Explain the basics of Linear Elastic Fracture Mechanics and the stress intensity factor.

LEFM analyzes crack behavior using stress intensity factor K = Yσ√(πa), where Y is geometry factor, σ is nominal stress, and a is crack length. Fracture occurs when K reaches critical value Kc (fracture toughness). Three modes exist: Mode I (opening), Mode II (sliding), Mode III (tearing). LEFM is essential for damage tolerance design in aerospace, pressure vessels, and nuclear components where cracks must be managed safely.