Chapter 11: Fracture Mechanics

Fracture Mechanics transitions from classical theories of brittle fracture, such as the Griffith criterion, to modern modifications by Orowan and Irwin that account for the plastic deformation inherent in metals. Key concepts include the strain-energy release rate, which measures the energy available for crack propagation, and the stress intensity factor (K), a parameter that characterizes the stress field at the tip of a crack in linear-elastic materials. The text details the three fundamental modes of crack surface displacement—opening, sliding, and tearing—with a primary focus on Mode I tension. A major section is dedicated to defining and testing plane-strain fracture toughness (K-Ic), a critical material property, including the necessary specimen dimensions to ensure valid plane-strain conditions and avoid plane-stress effects. Limitations of linear elastic fracture mechanics (LEFM) are addressed through plasticity corrections, such as the Irwin and Dugdale plastic zone models, and the introduction of elastic-plastic parameters like Crack-Opening Displacement (COD) and the path-independent J-integral for tougher, more ductile materials. The chapter also explores the R-curve concept to describe resistance to stable crack growth, probabilistic fracture mechanics using the Weibull distribution to account for size effects and flaw statistics in brittle solids, and the microstructural variables—such as grain size, inclusions, and yield strength—that dictate the trade-off between strength and toughness in engineering alloys.