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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There are other essential failure mechanisms in ceramic materials: plastic deformation at high confining pressure(Lankford, 1996), crack nucleation, crack branching, etc. (Bhattacharya et al., 2016). Defining damage in the ceramics material is critical in developing the constitutive model. The damage definition in phenomenological models, such as the Johnson-Holmquist series model(Johnson & Holmquist, 1994, 2008a, 2008b), uses the inelastic strain, which has the following form. = ( , ) (1) Where, = plastic strain =plastic strain at failure. The damage definitions in the micromechanical model are mainly based on the crack area or crack density. The crack area or crack density changes with the crack propagation. This type of damage definition cannot capture the damage due to the other possible failure mechanisms. 3. Unified Mechanics Theory Newton's universal laws of motion and thermodynamics' first and second laws are combined at the ab initio level in Unified Mechanics Theory. According to UMT, material degradation can be evaluated based on the Thermodynamic State Index, (TSI), which varies from zero to one. The modified laws of motion based on UMT are; The second law of UMT (1 − ) = ( ) (2) Where F, m and v are force, mass and velocity. The third law of UMT, Reaction force due to the application of load, reduces with time because the stiffness degrades with time. 12 = 21 21 (1− ) (3) Where, 21 , and 21 are the stiffness and displacement of the reacting system. Thermodynamic State Index (TSI), = [1 − − ∆ ] (4) , ∆ , and R molar mass, entropy and gas constant. Entropy is calculated from the dissipated energy due to the extension of the crack. From equation 2, it is evident that an amount of (1- ) degrades the stiffness of the reacting body. 4. Constitutive model for Alumina at high strain rate loading. A representative volume element (RVE) with a pre-existing flaw (Figure 2) is used to develop the constitutive model. In this study, the Paliwal-Ramesh model (Paliwal & Ramesh, 2008) is modified by including entropy-based damage. The degradation in the material property can be quantified using the laws of unified mechanics theory; TSI is used for this purpose. The primary failure mechanism considered in the present study is crack propagation from the pre-existing flaw. The energy lost in the formation of a new crack surface is the energy dissipated, and it causes the entropy generation in the material. Constitutive relations: = (5)