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

215

2

silicon carbide, and boron carbide as the protective striking surface. In those applications, the main aim of the ceramic strike face is to blunt and erode the projectile so that the injuries to the personnel due to the projectile's impact can be reduced. Understanding and predicting their mechanical behaviour under different loading conditions is essential for designing and optimising structures and components incorporating ceramics. The microstructural features are significant in deciding their mechanical behaviour in static and dynamic loading. The dominant failure mechanism is crack growth from pre-existing flaws at lower strain rates, and inertia becomes significant at higher strain rates (Lankford, 1981). Many phenomenological and micro-mechanical models are available in the literature. The damage in the material is defined based on the inelastic strain in the phenomenological model and crack area or crack density in the micro-mechanical model(Deshpande et al., 2011; Paliwal & Ramesh, 2008; Ravichandran & Subhash, 1995). The way of expressing the damage in the model determines the applicability of the model in incorporating various damage-causing mechanisms. Entropy-based damage definition is an appropriate way to include multiple energy dissipation mechanisms. Unified Mechanics Theory uses entropy to define damage in the material using the Thermodynamic State Index (TSI)(Basaran, 2021). The entropy or degree of disorderness is normalised to get the value of TSI. Models for hydrogen embrittlement, high cycle fatigue, and low cycle fatigue use the UMT and TSI to determine the damage in the material (Basaran & Nie, 2007; Jamal M et al., 2021; Lee et al., 2022, 2023). The primary energy-dissipating mechanism in those models is plastic work (Noushad et al. et al., 2020). However, within ceramics, energy dissipation occurs through the propagation of cracks originating from pre-existing flaws. A thermodynamically consistent model for ceramic materials such as Alumina can be developed using the TSI as the damage metric. The main objective of this paper is to develop a thermodynamically consistent constitutive model and also to

study the effect of crack distribution on mechanical behaviour. 2. Failure mechanisms and various damage definitions

The primary failure mechanism in ceramic material like Alumina is crack propagation from pre-existing flaws. These flaws can be line cracks, surface cracks, pores, etc. Cracks propagating from the flaws will branch, and the final coalescence of all cracks will cause the absolute failure of the material. The strain rate sensitivity of ceramic strength depends on the crack propagation at a lower strain rate and inertia at a higher strain rate (Figure 1).

Strain rate> Transition strain rate

Inertia dependent: Sensitive

Thermally activated: Sensitive Eg: MgO

No subcritical crack growth: Insensitive Eg: Sintered Sic, B4C

Crack Nucleation

Strain rate < Transition strain rate

Athermal

Subcritical crack growth: Sensitive Eg: AL2O3, Hot pressed SiC

Figure 1. Mechanisms responsible for strain rate sensitivity (Lankford, 1981)