Crack growth resistance curve

In materials modeled by linear elastic fracture mechanics(LEFM), crack extension occurs when the energy release rate G equals R, the materials resistance to crack extension. A plot of R versus crack extension is called a resistance curve, or R curve and the corresponding plot of energy release rate versus crack extension is called a driving force curve.

Generally, materials display either a flat R curve or a rising R curve. For a flat R curve, the material resistance is constant with crack extension.When the resistance curve is flat, one can define a critical value of energy release rate Gc, unambiguously. A material with a rising R curve, however, cannot be uniquely characterized with a single toughness value. A flawed structure fails when the driving force curve is tangent to the R curve, but this point of tangency depends on the shape of the driving force curve, which depends on the configuration of the structure. Materials with rising R curves are generally characterized by the value of G at the beginning of crack growth, but the precise moment of initiation is difficult to determine. The R curve for an ideally brittle material is flat because the surface energy is a non changing property. Nonlinear behavior, like ductile fracture, can result in a rising R curve as the plastic zone at crack tip increases in size with extension. Falling R curves can are also seen, especially when a metal fails by cleavage. Cleavage propagation is unstable and very high strain rates are found near the crack tip. This suppresses plastic deformation.

Size and geometry also plays a role in determining the shape of the R curve. A crack in a thin sheet tends to produce a steeper R curve than a crack in a thick plate because there is a low degree of stress triaxiality at the crack tip in the thin sheet while the material near the tip of the crack in the thick plate may be in plane strain. The R curve can also be affected if the growing crack approaches a free boundary in the structure. Thus, a wide plate may exhibit a somewhat different crack growth resistance behavior than a narrow plate of the same material. Ideally, the R curve, as well as other measures of fracture toughness, should be a property only of the material and not depend on the size or shape of the cracked body. Much of fracture mechanics is predicated on the assumption that fracture toughness is a material property.