The crack extension force of a curved crack derived from the principle of virtual work

A general method to determine the crack extension force F related to a fini te segment of a curved crack is presented. A path independent integral expr ession that holds in curvilinear coordinates is derived from the principle of virtual work. An appropriate virtual displacement field allows variation of the position of a crack tip. F is related to the path independent integ ral expression through variation of a total energy expression. To illustrat e the applicability of the method F is derived for the conical crack in axi symmetric loading. For a plane crack with a straight front F is identical t o the J-integral, Rice (1968).