crackpropagation

Crack propagation is the growth of cracks within solid materials under applied stress, which may progress slowly during operation or rapidly under overload, and can culminate in catastrophic fracture. The process is governed by the material's fracture toughness and the applied load, and is analyzed within the framework of fracture mechanics. Propagation can occur under static loading, dynamic loading, or cyclic loading as in fatigue.

In linear elastic fracture mechanics, crack growth begins when the energy release rate or the stress intensity factor at the crack tip reaches a critical value. The stress intensity factor K characterizes the tip field for loading modes I, II, and III. Fracture occurs when K reaches K_IC or when the energy release rate G reaches G_IC. In polymers and metals, plastic zones and microcracking modify these criteria.

Fatigue crack growth is characterized by a progressive increase in crack length under cyclic loading. The relationship between crack growth per cycle da/dN and the stress-intensity range Delta K is often described by Paris' law: da/dN = C (Delta K)^m, with material constants C and m. A threshold Delta K_th exists below which cracks do not grow, and unstable propagation may occur if Delta K exceeds a critical value, leading to rapid failure.

Factors influencing crack propagation include microstructure (grain size, inclusions), residual stresses, temperature, loading rate, and environmental effects such as corrosion and hydrogen embrittlement. In composites and ceramics, crack paths may deviate or bifurcate, and mixed-mode loading can complicate propagation. Understanding crack growth informs design, inspection, and safety assessments in engineering structures.

Experimental characterization relies on fracture toughness tests and fatigue tests, while modeling uses fracture mechanics theory, finite element analysis, and cohesive zone models to predict crack growth and to establish safe design limits.