A criterion for low-stress brittle fracture of materials with crack or sharp notch based on combined micro-and-macro fracture mechanics

For fracture of solids with crack, the following two requisites should be satisfied:

1. (1) The local stress at or near the tip of the crack should exceed the ideal strength, that is, atomic cohesion, and

2. (2) The free energy should decrease with propagation of the crack, that is, the energy unstable condition should be satisfied.

In low-stress brittle fracture of materials with crack or sharp notch, it has been usually considered that the local stress at or near the tip of the crack could not reach the atomic cohesion level. Then many investigators have been led to the conclusions that critical displacement should be assumed instead of critical stress or energy unstable condition. This appears to be the reason why the COD concept has been widely assumed. Thus it is to be noted that the explanation of the phenomenon by the COD concept concerns essentially the rupture or slipping off mechanism rather than fracture.

On the other hand, when plastic flow occurs at or near the tip of the crack, dislocation will move and thus, if there are any obstacles near, then pile-up will occur. In this article, the stress concentration caused by such microscopic mechanism is considered, and thus the local stress near the tip of the crack will reach the ideal strength, say, atomic cohesion, and, that is, the first requisite mentioned above is satisfied.

Then, the energy balance condition as the second requisite is studied in the article.

Comparing the two critical stresses as satisfying the first and the second requisites respectively, the criterion for low-stress brittle fracture is discussed.

Furthermore, the experimental study was made on polymethyl-methacrylate, and the result is in good agreement with the energy unstable condition.