applied fracture mechanics

72Applied Fracture Mechanics2 2lLlUl t(8)2 E'lFigure 2. Griffith model for the crack growth introduced in a plate under stress: a) flat crack andinitial length Ll with increase dLl in size; b) rugged crack and initial length L with increase dL in size;c) fractal crack, showing increase dL in size.Analogously, the area of the unloaded elastic energy due to the introduction of a ruggedcrack of length L is given by2A m*L(9)where m * is a shape factor for the rugged crack. Thus, the elastic energy released by theintroduction of a rugged crack with length L is2 2rLUL m*t(10)2 E'Considering that the rugged crack is slightly larger than its projection, thenL L 0(11)Consequently, the change of elastic strain energy from the point of view of the projectedlength L0can be expressed as:where 0 r.2 20L0UL0 m*t(12)2 E'