fracturemechanics

Fracture mechanics is the field of mechanics concerned with the propagation of cracks in materials. It uses concepts from solid mechanics to predict the conditions under which cracks initiate and grow, and to assess the remaining life of structures.

Cracks concentrate stress; the intensity factors K characterize the state near a crack tip. In linear elastic fracture mechanics, the critical condition for crack growth is typically expressed as a fracture toughness K_IC, which marks the material's resistance to brittle fracture under Mode I loading. Related energy-based criteria use the energy release rate G or the J-integral to quantify the driving force for crack growth. Cracks can propagate in different modes: Mode I (opening), Mode II (sliding), Mode III (tearing). Mixed-mode loading combines these.

Two main frameworks govern analysis. Linear Elastic Fracture Mechanics assumes small-scale yielding and uses K or G; Elastic-Plastic Fracture Mechanics accounts for plastic deformation near the crack tip to extend validity to tougher materials. LEFM applies well to brittle materials and high-strength metals, while EPFM is more appropriate for ductile metals and welds.

For fatigue, empirical relations relate crack growth rate to the applied loading range; a common example is Paris law, which links da/dN to the stress intensity range ΔK via a power law. There is also the concept of a critical condition when K reaches K_IC or when the energy rate G reaches G_IC, beyond which rapid fracture can occur.

Practitioners combine experiments, analytical solutions, and numerical methods such as finite element analysis, boundary element methods, and cohesive zone models to compute K, G, or J and to simulate crack growth under realistic loading. Fracture mechanics informs design codes and failure analysis in aerospace, mechanical, civil, and energy sectors.

Origins lie in Griffith’s energy criterion of the 1920s and Irwin’s introduction of K and K_IC, with further developments by Paris and others in fatigue. Limitations include scale assumptions, material inhomogeneity, and environmental or dynamic effects.