The elastic energy released when a crack advances by a unit area. Written G, it equals K²/E in plane stress, and the crack advances when it reaches the critical value G_c.
Japanese name: エネルギー解放率
Energy release rate appears in 1 practice question across 1 topic, including Fracture mechanics and fatigue.
The energy release rate G is the energy released from the system of the body and its loading when a crack extends by unit area, and its unit is J/m². Despite the word rate in its name, it is not a quantity per unit time but per unit crack area. The value of G for a small crack extension is the same whether the load is held constant or the displacement is fixed. A crack grows when G reaches the energy needed to advance it, that is, the material's resistance R, so its critical value G_c is the fracture toughness expressed as an energy: the material's resistance to fracture.
In the linear elastic range, G and the stress intensity factor K are related by G = K²/E in plane stress and G = K²(1 − ν²)/E in plane strain. Converting fracture toughness into energy with these equations shows the differences between materials clearly. For soda-lime glass (K_IC about 0.75 MPa·√m, E about 70 GPa), G_c is about 8 J/m², the same order as the surface energy. For a steel with K_IC of about 50 MPa·√m and E of about 210 GPa, it is about 1×10⁴ J/m², showing that orders of magnitude more energy is used in plastic deformation at the crack tip.
If the ratio of load-point displacement to load P is taken as the compliance C (displacement/load), then for a specimen of thickness B, G = (P²/2B)(dC/da). By measuring or calculating how the compliance changes with crack length, G can be found without solving the stress distribution in detail. This method is often used for problems in which K is hard to obtain, such as delamination between the layers of fiber-reinforced plastics. For example, in the double cantilever beam (DCB) test, in which a starter crack is placed at the end of a laminate and the two arms are pulled apart, the mode I interlaminar fracture toughness G_IC is found.
In ductile materials and some ceramics, the resistance R to crack growth increases as the crack extends, because the plastic zone grows or bridging between the crack faces increases. This is called the R-curve. In such materials, fracture does not occur as soon as G reaches R; the crack grows a little and stops. The crack grows unstably when the rate at which G increases with crack extension exceeds the rate at which R increases. Under constant load G increases with crack length more readily than under fixed displacement, making instability more likely, so the test method and the way a structure is supported also affect how fracture proceeds.
Answer: A. Plastic deformation occurs at the crack tip, and a large amount of energy is consumed as plastic work
Orowan and Irwin extended Griffith's idea to metals and wrote the energy needed for a crack to advance as G_c = 2γs + γp. Here γp is the plastic work consumed in the plastic zone at the crack tip; in ductile steels it exceeds 10⁴ J/m², far larger than 2γs. The surface energy of metals is roughly 1–3 J/m², not different from that of ceramics by orders of magnitude. Metals also contain inclusions and cracks, and Griffith's energy balance is still used as the foundation, with the plastic work added. In materials that hardly deform plastically, such as glass, G_c is a small value of the same order as 2γs.
In the linear elastic range with a small plastic zone, both carry the same information and can be converted by G = K²/E in plane stress. K is often used in the design of metals, while G is often used to evaluate delamination of composites and adhesive joints. When modes are mixed, G, which can be added as an energy, is sometimes easier to handle.
The surface energy is the minimum energy needed to create new surface, while G_c is the energy actually needed to advance a crack. In glass the two are of the same order, but in metals the work of plastic deformation is added, so G_c is orders of magnitude larger than the surface energy.
Yes. Since J = N·m, J/m² can be written as N/m. G can also be thought of as a force per unit length of the crack front that tries to push the crack forward, and in that sense it is sometimes called the crack extension force.
Fatigue striations Griffith theory Miner's rule Modified Goodman diagram Paris law Stress concentration factor Stress intensity factor