Strictly speaking these properties are *Critical Energy Release Rates* (critical ERR), but I got tired of such a long name, so I decided to infringe on the known term *Fracture Toughness* that better conveys the meaning of these properties. *Excusez-moi !*

. Critical energy release rate for crack opening (mode I).

. Critical energy release rate for crack shear (mode II).

The critical energy release rate for crack tearing (mode III) is zero for laminates because the adjacent laminas prevent mode III of deformation.

The formulas used are shown in CADEC for mode I and mode II^{1}. But to use these formulas, there is an additional detail, which is a novel proposition made in the textbook, namely that .

Basically, is the size of the representative crack, which has been used in those formulas since it they were proposed by Dvorak. The representative crack is a well known concept in fracture mechanics literature. It represents the state of imperfections in a material. The problem was that no one could estimate or measure it. But, as it is explained in the textbook, the representative size is related to the transition thickness. The beauty of this is that transition thickness can be measured, as shown by Wang. All this is explained in the textbook.

**Footnotes**

- you have to login to see the formulas and use the software