**3.3 Determination of stress intensity factor under mode I**

Since the CSTBD specimen is closely linked to fracture toughness and stress intensity factor, this sub section is there for compare different solutions of stress intensity factor under mode I. We used the experimental data of the CSTBD samples to define KI, by applying the previous formulas Eq. (3) using two different term of Y (6) and Eq. (7) using the different term of dimensionless stress intensity factor (NI) (9) and (10), for different percentages of TCP additive calculation is launched for crack length a/R = 0.4.

According to our previously work [9], the used composite specimens reached their optimum in mechanical properties at 1600° C. **Figure 8** illustrates the evolution of the stress intensity factor under mode I fracture in relation to the percentage of TCP under optimal conditions at 1600°C for 1 hour using different methods. We note that the Cherepanov, SIF values are close to those by handbook, Shetty and Fowel and al. Hence, KI (Cherepanov) is basically consistent with KI (handbook) and KI (Shetty et all) and shows a good compromise in the results.

For the study of the effect of TCP, this figure has illustrated that the stress intensity factor KI increases with the addition of 10 wt.% of TCP until 8.452 MPa m1/2 using the formula mentioned in Cherepanov's book. Beyond this percentage of TCP, the overall stiffness falls gradually.

The initiation and propagation of each crack depends on the type of solicitation. According to this test condition, cracks propagates in a parallel manner to the direction of the notch, and as soon as it intersects with the surface, the sample is divided into two parts. These cracks are generated by principal stresses, under mode I loading (As shown in **Figure 9**).
