Griffith Theory of Fracture

Materials fracture through cracks. That sounds obvious when you think of something like a cracked piece of wood and that it will generally fracture along that crack. There can be interior cracks and exterior cracks which, when placed under stress, grow together to form a larger, single crack. Furthermore, the cracking action can be thought of as unzipping bonds one at a time. Cracking depends on the geometry of the crack and the applied stress.

To do this, we assume all cracks are elliptical in shape, which if you think about it, isn’t too far from the truth. If you take a triangular shaped crack and zoom in on it, eventually, it will begin to look elliptical. Once we accept that assumption, we can find the maximum stress at the crack tip to be:

s = 2n[1+2(a/p)^1/2)]

where s is the effective stress, n is the nominal applied tensile stress, p is the radius of curvature of the elliptical crack, and a is the crack length (or 1/2 the crack length in an internal crack). As the equation shows, an applied stress can be magnified and concentrated at the crack location by many times. We can define a stress concentration factor, K, as being s/n.