**3. Results**

#### *3.1. Stress-Extension Curves at Different Temperatures*

Using Deben Microtest CT5000-TEC device, an extension-force curve in the test can be obtained and recorded automatically, and the stress can be derived by the following expression [10],

$$
\sigma\_{xx} = \left(1 - \left(\frac{b}{R}\right)^2\right) \frac{2P}{\pi Dt} \tag{1}
$$

where *P* is the loading force and *D* and *t* are the specimen's diameter and the thickness, respectively, *b* is the contact half-width of the anvils and *R* is the radius of the specimen. This *b*/*R* ratio should be measured for the specimen in experiments. This ratio is recommended to be greater than 0.27, since this has been found the failure is to be purely tensile [10]. In this paper, all of the *b*/*R* ratios in every group of tests are around 0.28 to 0.30.

Through Formula (1), stress-extension curves in every test can be obtained. The curves at different temperature were shown in Figure 2.

**Figure 2.** Stress-extension curves at different temperatures, at each temperature there is a repeat group.

As we can see from Figure 2, all of the failure extensions are around 0.15 to 0.20 mm, the difference at the same temperature tests basically equals to the difference among different temperature groups. Therefore, the failure extension is not sensitive to the temperature, which agrees to the previous research [18]: temperature has little effect on tensile failure strain. As the temperature decreases, the binder hardens, the PBX modulus increases, and the failure stress increases accordingly. As the temperature increases, the binder changes to high elastic state, the viscosity increases, the PBX modulus decreases, and the failure stress reduces, accordingly. In low temperature conditions, such as room temperature, 0 ◦C and −20 ◦C, the brittleness is significant, the specimen loses its carrying capability at the fracture moment; and, at 55 ◦C, the load of specimen decreases a little after fracture; when temperature reaches 70 ◦C, the sample does not lose carrying capability, but continue to load, and an obvious creep occurs.

#### *3.2. CT Images and Digital Image Process*

A typical slice image from CT scan and image reconstruction is shown in Figure 3, (a) is the slice of fractured specimen and (b) is the slice of original one. Generally speaking, the grayscale of the image is proportional to the mass density, so different components in the specimen can be identified. However, in this kind of PBX, the mass densities of explosives (TATB molding powder) and binders (F2314) are very close. The density of TATB is 1.93 g/cm<sup>3</sup> and the density of F2314 is around 2.04 g/cm3. Because of beam hardening and other system errors that are caused by CT, components in the specimen cannot be simply identified and segmented only by grayscale histogram. In this paper, several digital image processing methods, including morphological image processing (such as open and close operations and so on) and various segmen<sup>t</sup> techniques (such as Otsu segmen<sup>t</sup> and so on) were used to segmen<sup>t</sup> explosives (TATB molding powder), binders (F2314), and cracks, and to process the CT slices into binary images. The algorithms and criterion of the grayscale threshold used in segmentation are same in all of the analyses of experiments. The typical cracks at different temperatures are shown in Figure 4a. Three-dimensional crack morphologies can be obtained through reconstruction of binary images, shown in Figure 4b, and more analysis of these binary slices are in the next section.

**Figure 3.** (**a**) Left one is the computed tomography (CT) slice with cracks. Because the loading head used in Brazilian test in this paper has fenders (as shown in Figure 1) in order to stabilize the specimen, two dark horizontal lines can be seen in the figure; (**b**) Right one is the CT slice without cracks.

**Figure 4.** (**a**) Typical slice images of cracks at different temperatures; (**b**) Three-dimensional (3D) crack morphology at different temperatures.

As is shown in Figure 4, the cracks are straighter at lower temperatures, while they are more tortuous at higher temperatures. This is because, at lower temperatures, the fracture has significant brittleness; while at higher temperatures, as the binders turn into high elastic state, the viscoelasticity of the specimen enhances, so crack paths are more along the grain boundaries, then a more tortuous crack will occur.

#### *3.3. Fracture Mode Comparison*

The fractured specimens at different temperatures were also detected by SEM. The result of SEM detection proves the result of fracture fractal dimension analysis. Figure 5 shows some typical images at different temperatures, −20 ◦C, 0 ◦C, 22 ◦C, 55 ◦C, and 70 ◦C, respectively:

(**c**) **Figure 5.** *Cont*.

**Figure 5.** (**a**) SEM images in −20 ◦C; (**b**) SEM images in 0 ◦C; (**c**) SEM images in 22 ◦C; (**d**) SEM images in 55 ◦C; (**e**) SEM images in 70 ◦C.

The SEM images show the grea<sup>t</sup> difference of the fractures at different temperatures. Figure 5a is SEM images in −20 ◦C, the rough fracture surface can be clearly seen and the main fracture mode is the break of particles and crystals. Because of the angular broken particles and crystals, the fracture surface is rougher, resulting in a larger fracture fractal dimension. Figure 5b is SEM images in 0 ◦C, a large amount of fractured particles drop out. Figure 5c is SEM images in 22 ◦C. These are images of the fracture surface, which can be seen directly that it is rough. Meanwhile, not only broken particles and crystals can be seen, but there are also some broken binders around the fracture surface. Figure 5d is SEM images in 55 ◦C. The binders bridging the gap of particles in cracks can be seen clearly, as shown in the left image. Some large single particles drop out, a smooth surface that is covered with binders can be seen clearly, which implies a smaller fracture fractal dimension. Because the glass transition temperature of the binder is around 50 ◦C, in and above this temperature the fracture mode is mainly transgranular and debonding. Figure 5e is SEM images in 70 ◦C. There are lots of binders bridging the cracks along the crack path. The main fracture mode can be clearly and directly seen through SEM images, which agrees with the previous researches and the result of fracture fractal dimension, which will be discussed in the next section.
