Dynamic tensile stress–strain characteristics of carbon/epoxy laminated composites in through-thickness direction

The effect of strain rate up to approximately ε̇ = 102/s on the tensile stress–strain properties of unidirectional and cross-ply carbon/epoxy laminated composites in the through-thickness direction is investigated. Waisted cylindrical specimens machined out of the laminated composites in the through-thickness direction are used in both static and dynamic tests. The dynamic tensile stress–strain curves up to fracture are determined using the split Hopkinson bar (SHB). The low and intermediate strain-rate tensile stress–strain relations up to fracture are measured on an Instron 5500R testing machine. It is demonstrated that the ultimate tensile strength and absorbed energy up to fracture increase significantly, while the fracture strain decreases slightly with increasing strain rate. Macroand micro-scopic examinations reveal a marked difference in the fracture surfaces between the static and dynamic tension specimens.

The primary objective of the present work is to determine the tensile stress-strain relations of unidirectional and cross-ply carbon/epoxy laminated composites in the through-thickness direction at strain rates up to nearly 10 2 /s in the split Hopkinson bar (SHB).Waisted cylindrical specimens were used in both static and dynamic tests.The tensile stress-strain curves at low and intermediate strain rates were measured on an Instron 5500R testing machine.The influence of strain rate on the ultimate tensile strength, fracture strain and absorbed energy up to fracture was examined.Macro-and micro-scopic examinations were conducted to discuss the effect of strain rate on the fracture modes in the specimens.

Test composites and specimen preparation
42-ply unidirectional ([0 42 ]) and cross-ply ([0/90] 21s ) carbon/epoxy composite laminates with a nominal thickness of 10.05 mm were used.They were chosen to assess the effect of the reinforcement geometry on their tensile behavior.The laminates were prepared from pre-impregnated tapes each of size 500 × 500 mm 2 and processed in a heat press, i.e., the laminates were cured at a temperature of 125 • C for 1 hr under a pressure of 0.98 MPa and then cooled.The types of reinforcing fiber, matrix resin and fiber volume ratio are given in Table 1.The basic in-plane tensile characteristics of the unidirectional composite laminate in the longitudinal (L) and transverse (T) directions are listed in Table 2.The longitudinal (or fiber) and in-plane transverse directions are, respectively, represented by 1 and 2, and the through-thickness direction is represented by 3 (see, Fig. 1).Specimens were machined from the composite laminates in the through-thickness direction into short waisted cylinders.Figure 1 shows the shape and dimensions of the waisted tension specimen.The diameter (d = 15 mm) of the specimen ends was set equal to that of the Hopkinson bars.To ensure fracture in the gage (parallel) section, the specimen diameter was reduced to 5 mm.The gage length (l S = 4 mm) to diameter (d = 5 mm) ratio of the specimen was taken as 0.8, approximately corresponding to the specimen geometry suggested by Medina and Harding [26], and Ferguson et al. [29].To enable the specimens to be loaded in tension, magnesium end-caps were bonded to each end of the specimen using a high strength two-part epoxy adhesive (Sumitomo 3-M, Scotch weld R DP-460).A simple fixture (see, Fig. 2) was used to provide alignment of the end-caps with the specimen during bonding.

Low and intermediate strain-rate tension testing
The low and intermediate strain-rate tension tests were performed using the waisted specimens in the Instron 5500R testing machine at crosshead speeds V c of 1 and 50 mm/min, respectively.The end-caps was screwed into two fixtures and loaded until fracture.The tensile stress in the specimen was obtained from the force recorded with a 100-kN capacity load cell (Instron: Model 2525-801).The tensile strain in the specimen was determined from strain gages (Kyowa: KFG-2-120-C1-5) attached directly to the specimen parallel section.Both stress and strain data were recorded at sampling rates of 5 Hz for V c = 1 mm/min and 500 Hz for V c = 50 mm/min.

Split Hopkinson bar testing
Figure 3 indicates a schematic of the tensile SHB system used, which consists principally of AZ80A-F Mg alloy input and output bars, an AZ80A-F Mg alloy striker tube, a gun barrel and an associated recording system (not shown here).The specifications for the SHB system are listed in Table 3.The Mg alloy bars with low mechanical impedance were used to reduce a drastic impedance mismatch between the composite specimen (through-thickness acoustic impedance Z 4 × 10 6 kg/(m 2 s)) and conventional steel bars (Z 40 × 10 6 kg/(m 2 s)), resulting in a transmitted strain signal with a very low signal-to-noise ratio.The end-caps are screwed into the Hopkinson bars (see the inset in Fig. 3).Two pairs of strain gages (Kyowa: KFG-2-120-C1-5) were attached directly to the specimen parallel section to accurately measure the strain in the specimen.A pulse shaping technique [30] is applied to generate well-defined tensile strain pulses without higher frequency components in the input bar.Namely, a 0.8 mm-thick 1050 Al ring of a 16 mm inside diameter and a 21 mm outside diameter is attached onto the impact (right) side of the loading block with a thin layer of petroleum jelly.Details of the test procedure are given elsewhere [31].
From the elementary one-dimensional theory of elastic wave propagation [32], we can determine the nominal strain ε(t), strain rate ε(t) and stress σ (t) in the specimen from the tensile SHB test records as Here u and P are the displacement and the axial force on both ends of the specimen, respectively, (where subscripts 1 and 2 denote the left and right interfaces, respectively; see the inset in Fig. 3 where In the above derivations, the incident and reflected strain pulses are time-shifted to the specimen-input bar interface, and the transmitted strain pulse is time-shifted to the specimen-output bar interface.

Dynamic tensile behavior
A number of the tensile SHB tests were conducted using the composite specimens at room temperature.Figure 4 indicates a typical set of oscilloscope records from the SHB test on the unidirectional carbon/epoxy laminated composite.The upper trace gives the incident and reflected strain pulses (ε i and ε r ), the middle trace gives the strain pulse (ε t ) transmitted through the specimen, and the lower trace gives the strain pulse (ε sp ) from the specimen strain gage.The output signals from the strain gages were recorded at a sampling rate of 1 MHz.The recorded signal data are neither smoothed nor averaged electronically.Note that the duration ( 80 µs) of the transmitted strain pulse is much shorter than that ( 250 µs) of the incident and reflected strain pulses.This implies that a tensile fracture took place in the specimen during stress wave loading, because if a fracture occurs, a tensile strain pulse can no longer be propagated to the output bar. Figure 5 gives the time variations of the applied tensile forces P 1 and P 2 obtained from Eq. ( 5).It is experimentally verified that the dynamic force equilibrium across the specimen is valid.Figure 6 presents the time histories for the dynamic tensile stress σ (t) and strain ε(t) determined from the SHB analysis, or Eqs. ( 1) and ( 3), and the strain ε sp (t) measured by the strain gage on the specimen.Note that the strain calculated from the SHB analysis is larger than that from the specimen strain gage.This is primarily due to the occurrence of deformation in the fillets at the end of the gage length of the waisted specimen.Eliminating time t through σ (t) and ε sp (t) yields the dynamic tensile stress-strain relations.The crack initiation in the specimen took place at the peak stress (corresponding to the ultimate tensile strength σ UTS ) at 67 µs.The strain rate at fracture is expressed as εf = ε f /t f (t f : fracture initiation time).Figure 7 depicts the tensile stress-strain curves at three different strain rates.The initial slope (or initial modulus) and ultimate tensile strength σ UTS increase greatly with increasing strain rate.This may be due to the viscoelastic nature of the epoxy resin matrix itself [4].This result is consistent with a previous study [26] which reports that the initial modulus and tensile strength for a cross-ply    carbon/epoxy (T300/924) laminated composite increase significantly with strain rate in the range of 10 −4 to 10 3 /s.In contrast, the fracture strain ε f decreases slightly with increasing strain rate.The absorbed energy U T is obtained by numerical integration of the tensile stressstrain curveup to fracture strain measured in the static  and dynamic tests.In an attempt to evaluate the effect of strain rate on the tensile behavior for the unidirectional and cross-ply carbon/epoxy laminated composites, σ UTS , ε f and U T are plotted in Figs. 8 to 10 as functions of the strain rate at fracture.The test results display a significant amount of experimental scatter.This scatter is caused by inhomogeneity within the specimen.For both unidirectional and cross-ply carbon/epoxy laminated composites, the ultimate tensile strength and absorbed energy up to fracture increase dramatically, whereas the fracture strain decreases marginally with increasing strain rate at fracture.Furthermore, σ UTS , ε f and U T for the unidirectional carbon/epoxy laminated composite are slightly higher than those for the cross-ply one at low and high rates of strain.

Effect of strain rate on fracture mode
In an effort to validate the test results, we observed the macro-and micro-scopic fracture modes in both the static and dynamic tension specimens.Figure 11 depicts fracture appearance of the unidirectional specimens after static and dynamic testing.Typical tensile fracture occurs in the plane perpendicular to the specimen axis at all strain rates.Little effect of strain rate on the fracture mode can be found from a macroscopic point of view.Figures 12 and 13 show SEM micrographs of the static and dynamic fracture surfaces.For both the unidirectional and cross-ply specimens, the dynamic fracture surface is much rougher and more uneven than the static one.At low strain rates, the fracture surfaces exhibit fiber-matrix interfacial fracture for both the specimens.In contrast, in the dynamic fracture surfaces, we can observe the

01039-p.5
EPJ Web of Conferences fiber-matrix interfacial cracking and matrix cracking for the unidirectional specimens, and interlaminar delamination for the cross-ply ones.The different tensile stressstrain behavior at low and high rates of strain is supported by the different fracture surfaces in the specimens.Furthermore, there is significant effect of reinforcement geometry on the fracture surface at high strain rates.

Conclusions
The effect of strain rate up to nearly ε = 10 2 /s on the tensile stress-strain characteristics of the unidirectional and cross-ply carbon/epoxy laminated composites in the through-thickness direction has been examined in detail.From the present experimental investigation, we can draw the following conclusions: (1) The ultimate tensile strength and absorbed energy up to fracture exhibit a positive strain-rate sensitivity, whereas the fracture strain exhibits a negative one.(2) The ultimate tensile strength, fracture strain and absorbed energy of the unidirectional carbon/epoxy laminated composite are slightly higher than those of the cross-ply one at any strain rate.(3) The fracture surfaces are strongly affected by the strain rate and reinforcement geometry.

Figure 1 .
Figure 1.Geometry of static and dynamic waisted tension specimens (dimensions in mm).

Figure 2 .
Figure 2. Alignment fixture for bonding end-caps to waisted specimen.
); A, E and c o are the cross-sectional area, Young's modulus and the longitudinal elastic wave velocity of the Hopkinson (Mg alloy) bars; A S and l S denote the cross-sectional area ( π 5 2 /4 = 19.63 mm 2 ) and original gage length (= 4 mm) of the specimen.Eqs.(1) to (3) are derived under the assumption of dynamic force equilibrium across the specimen, i.e., P 1 (t) = P 2 (t) or

Figure 4 .
Figure 4. Typical set of oscilloscope records from tensile SHB test on unidirectional carbon/epoxy laminated composite (striker tube velocity: V s = 3.9 m/s).

Figure 8 .Figure 9 .
Figure 8.Effect of strain rate at fracture on ultimate tensile strength for two different carbon/epoxy laminated composites.

Figure 10 .
Figure 10.Effect of strain rate at fracture on absorbed energy for two different carbon/epoxy laminated composites.

Table 1 .
Types of reinforcing fiber and matrix resin used in two kinds of carbon/epoxy laminated composites.