Research on Fracture Toughness of Flattened Brazilian Disc Specimen after High Temperature

Test scheme design

Granite and marble are igneous and metamorphic rocks, respectively, with a wide range distribution. So in this experiment, choosing granite and marble as research samples, the test results have representative significance. In order to avoid the influence of cleavage layer on test results, select the thick rock block to prepare specimens. The Poisson ratios of two rocks are 0.2 and 0.3, respectively, and the density of 2,750 and 2,600 kg/m³. Rock samples are processed to be the flattened Brazilian disc specimen with Φ 50 mm × 25 mm that the upper and lower surface parallelism is within 0.05 mm, and surface flatness is within 0.02 mm according to International Society for Rock Mechanics (ISRM) [21]. To avoid that the bearing point of Brazilian disc specimen without platform may be fractured first due to local stress concentration, two mutually parallel planes are introduced as loading platforms in specimens especially with loading platform angle of 20° (as shown in Figure 1). Carry out the ultrasonic test on flattened Brazilian disc specimens to exclude specimens with significantly low longitudinal wave velocity, reducing the effect of the differences among the samples on test results. Test temperature is designed to fall into seven groups: room temperature, 100°C, 200°C, 400°C, 600°C, 800°C and 1,000°C, each group equipped with no less than three specimens and with heating rate of 10°C/min. The predetermined temperature, once reached, is kept constant for 2 h. After that the specimens are left in the furnace to cool down to room temperature.

Figure 1:

Flattened Brazilian disc specimen under compression load.

Load–displacement curve

Sample is placed correctly on test machine and applied axial load along the platform surface. Figure 2 shows the load–displacement curves of granite flattened Brazilian disc samples. As can be seen, the load–displacement curves show linearly before the load reaches peak. Then, the load–displacement curves will experience two inflections that the load decreases from the peak to a local minimum first, and after that the load will continue to rise as the displacement increases, which is still significantly less than peak load. The main mechanical parameters of test are shown in Table 1.

Figure 2:

Typical load–displacement curves of granite.

Fracture toughness

The center cracks are generated symmetrically in flattened Brazilian disc specimen along the vertical direction to loading surface subjected to compression loads. According to the suggested method by ISRM [22], the stress strength factor of rock sample can be expressed as [23]:

where KI stands for the stress strength factor; Y stands for the dimensionless stress strength factor; P stands for the uniform pressure force; R stands for the radius of disc; 2α stands for the load angle of platform; b stands for the thickness of disc; 2a stands for the length of central crack.

Because fracture toughness KIC is a material constant, and according to the fracture principle, the fracture toughness is equal to stress strength factor, but it is very troublesome. However, the variation of load with crack is corresponding to change in dimensionless stress strength factor Y, of which the maximum Ymax is corresponding to the local minimum load Pmin. So KIC can be calculated by eq. (1), according to the maximum dimensionless stress strength and the local minimum load as follows:

The formula to calculate the fracture toughness of flattened Brazilian disc specimens with loading platforms angle of 20° is expressed as follows [10]:

The variations of fracture toughness of granite and marble with temperature are shown in Figures 3 and 4. As can be seen, the fracture toughness of two kinds of rock decreases gradually with increasing temperature, but there exist differences: On the one hand, the fracture toughness of granite decreases approximately linearly while that of marble decreases approximately as exponential function with increasing temperature. On the other hand, the sensitivity of temperature to fracture toughness is also related to the type of rock. After 800°C and 1,000°C, fracture toughness of granite is decreased by 59.30% and 59.30%, respectively, compared with room temperature, while fracture toughness of marble is decreased by 78.86% and 84.24%, respectively. Therefore, compared to granite, the fracture toughness of marble is much more sensitive to temperature, which is caused by the different mineral compositions and structural features of two rocks. As a result, not only heat treatment temperature, but also the rock types significantly affect the fracture toughness of rock.

Figure 3:

Relationship between fracture toughness and temperature of granite.

Figure 4:

Relationship between fracture toughness and temperature of marble.

Splitting tensile strength

According to ISRM [21], based on the formula to calculate splitting tensile strength of the flattened Brazilian disc specimens proposed in [10], the splitting tensile strength of flattened Brazilian disc specimen with loading platforms angle of 20° is expressed as follows:

where σt stands for the splitting tensile strength; Pmax stands for the peak load; D stands for the diameter of disc.

The variations of splitting tensile strength of granite and marble with temperature are shown in Figures 5 and 6. As can be seen, overall, the splitting tensile strength of two rocks decreases gradually with increasing temperature, but there exist differences: For granite, the splitting tensile strength decreases almost linearly with increasing temperature. For marble, at 100°C, the splitting tensile strength increases slightly compared with the room temperature, but decreases gradually after 100°C. Therefore, the ways of temperature effect on the splitting tensile strength of two rocks are different. The temperature mainly has a weakening effect on granite. However, there exists a threshold temperature of marble; the temperature mainly has a reinforcement effect on marble before the threshold temperature while it has a weakening effect on marble after the threshold temperature.

Figure 5:

Relationship between splitting tensile strength and temperature of granite.

Figure 6:

Relationship between splitting tensile strength and temperature of marble.

Elastic modulus

It is nearly impossible to obtain accurate elasticity displacement and stress solutions for the flattened Brazilian disc specimens under uniform compression loads. Therefore, use finite element and approximate elastic analysis to solve this problem. According to [10, 24], the approximation formula of compression displacement of the loading diameter is as follows:

Then the elastic modulus is obtained:

where E stands for the elastic modulus; ΔW stands for the compression displacement of the loading diameter; μ stands for the Poisson ratio, at room temperature, granite of 0.2 and marble of 0.3. According to eq. (6), the elastic modulus can be calculated by initial linear portion of the load–displacement curves. The variations of elastic modulus of granite and marble with temperature are shown in Figures 7 and 8. As can be seen, overall, the elastic modulus of two rocks decreases gradually with increasing temperature, among which, the elastic modulus of granite decreases approximately linearly while that of marble decreases approximately as exponential function.

Figure 7:

Relationship between elastic modulus and temperature of granite.

Figure 8:

Relationship between elastic modulus and temperature of marble.

Relationship between splitting tensile strength, elastic modulus and fracture toughness

In the splitting tensile test on rock after high temperature, the fracture toughness is an important physical quantity in rock fracture mechanics, while the splitting tensile strength and elastic modulus are important parameters in the rock thermodynamics. To establish this, the relations between splitting tensile strength, elastic modulus and fracture toughness can provide a basic reference for the study on the relationship between fracture mechanics and thermodynamics. The variations of splitting tensile strength and elastic modulus with fracture toughness are shown in Figures 9 and 10.

Figure 9:

Relationship between splitting tensile strength, elastic modulus and fracture toughness of granite.

Figure 10:

Relationship between splitting tensile strength, elastic modulus and fracture toughness of marble.

As can be seen, there is a connection between splitting tensile strength, elastic modulus and fracture toughness. Through regression analysis, the relationships between splitting tensile strength, elastic modulus and fracture toughness conform to the following equations:

In theory, the higher the tensile strength is, the greater the fracture toughness is. According to test results, the fracture toughness of two rocks increases with increasing tensile strength, so the theoretical results are consistent with actual results. For example, for marble, at 100°C, the splitting tensile strength increases slightly compared with room temperature, and decreases gradually after 100°C. At this time, the fracture toughness also shows the same changing rules with increasing temperature, namely that first increases and then gradually decreases. That is, the splitting tensile strength and fracture toughness have same threshold temperature, indicating that there is a close connection between splitting tensile strength and fracture toughness. Since the test method of tensile strength is relatively simple and that of fracture toughness is complex, fracture toughness can be roughly estimated by tensile strength based on the above formula.