Rcurves

R-curves, short for resistance curves, are curves used in fracture mechanics to characterize how the fracture resistance of a material changes with crack extension. The curve presents either the stress intensity factor K or the energy release rate G (or the J-integral) required to propagate a crack by an incremental amount da. The abscissa is crack extension and the ordinate is the corresponding fracture resistance value (K_R, G_R, or J_R).

R-curves are particularly relevant for materials that undergo toughening mechanisms during crack growth, such as metals with plastic blunting and bridging, ceramic composites with fiber bridging, or polymers with crazing. In such materials the fracture resistance increases as the crack grows, leading to stable tearing behavior; in brittle materials the R-curve is flat or decreasing.

Experimentally, R-curves are obtained using standard fracture tests, such as compact tension or three-point bending, where the applied load, crack length, and geometry are measured to compute K, G, or J. A plot of K_I or G_I versus crack extension yields the R-curve.

They are used to assess structural integrity by comparing the maximum expected service driving force to the material's R-curve. A structure is considered safe if the expected load does not exceed the R-curve at the corresponding crack length.

Limitations include dependence on specimen size, mode mix, temperature, environment, and constraint; R-curves are not universal and must be determined for each material, geometry, and loading condition.

See also: fracture mechanics, fracture toughness, J-integral, tearing resistance.