According to the one dimensional stress wave theory

According to the one-dimensional stress wave theory, the train , stress and strain rate of the specimen can be calculated by two-wave methodwhere and are the time-resolved reflected and transmitted strains in the incident and transmission bars with cross-sectional area A; E is the Young\'s modulus of bar material; is the elastic bar wave speed in the bar material; and L are the cross-sectional area and the original length of specimen, respectively. A pulse shaping technique is used to get the ideal waves. In other words, the purpose is to facilitate the stress equilibrium and constant strain rate deformation of specimen. As shown in Fig. 1, a pulse shaper is put between the striker and incident bar. The most ideal pulse shaping material depends on the mechanical characteristics of the specimen and the speed of the striker. In the paper, we mainly adopt asbestos tips as the pulse shaping material. The shapes of the tips are circular, and their diameters equal that SCR7 of bar. Fig. 3 illustrates the comparison of waveforms with and without pulse shaper. It can be seen from the above figures that the waveform with pulse shaper has less high frequency oscillation than that without pulse shaper, so the influence of high frequency oscillation on the experiment data can be reduced. The increase in the rising time of incident wave is beneficial to achieve the stress equilibrium. After pulse shaping, there is a plateform on the reflected wave. According to Eq. (3), we can know that the strain rate is proportional to the reflected signal. Therefore, the reflected wave should be kept constant in order to achieve a constant strain rate during the deformation progress. In conclusion, Fig. 3 shows that the pulse shaping technique meets the requirements above mentioned.
Experimental results and discussion Fig. 4 shows the compressive true stress–true strain curves of PTFE obtained at the strain rates ranging from 10−2 s−1 to 104 s−1. It can be seen from Fig. 4 that the mechanical characteristics of PTFE are strain rate-dependent and the initial modulus of dynamic increases markedly; After yielding, the material manifests strain hardening that can continue to a large strain range; The rising trend is roughly the same at different strain rates, which indicates the strain rate effect is unconspicuous in plastic section; The dynamic compressive true stress–true strain curves show the oscillations which may be due to the instability under impact loading during experimental measurement. The ends of dynamic compressive true stress–true strain curves decline. That is because the length of striker limits the width of loading pulse but not the material characteristics. The yield stresses at the different strain rates are presented in Table 1. It can be seen from Table 2 that the yield stresses increase with the increase in strain rates, and the dynamic yield stresses are about two times of quasi-static yield stresses. Walley and Field [4], Rae and Dattelbaum [5,6], Jennifer and Clive [7] got the stresses of PTFE at 15% of strain at room temperature, as shown in Fig. 5. The result in this paper is consistent with others, which further proves the reliability of the result. A lot of scholars do some research on the relation of yield stress–strain rate of polymer materials. Hu et al. [8] used a power-law constitutive model for the description of polycarbonate (PC)where A, B and m are three undetermined coefficients. Richeton et al. [9] and Fu S. et al. [10] proposed the modified models on the basis of Eyring theory. Mohd et al. [11] adopted the thermal activation to describe the yield stresses of polycarbonate (PC), polyethylene (PE) and polypropylene (PP). The thermal activation has the following formwhere is the internal stress, k is Boltzmann\'s constant, T is the absolute temperature, v is the activation volume, n is the material parameter, and is the characteristic strain rate. can be served as an unknown factor during numerical fitting.