is influenced by the tow architecture and the constituent material properties [12]. 2. SHPB method The SHPB test procedure has been developed and refined over several decades, starting with pioneering work by Kolsky [13].
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Most routine SHPB tests are based on a 1D wave propagation analysis in a solid as described in [5]. The results obtained from such an analysis of the experimental data are used to obtain the effective stress–strain curve of the material as obtained from strain gauge data. These results are also validated using DIC techniques to better understand the full field strain field and interpret the inferred results since, traditionally, SHPB testing is carried out for homogeneous monolithic materials. In the present study, DIC measurements were taken on all of the samples during deformation to determine the effective strain field of the samples. This aspect is very important since it shows the ‘‘synthesis’’ of the strain signal that is recorded through the strain gages in the incident and transmitted bars, due to a highly complex stress and strain field that is present in a non-homogeneous 3DWC sample. Fig. 1 shows the specimen as it would be situated between the two bars. It is necessary that the specimen is perfectly flat between the two bars otherwise there will be poor transmission of the stress waves, at the interfaces between the incident bar, the 3DWC specimen, and the transmission bar. The samples were ground flat using a precision surface grinder.The strain rate was changed in the samples through a combination of changing the length of the pulse shapers and through changing the velocity of the impact bar. Material properties for the bars are provided in Table 1, and bar lengths and dimensions are given in Table 2. To record and capture digital images at high rates, a Photron SA.5 camera was used. A sequence of raw images captured in a SHPB test will be presented in a later section. 3. DIC data interpretation The DIC data was used to not only synthesize the strain gage measurements, but also for further information on failure mechanisms and strain field non-uniformity. Preliminary tests showed that the spatially averaged strain in the sample agreed well with the strain measured from strain gauges in the bars. When the two measurements are plotted as a function of time, the two results show good agreement, however the results diverge at a certain point, see Fig. 2. The DIC results show that the strain reaches a critical value, however the strain gauges continue to predict ‘‘strain’’. From the DIC images, it is seen that the inferred measurement (from strain gages) often produces more strain than measured in the specimen, therefore the DIC data was used to determine where to truncate the data points that are used to
Table 1 Physical properties of incident and transmitted bars. Material
440C stainless steel
Density
Kg 7620 m 3 220 GPa 1965 MPa 580
Young’s modulus Ultimate tensile strength Brinell hardness
Table 2 Length of bars.
Bar diameter Incident bar length Transmitted bar length Striker bar length
Small bar
Big bar
12.7 mm 1.83 m 1.22 m 0.30 m
38.1 mm 2.438 m 1.527 m 0.457 m
construct an effective stress–strain relation, derived from the strain gauge responses. The reason for ‘‘more’’ strain production in the bars is due to the fact that this is an inferred measurement. The strain recorded in the bars is based on the integral of the reflected signal. Therefore such a measurement is insensitive to failure occurring within the specimen volume. Additionally, when the strain field in the specimen becomes highly localized due to failure, the specimen will soften and continue to compress, however, strain relaxation in other areas of the specimen leads to a net decrease in the DIC data. Strain relaxation cannot occur in the 1D wave analysis since a negative reflected signal would need to occur. The ARAMIS DIC software was used with a facet size of 17 pixels and a step size of 1 pixel for image processing. Additionally, it should be noted that the large variation in strain is due to the matrix and fiber tows within the 3DWC undergoing different strain histories. These differences are related to the different wave speeds within each constituent. 4. Material The material studied here is a 6% Z-fiber reinforced architecture. The Z-fiber reinforced architecture consists of a system of warp and weft fibers (in the remainder of this paper, the word fiber and fiber tow are interchangeably used to refer to a fiber tow). Fig. 3a shows
Fig. 1. SHPB setup showing the placement of the specimen in the apparatus. The specimen is held between the two bars. The specimen shown here is not one of the specimens tested as the one shown here is round and the ones tested were square.
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RUC Warp tow Weft tow
Fig. 2. Comparison of strain gauge and DIC data obtained from a typical SHPB test.
Length
Thickness
(mm)
(in.)
(mm)
(in.)
(mm)
(in.)
6.80 2.71 3.11
0.2676 0.1065 0.1225
8.03 8.03 6.80
0.3162 0.3162 0.2676
6.35 0.63 0.60
0.2500 0.0248 0.0235
fraction of Z-fibers (as a percentage of all fibers) used in the binding process. Fig. 3b shows the actual architecture from the 6% Z-fiber material along with details of the path followed by the Z-fibers. 6% of the fibers are used as binding while the remaining is split between the warp and weft directions. The warp and weft layers are essentially layers of unidirectional fiber tow bundles that act like a laminate. The Z-fiber bundle moves from the top row to the bottom. The tow will pass under two rows of weft fibers and then move to the top where it will pass over two rows of weft fibers. This alternating process creates a bridging of the weak matrix layers. The thickness of the material is approximately 6.35 mm in a cured state. The overall fiber volume fraction is 46% for the composite. General dimensions of the individual fiber two bundles have been presented in Table 3, which identifies each tow and the volume that it would occupy. 4.1. Fabrication The panels were made using a Vacuum Assisted Resin Transfer Mold (VARTM) system. VARTM is a derived process from the Resin Transfer Mold Process (RTM). The main difference between the two is that in VARTM, a vacuum bag replaces one half of the mold and the matrix is then drawn through the material to ensure proper impregnation of the fibers through the assistance of a vacuum suction on the resin flow [14]. There are many benefits to this process some of which include, shorter mold time, lower tooling costs, reduced volatile emissions, lower injection pressures, and the ability to do much larger structures [15]. The VARTM process was performed at the Army Research Laboratories (ARL), Aberdeen proving ground, MD. 4.2. SC-15 material The material used as resin to infuse the panels was SC-15 epoxy, a thermoset polymer. SC-15 is a low-viscosity two-phase toughened epoxy resin system consisting of part A (resin mixture of diglycidylether epoxy toughener) and part B (hardener mixture of cycloaliphaic amine poluoxylalkylamine) [16]. Due to the low viscosity of the material it was a good choice for the VARTM process because it was able to flow well under vacuum to completely impregnate the material. 5. Experimental results Hopkinson bar testing was carried out in both in-plane orientations, warp and weft, with a third direction being tested
Fig. 3. Details of Z-fiber architectures. (a) The Z-fiber path path is shown in yellow and represents the course that the Z-fiber follows during the weaving process. (b) Details of 6% Z-fiber architecture. (c) Details of the RUC in the material.
a schematic of this, with the weft fibers denoted by red and the warp fibers represented as blue. The yellow fiber representing the Z-fiber binds all of these layers together. The 6% refers to the
Fig. 4. Through-the-thickness compression specimen, post failure image showing side view.
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Fig. 5. Through-the-thickness stress–strain and strain rate-strain plots obtained from SHPB tests of small specimens.
Fig. 6. _ vs. R: Strain rate dependency of SC-15, where R ¼ rr0 .
through-the-thickness. Each of the orientations were subjected to four separate strain rates. Failure was observed in all of the orientations producing stress–strain responses until failure. The throughthe-thickness test results will be examined first. 5.1. SHPB testing through-the-thickness One of the more critical aspects of this study was the throughthe-thickness response of the 3DWC material, since this is related to how the material will respond to a distributed pressure pulse loading over a small surface area. Additionally the information about how the material would fail either from shear banding or delamination was also of interest. A quasi-static test, using a standard laboratory testing frame, was also performed to characterize the through-the-thickness compressive response of the material. This test was performed to determine a baseline response of the material to understand differ-
ences induced by different loading rates. The effective quasi-static stress–strain response will be used later on in many of the comparisons. The test was run at a rate of 0.01 mm/s (0.0004 in/s) on specimens identical to that used in the SHPB testing. The specimen dimensions are, 15.8 mm (0.622 in.) by 15.5 mm (0.611 in.) and 5.95 mm (0.234 in.) thick. The specimens contain about 4–8 repeat unit cells of the nearly periodic woven architecture. The material failed through individual fiber tow delamination and matrix failure in compression as shown in Fig. 4. It can be seen that the matrix and fiber tows have separated apart in all of the layers, which can be characterized as delamination of the fiber tows. The matrix material has plastically deformed while the fiber tow bundles remain somewhat intact. Some tow bundles have failed due to the large strains. The outline of the tows can clearly be seen in the matrix material that is separating. Following quasi-static testing, SHPB tests were performed. Through-the-thickness tests were performed using bars with a diameter of 38.1 mm. The larger bar was needed to ensure that all of the unit cells were loaded equally. The incident bar was 2.438 m long and the transmitted bar was 1.524 m in length. The striker bar was 0.457 m long. The raw strain gauge signals from the SHPB can be seen in Fig. 5c. The effective through-the-thickness stress–strain response can be seen in Fig. 5. The plot shows the material response subjected to four different constant strain rates of 750, 1000, 1500, 1750 strain per second, which were all achieved through different methods of pulse shaping. The stress– strain response had nearly identical results. The data does not suggest any form of rate dependent behavior in the material at these rates. All of the specimens had a maximum stress of about 600 MPa and a maximum strain of about 7.5%. The small amount of variation seen is within experimental scatter. However, it is noted that there is an increase in strength in comparison with the quasi-static compression strength. This increase is from
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Fig. 7. The high speed image sequence taken of the through-the-thickness test.
500 MPa at 6.5% strain to 600 MPa at 7.5% strain. This increase is attributed to the rate dependent properties of the matrix material. The results show an absence of rate dependent modulus behavior (stress–strain response) at low straining rates (up to 1750 per second), but an increase in the failure strength, showing a rate dependent strength response. Fig. 6 shows the rate-dependent behavior of the pure SC-15 matrix material. These results were obtained from SHPB tests using a 12.7 mm diameter bar and samples were prepared as described in [5]. The rate dependent failure results are presented here. More details can be found in reference [17], which describes these experiments in more detail and shows that the modulus of the material is rate independent. The plot shows an increase in yield stress as a function of loading rate. Note that ro is a reference (static) yield stress, while r is the current yield stress corresponding to the strain rate being considered. Beyond a strain rate of about 3000 per second it is seen that R, the yield stress ratio, approaches a fairly constant value suggesting that for strain rates larger than this, the matrix would be less sensitive to strain rate, based on the theoretical fit. Thus, when 3DWC are examined using the SHPB, rate dependency can be expected at strain rates corresponding to matrix strain rates of 0–3000 per second. Although the bulk of the material is under 1750 per second at the highest rate, the matrix material could be experiencing much higher strain rates. The failure mode of 3DWC material contains a shear band forming in the specimen. Fig. 7 shows the raw image files. It can be seen that in the later images, there is indication of material failure and out of plane deformation causing blurred images. This blurring can lead to image non-correlation in the DIC analysis. Fig. 8 shows the full field strain data as a function of time. In the later DIC images, the formation of a localized dark blue band of high strain, which
can be seen in subfigure o, indicates the failure path, in this case corresponding to a shear band failure. The band corresponds to the shear plane that is formed in the specimen. In the subsequent images one can see the shear band consolidate. The different strain contours are directly related to the different layers of fiber tows that occur in the material. Due to material mismatch, the wave speed in the fiber tows and the matrix material are different, causing the strain to build differently in different constituents. Image O and P are the points corresponding to where failure is occurring. Theoretically, from the SHPB bar data, strain corresponding to these points would not be accurate anymore. They are just later points in the test, but do not correlate with the stress–strain curve, since the material has failed catastrophically. Therefore they have been removed from the stress–strain response plot. The line contour plot shows the strain evolution history, with the corresponding times shown on the right hand side of the figure. It can be seen that, initially, the strain distribution shows a fairly uniform spatially periodic build-up that corresponds to the different fiber tows. With increasing time, the initiation of strain localization (image (h)) results in a subsequent evolution that corresponds to pronounced non-uniformity (images (i) and (j)) . In these latter images, the correlation drops on the left hand side due to some motion blur.The strain amplitudes are quite large (in excess of 6%), indicating failure within this band. The surface oriented at ninety degrees to the shear band shows a different phenomenon. Fig. 9 shows this opposite face as the specimen deforms. This surface again does not show a constant strain, but rather distinct bands corresponding to locations where the matrix and fibers exist in the different layers. Since the shear band occurs in the plane that is ninety degrees to this face, failure on this specimen will appear as a separation of layers which can be
M. Pankow et al. / Composites Science and Technology 71 (2011) 1196–1208
Fig. 8. The evolution of
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x obtained from DIC in a through-the-thickness SHPB test. Stress–strain relationship is shown in Fig. 7 along with loading diagram.
seen in sub-image k. The right most layer has separated, and this is where the shear band is exiting the sample. This shear failure follows closely the textile tow architecture of the material, as can be seen in Figs. 10 and 11. These images of a specimen after SHPB testing shows some of the different constituents in the architecture. The shear band that formed followed many of the different warp and weft fiber tows in the material. Often the individual tows will remain intact except where they have sheared across and the matrix will be turned into ‘‘powder’’ from the coalescence of matrix micro-cracks. Fiber tow bundles near the edges of the material will often fail earlier by shearing out before ultimate failure of the specimen. This type of shear banding failure leads to a significant loss in load carrying capacity. The compression response of the 6% Z-fiber reinforced material offers insight into the rate-dependent behavior of the 3DWC material and shows a transition in failure mode with an increase in loading rate. As the material is stressed at higher rates it does not fail by delamination as noticed in the static test, but rather through a shear band formation. This transition in failure mode is important to note. The transition is likely due to the rate dependent yield stress of the matrix. At low rates, delamination is preferred since this mode of failure leads to a larger dissipation and is initiated by matrix cracking occurring at the free edges due to mismatch in properties between the tows and the matrix, and because shear banding is controlled by the matrix inelasticity. At higher rates, the rate of increase of yield strength appears to be less than the rate of increase of matrix cracking strain (strength). Thus, shear banding is the preferred mode of failure at higher rates. This
transition is important in understanding how to design 3DWC structures. 5.2. In-plane loading The in-plane quasi-static compression response of the material was also investigated. The test was run at a rate of 0.01 mm/s (0.0004 in/s) using an identical specimen to that used in the SHPB tests. The specimens measured 12.7 mm (0.500 in.) by 12.7 mm (0.500 in.) and 6.60 mm (0.260 in.) thick. The results show that the weft direction has a higher initial modulus while the warp direction is able to sustain a higher failure load. The material failed by delamination between the layers in the center with kink bands forming on the outer layers of the material, occurring in both the warp and weft directions, as shown in Fig. 12. The stress–strain responses for each of these orientations are shown in Fig. 13. The strain to failure was approximately 1%, for both in-plane directions. Additional tests were performed to determine if there was any variation in load with respect to size of the specimen. Larger panels were tested with a size of 152.4 mm (6 in.) by 101.6 mm (4 in.) with a thickness of 12.7 mm (0.50 in.). These panels were tested in compression with a fixture that has anti-buckling guides. The material was tested in two configurations, one with a uniform panel and one with a reduced cross section to promote failure in the test section. The stress–strain responses with a comparison with the corresponding response from a smaller sample size is shown in Fig. 14. The material response had very similar characteristics. The material failed in the weft direction at approximately
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Fig. 9. The evolution of
x obtained from DIC in a through-the-thickness SHPB test, viewed at 90° to the face corresponding to results presented in Fig. 8.
Fig. 10. Failed 6% Z-fiber specimen after through-the-thickness compression test. It should be noted that this specimen suffered catastrophic damage and not all of the surface can be seen.
250 MPa and at about 200 MPa in the warp direction. The failure strain was approximately 1% for both orientations. The failure mode was, again, kink band formation, as shown in Fig. 15. The in-plane SHPB tests were performed on a smaller diameter bar, 12.7 mm (0.5 in.), where specimens were cut into squares of
dimensions 12.7 mm (0.50 in.) by 12.7 mm (0.50 in.) and 6.60 mm (0.260 in.). The specimens were kept as large as possible to ensure that there were approximately four repeat unit cells present in each of the specimens. The dimensions of the specimens were matched to the 12.7 mm (0.50 in.) incident and transmitted bars. The warp direction was tested first, and four separate strain rates were achieved. The raw strain gauge signals from a test can be seen in Fig. 16c. An interesting phenomenon in the response was observed. In all of the in-plane tests, the strain rate would reach a peak of about 0.5% strain and then begin decreasing. In examining the strain gauge signals from the bars, the reason for this occurrence becomes clear. The incident wave is essentially a square wave while the transmitted wave is similar to a linearly increasing wave. Initially, the separation between the two gauges is large causing a high strain rate, but as the transmitted bar value approaches the square wave value it causes the strain rate to decrease. This is due to the fact that a wave is propagating through a highly non-homogeneous material. The waves enter the specimen cleanly, but due to the complex microstructure of the 3DWC, internal reflections cause wave interactions. This result is consistent with every in-plane SHPB test. The difficult part is determining what strain rate the response actually occurs at. In a typical SHPB test the rate will be fairly constant until failure. However with these materials the strain rate is not constant. There is typically a maximum seen and then a decrease until failure. The maximum strain rate achieved will be reported and used to discriminate between different cases.
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Fig. 11. Failed 6% Z-fiber specimen after through-the-thickness compression test indicating the fiber tow shear failure.
Fig. 12. Failed in-plane specimens for the warp and weft directions. The failure mechanism corresponds to kink band formation in the tows.
Fig. 13. Static compression test results for 6% Z-fiber reinforced composite material.
Fig. 14. Static compression test results for 6% Z-fiber reinforced composite material.
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Fig. 15. Weft specimen failed in kink band formation.
The warp direction results can be seen in Fig. 16, which clearly shows the decrease in strain rate as the specimen deforms further.
The figure also contains a static compression test for comparison. The SHPB experimental responses clearly follow the same material modulus (based on averaged stress and strain values) as the static test case. Additionally, the strength of the material increases with strain rate. The quasi-static test showed failure in the material at 275 MPa, while the SHPB testing revealed a maximum stress of 375–450 MPa. There is clearly a strain rate dependence of the material strength, with an increase in strength as a function of strain rate. Additionally, as the strain rate increases, the samples were able to undergo larger strains before failure. Since the material had the same modulus this result is expected. The DIC time history is shown in Fig. 17. The plots show that the material does not experience a uniform strain. The strain field shows areas of elevated and localized concentrations. The onset of failure corresponds to one end of the specimen initiating failure, and releasing the built-up internal strain energy. The data in Fig. 17 shows that the right end has failed, while the left end returns to near zero strain. The failure seen in the DIC data corresponds to delamination of the individual tows. There were no kink bands formed. This result is consistent with the longer specimens initially tested. In the quasi-static test, the specimen failed through kink band formation which initiates delamination. Thus, here a clear transition in failure mode from kink banding at low rates to only delamination at higher rates is observed. Notice that in these in-plane tests, while the fiber tows are directly compressed axially, they are free to move out-of-plane, since there is no lateral confinement. Thus, end ‘‘brooming’’ or splitting which is controlled by the mode-I fracture toughness of the matrix dominates because the tow kinking, which is controlled by the matrix yield strength is now elevated due to the increased matrix yield strength at elevated rates. The competition between splitting and fiber kinking has
Fig. 16. Stress–strain, and strain rate–strain plots for small specimens subjected to compression in the Warp direction.
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Fig. 17.
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x DIC time history in the warp direction.
been addressed before in Yerramalli and Waas [18]. To get an actual failure mode of a panel one would need to perform the same
Fig. 18. Failed in-plane specimens for the warp direction. The failure mode transitions from kink band formation and delamination, to delamination only at higher rates of loading.
tests with lateral confinement at the end to prevent tow failure from occurring. This would likely result in a much higher strength and strain in the sample. Fig. 18 shows a comparison of the two failed specimens, it is evident that there are different failure mechanisms corresponding to the different loading rates. At higher rates, since the matrix shows elevated yield strength, the kink band mode of failure appears to be suppressed in favor of the splitting which is controlled by the fracture toughness. It is also interesting to note that the result for in-plane response is reversed from that observed in the through-the-thickness case. In that case, delamination occurred at low rates (controlled by matrix cracking strain, or strength of the matrix) and shear banding at elevated rates (controlled by the matrix yield strength). In those tests, the weft and warp fiber tows are not directly loaded so failure modes that involve fiber tow axial failure, such as fiber tow kinking, see Song et al. [19] is absent. The warp direction shows a significant strain rate dependency, in both the maximum stress, but also in the failure mode. The kink bands associated with the static test disappear and only delamination is seen to occur in the specimens. This is because of the
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Fig. 19. Stress–strain and strain rate–strain plots for small specimens subjected to compression in the weft direction.
elevated yield stress of the matrix at higher rates which pushes the stress to initiate the kink banding to higher values. The weft direction had very similar results and trends. The raw strain gauge signals from a test can be seen in Fig. 19c. Fig. 19 shows the correlations obtained experimentally. These results show that there seems to be a rate dependency in the material once again. There is not as much dependency in the maximum strain, but rather in the load achieved. The result also shows a quasi-static compression test for comparison, which again shows that the modulus is not affected by strain rate. The weft directions response has similar trends to that of the warp direction, however the failure strength has increased from 250 MPa to 500 MPa and the strain has increased from 1% to 2% as a function of loading rate. While these results are very similar to the results seen in the warp direction, the strength has doubled. This is a very significant increase due to the rate dependency of the material. The DIC time history is shown in Fig. 20. The specimen is observed to be not in equilibrium, however there is less deviation in the warp and weft direction responses compared to the through-the-thickness direction response. It appears that the in-plane responses are closer to strain equilibrium than the through-the-thickness direction response. There are some strain concentrations near the end, and this is the location of failure in the specimen. Failure relieves the strain energy of the specimen, relaxing much of the strain in the un-failed region except near the actual failure site, where permanent deformation has occurred. The observed failure modes and mechanisms in the weft specimens were identical to the warp specimens. Delaminations occurred in the material causing the different tows to separate
from the matrix. Fig. 21 shows a comparison of the static and higher rate failure modes. The transition in failure mode from kink band dominated to delamination dominated observed in the warp direction is also noticed in the weft direction. All of the SHPB testing revealed a transition in failure mode as a function of loading rate, principally controlled by the rate-dependent behavior of the matrix. 6. Conclusions The SHPB tests provided a means for evaluating the rate dependence of the through-the-thickness and in-plane compression response of 3D 6% Z-fiber woven composite. Through-the-thickness testing revealed information about the rate dependent parameters and a transition in failure mode at higher rates. Architecture dependent strains were noticed in the DIC results, showing distinct bands where tows and matrix existed in regimes of different strain states. The in-plane results revealed similar trends to the through-thethickness results, however a large difference in measured values was observed. The in-plane, elevated rate strength of the material nearly doubled when compared to the quasi-static strength. The material had a clear transition in failure mode dominated by kink band formation at low rates to delamination at much higher rates. The in-plane compression response showed the largest rate dependent properties. The non-constant decreasing strain rate is unique to the 3DWC as well, due to the complex architecture causing interaction of waves between constituents within the specimen. Further, the failure mode transition from delamination to shear banding observed in the through-the-thickness testing was reversed for the warp and weft in-plane responses. This was
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Fig. 20.
x DIC time history in the weft direction.
Fig. 21. Failed in-plane specimens in the weft direction. The failure mode transitions from kink band formation to delamination at higher rates of loading.
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explained by examining the load bearing role of fiber tows in conjunction with the rate dependent response of the matrix. These experimental results are currently being used to develop a computational model in a follow-on paper [12], for predicting high rate 3DWC response, as reported in [20] Acknowledgement The authors would like to thank the Army Research Laboratories, Aberdeen proving ground, for their continued financial support. References [1] Wang S, Zahlan N, Suemasu H. Compressive stability of delaminated random short-fiber composites, part ii-experimental and analytical results. J Compos Mater 1985;19:317–33. [2] Stobbe D, Mohamed M. 3d woven composites: cost and performance viabiliity in comercial applications. in: 48th international SAMPE symposium, SAMPE; 2003. [3] Donadon M, Falzon B, Iannucci L, Hodgkinson J. A 3-d micromechanical model for predicting the elastic behaviour of woven laminates. Compos Sci Technol 2007;67:2467–77. [4] Garry III GT, ASM handbooks online. vol. 8, ASM International; 2004.
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