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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∝ ̇ 0.27

Compressive strength (MPa)

∝ ̇ 1/52

Normal distribution

Curve fit

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Log of strain rate

Figure 11. Comparison between predicted response and Lankford strain rate sensitivity relation(Lankford, 1981)

Figure 11 shows the compressive strength vs strain rate for normal distribution and curve fit from Lankford strain rate sensitivity relations, and it displays a good match between the predicted response and Lankford relations. So, the RVE containing pre-existing flaws and TSI as a damage metric can predict the mechanical response of Alumina. The evaluation of damage in ceramics depends on the quantification of energy dissipation during crack propagation, determined by the thermodynamic state index (TSI) derived from the principles of the second law of thermodynamics. As a result, the developed model strictly adheres to thermodynamic principles. The principal advantage of utilising TSI as a metric for damage lies in its utilisation of entropy to measure energy dissipation resulting from the inherently irreversible crack propagation process. It effectively accommodates a range of mechanisms for dissipating energy in the deformation of ceramic materials, including phenomena like the initiation of cracks, the branching of cracks, plastic deformation under high confining pressure, and additional factors. In contrast, damage definitions not based on entropy do not possess the capability to integrate different mechanisms for dissipation within a unified definition of damage. Conversely, entropy-based damage assessment through TSI comprehensively addresses damage resulting from various energy-dissipating mechanisms. 6. Conclusions This paper discusses a thermodynamically consistent constitutive model for Alumina at a high strain rate loading. Damage in ceramic materials due to crack propagation is defined based on the entropy and TSI. The effect of various distributions of cracks in the materials is studied. At a lower strain rate, the stress-strain response largely depends on the type of distribution, but at a higher strain rate, it becomes less important. The selection of a particular distribution of cracks depends on the micrograph studies. The developed model can capture the strain rate sensitivity of the Alumina. References Agrawal, D. C. (1995). Mechanical properties of alumina ceramics. Transactions of the Indian Ceramic Society , 54 (5), 185 – 189. https://doi.org/10.1080/0371750X.1995.10804717 Basaran, C. (2021). Introduction to Unified Mechanics Theory with Applications. Introduction to Unified Mechanics Theory with Applications . https://doi.org/10.1007/978-3-030-57772-8 Basaran, C., & Nie, S. (2007). A thermodynamics based damage mechanics model for particulate composites. International Journal of Solids and Structures , 44 (3 – 4), 1099 – 1114. https://doi.org/10.1016/j.ijsolstr.2006.06.001