2.2.2. SHPB Experiment

The SHPB apparatus is widely used to investigate the dynamic behavior of materials. The device typically consists of a striker bar, an incident bar, a transmission bar, and a gas gun, among other things, as shown in Figure 3. The strain gauge, digital storage oscilloscope, and ultrahigh dynamic extensometer are used to calibrate and measure the time history curves of incident, reflected, and transmitted waves. The cylindrical specimen is placed between the incident bar and the transmission bar. When the striker is propelled from the gas gun to impact the incident bar, a compressive elastic wave is generated and propagated through the incident bar. Once the wave reaches the specimen, part of the wave reflects on the interface of the specimen, while the remaining portion passes through the transmission bar. The traveling waves in the incident bar and the transmitted bar can be quantitatively captured by strain gauges mounted on these two bars. Thus, the strain–time histories of the incident, reflected, and transmitted waves can be recorded using the oscilloscope.

**Figure 3.** Schematic of the SHPB device.

The engineering stress, engineering strain, and strain rate can be calculated using the following equations [23]:

$$
\sigma\_{\mathfrak{e}}(t) = \frac{EA\_0}{A\_{\mathfrak{s}}} \varepsilon\_{\mathfrak{t}}(t),
\tag{1a}
$$

$$\varepsilon\_{\mathbf{e}}(t) = -\frac{2\mathcal{C}\_0}{L\_{\mathbf{s}}} \int\_0^t \varepsilon\_{\mathbf{t}}(t) \mathbf{d}t,\tag{1b}$$

$$
\dot{\varepsilon}(t) = -\frac{2\mathcal{C}\_0}{L\_\text{s}} \varepsilon\_\text{r}(t),
\tag{1c}
$$

where *E*, *C*0, and *A*0 denote Young's modulus, stress wave speed, and the cross-section area of the incident bar, respectively. *A*s and *L*s represent the cross-section area and length of the specimen, respectively. *<sup>ε</sup>*t(*t*) and *<sup>ε</sup>*r(*t*) refer to the amplitude of the transmitted wave and the reflected wave as functions of time *t*, respectively. *<sup>σ</sup>*e(*t*) and *<sup>ε</sup>*e(*t*) denote engineering stress and strain, respectively.

Furthermore, the true stress–strain relationship can be obtained using the following equations:

$$
\sigma(t) = \sigma\_\mathfrak{e}(t)(1 - \varepsilon\_\mathfrak{e}(t)),
\tag{1d}
$$

$$
\varepsilon(t) = \ln(1 - \varepsilon\_{\rm e}(t)),
\tag{1e}
$$

where *σ*(*t*) and *ε*(*t*) are the true stress and the true strain, respectively.

In the present study, the detailed parameters of the SHPB apparatus were as follows: the striker measured 300 mm in length and 12 mm in diameter; both the incident bar and the transmitted bar were 1200 mm in length and 12 mm in diameter; and the three bars were made of steel. The experiments were conducted at different strain rates: 1300 s<sup>−</sup><sup>1</sup> and 2200 s<sup>−</sup>1. Two repeated experiments were conducted at each strain rate to ensure the repeatability of the experimental results.
