- Email: [email protected]
High rate test method for fiber-matrix interface characterization
Polymer Testing 52 (2016) 174e183
Contents lists available at ScienceDirect
Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Test method
High rate test method for fiber-matrix interface characterization Sandeep Tamrakar a, c, *, Bazle Z. (Gama) Haque a, d, John W. Gillespie Jr. a, b, c, d a
Center for Composite Materials (UD-CCM), University of Delaware, Newark, DE 19716, USA Department of Materials Science & Engineering, University of Delaware, Newark, DE 19716, USA c Department of Civil & Environmental Engineering, University of Delaware, Newark, DE 19716, USA d Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 March 2016 Accepted 23 April 2016 Available online 25 April 2016
A new test method to directly characterize fiber-matrix interface properties under high rate of loading has been developed. A tensile Hopkinson bar with a modified incident bar is used to load a microdroplet test specimen. Numerical simulations were carried out to design the test specimen geometry and validate data reduction procedures for the dynamic interface experiments. Stress wave propagation in an S-2 Glass/Epoxy microdroplet specimen was studied with different droplet sizes (100 mme200 mm) and fiber gage lengths (2 mme6 mm). Simulation results indicate that dynamic equilibrium can be maintained up to a displacement rate of 10 m/s. Dynamic microdroplet experiments were conducted at a displacement rate of 1 m/s on S-2 glass/epoxy interface. Experimental results and post-failure inspection of the fiber matrix interface showed that the new test method is effective in measuring high rate interface properties of composites. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Interface Hopkinson bar High rate loading Microdroplet test
1. Introduction Fiber reinforced polymer composites have been widely used for lightweight structures subjected to dynamic loading conditions. High specific stiffness, strength and energy absorption makes composites an attractive lightweight alternative to conventional materials. Dynamic response of a composite material can depend on the strain rate dependent properties of the fiber, matrix and fiber-matrix interface that transfers load between the constituents. A strong bond between fiber and matrix is desirable for structural application, whereas a weak and ductile interface increases the toughness and is more suitable for impact and ballistic applications [1e3]. Energy absorption in a composite occurs through various mechanisms such as matrix cracking and delamination at the macroscale, and fiber breakage, fiber-matrix debonding and frictional sliding at the microscale. Macromechanical test techniques such as drop weight and dynamic punch shear tests provide insight into the role of interface on composite properties. Moreover, a strong correlation between the interfacial properties at microscale and the mechanical properties of composite materials at the macroscale has been reported [4e6]. Gao et al. [7] established a
* Corresponding author. Center for Composite Materials (UD-CCM), University of Delaware, Newark, DE 19716, USA. E-mail address: [email protected] (S. Tamrakar). http://dx.doi.org/10.1016/j.polymertesting.2016.04.016 0142-9418/© 2016 Elsevier Ltd. All rights reserved.
linear relationship between the interfacial shear strength (IFSS) obtained from microdroplet testing of a wide range of fiber sizings and punch shear strength of composite laminates fabricated from the same constituents. Mechanisms that govern the energy absorption process at the microscale have been found to be more significant than that at the macroscale [2]. Consequently, an opportunity to tailor the interface properties at the nano to micro length scale opens up methodologies to improve composite performance. Several test methods are available to quantify the interfacial properties at microscale such as microdroplet test, single fiber fragmentation test, fiber push out and fiber pull out tests [8e10]. However, most of these test methods have been employed only within a quasi-static loading regime. Tanoglu et al. [11] developed a dynamic interphase loading apparatus to load the interphase through micro-indentation method up to a displacement rate of 3 mm/s. Other researchers have used the microdroplet test method or its modified version (cylinder test) to study the rate sensitivity of the interface (See Table 1) up to about 4 mm/s. Greenfield et al. [12] developed a test method to load a single fiber fragmentation test specimen at high displacement rate of 1250 mm/s, which is the only study found in the literature to conduct micromechanical test in the meters per second range. In a fragmentation test, IFSS is back calculated based on the critical length of fragmented fibers and the energy absorbed during fiber matrix debonding, and frictional
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
175
Table 1 Various test methods and displacement rates from literature.
Tanoglu et al. [11] Gao [13] Morlin and Czigany [14] Greenfield et al. [12] Current study
Displacement rate (mm/s)
Test method
Properties
0.3e3.00 0.003 0.0002e3.33 1250 0.001e1000
Dynamic push out test Microdroplet test Cylinder test Single fiber fragmentation test Microdroplet test
IFSS and energy absorption IFSS and energy absorption IFSS IFSS IFSS and energy absorption
sliding is not measured. In order to characterize the interface properties at higher rate of loading, an experimental setup has been designed which utilizes a modified version of a tensile Hopkinson bar. The incident bar is modified to load a microdroplet test specimen to directly measure IFSS and the energy absorbed during fiber-matrix debonding.
determined in accordance with ASTM C1557. Apparent compliance (DL/F) was plotted against fiber gage length, and the fitted curve was extrapolated back to zero gage length. Fixture compliance (Cs) for the quasi-static test setup was 0.13 mm/N. Corrected modulus of elasticity was then calculated by correcting the displacement for fixture compliance as shown in Eq. (1).
2. Experimental methods
DLcorr ¼ ðDL Cs $FÞ
2.1. Materials S-2 glass fibers with (3-glycidoxypropyl) trimethoxy silane coupling agent and epoxy film former sizing obtained from Owens Corning Corporation were used. Epoxy resin DER 353 (Dow Chemical Company) was mixed with bis (p-aminocyclohexyl) methane (PACM-20) curing agent (Air Products and Chemicals, Inc.) at a stoichiometric ratio of 100:28 (weight ratio) to form the droplets. Detailed procedure regarding the preparation of microdroplet specimens is presented elsewhere [13]. 2.2. Quasi-static tests 2.2.1. Single fiber tensile test Quasi-static tensile tests were conducted on single S-2 glass fibers with two gage lengths (8 mm and 25.4 mm) at a strain rate of 0.002/s to determine the axial modulus, which will later be used for data reduction in microdroplet tests. Tensile tests were conducted using an Instron model 5848 MicroTester with 0.020 mm position resolution. A 5 N load cell was used to monitor force in the fibers. Using epoxy adhesive, a single fiber was glued to cardboard, which was then clamped to the Instron for tensile testing. S-2 glass fibers exhibited a linear force e displacement response until failure. Total displacement measured by the Instron includes axial elongation of fiber and displacement due to fiber slippage in the adhesive and clamped region. The influence of the compliance arising from the bonding technique diminishes as the gage length increases [15]. For accurate determination of the axial elongation of the fiber, fixture compliance for the quasi-static test setup was
(1)
where, DL is the total displacement corresponding to the force (F) in the fiber. The corrected modulus was calculated to be about 85e86 GPa, which lies within the range of the published data from the manufacturers [16]. The tensile strength of the S-2 glass fibers for gage lengths of 8 mm and 25.4 mm are 3.7 ± 0.5 GPa and 3.4 ± 0.5 GPa, respectively (Table 2). 2.2.2. Microdroplet test The microdroplet test method developed by Miller et al. [17] was adopted to quantify the fiber-matrix interface properties. A microdroplet specimen consists of a single droplet of resin matrix deposited and cured on a single fiber to create a realistic composite interface. One end of the fiber is attached to a load cell while a set of knives are used to shear off the droplet such that the failure occurs along the interface. Microdroplet experiments under quasi-static loading rate of 1 mm/s were conducted to establish a baseline using the custom setup built by Gao [18]. Using the force e displacement data, the average IFSS was calculated based on the measured failure load and interface shear area using Eq. (2).
t¼
F
(2)
pdf le
where, t refers to IFSS, F is the tensile failure load in the fiber at interface debonding, df is the diameter of the fiber and le is the embedded length of the microdroplet. Energies were normalized to allow for comparison of specimens that may have differences in fiber diameter, gage length and droplet
Table 2 Tensile properties of S-2 Glass fibers under quasi-static loading. Gage length (mm)
Strain rates (1/s)
Tensile strength (GPa)
Strain at failure (%)
Modulus of elasticity (GPa)
25.4 8
0.002
3.4 ± 0.5 3.7 ± 0.5
4.0 ± 0.9 4.3 ± 0.5
85.6 ± 4.9 85.9 ± 3.2
Table 3 Calculation of maximum droplet size based on statistical distribution of tensile strength [19]. Probability of fiber failure (%)
Tensile strength of fiber, sfiber (MPa)
Maximum allowable droplet size, le (mm)
1 2 5 40
1700 2000 2400 4000
85 100 120 200
176
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
Fig. 3. Typical incident and reflected signal in the incident bar showing specimen loading period.
Fig. 1. . Typical force displacement response of a microdroplet experiment (Data obtained during dynamic sliding is not considered for calculation).
size. In addition, the load-displacement curves were corrected for fixture compliance following the methodology of Gao [13]. Specific debonding energy (Eq. (3)) and specific energy during frictional sliding (Eq. (4)) were calculated as follows:
Z ddeb sp
Edeb ¼
di
F dd
pdf le
(3)
Z dmax
F dd d sp Efs ¼ fric; i pdf le le
(4)
Fig. 4. Calibration curve for laser displacement sensor (R2 ¼ 1).
For quasi-static loading, test specimen design criteria established by Gao [13] consider fiber strength statistics (smaller gage lengths exhibit higher strength) that places limits on maximum droplet embedded length for a given IFSS to ensure interfacial failure prior to fiber tensile failure (Eq. (5)).
sfiber 1 le < df 4 sIFSS
Fig. 2. Schematic representation of dynamic microdroplet test apparatus and details on modified end of the incident bar.
Fig. 5. Force displacement response of single fiber tensile test with 4 mm gage length (Loading rate: 3e5 m/s).
(5)
where, sfiber is the tensile strength of the fiber and sIFSS is the IFSS.
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
177
Table 4 Dynamic tensile properties of S-2 glass fibers. Gage length Strain rates Tensile Uncorrected Modulus of (mm) (1/s) strength (GPa) elasticity (GPa) 8 4 2
500 900 1800
4.8 ± 0.5 5.1 ± 0.5 5.4 ± 0.5
92.1 ± 3.6 80.6 ± 2.5 59.3 ± 3.7
Modulus of elasticity corrected for fixture Corrected Modulus of elasticity Corrected strain at compliance (GPa) (GPa) a ¼ 1.28 failure (%) 112.3 ± 5.3 116.3 ± 4.8 109.1 ± 13.5
87.3 ± 3.4 91.1 ± 2.8 85.7 ± 5.3
5.5 ± 0.7 5.6 ± 0.7 6.3 ± 0.9
is exerted by the matrix on to the fiber due to resin shrinkage during cure and the mismatch in coefficient of thermal expansion (CTE) between fiber and matrix that arises as the specimen cools to room temperature, and due to the surface roughness of the fiber. IFSS for this specific S-2 glass/epoxy system was calculated to be 47.8 ± 3.8 MPa. Specific energy up to complete debonding and during frictional sliding were 760 ± 350 J/m2 and 9300 ± 3000 kJ/ m3, respectively.
2.3. High rate tests
Fig. 6. Calculation of fixture compliance from zero gage length intercept of the fitted curve.
For a gage length of 2 mm, fiber diameter of 10 mm and assuming an IFSS of 50 MPa, maximum droplet size can be calculated based on the failure probability of a fiber with Weibull strength distribution (See Table 3). Weibull parameters were obtained from the literature for S-2 glass fibers [19]. Probability of fiber failure increases with increase in droplet size. Microdroplet experiments were conducted on droplet sizes ranging from 80 to 120 mm. A probability of fiber failure of less than 5% (i.e. 95% probability of interface failure) was deemed acceptable in our experimental design, particularly since smaller droplet sizes are difficult to achieve during specimen preparation. A gage length of 1e2 mm was maintained. At least 10 valid tests were considered for further data reduction. Microdroplet specimens exhibited a fairly linear force-displacement response until complete debonding, followed by dynamic sliding and a frictional sliding regime (Fig. 1). During frictional sliding, a fairly constant compressive force
2.3.1. Tensile hopkinson bar A tensile Hopkinson bar has been adapted [20,21] for high rate loading of the microdroplet specimen. The test fixture consists of an incident bar with a flange at the end and a hollow striker bar made of 7075-T6 aluminum alloy (Fig. 2). The incident bar is 6.35 mm in diameter and 1.52 m in length. The outer diameter of the circular flange attached to the end of the incident bar is 12.7 mm. The
Fig. 8. 2D axisymmetric LS-DYNA model.
Fig. 7. Specimen holder attached to the load cell, miniature knife edge attached to the incident bar and microdroplet test specimen.
178
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
Table 5 Material properties for aluminum, fiber and epoxy [16,24]. Properties, unit
Aluminum knife
S-2 glass fiber
Epoxy droplet
Density, gm/cc Young's modulus, GPa Poisson's ratio Bar velocity, m/s
2.70 69.00 0.285 5000
2.49 86.00 0.230 5470
1.27 4.3 0.35 1840
striker bar has an outer diameter of 12.7 mm and is 203.2 mm in length. During the experiment, a spring launcher accelerates the striker bar to a target velocity, which strikes the flange attached to the incident bar. A 70 mm thick soft paper soaked in petroleum jelly is used as pulse shaper to eliminate the high frequency noise generated when the striker bar impacts the flange. A semiconductor strain gage attached on the surface of the incident bar captures the resulting stress waves, which propagate in the direction opposite to the impact direction. A smooth tensile wave with constant amplitude loads the specimen for a period of about 100 ms, as indicated by the shaded area in Fig. 3. Velocity of wave propagation in the incident bar, calculated based on the monitored signal, was about 5000 m/s, which is in good agreement with theoretical value for aluminum. The tensile force induced in the specimen is directly measured by a fast response quartz piezoelectric load cell (Kistler 9712B5) with a capacity of 22.24 N. It has a frequency response of 115 kHz, which implies that the test duration of 100 ms is sufficient to collect at least 10 meaningful data points. Axial displacement at the loading end of the incident bar is monitored using a laser displacement sensor. A laser diode (110 mW output and 660 nm wavelength) with a circular beam is used. The laser beam passes through a beam expander and a line generator, which forms a horizontal laser line. The laser line is passed through the gap between the specimen holder and incident bar, and is collected on the sensor area (75.4 mm2) of the photodetector (DET100A) through a focusing lens. The data acquisition rate was 5 MHz, while the frequency response of the detector was 8 MHz. The laser sensor was calibrated by monitoring the voltage output while changing the gap width with a known distance. The linear relationship between the output voltage and the gap width
(Fig. 4) suggests that the intensity of the laser line is uniform along the length. This relationship was used to calculate the displacement of the loading end of the incident bar. 2.3.2. Single fiber dynamic tensile test Although the laser displacement sensor measures end displacements accurately, other sources of compliance exist and must be accounted for. Calculations of IFSS and energy absorption in a microdroplet test require accurate load and displacement measurement. Our approach is to validate calibration by conducting dynamic tensile tests of single S-2 glass fibers with rate independent axial modulus of elasticity. Load is measured directly and is accurate when dynamic equilibrium is achieved (see Section 3). Dynamic compliance calibration first considers compliance from the fixture and, secondly, a dynamic correction factor to provide accurate correction to our fiber standard. A similar dynamic correction measure has been employed in other studies [22]. Dynamic tensile tests were conducted on single fibers with a nominal diameter of 10 mm and gage lengths of 2 mm, 4 mm and 8 mm at a displacement rate of 3e5 m/s. The fiber was glued to the specimen holders attached to the load cell and the incident bar. Fig. 5 shows a fairly linear force displacement response up to failure for the S-2 glass fiber with 4 mm gage length. Since all dynamic tests were conducted within the same range of loading velocity, the strain rate increased with reduced gage length. Higher tensile strength resulted for lower gage length due to both size effect as well as strain rate effects. However, for the same gage length of 8 mm, the tensile strength increased from 3.7 GPa at 0.002/s (Table 2) to 4.8 GPa at 500/s (Table 4), showing strain rate dependency. Uncorrected modulus of elasticity for high rate of loading decreased from 92.1 GPa to 59.3 GPa when the gage length decreased from 8 mm to 2 mm (Table 4). This is due to the fact that the fixture compliance is large compared to the compliance of the 2 mm fiber, and its influence decreases at higher gage lengths, as described in Section 2.2.1. Analogous to the quasi static method, the fixture compliance must be accounted for to correct the axial elongation. 2.3.2.1. Fixture compliance. Fixture compliance of the tensile Hopkinson bar was determined in accordance with ASTM C1557. Fig. 6
Fig. 9. (a) Shear stress and (b) Radial stress distribution along the interface at force level 0.1 N (red) and 0.2 N (black) for quasi-static loading for a 200 mm droplet. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
shows the apparent compliance (DL/F) plotted as a function of fiber gage length (L0) normalized by its cross sectional area (A). DL is the displacement measured at the end of the incident bar by the laser sensor and F is the corresponding force. Fixture compliance of the system (Cs), given by the intercept of the curve at zero gage length, is 0.189 mm/N. The modulus corrected for fixture compliance now becomes gage length independent (Table 4). However, the modulus is consistently higher (about 30%) than the known properties of S-2 Glass fiber (Table 4).
2.3.2.2. Dynamic compliance correction factor. The modulus of elasticity for longer gage length is over-predicted in the dynamic tests, which has been reported in the literature for a similar testing system [20]. To ensure accurate displacement measurements, a dynamic correction factor (a) is applied after fixture compliance and gage length effects are accounted for in Eq. (6). The corrected displacement is calculated as follows:
DLcorr ¼ ðDL Cs $FÞ a
179
(6)
The compliance calibration factor (a) is chosen such that the corrected displacement would yield the published modulus of our calibration standard (85e90 GPa for S-2 Glass). In this particular case, a value of 1.28 was defined and gives excellent agreement for all gage lengths, as presented in Table 4. This dynamic correction factor was used in the dynamic microdroplet tests. 2.3.3. Dynamic microdroplet test The procedure to conduct dynamic microdroplet tests includes positioning the knife edges to have a gap of nominally 14 mm which is slightly larger than the fiber diameter (i.e. the end of the knife edges are 2 mm from the fiber surface) to load the droplet. On the other end of the specimen, the fiber was glued to the specimen holder attached to the load cell (Fig. 7). The specimen was preloaded and inspected to ensure the droplet was not loaded eccentrically. A tensile pulse was sent using a hollow striker bar, as
Fig. 10. Dynamic effects in interfacial shear stress distribution at force level 0.1 N (red) and 0.2 N (black) for droplet size 200 mm and fiber gage length 2 mm at displacement rates (a) 60 m/s, (b) 20 m/s, (c) 10 m/s and (d) 5 m/s.
180
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
3. Specimen design for dynamic loading
When the knife edge, with a much larger mass, comes in contact with the droplet at a certain velocity, the momentum transfer causes the droplet to accelerate to a velocity higher than the knife edge, causing the droplet to momentarily lose contact with the knife edge. Then, the droplet starts to decelerate and eventually springs back and comes in contact with the knife edge again. This sequence of event repeats until the knife edges and drop attain the same velocity. The larger drop of higher mass is accelerated to a less extent, and hence takes less time to achieve dynamic equilibrium (Videos of these mechanisms can be seen in the supplemental information provided). As such, the combination of the largest droplet (200 mm) and the smallest gage length (2 mm) was found to achieve equilibrium in the shortest time. However, it should be noted that the probability of fiber failure increases with larger droplets that require higher debonding forces (Table 3). Supplementary video related to this article can be found at http://dx.doi.org/10.1016/j.polymertesting.2016.04.016 The shear stress and radial stress distribution at different load levels for the quasi-static case is presented in Fig. 9. The load levels correspond to the axial force in the fiber gage length. The coordinates along the interface have been normalized with respect to the total embedded length of the droplet. There is a stress
Apart from developing the data reduction scheme and displacement correction methods, it is imperative to ensure dynamic equilibrium is achieved in the gage length and interface region during loading of the microdroplet. During a dynamic test, the microdroplet is subjected to compressive stresses as the tensile wave reaches the modified end of the incident bar. Consequently, shear stresses are induced in the fiber-matrix interface region, which in turn loads the fiber in tension. A complex series of wave propagation and reflections develop within the specimen. Finite element modeling of a microdroplet (Fig. 8) was conducted to study the dynamic effects and select appropriate test specimen geometry. A 2D axisymmetric FE model was developed and analyses were done using the commercially available finite element code LS-DYNA 971 [23]. Linear elastic elements were used and perfect bonding was assumed between fiber and droplet. Mesh size of 0.625 mm was chosen along the droplet length (adjacent to the fiber) to accurately describe the spatial gradients in interfacial stress along the embedded length. Explicit time steps are governed by the higher wave speed of the fiber (0.00011 ms). A characteristic time is defined based on the specimen geometry and wave speed of the respective materials presented in Table 5. For example, the characteristic time for wave propagation along the fiber with a 2 mm gage length is 0.37 ms Consequently, the numerical model is suitably refined with enough time resolution to study the wave propagation along the fiber and interface. Wave propagation in the fiber gage length and dynamic effects in the interfacial region were investigated for different combination of gage length (2 mme6 mm) and droplet sizes (100 mme200 mm) at different displacement rates (5 m/s to 60 m/s). When the gage length was reduced for a constant droplet size, the time to achieve dynamic equilibrium in the gage length decreases. Dynamic equilibrium refers to the specimen configuration where the difference between the forces measured by the load cell on one end and the load applied to the droplet by the knife edge at the other end of the gage length is an acceptable small error throughout the duration of the test [25]. For this study, dynamic equilibrium was said to be achieved when this error in forces at the two ends of the gage length (F1 and F2 in Fig. 8) became less than 5%. In general, it took about 4e6 wave reflections within the gage length to reach equilibrium. When the gage length was kept constant, the time to reach dynamic equilibrium decreased with increase in droplet size.
Fig. 11. Typical signal recorded during the dynamic microdroplet test. (a) Force signal measured from the piezoelectric load cell, (b) Displacement signal measured from the laser sensor.
described earlier, to begin the test. The compliance correction for the microdroplet test must be modified since only one end of the specimen is glued, while the droplet on the other end is loaded by the knife edge (Fig. 7). Since both ends of the single fiber tests are identical, it is assumed that the compliance due to bonding from each end is equivalent. A value of 0.0945 mm/N was used as the fixture compliance (Cs) for the microdroplet test. Then, the corrected displacement (d) applied to the droplet by the loading knives was calculated using Eq. (7). In this equation, the measured laser displacement (DL) was corrected for fixture compliance and dynamic compliance correction. The displacement associated with fiber stretching (the second term in Eq. (7)) was also subtracted to obtain the droplet displacement used to calculate energy absorption during debonding and sliding (see Eqs. (3) and (4)).
d ¼ DL
Cs $F 2
a
F$Lo A$E
(7)
where, a ¼ 1.28 and E ¼ 85 GPa.
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
concentration at the loading end of the droplet (present in all of the interface test methods), which decreases to zero at the other end of the droplet. The mechanical loading places the interface under radial tension near the loading end of the droplet. This suggests that the crack initiation near the loading tip is due to mixed mode loading [26e28]. Fig. 10 shows the comparison between the quasi-static and high rate loading cases at two load levels for different displacement rates. The state of stress for high rate tests converge to the quasistatic tests when the velocity is 10 m/s or less, indicating wave propagation and inertial effects have been minimized. In this case, the data reduction equations presented in Eqs. (2)e(4) can be used for high rate tests. It should be noted that this same rationale is used to establish dynamic equilibrium in compression testing using a split Hopkinson pressure bar at high strain rates [29,30]. 4. Results and discussion Dynamic microdroplet experiments were conducted on droplets with embedded length ranging from 80 to 120 mm at an average displacement rate of 1 m/s. Duration of the loading to reach failure load was in the range of 75e220 ms. Typical force and displacement signals are shown in Fig. 11. The displacement signal increases monotonically while the specimen is being loaded, indicating a constant velocity during the test. The load cell vibrates at its natural frequency of 115 kHz immediately after failure occurs. As a result, the frictional sliding between the fiber and the failed droplet could not be captured. However, since droplets were still attached to the fiber after the test, it is possible to reload the specimen to measure the sliding energy.
181
Post-test inspections were carried out to check the validity of the tests. The specimens were inspected under scanning electron microscope to ensure that the droplet did not have major fractures within the drop other than the desired interfacial failure near the fiber surface, and that the indentation due to knife edge was minimal (See Fig. 12a). The residual epoxy at the top of the drop (Fig. 12b), which is the location of crack initiation due to the tensile stresses near the loading end [28], should be localized (See Fig. 9). Also, to ensure that the failure occurred along the fiber matrix interface region, the surface of the fiber was investigated. Fig. 12c and d shows a fairly smooth fracture surface with a few traces of epoxy. After all these criteria have been met, IFSS and the energy absorbed by the interface were calculated using Eqs. (2)e(3). Fig. 13 shows a fairly linear force displacement response until complete debonding of the interface occurs. Average IFSS increased to 80.6 MPa for high rate loading (1 m/s) from 47.8 MPa at quasistatic loading rate (1 mm/s). The difference between IFSS for high rate of loading and quasi-static loading is statistically significant. Also, the energy absorbed by the interface up to debond increased from 760 J/m2 to 1950 J/m2 with increase in the displacement rate (Table 6). These results suggest that this S-2 Glass/epoxy/sizing system has fiber matrix interface properties that are sensitive to the rate of loading. The coefficient of variation (COV) in the IFSS for quasi-static loading rates are on the lower side (8%) compared to most of the studies reported in literature that can be as high as 33% [10]. However, the COV increases to 15% for the high rate test, which is still within the acceptable range for such test methods. IFSS is sensitive to the gap width and the symmetricity of the droplet loading by the knife edges. Very small differences in the point of contact of the knife edges can cause rotation and bending of the
Fig. 12. SEM images of tested microdroplet specimen (a) Debonded microdroplet, (b) Residual epoxy at the loading end of the tested specimen, (c) Fracture surface at the top of the specimen, (d) Fracture surface along the embedded length.
182
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
1 mm/s to 1 m/s. Acknowledgments Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-12-2-0022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. The authors would like to thank Prof. Weinong Chen and Matthew Hudspeth for collaborations on the development of the tensile Hopkinson bar. References Fig. 13. Force vs. raw displacement response from dynamic microdroplet experiments.
Table 6 Comparison of experimental results. Velocity (mm/s) Quasi-Static Test High Rate Test
IFSS (MPa)
COV (%)
Specific energy debond (J/m2)
COV (%)
1
47.8
8
760
45
106
80.6
15
1950
44
fibers prior to dynamic loading, and significantly affect the interfacial shear stress distribution and, ultimately, IFSS even at quasi static loading rates [31]. To ensure uniform loading, we monitored the bending of the fiber during static preload and adjusted the stages holding the knife edges. Another way to reduce such variability would be to use a disk with a concentric hole to load the microdroplet [26]. During dynamic testing, bouncing of the droplet can also be an added source of variability. When there is not enough preloading, or if there is a gap between knife edge and the droplet, loading and unloading of the droplet can be seen in the force-time signal. Such results are discarded before further data reduction. 5. Conclusions An experimental method for characterizing fiber matrix interface properties at high rate of loading has been developed. The experimental method presented in this study is the first of its kind to characterize fiber-matrix interface properties (i.e. strength and debonding energy) in the meters per second range. The experimental setup consists of a tensile Hopkinson bar with a modified end to load a microdroplet test specimen. Finite element analysis was carried out to design optimum specimen geometry, including the fiber gage length and droplet size, and acceptable displacement rates within which the specimen would be in dynamic equilibrium. Simulation results showed that the shear stress distribution along the interface would be in dynamic equilibrium up to a displacement rate of 10 m/s. The combination of 2 mm gage length and 200 mm droplet has the shortest time to reach equilibrium without fiber failure and, therefore, has the highest loading rate potential. Our experimental set-up was used to test microdroplet specimen with S-2 glass/epoxy system. Experimental results suggest that the IFSS and specific energy absorption capacity are sensitive to the rate of loading. IFSS and debond energy increased by a factor of 1.7 and 2.6, respectively, when the displacement rate was increased from
[1] M. Labronici, H. Ishida, Toughening composites by fiber coating: a review, Compos. Interfaces 2 (1994) 199e234. [2] M. Tanoglu, S.H. McKnight, G.R. Palmese, J.W. Gillespie Jr., The effects of glassfiber sizings on the strength and energy absorption of the fiber/matrix interphase under high loading rates, Compos. Sci. Technol. 61 (2001) 205e220. [3] L.J. Broutman, B. Das Agarwal, A theoretical study of the effect of an interfacial layer on the properties of composites, Polym. Eng. Sci. 14 (1974) 581e588. [4] B. Harris, P. Beaumont, E. De Ferran, Strength and fracture toughness of carbon fibre polyester composites, J. Mater. Sci. 6 (1971) 238e251. €der, K. Grundke, H. Jacobasch, G. Wachinger, Surface, interphase and [5] E. Ma composite property relations in fibre-reinforced polymers, Composites 25 (1994) 739e744. [6] J. Sun, L. Gao, Development of a dispersion process for carbon nanotubes in ceramic matrix by heterocoagulation, Carbon N. Y. 41 (2003) 1063e1068. [7] X. Gao, J.W. Gillespie, R.E. Jensen, W. Li, B.Z. (Gama) Haque, S.H. McKnight, Effect of fiber surface texture on the mechanical properties of glass fiber reinforced epoxy composite, Compos. Part A Appl. Sci. Manuf. 74 (2015) 10e17. [8] J. Kim, Y. Mai, Engineered Interfaces in Fiber Reinforced Composites, first ed., Elseview Science Ltd, 1998. [9] U. Gaur, B. Miller, Microbond method for determination of the shear strength of a fiber/resin interface: evaluation of experimental parameters, Compos. Sci. Technol. 34 (1989) 35e51. [10] M.J. Pitkethly, J.P. Favre, U. Gaur, J. Jakubowski, S.F. Mudrich, D.L. Caldwell, et al., A round-robin programme on interfacial test methods, Compos. Sci. Technol. 48 (1993) 205e214. [11] M. Tanoglu, S.H. McKnight, G.R. Palmese, J.W. Gillespie, A new technique to characterize the fiber/matrix interphase properties under high strain rates, Compos. Part A Appl. Sci. Manuf. 31 (2000) 1127e1138. [12] M. Greenfield, A. Pedicini, L. Penn, Development of a single fiber fragmentation test for high strain rates, Int. J. Adhes. Adhes. 20 (2000) 403e407. [13] X. Gao, Tailored Interphase Structure for Improved Strength and Energy Absorption of Composites, University of Delaware, 2006. [14] B. Morlin, L.M. Vas, T. Czigany, Investigation of fiber/matrix adhesion: test speed and specimen shape effects in the cylinder test, J. Mater. Sci. 48 (2013) 3185e3191. [15] D. Turek, On the tensile testing of high modulus polymers and the compliance correction, Polym. Eng. Sci. 33 (1993) 328e333. [16] AGY, Advanced Materials: Solutions for Demanding Applications, 2004. [17] B. Miller, P. Muri, L. Rebenfeld, A microbond method for determination of the shear strength of a fiber/resin interface, Compos. Sci. Technol. 28 (1987) 17e32. [18] X. Gao, R.E. Jensen, W. Li, J. Deitzel, S.H. McKnight, J.W. Gillespie, Effect of fiber surface texture created from silane blends on the strength and energy absorption of the glass fiber/epoxy interphase, J. Compos. Mater 42 (2008) 513e534. [19] M.R. Gurvich, A.T. DiBenedetto, S.V. Ranade, A new statistical distribution for characterizing the random strength of brittle materials, J. Mater. Sci. 32 (1997) 2559e2564. [20] J. Lim, W.W. Chen, J.Q. Zheng, Dynamic small strain measurements of Kevlar® 129 single fibers with a miniaturized tension Kolsky bar, Polym. Test. 29 (2010) 701e705. [21] M. Hudspeth, X. Nie, W. Chen, R. Lewis, Effect of loading rate on mechanical properties and fracture morphology of spider silk, Biomacromolecules 13 (2012) 2240e2246. [22] C. Albertini, M. Montagnani, Dynamic Material Properties of Several Steels for Fast Breeder Reactor Safety Analysis, Report EUR 5787 EN, Applied Mechanics Division, Joint Research Centre, Ispra, Italy, 1977. [23] LSTC, LS-DYNA Keyword User's Manual, Vol. 971, 2012.
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183 [24] I.M. Daniel, O. Ishai, Engineering Mechanics of Composite Materials, Oxford University Press, New York, 1994. [25] W.W. Chen, B. Song, Split Hopkinson (Kolsky) Bar: Design, Testing and Applications, Springer, New York, 2011. [26] N.-S. Choi, J.-E. Park, S.-K. Kang, Quasi-disk type microbond pull-out test for evaluating fiber/matrix adhesion in composites, J. Compos. Mater 43 (2009) 1663e1677. [27] S. Kang, D. Lee, N. Choi, Fiber/epoxy interfacial shear strength measured by the microdroplet test, Compos. Sci. Technol. 69 (2009) 245e251. [28] S. Tamrakar, Q. An, E.T. Thostenson, A.N. Rider, B.Z. (Gama) Haque,
183
J.W. Gillespie, Tailoring interfacial properties by controlling carbon nanotube coating thickness on glass fibers using electrophoretic deposition, ACS Appl. Mater. Interfaces 8 (2016) 1501e1510. [29] B. Gama, S.L. Lopatnikov, J.W. Gillespie, Hopkinson bar experimental technique: a critical review, Appl. Mech. Rev. 57 (2004) 223. [30] S.L. Lopatnikov, A.S. Lim, J.W. Gillespie, Split hopkinson pressure bar data reduction methodology for linear materials with memory, J. Eng. Mech. 138 (2012) 1157e1164. [31] P.J. Herrera-Franco, L.T. Drzal, Comparison of methods for the measurement of fibre/matrix adhesion in composites, Composites 23 (1992) 2e27.
Contents lists available at ScienceDirect
Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Test method
High rate test method for fiber-matrix interface characterization Sandeep Tamrakar a, c, *, Bazle Z. (Gama) Haque a, d, John W. Gillespie Jr. a, b, c, d a
Center for Composite Materials (UD-CCM), University of Delaware, Newark, DE 19716, USA Department of Materials Science & Engineering, University of Delaware, Newark, DE 19716, USA c Department of Civil & Environmental Engineering, University of Delaware, Newark, DE 19716, USA d Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 March 2016 Accepted 23 April 2016 Available online 25 April 2016
A new test method to directly characterize fiber-matrix interface properties under high rate of loading has been developed. A tensile Hopkinson bar with a modified incident bar is used to load a microdroplet test specimen. Numerical simulations were carried out to design the test specimen geometry and validate data reduction procedures for the dynamic interface experiments. Stress wave propagation in an S-2 Glass/Epoxy microdroplet specimen was studied with different droplet sizes (100 mme200 mm) and fiber gage lengths (2 mme6 mm). Simulation results indicate that dynamic equilibrium can be maintained up to a displacement rate of 10 m/s. Dynamic microdroplet experiments were conducted at a displacement rate of 1 m/s on S-2 glass/epoxy interface. Experimental results and post-failure inspection of the fiber matrix interface showed that the new test method is effective in measuring high rate interface properties of composites. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Interface Hopkinson bar High rate loading Microdroplet test
1. Introduction Fiber reinforced polymer composites have been widely used for lightweight structures subjected to dynamic loading conditions. High specific stiffness, strength and energy absorption makes composites an attractive lightweight alternative to conventional materials. Dynamic response of a composite material can depend on the strain rate dependent properties of the fiber, matrix and fiber-matrix interface that transfers load between the constituents. A strong bond between fiber and matrix is desirable for structural application, whereas a weak and ductile interface increases the toughness and is more suitable for impact and ballistic applications [1e3]. Energy absorption in a composite occurs through various mechanisms such as matrix cracking and delamination at the macroscale, and fiber breakage, fiber-matrix debonding and frictional sliding at the microscale. Macromechanical test techniques such as drop weight and dynamic punch shear tests provide insight into the role of interface on composite properties. Moreover, a strong correlation between the interfacial properties at microscale and the mechanical properties of composite materials at the macroscale has been reported [4e6]. Gao et al. [7] established a
* Corresponding author. Center for Composite Materials (UD-CCM), University of Delaware, Newark, DE 19716, USA. E-mail address: [email protected] (S. Tamrakar). http://dx.doi.org/10.1016/j.polymertesting.2016.04.016 0142-9418/© 2016 Elsevier Ltd. All rights reserved.
linear relationship between the interfacial shear strength (IFSS) obtained from microdroplet testing of a wide range of fiber sizings and punch shear strength of composite laminates fabricated from the same constituents. Mechanisms that govern the energy absorption process at the microscale have been found to be more significant than that at the macroscale [2]. Consequently, an opportunity to tailor the interface properties at the nano to micro length scale opens up methodologies to improve composite performance. Several test methods are available to quantify the interfacial properties at microscale such as microdroplet test, single fiber fragmentation test, fiber push out and fiber pull out tests [8e10]. However, most of these test methods have been employed only within a quasi-static loading regime. Tanoglu et al. [11] developed a dynamic interphase loading apparatus to load the interphase through micro-indentation method up to a displacement rate of 3 mm/s. Other researchers have used the microdroplet test method or its modified version (cylinder test) to study the rate sensitivity of the interface (See Table 1) up to about 4 mm/s. Greenfield et al. [12] developed a test method to load a single fiber fragmentation test specimen at high displacement rate of 1250 mm/s, which is the only study found in the literature to conduct micromechanical test in the meters per second range. In a fragmentation test, IFSS is back calculated based on the critical length of fragmented fibers and the energy absorbed during fiber matrix debonding, and frictional
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
175
Table 1 Various test methods and displacement rates from literature.
Tanoglu et al. [11] Gao [13] Morlin and Czigany [14] Greenfield et al. [12] Current study
Displacement rate (mm/s)
Test method
Properties
0.3e3.00 0.003 0.0002e3.33 1250 0.001e1000
Dynamic push out test Microdroplet test Cylinder test Single fiber fragmentation test Microdroplet test
IFSS and energy absorption IFSS and energy absorption IFSS IFSS IFSS and energy absorption
sliding is not measured. In order to characterize the interface properties at higher rate of loading, an experimental setup has been designed which utilizes a modified version of a tensile Hopkinson bar. The incident bar is modified to load a microdroplet test specimen to directly measure IFSS and the energy absorbed during fiber-matrix debonding.
determined in accordance with ASTM C1557. Apparent compliance (DL/F) was plotted against fiber gage length, and the fitted curve was extrapolated back to zero gage length. Fixture compliance (Cs) for the quasi-static test setup was 0.13 mm/N. Corrected modulus of elasticity was then calculated by correcting the displacement for fixture compliance as shown in Eq. (1).
2. Experimental methods
DLcorr ¼ ðDL Cs $FÞ
2.1. Materials S-2 glass fibers with (3-glycidoxypropyl) trimethoxy silane coupling agent and epoxy film former sizing obtained from Owens Corning Corporation were used. Epoxy resin DER 353 (Dow Chemical Company) was mixed with bis (p-aminocyclohexyl) methane (PACM-20) curing agent (Air Products and Chemicals, Inc.) at a stoichiometric ratio of 100:28 (weight ratio) to form the droplets. Detailed procedure regarding the preparation of microdroplet specimens is presented elsewhere [13]. 2.2. Quasi-static tests 2.2.1. Single fiber tensile test Quasi-static tensile tests were conducted on single S-2 glass fibers with two gage lengths (8 mm and 25.4 mm) at a strain rate of 0.002/s to determine the axial modulus, which will later be used for data reduction in microdroplet tests. Tensile tests were conducted using an Instron model 5848 MicroTester with 0.020 mm position resolution. A 5 N load cell was used to monitor force in the fibers. Using epoxy adhesive, a single fiber was glued to cardboard, which was then clamped to the Instron for tensile testing. S-2 glass fibers exhibited a linear force e displacement response until failure. Total displacement measured by the Instron includes axial elongation of fiber and displacement due to fiber slippage in the adhesive and clamped region. The influence of the compliance arising from the bonding technique diminishes as the gage length increases [15]. For accurate determination of the axial elongation of the fiber, fixture compliance for the quasi-static test setup was
(1)
where, DL is the total displacement corresponding to the force (F) in the fiber. The corrected modulus was calculated to be about 85e86 GPa, which lies within the range of the published data from the manufacturers [16]. The tensile strength of the S-2 glass fibers for gage lengths of 8 mm and 25.4 mm are 3.7 ± 0.5 GPa and 3.4 ± 0.5 GPa, respectively (Table 2). 2.2.2. Microdroplet test The microdroplet test method developed by Miller et al. [17] was adopted to quantify the fiber-matrix interface properties. A microdroplet specimen consists of a single droplet of resin matrix deposited and cured on a single fiber to create a realistic composite interface. One end of the fiber is attached to a load cell while a set of knives are used to shear off the droplet such that the failure occurs along the interface. Microdroplet experiments under quasi-static loading rate of 1 mm/s were conducted to establish a baseline using the custom setup built by Gao [18]. Using the force e displacement data, the average IFSS was calculated based on the measured failure load and interface shear area using Eq. (2).
t¼
F
(2)
pdf le
where, t refers to IFSS, F is the tensile failure load in the fiber at interface debonding, df is the diameter of the fiber and le is the embedded length of the microdroplet. Energies were normalized to allow for comparison of specimens that may have differences in fiber diameter, gage length and droplet
Table 2 Tensile properties of S-2 Glass fibers under quasi-static loading. Gage length (mm)
Strain rates (1/s)
Tensile strength (GPa)
Strain at failure (%)
Modulus of elasticity (GPa)
25.4 8
0.002
3.4 ± 0.5 3.7 ± 0.5
4.0 ± 0.9 4.3 ± 0.5
85.6 ± 4.9 85.9 ± 3.2
Table 3 Calculation of maximum droplet size based on statistical distribution of tensile strength [19]. Probability of fiber failure (%)
Tensile strength of fiber, sfiber (MPa)
Maximum allowable droplet size, le (mm)
1 2 5 40
1700 2000 2400 4000
85 100 120 200
176
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
Fig. 3. Typical incident and reflected signal in the incident bar showing specimen loading period.
Fig. 1. . Typical force displacement response of a microdroplet experiment (Data obtained during dynamic sliding is not considered for calculation).
size. In addition, the load-displacement curves were corrected for fixture compliance following the methodology of Gao [13]. Specific debonding energy (Eq. (3)) and specific energy during frictional sliding (Eq. (4)) were calculated as follows:
Z ddeb sp
Edeb ¼
di
F dd
pdf le
(3)
Z dmax
F dd d sp Efs ¼ fric; i pdf le le
(4)
Fig. 4. Calibration curve for laser displacement sensor (R2 ¼ 1).
For quasi-static loading, test specimen design criteria established by Gao [13] consider fiber strength statistics (smaller gage lengths exhibit higher strength) that places limits on maximum droplet embedded length for a given IFSS to ensure interfacial failure prior to fiber tensile failure (Eq. (5)).
sfiber 1 le < df 4 sIFSS
Fig. 2. Schematic representation of dynamic microdroplet test apparatus and details on modified end of the incident bar.
Fig. 5. Force displacement response of single fiber tensile test with 4 mm gage length (Loading rate: 3e5 m/s).
(5)
where, sfiber is the tensile strength of the fiber and sIFSS is the IFSS.
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
177
Table 4 Dynamic tensile properties of S-2 glass fibers. Gage length Strain rates Tensile Uncorrected Modulus of (mm) (1/s) strength (GPa) elasticity (GPa) 8 4 2
500 900 1800
4.8 ± 0.5 5.1 ± 0.5 5.4 ± 0.5
92.1 ± 3.6 80.6 ± 2.5 59.3 ± 3.7
Modulus of elasticity corrected for fixture Corrected Modulus of elasticity Corrected strain at compliance (GPa) (GPa) a ¼ 1.28 failure (%) 112.3 ± 5.3 116.3 ± 4.8 109.1 ± 13.5
87.3 ± 3.4 91.1 ± 2.8 85.7 ± 5.3
5.5 ± 0.7 5.6 ± 0.7 6.3 ± 0.9
is exerted by the matrix on to the fiber due to resin shrinkage during cure and the mismatch in coefficient of thermal expansion (CTE) between fiber and matrix that arises as the specimen cools to room temperature, and due to the surface roughness of the fiber. IFSS for this specific S-2 glass/epoxy system was calculated to be 47.8 ± 3.8 MPa. Specific energy up to complete debonding and during frictional sliding were 760 ± 350 J/m2 and 9300 ± 3000 kJ/ m3, respectively.
2.3. High rate tests
Fig. 6. Calculation of fixture compliance from zero gage length intercept of the fitted curve.
For a gage length of 2 mm, fiber diameter of 10 mm and assuming an IFSS of 50 MPa, maximum droplet size can be calculated based on the failure probability of a fiber with Weibull strength distribution (See Table 3). Weibull parameters were obtained from the literature for S-2 glass fibers [19]. Probability of fiber failure increases with increase in droplet size. Microdroplet experiments were conducted on droplet sizes ranging from 80 to 120 mm. A probability of fiber failure of less than 5% (i.e. 95% probability of interface failure) was deemed acceptable in our experimental design, particularly since smaller droplet sizes are difficult to achieve during specimen preparation. A gage length of 1e2 mm was maintained. At least 10 valid tests were considered for further data reduction. Microdroplet specimens exhibited a fairly linear force-displacement response until complete debonding, followed by dynamic sliding and a frictional sliding regime (Fig. 1). During frictional sliding, a fairly constant compressive force
2.3.1. Tensile hopkinson bar A tensile Hopkinson bar has been adapted [20,21] for high rate loading of the microdroplet specimen. The test fixture consists of an incident bar with a flange at the end and a hollow striker bar made of 7075-T6 aluminum alloy (Fig. 2). The incident bar is 6.35 mm in diameter and 1.52 m in length. The outer diameter of the circular flange attached to the end of the incident bar is 12.7 mm. The
Fig. 8. 2D axisymmetric LS-DYNA model.
Fig. 7. Specimen holder attached to the load cell, miniature knife edge attached to the incident bar and microdroplet test specimen.
178
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
Table 5 Material properties for aluminum, fiber and epoxy [16,24]. Properties, unit
Aluminum knife
S-2 glass fiber
Epoxy droplet
Density, gm/cc Young's modulus, GPa Poisson's ratio Bar velocity, m/s
2.70 69.00 0.285 5000
2.49 86.00 0.230 5470
1.27 4.3 0.35 1840
striker bar has an outer diameter of 12.7 mm and is 203.2 mm in length. During the experiment, a spring launcher accelerates the striker bar to a target velocity, which strikes the flange attached to the incident bar. A 70 mm thick soft paper soaked in petroleum jelly is used as pulse shaper to eliminate the high frequency noise generated when the striker bar impacts the flange. A semiconductor strain gage attached on the surface of the incident bar captures the resulting stress waves, which propagate in the direction opposite to the impact direction. A smooth tensile wave with constant amplitude loads the specimen for a period of about 100 ms, as indicated by the shaded area in Fig. 3. Velocity of wave propagation in the incident bar, calculated based on the monitored signal, was about 5000 m/s, which is in good agreement with theoretical value for aluminum. The tensile force induced in the specimen is directly measured by a fast response quartz piezoelectric load cell (Kistler 9712B5) with a capacity of 22.24 N. It has a frequency response of 115 kHz, which implies that the test duration of 100 ms is sufficient to collect at least 10 meaningful data points. Axial displacement at the loading end of the incident bar is monitored using a laser displacement sensor. A laser diode (110 mW output and 660 nm wavelength) with a circular beam is used. The laser beam passes through a beam expander and a line generator, which forms a horizontal laser line. The laser line is passed through the gap between the specimen holder and incident bar, and is collected on the sensor area (75.4 mm2) of the photodetector (DET100A) through a focusing lens. The data acquisition rate was 5 MHz, while the frequency response of the detector was 8 MHz. The laser sensor was calibrated by monitoring the voltage output while changing the gap width with a known distance. The linear relationship between the output voltage and the gap width
(Fig. 4) suggests that the intensity of the laser line is uniform along the length. This relationship was used to calculate the displacement of the loading end of the incident bar. 2.3.2. Single fiber dynamic tensile test Although the laser displacement sensor measures end displacements accurately, other sources of compliance exist and must be accounted for. Calculations of IFSS and energy absorption in a microdroplet test require accurate load and displacement measurement. Our approach is to validate calibration by conducting dynamic tensile tests of single S-2 glass fibers with rate independent axial modulus of elasticity. Load is measured directly and is accurate when dynamic equilibrium is achieved (see Section 3). Dynamic compliance calibration first considers compliance from the fixture and, secondly, a dynamic correction factor to provide accurate correction to our fiber standard. A similar dynamic correction measure has been employed in other studies [22]. Dynamic tensile tests were conducted on single fibers with a nominal diameter of 10 mm and gage lengths of 2 mm, 4 mm and 8 mm at a displacement rate of 3e5 m/s. The fiber was glued to the specimen holders attached to the load cell and the incident bar. Fig. 5 shows a fairly linear force displacement response up to failure for the S-2 glass fiber with 4 mm gage length. Since all dynamic tests were conducted within the same range of loading velocity, the strain rate increased with reduced gage length. Higher tensile strength resulted for lower gage length due to both size effect as well as strain rate effects. However, for the same gage length of 8 mm, the tensile strength increased from 3.7 GPa at 0.002/s (Table 2) to 4.8 GPa at 500/s (Table 4), showing strain rate dependency. Uncorrected modulus of elasticity for high rate of loading decreased from 92.1 GPa to 59.3 GPa when the gage length decreased from 8 mm to 2 mm (Table 4). This is due to the fact that the fixture compliance is large compared to the compliance of the 2 mm fiber, and its influence decreases at higher gage lengths, as described in Section 2.2.1. Analogous to the quasi static method, the fixture compliance must be accounted for to correct the axial elongation. 2.3.2.1. Fixture compliance. Fixture compliance of the tensile Hopkinson bar was determined in accordance with ASTM C1557. Fig. 6
Fig. 9. (a) Shear stress and (b) Radial stress distribution along the interface at force level 0.1 N (red) and 0.2 N (black) for quasi-static loading for a 200 mm droplet. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
shows the apparent compliance (DL/F) plotted as a function of fiber gage length (L0) normalized by its cross sectional area (A). DL is the displacement measured at the end of the incident bar by the laser sensor and F is the corresponding force. Fixture compliance of the system (Cs), given by the intercept of the curve at zero gage length, is 0.189 mm/N. The modulus corrected for fixture compliance now becomes gage length independent (Table 4). However, the modulus is consistently higher (about 30%) than the known properties of S-2 Glass fiber (Table 4).
2.3.2.2. Dynamic compliance correction factor. The modulus of elasticity for longer gage length is over-predicted in the dynamic tests, which has been reported in the literature for a similar testing system [20]. To ensure accurate displacement measurements, a dynamic correction factor (a) is applied after fixture compliance and gage length effects are accounted for in Eq. (6). The corrected displacement is calculated as follows:
DLcorr ¼ ðDL Cs $FÞ a
179
(6)
The compliance calibration factor (a) is chosen such that the corrected displacement would yield the published modulus of our calibration standard (85e90 GPa for S-2 Glass). In this particular case, a value of 1.28 was defined and gives excellent agreement for all gage lengths, as presented in Table 4. This dynamic correction factor was used in the dynamic microdroplet tests. 2.3.3. Dynamic microdroplet test The procedure to conduct dynamic microdroplet tests includes positioning the knife edges to have a gap of nominally 14 mm which is slightly larger than the fiber diameter (i.e. the end of the knife edges are 2 mm from the fiber surface) to load the droplet. On the other end of the specimen, the fiber was glued to the specimen holder attached to the load cell (Fig. 7). The specimen was preloaded and inspected to ensure the droplet was not loaded eccentrically. A tensile pulse was sent using a hollow striker bar, as
Fig. 10. Dynamic effects in interfacial shear stress distribution at force level 0.1 N (red) and 0.2 N (black) for droplet size 200 mm and fiber gage length 2 mm at displacement rates (a) 60 m/s, (b) 20 m/s, (c) 10 m/s and (d) 5 m/s.
180
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
3. Specimen design for dynamic loading
When the knife edge, with a much larger mass, comes in contact with the droplet at a certain velocity, the momentum transfer causes the droplet to accelerate to a velocity higher than the knife edge, causing the droplet to momentarily lose contact with the knife edge. Then, the droplet starts to decelerate and eventually springs back and comes in contact with the knife edge again. This sequence of event repeats until the knife edges and drop attain the same velocity. The larger drop of higher mass is accelerated to a less extent, and hence takes less time to achieve dynamic equilibrium (Videos of these mechanisms can be seen in the supplemental information provided). As such, the combination of the largest droplet (200 mm) and the smallest gage length (2 mm) was found to achieve equilibrium in the shortest time. However, it should be noted that the probability of fiber failure increases with larger droplets that require higher debonding forces (Table 3). Supplementary video related to this article can be found at http://dx.doi.org/10.1016/j.polymertesting.2016.04.016 The shear stress and radial stress distribution at different load levels for the quasi-static case is presented in Fig. 9. The load levels correspond to the axial force in the fiber gage length. The coordinates along the interface have been normalized with respect to the total embedded length of the droplet. There is a stress
Apart from developing the data reduction scheme and displacement correction methods, it is imperative to ensure dynamic equilibrium is achieved in the gage length and interface region during loading of the microdroplet. During a dynamic test, the microdroplet is subjected to compressive stresses as the tensile wave reaches the modified end of the incident bar. Consequently, shear stresses are induced in the fiber-matrix interface region, which in turn loads the fiber in tension. A complex series of wave propagation and reflections develop within the specimen. Finite element modeling of a microdroplet (Fig. 8) was conducted to study the dynamic effects and select appropriate test specimen geometry. A 2D axisymmetric FE model was developed and analyses were done using the commercially available finite element code LS-DYNA 971 [23]. Linear elastic elements were used and perfect bonding was assumed between fiber and droplet. Mesh size of 0.625 mm was chosen along the droplet length (adjacent to the fiber) to accurately describe the spatial gradients in interfacial stress along the embedded length. Explicit time steps are governed by the higher wave speed of the fiber (0.00011 ms). A characteristic time is defined based on the specimen geometry and wave speed of the respective materials presented in Table 5. For example, the characteristic time for wave propagation along the fiber with a 2 mm gage length is 0.37 ms Consequently, the numerical model is suitably refined with enough time resolution to study the wave propagation along the fiber and interface. Wave propagation in the fiber gage length and dynamic effects in the interfacial region were investigated for different combination of gage length (2 mme6 mm) and droplet sizes (100 mme200 mm) at different displacement rates (5 m/s to 60 m/s). When the gage length was reduced for a constant droplet size, the time to achieve dynamic equilibrium in the gage length decreases. Dynamic equilibrium refers to the specimen configuration where the difference between the forces measured by the load cell on one end and the load applied to the droplet by the knife edge at the other end of the gage length is an acceptable small error throughout the duration of the test [25]. For this study, dynamic equilibrium was said to be achieved when this error in forces at the two ends of the gage length (F1 and F2 in Fig. 8) became less than 5%. In general, it took about 4e6 wave reflections within the gage length to reach equilibrium. When the gage length was kept constant, the time to reach dynamic equilibrium decreased with increase in droplet size.
Fig. 11. Typical signal recorded during the dynamic microdroplet test. (a) Force signal measured from the piezoelectric load cell, (b) Displacement signal measured from the laser sensor.
described earlier, to begin the test. The compliance correction for the microdroplet test must be modified since only one end of the specimen is glued, while the droplet on the other end is loaded by the knife edge (Fig. 7). Since both ends of the single fiber tests are identical, it is assumed that the compliance due to bonding from each end is equivalent. A value of 0.0945 mm/N was used as the fixture compliance (Cs) for the microdroplet test. Then, the corrected displacement (d) applied to the droplet by the loading knives was calculated using Eq. (7). In this equation, the measured laser displacement (DL) was corrected for fixture compliance and dynamic compliance correction. The displacement associated with fiber stretching (the second term in Eq. (7)) was also subtracted to obtain the droplet displacement used to calculate energy absorption during debonding and sliding (see Eqs. (3) and (4)).
d ¼ DL
Cs $F 2
a
F$Lo A$E
(7)
where, a ¼ 1.28 and E ¼ 85 GPa.
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
concentration at the loading end of the droplet (present in all of the interface test methods), which decreases to zero at the other end of the droplet. The mechanical loading places the interface under radial tension near the loading end of the droplet. This suggests that the crack initiation near the loading tip is due to mixed mode loading [26e28]. Fig. 10 shows the comparison between the quasi-static and high rate loading cases at two load levels for different displacement rates. The state of stress for high rate tests converge to the quasistatic tests when the velocity is 10 m/s or less, indicating wave propagation and inertial effects have been minimized. In this case, the data reduction equations presented in Eqs. (2)e(4) can be used for high rate tests. It should be noted that this same rationale is used to establish dynamic equilibrium in compression testing using a split Hopkinson pressure bar at high strain rates [29,30]. 4. Results and discussion Dynamic microdroplet experiments were conducted on droplets with embedded length ranging from 80 to 120 mm at an average displacement rate of 1 m/s. Duration of the loading to reach failure load was in the range of 75e220 ms. Typical force and displacement signals are shown in Fig. 11. The displacement signal increases monotonically while the specimen is being loaded, indicating a constant velocity during the test. The load cell vibrates at its natural frequency of 115 kHz immediately after failure occurs. As a result, the frictional sliding between the fiber and the failed droplet could not be captured. However, since droplets were still attached to the fiber after the test, it is possible to reload the specimen to measure the sliding energy.
181
Post-test inspections were carried out to check the validity of the tests. The specimens were inspected under scanning electron microscope to ensure that the droplet did not have major fractures within the drop other than the desired interfacial failure near the fiber surface, and that the indentation due to knife edge was minimal (See Fig. 12a). The residual epoxy at the top of the drop (Fig. 12b), which is the location of crack initiation due to the tensile stresses near the loading end [28], should be localized (See Fig. 9). Also, to ensure that the failure occurred along the fiber matrix interface region, the surface of the fiber was investigated. Fig. 12c and d shows a fairly smooth fracture surface with a few traces of epoxy. After all these criteria have been met, IFSS and the energy absorbed by the interface were calculated using Eqs. (2)e(3). Fig. 13 shows a fairly linear force displacement response until complete debonding of the interface occurs. Average IFSS increased to 80.6 MPa for high rate loading (1 m/s) from 47.8 MPa at quasistatic loading rate (1 mm/s). The difference between IFSS for high rate of loading and quasi-static loading is statistically significant. Also, the energy absorbed by the interface up to debond increased from 760 J/m2 to 1950 J/m2 with increase in the displacement rate (Table 6). These results suggest that this S-2 Glass/epoxy/sizing system has fiber matrix interface properties that are sensitive to the rate of loading. The coefficient of variation (COV) in the IFSS for quasi-static loading rates are on the lower side (8%) compared to most of the studies reported in literature that can be as high as 33% [10]. However, the COV increases to 15% for the high rate test, which is still within the acceptable range for such test methods. IFSS is sensitive to the gap width and the symmetricity of the droplet loading by the knife edges. Very small differences in the point of contact of the knife edges can cause rotation and bending of the
Fig. 12. SEM images of tested microdroplet specimen (a) Debonded microdroplet, (b) Residual epoxy at the loading end of the tested specimen, (c) Fracture surface at the top of the specimen, (d) Fracture surface along the embedded length.
182
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183
1 mm/s to 1 m/s. Acknowledgments Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-12-2-0022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. The authors would like to thank Prof. Weinong Chen and Matthew Hudspeth for collaborations on the development of the tensile Hopkinson bar. References Fig. 13. Force vs. raw displacement response from dynamic microdroplet experiments.
Table 6 Comparison of experimental results. Velocity (mm/s) Quasi-Static Test High Rate Test
IFSS (MPa)
COV (%)
Specific energy debond (J/m2)
COV (%)
1
47.8
8
760
45
106
80.6
15
1950
44
fibers prior to dynamic loading, and significantly affect the interfacial shear stress distribution and, ultimately, IFSS even at quasi static loading rates [31]. To ensure uniform loading, we monitored the bending of the fiber during static preload and adjusted the stages holding the knife edges. Another way to reduce such variability would be to use a disk with a concentric hole to load the microdroplet [26]. During dynamic testing, bouncing of the droplet can also be an added source of variability. When there is not enough preloading, or if there is a gap between knife edge and the droplet, loading and unloading of the droplet can be seen in the force-time signal. Such results are discarded before further data reduction. 5. Conclusions An experimental method for characterizing fiber matrix interface properties at high rate of loading has been developed. The experimental method presented in this study is the first of its kind to characterize fiber-matrix interface properties (i.e. strength and debonding energy) in the meters per second range. The experimental setup consists of a tensile Hopkinson bar with a modified end to load a microdroplet test specimen. Finite element analysis was carried out to design optimum specimen geometry, including the fiber gage length and droplet size, and acceptable displacement rates within which the specimen would be in dynamic equilibrium. Simulation results showed that the shear stress distribution along the interface would be in dynamic equilibrium up to a displacement rate of 10 m/s. The combination of 2 mm gage length and 200 mm droplet has the shortest time to reach equilibrium without fiber failure and, therefore, has the highest loading rate potential. Our experimental set-up was used to test microdroplet specimen with S-2 glass/epoxy system. Experimental results suggest that the IFSS and specific energy absorption capacity are sensitive to the rate of loading. IFSS and debond energy increased by a factor of 1.7 and 2.6, respectively, when the displacement rate was increased from
[1] M. Labronici, H. Ishida, Toughening composites by fiber coating: a review, Compos. Interfaces 2 (1994) 199e234. [2] M. Tanoglu, S.H. McKnight, G.R. Palmese, J.W. Gillespie Jr., The effects of glassfiber sizings on the strength and energy absorption of the fiber/matrix interphase under high loading rates, Compos. Sci. Technol. 61 (2001) 205e220. [3] L.J. Broutman, B. Das Agarwal, A theoretical study of the effect of an interfacial layer on the properties of composites, Polym. Eng. Sci. 14 (1974) 581e588. [4] B. Harris, P. Beaumont, E. De Ferran, Strength and fracture toughness of carbon fibre polyester composites, J. Mater. Sci. 6 (1971) 238e251. €der, K. Grundke, H. Jacobasch, G. Wachinger, Surface, interphase and [5] E. Ma composite property relations in fibre-reinforced polymers, Composites 25 (1994) 739e744. [6] J. Sun, L. Gao, Development of a dispersion process for carbon nanotubes in ceramic matrix by heterocoagulation, Carbon N. Y. 41 (2003) 1063e1068. [7] X. Gao, J.W. Gillespie, R.E. Jensen, W. Li, B.Z. (Gama) Haque, S.H. McKnight, Effect of fiber surface texture on the mechanical properties of glass fiber reinforced epoxy composite, Compos. Part A Appl. Sci. Manuf. 74 (2015) 10e17. [8] J. Kim, Y. Mai, Engineered Interfaces in Fiber Reinforced Composites, first ed., Elseview Science Ltd, 1998. [9] U. Gaur, B. Miller, Microbond method for determination of the shear strength of a fiber/resin interface: evaluation of experimental parameters, Compos. Sci. Technol. 34 (1989) 35e51. [10] M.J. Pitkethly, J.P. Favre, U. Gaur, J. Jakubowski, S.F. Mudrich, D.L. Caldwell, et al., A round-robin programme on interfacial test methods, Compos. Sci. Technol. 48 (1993) 205e214. [11] M. Tanoglu, S.H. McKnight, G.R. Palmese, J.W. Gillespie, A new technique to characterize the fiber/matrix interphase properties under high strain rates, Compos. Part A Appl. Sci. Manuf. 31 (2000) 1127e1138. [12] M. Greenfield, A. Pedicini, L. Penn, Development of a single fiber fragmentation test for high strain rates, Int. J. Adhes. Adhes. 20 (2000) 403e407. [13] X. Gao, Tailored Interphase Structure for Improved Strength and Energy Absorption of Composites, University of Delaware, 2006. [14] B. Morlin, L.M. Vas, T. Czigany, Investigation of fiber/matrix adhesion: test speed and specimen shape effects in the cylinder test, J. Mater. Sci. 48 (2013) 3185e3191. [15] D. Turek, On the tensile testing of high modulus polymers and the compliance correction, Polym. Eng. Sci. 33 (1993) 328e333. [16] AGY, Advanced Materials: Solutions for Demanding Applications, 2004. [17] B. Miller, P. Muri, L. Rebenfeld, A microbond method for determination of the shear strength of a fiber/resin interface, Compos. Sci. Technol. 28 (1987) 17e32. [18] X. Gao, R.E. Jensen, W. Li, J. Deitzel, S.H. McKnight, J.W. Gillespie, Effect of fiber surface texture created from silane blends on the strength and energy absorption of the glass fiber/epoxy interphase, J. Compos. Mater 42 (2008) 513e534. [19] M.R. Gurvich, A.T. DiBenedetto, S.V. Ranade, A new statistical distribution for characterizing the random strength of brittle materials, J. Mater. Sci. 32 (1997) 2559e2564. [20] J. Lim, W.W. Chen, J.Q. Zheng, Dynamic small strain measurements of Kevlar® 129 single fibers with a miniaturized tension Kolsky bar, Polym. Test. 29 (2010) 701e705. [21] M. Hudspeth, X. Nie, W. Chen, R. Lewis, Effect of loading rate on mechanical properties and fracture morphology of spider silk, Biomacromolecules 13 (2012) 2240e2246. [22] C. Albertini, M. Montagnani, Dynamic Material Properties of Several Steels for Fast Breeder Reactor Safety Analysis, Report EUR 5787 EN, Applied Mechanics Division, Joint Research Centre, Ispra, Italy, 1977. [23] LSTC, LS-DYNA Keyword User's Manual, Vol. 971, 2012.
S. Tamrakar et al. / Polymer Testing 52 (2016) 174e183 [24] I.M. Daniel, O. Ishai, Engineering Mechanics of Composite Materials, Oxford University Press, New York, 1994. [25] W.W. Chen, B. Song, Split Hopkinson (Kolsky) Bar: Design, Testing and Applications, Springer, New York, 2011. [26] N.-S. Choi, J.-E. Park, S.-K. Kang, Quasi-disk type microbond pull-out test for evaluating fiber/matrix adhesion in composites, J. Compos. Mater 43 (2009) 1663e1677. [27] S. Kang, D. Lee, N. Choi, Fiber/epoxy interfacial shear strength measured by the microdroplet test, Compos. Sci. Technol. 69 (2009) 245e251. [28] S. Tamrakar, Q. An, E.T. Thostenson, A.N. Rider, B.Z. (Gama) Haque,
183
J.W. Gillespie, Tailoring interfacial properties by controlling carbon nanotube coating thickness on glass fibers using electrophoretic deposition, ACS Appl. Mater. Interfaces 8 (2016) 1501e1510. [29] B. Gama, S.L. Lopatnikov, J.W. Gillespie, Hopkinson bar experimental technique: a critical review, Appl. Mech. Rev. 57 (2004) 223. [30] S.L. Lopatnikov, A.S. Lim, J.W. Gillespie, Split hopkinson pressure bar data reduction methodology for linear materials with memory, J. Eng. Mech. 138 (2012) 1157e1164. [31] P.J. Herrera-Franco, L.T. Drzal, Comparison of methods for the measurement of fibre/matrix adhesion in composites, Composites 23 (1992) 2e27.