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 ${\displaystyle G_{R}}$.

Conceptually, ${\displaystyle G}$ can be thought of as the energetic gain associated with an additional infinitesimal increment of crack extension, while ${\displaystyle G_{R}}$ can be thought of as the energetic penalty of an additional infinitesimal increment of crack extension. At any moment in time, if ${\displaystyle G\geq G_{R}}$ then crack extension is energetically favorable. A complication to this process is that in some materials, ${\displaystyle G_{R}}$ is not a constant value during the crack extension process. 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. A plot of energy release rate ${\displaystyle G}$ versus crack extension ${\displaystyle \Delta a}$ for a particular loading configuration is called the driving force curve. The nature of the applied driving force curve relative to the material's R-curve determines the stability of a given crack.

The usage of R-curves in fracture analysis is a more complex, but more comprehensive failure criteria compared to the common failure criteria that fracture occurs when ${\displaystyle G\geq G_{c}}$ where ${\displaystyle G_{c}}$ is simply a constant value called the critical energy release rate. An R-curve based failure analysis takes into account the notion that a material's resistance to fracture is not necessarily constant during crack growth.

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 ${\displaystyle a}$.