In the ASTM D1822 tensile-impact energy standard test method [23] for breaking plastics and electrical insulating materials, the energy to fracture a specimen by shock in tension is determined by the kinetic energy extracted from the pendulum of an impact machine in the process of breaking the specimen. Qualitatively, it is reported to present intermediate strain rates when compared with the high rate of the Izod test (ASTM D256 standard [24]) and the low rate of the common tension test (ASTM D638 standard [25]), and thus, its principle was selected as the basis of this research.

The head pendulum of a Charpy machine was modified in agreement with ASTM D1822 standard for tensile-impact testing. One of the specimen’s end is attached to the pendulum head with a bolt as shown in Fig. 2. In the other end, a longer bolt is attached. When the pendulum is released, the longer bolt hits the anvil at the bottom of the pendulum trajectory, and at that point the tensile-impact event starts: one end of the specimen is tensed by the pendulum head that continues its travel and the other end is constrained by the anvil.

Figure 2 Source: The Authors.

The machine is instrumented to acquire acceleration and displacement data, enabling to obtain the stress-strain curve. A Dytran 2W033 accelerometer with a frequency response of 51.2 kHz was used to record the instantaneous accelerations with which the forces were calculated. An encoder with 1000 pulses per revolution was used to record the displacements in terms of the angular position. Because the pendulum trajectory is much longer than the deformation region of the specimen, which is hit at the bottom of the pendulum trajectory, a light barrier was used as an initial filter in order to save only the tensile-impact region data. The information transmitted by the sensors was acquired by an NI cDAQ 9174 and a SMT32Discovery, while the light barrier information was attained by a NI 6212 DAQ with a sampling frequency of 400 kHz. The data acquired by the acquisition cards were filtered with a low-pass filter in LabVIEW, following the recommendations of the SAE J2749 standard [26], so that experimental tests of resonance were performed on the modified Charpy machine giving results between 10-12 kHz, so that the resonance frequencies of the Charpy machine do not interfere with the obtained results. Eliminating these frequencies is more complex to achieve in dynamic tests than in quasi-static tests [19,27].

Additionally, a Phantom V9-3072MC high-speed camera was used to record the test in such a way that the precise moment of impact between the bolt in the specimen and the anvil could be determined. The camera has a speed of 1016-23391 fps with 1632x1200 and 480x120 resolution. The camera began recording 100 ms after the light barrier was activated, setting this time as the initial (zero) time of the test.

Because there are no standard procedures for obtaining stress-strain curves during tensile- impact tests on plastic materials [1], two specimen types were used: 1) ASTM D1822 type S specimen (Fig. 1a), the same used for quasi-static tests, and 2) ASTM D638 type V specimen (Fig. 1b). Both specimens were die cut from 3 mm thick injection molded plates. Although the ASTM D1822 standard has another type of specimen, the type L, it is almost identical to the D638 specimen and therefore, type S was selected.

Tests were performed at temperatures between 29°C, similar to those of the quasi-static tests. The pendulum head was released from an initial position of 45°, reaching a speed of 3.1 m/s at the bottom of its trajectory where the specimen hits the anvil. Twenty replicate samples per material were used. The elastic modulus, E, yield strength at 0.2% offset, σ _y , maximum strength, σ _max , and percent elongation at break or rupture strain, e _break were calculated from the stress-strain curves according to Annex 1 of ASTM D638 standard [25].

Once the tensile-impact machine was instrumented, tests were performed in order to evaluate the repeatability of the acquired data. These tests consisted on positioning the pendulum at an initial position of 90°, and then leaving it in free fall, acquiring angular position and acceleration data with the encoder and accelerometer, respectively (Fig. 4). Ten tests were performed. A 99.46% and 81.48% of repeatability was found for angular position and acceleration, respectively, which, according to Belingardi [28] and Chapra [29] are adequate for this type of dynamic testing.

Figure 4 Source: The Authors.

Linear displacements were calculated from the angular displacements through the pendulum arm length (69 cm). Fig. 5a shows the displacement vs time curve during a tensile-impact test, the angular displacement from the impact to the fracture of the specimen was 0.3 degrees which represents linearly 3.6 mm, for this reason it was assumed that the movement was always linear and approximate the calculation of the force to Newton's second law, which represents for this study, a difference of 4x10^-4% from the linear to the rotational. At each time step the engineering strain (e) is calculated as the equation 1

Figure 5 Source: The Authors.

where ∆L is the elongation and L₀ the initial gage length. For the D638 specimen L₀ is 9.53 mm. However, for the D1822 type S specimen there is no gage length zone so 9.53mm was also used for comparison between the different specimens, because equation 1 requires a L₀ it was decided to be the same as the test specimen to be compared for ease of calculation. Note that the rest of the specimen dimensions are very similar to the D638 standard.

From the acceleration (a) vs time curve (Fig. 5b) the force (F) was estimated as the eq. 2. A program in LabVIEW obtained the accelerations (see section 2.3.1) and following Newton's law, the acceleration multiplied by the mass of the body which was assumed totally inelastic at the time of impact. Because the mass of the anvil is much bigger than the specimen, it was assumed that during its deformation until the fracture it is a single body.

where m _p is the mass of the pendulum arm and head (8.2 kg).

Stresses (σ) were calculated as the equation 3

where A ₀ is the initial area of the cross-section (9.54 mm²). Fig. 5c shows the obtained stress-strain curve for this case.

The engineering stress-strain curves obtained from the tensile-impact tests at an initial arm position of 45° on PP-Co, PP-Ho and HDPE are shown in Fig. 6 for both types of specimens (D638 and D1822). Note that for tests with the D1822 specimen’s dispersion in the curves seems to be lower. Coefficients of variation were calculated for each test and are shown in Table 2. Effectively, the variation in tests with D1822 is lower than with D638 specimens, which has been reported in other studies [30,31].

Figure 6 Source: The Authors.

Table 2

Source: The Authors.

To obtain the average stress-strain curve for each test, outliers were eliminated (Fig. 8) with a boxplot analysis. A repeatability higher than 75% was found for all the tests. A boxplot analysis was used because the distribution was not normal, since the average ( ) and the median (Me) is very far and the sizes of the boxes were not symmetrical as shown in the Fig. 7. Also, analysis of variance (ANOVA) was performed to find the repeatability of the data with a confidence level of 95%. The standard deviation and mean are a function of the sample time. As a result, a repeatability of approximately 75% was found. The average stress-strain curves for each material during the quasi-static and tensile-impact tests with both specimens are shown in Fig. 8 for comparison. Fig. 7 shows Young's module for HDPE tests with specimen D1822 in a boxplot analysis, where a) we can see outliers that after being removed become b), and thus obtained the values of the mechanical properties of each material. In Table 1 the mechanical properties obtained from these curves are summarized.

Figure 7 Source: The Authors.

Figure 8 Source: The Authors.

It is observed that at higher strain rates the elastic modulus is upper. Curves from specimen D638 presented the highest values. As expected, opposite behavior is observed for rupture strain, which decreases as strain rate increases. Yield and maximum strength also increased, but in this case, values are very similar for both specimens D638 and D1822. At the beginning of the curves presented in Fig. 9, the results show that the stresses values of quasi-static data exceed those of high speed by a fraction of 5% deformation, after many observations this value was attributed to the adjustment of the specimens in the head pendulum at the moment of impact.

Figure 9 Source: The Authors.

The conventional or engineering strain rate is expressed in terms of engineering strain as the equation 4 [32]

where 𝑣(𝑡)=𝑑L/𝑑t

In Fig. 10 the strain rates during quasi-static tests and tensile-impact tests with specimens D638 and D1822 for PP-Co, PP-Ho and HDPE are shown. For the quasi-static tests an average strain rate of 6.63x10^-3 s^-1 was found. This corresponds to a crosshead speed of approximately 4 mm/min rather than 5 mm/min as programmed in the machine. Analyzing the data, it was found that the maximum crosshead speed reached during the tests was 3.9 mm/min. Note how the strain rate increases from zero until it reaches a constant value once the inertia of the system is overcome. For the tensile-impact tests an opposite behavior is observed: when the specimen hits the anvil and its deformation starts, there is a significant drop in the strain-rate, which then converges to certain value. Note also the difference in the time scale, while the quasi-static tests ran for more than 100 s, the tensile-impact tests are in the range of 2 ms. Strains rates were estimated according to equation 4. In Table 3 the strain rates of PP-Co, PP-Ho and HDPE during the quasi-static and tensile-impact tests are summarized. It is observed that with PP-Co the highest strain rate is achieved, followed by HDPE and PP-Ho. If the fracture toughness of each material (Table 3) is analyzed, it can be observed that the tougher the material is, the more energy it is absorbed, and thus the lower strain rate during the test.

Figure 10 Source: The Authors.

Table 3

Source: The Authors.