Crack growth resistance curve

In fracture mechanics, a crack growth resistance curve shows the energy required for crack extension as a function of crack length in a given material. For materials that can be modeled with linear elastic fracture mechanics (LEFM), crack extension occurs when the applied energy release rate ${\displaystyle G}$ exceeds the material's resistance to crack extension ${\displaystyle G_{R}}$. A plot of crack growth resistance ${\displaystyle G_{R}}$ versus crack extension ${\displaystyle \Delta a}$ is called a crack growth resistance curve, or R-curve.

R-curves can alternatively be discussed in terms of stress intensity factors ${\displaystyle (K)}$ rather than energy release rates ${\displaystyle (G)}$, where the R-curves can be expressed as the fracture toughness (${\displaystyle K_{Ic}}$, sometimes referred to as ${\displaystyle K_{R}}$) as a function of crack length ${\displaystyle a}$.