JNTU B.Tech IV FAILURE ANALYSIS Previous Question Paper (July/August - 2022 - R18)

Fracture is the separation of a body into two or more pieces under the action of stress, occurring when the applied load exceeds the material's cohesive strength. It is broadly classified into ductile fracture, characterized by significant plastic deformation, and brittle fracture, which occurs with little to no macroscopic deformation.

The Griffith crack theory explains brittle fracture by proposing that materials contain microscopic flaws or cracks that act as stress concentrators. Griffith postulated that a crack will propagate if the energy released by the relaxation of elastic strain energy during crack growth is greater than or equal to the energy required to create new crack surfaces.

The critical stress for crack propagation is given by the formula:

Where σ is the critical stress, E is Young's modulus, γ is the specific surface energy of the material, and a is the half-length of the internal crack. This theory demonstrates that the actual fracture strength of brittle materials is significantly lower than the theoretical cohesive strength due to the presence of these flaws.

Theoretical strength refers to the stress required to break the atomic bonds across a plane in a perfect crystal lattice, assuming no defects. Based on the Orowan model, this is approximately E/10 to E/30. In practice, real materials exhibit strengths orders of magnitude lower than this because of the presence of dislocations and structural defects.

Fracture criteria provide the mathematical conditions under which a crack will grow or a material will fail. Key criteria include:

• Energy Criterion (Griffith): Focuses on the balance between elastic strain energy release and surface energy creation.
• Stress Intensity Factor (K): Defines the stress state at the crack tip. Fracture occurs when the stress intensity factor reaches a critical value, known as the fracture toughness (K_Ic). The criterion is K ≥ K_Ic.
• J-Integral: An energy-based criterion used for materials undergoing significant plastic deformation at the crack tip, where linear elastic fracture mechanics (LEFM) is no longer valid.
• Maximum Principal Stress Criterion: Often used for brittle materials, stating that fracture occurs when the maximum normal stress reaches the ultimate tensile strength of the material.