A2 Fracture

Topic

When the stress acting on a pre-existing crack within the metal reaches a certain threshold, the crack ceases to grow slowly and stably and begins to propagate unstably, resulting in the catastrophic fracture of the component; this unstable propagation of a pre-existing crack is precisely what this model defines as fracture. The fact that the crack propagates unstably—rather than arresting once growth begins—causes the metal to fracture suddenly, without prior warning.

The stress threshold at which the pre-existing crack begins to propagate unstably is the brittle fracture stress; this stress is determined by a combination of the metal's elastic constants—established in another model within this set—and the surface energy released during the creation of the two new crack surfaces, in accordance with the Griffith criterion. According to this criterion, a higher surface energy or a smaller initial crack size results in a higher brittle fracture stress required for unstable propagation.

However, the Griffith criterion underestimates the metal's actual fracture stress because it fails to account for the plastic deformation of the metal at the crack tip prior to crack advancement, and the fact that this plastic work consumes energy in addition to the surface energy. The Griffith-Irwin criterion extends the original Griffith criterion by adding this plastic work to the surface energy component, thereby making it applicable to metals that exhibit some plasticity at the crack tip rather than undergoing purely brittle fracture. The fact that the plastic work at the crack tip is greater means—according to this extended Griffith-Irwin criterion—that the required fracture stress is also higher than what the original Griffith criterion alone would predict.

Consequently, this model—incorporating the pre-existing crack and the brittle fracture stress that initiated it—expresses the fracture failure criterion in an equivalent yet more practical way: fracture occurs the moment the stress intensity factor applied to this pre-existing crack reaches the metal's fracture toughness. This single parameter encapsulates both the surface energy and the plastic work accounted for by the combined Griffith and Griffith-Irwin criteria. Since this same fracture toughness can be estimated—albeit more simply, if less directly—via another model in this set (the one describing the Charpy test for the metal), that test serves as a practical experimental correlation for the property; furthermore, because hydrogen embrittlement reduces the metal's effective fracture toughness (according to yet another model in the set), the fracture failure criterion is met at a lower applied stress intensity factor than would be the case without such embrittlement.

ID:4441