PSI - Issue 60

Brahmadathan V B et al. / Procedia Structural Integrity 60 (2024) 214–221 Brahmadathan V B, C Lakshmana Rao / Structural Integrity Procedia 00 (2019) 000 – 000

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Table 1. Properties of Alumina(Agrawal, 1995)

Critical stress intensity factor ( ) 2.7 MPa

Elastic Modulus

Poisson ratio

386 GPa

0.24

Figure 2 shows the simplified schematic representation of the material with pre-existing micro cracks. The distribution of cracks will determine the mechanical behaviour of the ceramic. Therefore, four different probability density functions are assumed to include the effect of various crack orientations and lengths (Figure 3). The Weibull distribution's skew parameters 1.2 and 2.4 are taken to get different crack distributions.

Figure 3. Probability distribution function

5. Results and discussions The stress-strain curves for different strain rates are shown in Figures 4,6 and 8. Four different types of probability distribution functions are assumed in the study. The actual distribution will depend on the real micro-graph studies. At a lower strain rate, the expected sudden drop after the post-peak is obtained in the case of exponential and Weibull distribution (skew parameter 1.2). However, the sudden drop in the stress value after the peak stress is not visible in the other two cases. The peak stress value obtained is highest for the Weibull distribution with skew parameter 2.4. The reason behind the deviation of behaviour obtained from the Weibull distribution (skew parameter 2.4) is the probability of finding a 0-15µm crack size is more out of the 0- 50μm crack range. It indicates that the crack's entropy contribution will be less in the Weibull distribution (skew parameter 2.4). In the other three distributions, a wider range of cracks contributes to the entropy generation; therefore, the material degrades quickly. A similar trend can be seen in TSI evolution (Figures 5,7 and 9).

Figure 4. Stress strain response at ̇ =10 1 −1

Figure 5. TSI evolution at ̇ =10 1 −1