Strain Rate Response of Cross-Linked Polymer Epoxies under Uni-Axial Compression (Dynamic Behavior of Materials)

ABSTRACT

The strain rate responses of several cross-linked polymer epoxy materials were investigated under uni-axial compression at low to high strain rates. The properties of the epoxy were tailored through a variety of monomer choices including aromatic, which provide stiff, high glass transition structural materials, and aliphatic, which can form elastomers. The molecular weight and molecular weight distribution as well as the chemical functionality of the monomers can be varied to provide further control over the mechanical response. High rate experiments (greater than 1/sec rates) were conducted using a modified split-Hopkinson Pressure bar (SHPB) with pulse-shaping to ensure that the compressive loading of the specimen was at constant strain rate under dynamic stress equilibrium. In this paper, moduli and yield strengths as a function of strain-rate of the epoxies are presented and compared in an effort to understand the effect of the different tailoring to their mechanical response.

INTRODUCTION

In general, there are two types of epoxies, the glycidyl and non-glycidyl epoxy resins. Each differs in the way that the epoxies are prepared. Glycidyl epoxies use a condensation reaction of dihydroxy compound, dibasic acid, and or a diamine and epichlorohydrin. Whereas, non-glycidyl epoxies are created using peroxidation of olefinic double bond. Each type of epoxy can be tailored to have a rubbery to a brittle toughness by changing the molecular weight, cross-link density, or adding a dispersed toughener into the cured epoxy.


These chemically cross-linked thermosetting polymer networks are used in a wide range of applications including composite laminates, anticorrosive coatings, polymer membranes, and electronics. Epoxies can range from glassy structures to flexible gels [1]. In order for epoxies to be used for composite laminates for armor applications, the material response under a variety of strain rates needs to be fully understood to develop complete material models.

As discussed in Rittel [2], as the epoxies undergo deformation majority of the mechanical energy is transformed into heat. The heat causes the specimens to undergo intrinsic strain softening followed by strain hardening. This phenomenon is described by Govaert et al. [3]. In 1995 Arruda et al. used an infrared detector to analyze the temperature effects of PMMA during quasi-static to intermediate strain rate compression testing. Arruda then reported that softening of the material occurring after the yield is a result from the combination of strain hardening/softening and thermal softening [4].

In this work, uni-axial compression experiments conducted on two epoxies are used to understand the mechanical responses from low to high strain rates. Quasi-static experiments were conducted using a servo-hydraulic Instron. High strain rate compression testing was carried out on a Kolsky bar which is also referred to as a Split-Hopkinson Pressure Bar (SHPB).

The SHPB technique allows for the study of materials under a dynamic loading with high strain-rate deformation. Jordan et al. [5] investigated the compressive behaviors of Epon 826/DEA epoxy from strain rates of 10-3 up to 104 s-1. Similarly, Chen et al. [6] used a modified SHPB from high strength aluminum to study the dynamic response of Epon 828/T-403. Moy et al. [7] used the same testing techniques to study the mechanical behavior of PMMA at various strain rates. All showed results describing the effects of increasing yield strength and modulus as a function of strain rate.

MATERIAL

The epoxies used in this experimental investigation are Di-Glycidyl of Bisphenol A cross-linked with Jeffamine Diamine D400 (DGEBA D400), and Di-Glycidyl of Bisphenol F cross-linked with Jeffamine Diamine D400 (DGEBF D400). The polymers bisphenol (resin) and Jeffamine (curing agent) were acquired from Aldrich Chemical Company. The epoxy resin and curing agent were mixed and cured at the Army Research Laboratory

Each epoxy mixture were poured into a custom fabricated stainless steel mold designed to provide a specimen diameter of 6.35 mm. The molded epoxy, right cylinder is about 152.4 mm long. Figure 1 shows a picture of each half of the mold. The bottom of the fixture is completely enclosed and the top has a threaded opening. Prior to the casting, mold release was used to ensure the epoxy can be easily removed from the steel mold. Otherwise forcible removal can damage the relatively thin epoxy rod. All compression experiments were conducted at room temperature.

Once the epoxy has completely cured, right cylinder 3.18 mm gage length compression test specimens were then fabricated. Diameter to length ratio of these compression specimens is 2:1. Then, the specimen faces at both ends were machined to be flat and parallel to each other with a smooth surface finish. After the final machining, the test samples for DGEBA D400 and DGEBF D400 were then annealed in an oven at 76°C and 66°C respectively for 4 hours to eliminate any residual stresses caused from the cutting tool during machining. This annealing temperature is 20°C above the glass transition temperature, Tg for DGEBA D400 and DGEBF D400 which is 56°C and 46°C, respectively.

Epoxy Molds for Compression Specimens

Figure 1: Epoxy Molds for Compression Specimens

LOW RATE EXPERIMENTS

The quasi-static (10-/sec), (10-/sec), and intermediate (1/sec) strain rate experiments were conducted on an Instron 1331 servo-hydraulic test frame. A LabView-based program was used to generate an exponentially decaying waveform through a WaveTek function generator to command the Instron controller. This process allowed for a constant true-strain rate compression experiments to be achieved. The load and displacement data were acquired using a separate LabView data acquisition program. Mineral oil was used as lubrication on the specimen ends to minimize friction during the compression. Hardened steel compression platens with a swivel base were used to compensate for any minor misalignment in the loading train. In order to correct the displacement data for the effect of machine compliance, the compliance of the Instron test machine was measured and the displacement due to machine compliance was subtracted from the measured machine displacement..

HIGH RATE EXPERIMENTS

High rate experiments were conducted on a modified SHPB. A SHPB consists of a striker, an incident bar, and a transmission bar as shown in figure 2. The working principle of such setup is well documented [8, 9]. The bars used for the incident bar and transmit bar in the test setup were made from high strength Al 7075 that were specified to be centerless grounded to a diameter of 19 mm. Various annealed copper disks with different diameters and thicknesses were used for pulse shaping.

Schematic of pulsed-shaped SHPB Set-up

Figure 2: Schematic of pulsed-shaped SHPB Set-up

Assumptions were made during the SHPB testing that homogeneous deformation in the specimen occurs, identical incident and transmitted bars, and lastly analysis was based on one-dimensional wave theory [10]. The nominal strain rate described by Kolsky in the specimen is

tmp19-66_thumb

Where c0 is the elastic bar-wave velocity of the bar material, L is the original specimen gage length, and eR(t) is the time-resolved strain from the reflective pulse from the incident bar. Integration of equation 1 with respect to time yields the time-resolved axial strain of the specimen. The axial stress, a, of the specimen is determined using the equation

tmp19-67_thumb

Where As is the cross-sectional area of the specimen, At is the cross-sectional area, Et is the Young’s modulus, and st(t) is the time-resolved axial strain from the transmission bar.

RESULTS AND DISCUSSION

Figure 3 shows a typical set of stress pulses from the input and output bars from the SHPB with pulse shaping. The stress waves (incident, reflected, and transmitted) are identified on the graph.

Typical input and output stress pulses

Figure 3: Typical input and output stress pulses

Plotting the true strain as a function of time (Figure 4) for the high rate experiment shows that the epoxy sample is undergoing a near constant strain rate. Since a majority of the curve is linear, a valid constant strain rate compression test has been achieved.

Compressive True Strain as a function of Time

Figure 4: Compressive True Strain as a function of Time

Stresses in the specimen/bar interface at each ends are shown in Figure 5. This indicates that dynamic stress equilibrium in the high rate experiments is achieved through pulse-shaping of the incident wave. This ensures that uniform loading is accomplished throughout the test without cyclic loading pulses going through the material from the incident stress wave.

summarizes the mechanical response for DGEBF D400 from low to high strain rates. The individual plots with either an "X" or "O" states whether the specimen has failed or not failed, respectively. The "failed" compression test specimens are deemed by evidence of visible cracks. As a result, the epoxy specimens tested at 2000/sec strain rate and higher have various cracks in the direction of loading. In this paper, no high rate experiments were completed for the DGEBA D400.

Figure 6 summarizes the mechanical response for DGEBF D400 from low to high strain rates. The individual plots with either an "X" or "O" states whether the specimen has failed or not failed, respectively. The "failed" compression test specimens are deemed by evidence of visible cracks. As a result, the epoxy specimens tested at 2000/sec strain rate and higher have various cracks in the direction of loading. In this paper, no high rate experiments were completed for the DGEBA D400.


Figure 5: Stresses at Specimen/Bar Interfaces for DGEBF D400 at 4200s

Strain Rate with Pulse-Shaping

Specimen failure did not occur for the test at 1500/sec. Just like the specimens at the lower rate, this specimen did not have any visible signs of cracks. The specimen’s initial gage length was 3.19 mm. The total measured deformation is about 20%. Eight hours after testing, the specimen recovered to a near 100% of the initial gage length. It is quite evident that adiabatic heating effects are present at this strain rate. When the temperature for this epoxy material reaches above the Tg the behavior would change to behaving similarly to an elastomer. Thus, the value for the yield strength at 1500/sec cannot be confirmed.

True Stress as a Function of True Strain for DGEBF D400

Figure 6.True Stress as a Function of True Strain for DGEBF D400

Figure 7 shows the stress-strain behavior for the epoxies DGEBA D400 and DGEBF D400 at the lower strain rates. The DGEBA D400 has a significant lower flow stress for a given strain rate than the DGEBF. For all quasi and intermediate experiments, strain hardening was evident at strains approximately 0.04. Interestingly, the stress-strain behavior for DGEBF at 0.001/sec is similar to DGEBA at 1/sec.

True Stress as a Function of True Strain for DGEBA D400 and DGEBF D400 at Quasi-Static through Intermediate Strain Rates

Figure 7: True Stress as a Function of True Strain for DGEBA D400 and DGEBF D400 at Quasi-Static through Intermediate Strain Rates

To illustrate the effects of strain rate on the different epoxies, the yield strength and modulus as a function of strain rate are shown in Figure 8 and Figure 9, respectively. From both figures, it demonstrates that the DGEBF epoxy is rate sensitive. As stated earlier, high rate experiments were not conducted for DBEBA. Furthermore, these results show a bi-linear behavior for the DGEBF in both plots.

Yield Strength as a Function of Strain Rate for DGEBA D400 and DGEBF D400

Figure 8: Yield Strength as a Function of Strain Rate for DGEBA D400 and DGEBF D400

Modulus as a Function of Strain Rate for DGEBA D400 and DGEBF D400

Figure 9: Modulus as a Function of Strain Rate for DGEBA D400 and DGEBF D400

Figure 10 shows the pictures of both (a) DGEBA D400 and (b) DGEBF D400 epoxy compression specimens tested at the1/sec intermediate strain rate. In both cases, no signs of cracks were present.

Photo of the Tested Compression Experiments for (a) DGEBA and (b) DGEBF at 1/sec

Figure 10: Photo of the Tested Compression Experiments for (a) DGEBA and (b) DGEBF at 1/sec

Photo of the Tested Compression Epoxy DGEBF at (a) 1500/sec, (b) 2000/sec, and (c) 2600/sec

Figure 11: Photo of the Tested Compression Epoxy DGEBF at (a) 1500/sec, (b) 2000/sec, and (c) 2600/sec

Figure 11a, 11b, and 11c shows the pictures of the compression tested DGEBF D400 specimens tested at 1500/sec, 2000/sec, and 2600/sec, respectively. Since the specimen tested at 1500/sec did not have any cracks, the final gage length was measured at 3.18 mm which is only 0.24% of the initial gage length. Yet, the maximum strain from the SHPB calculations is about 20%. This proves that the epoxy transitioned from a glassy state to a rubbery state. The specimen DGEBF D400 at strain rate of 2000/sec showed cracking in the center of the specimen along with cracks radiating outward. Although the specimen failed, the specimen continued to remain intact. This specimen was tested to strain of 8%.

Figure 11c shows DGEBF D400 at a strain rate of 2600/sec. This specimen was tested to strain of 9%. At this strain rate, the specimen showed many more cracks then the previous specimen tested at a strain rate of 2000/sec. The specimen exhibit cracking located in the center of the specimen which is in a circular pattern. The specimen also has radial cracks moving outward towards the specimen edges where the edges start to split apart from the body of the specimen. Although the damage is severe the specimen remains intact. Specimens tested at strain rates of 3500/sec and 4200/sec were pulverized during testing. In fact, at these higher strain rates, some of the recovered pieces show evidence of melting and fusing together of the debris. The specimens tested at the strain rate of 3500/sec had larger fragments compared to the specimens tested at 4200/sec.

SUMMARY

Compression testing on two epoxies, DGEBA D400 and DGEBF D400, was conducted at quasi-static, intermediate, and high strain rates. A near constant strain rate was achieved for the SHPB experiments by stress pulse-shaping the incident wave. Summary of the stress-strain responses for DGEBF show that the epoxy is rate sensitive. Both the yield strength and modulus increase with the increase in the strain rate. Furthermore, results indicate a bi-linear mode from the yield strength and modulus as the function of strain rate graphs. Adiabatic heating effects are quite evident. In particularly to the compression experiment conducted at 1500/sec. The specimen at this rate recovered to a near 100%. Future efforts will investigate the adiabatic heating effects for the high rate experiments as well as other epoxy groups.

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