JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech IV FAILURE ANALYSIS Previous Question Paper (September - 2022 - R18)

A stress concentration factor (denoted as K_t) is a dimensionless coefficient that quantifies how much the local stress at a geometric discontinuity exceeds the nominal stress calculated for a uniform section. Discontinuities such as holes, notches, fillets, keyways, or sharp corners disrupt the smooth flow of stress lines, causing them to crowd together, which leads to localized stress peaks.

The factor is defined by the ratio:

where σ_max is the peak stress at the discontinuity and σ_nom is the nominal stress calculated based on the net cross-sectional area. In ductile materials, localized yielding often redistributes these stresses, reducing the effective impact of the concentration. However, in brittle materials or under fatigue loading, these high-stress regions act as initiation sites for crack propagation, significantly reducing the service life of the component. Designers mitigate these effects by increasing fillet radii, using transition tapers, or optimizing geometry to ensure a more gradual change in cross-section.

The Griffith criterion provides a thermodynamic basis for brittle fracture by proposing that a crack will propagate only when the energy released by the relaxation of elastic strain energy is sufficient to provide the energy required to create new fracture surfaces.

Griffith established that for a crack of length 2a in an infinite plate under tensile stress σ, the elastic energy released per unit thickness as the crack extends is proportional to the square of the applied stress and the crack length. Conversely, the energy required to form two new surfaces is proportional to the surface energy (γ_s) of the material. The critical stress (σ_c) at which fracture occurs is given by:

where E is Young's modulus and a is the half-length of the internal crack. This theory demonstrates that the strength of a brittle material is governed by the size of its largest pre-existing flaw. While originally developed for perfectly brittle materials, it was later modified by Irwin and Orowan to include plastic work at the crack tip (replacing γ_s with G_c or the strain energy release rate), forming the foundation of modern linear elastic fracture mechanics.