Stress corrosion cracking (SCC) is another sub-critical crack growth mechanism which is very suitable for LEFM treatment, because applied stress intensity values are usually low in this cracking regime. One of the problems with SCC is that crack growth velocities increase very sharply with increase in K, and the lifetime may be correspondingly short. Hence, if the combination of likely defect size and applied, or residual, tensile stress cause the threshold for stress corrosion cracking (K1SCC) to be exceeded (see the theory
box), it is usually necessary to avoid the possibility of SCC. This is likely to
require either a change in alloy, or surface protection. Nonetheless, it is useful to illustrate the application of fracture mechanics to SCC lifetime determination.
This first problem is straightforward and shows a typical application that might arise in, for example, failure analysis, although the question is phrased as a manufacturer's assessment of life. It should take perhaps 20 minutes to complete.
A glass shelf in a bookcase can be considered as simply supported
beam subject to a uniformly distributed load. A particular manufacturer produces
bookcases with shelves that are 1.5 m in length (L), have a width (b) of 200 mm and a thickness (t) of 10 mm. The design load on the shelves is estimated as w = 100 N/m2.
The manufacturer knows that handling of the glass shelves during fabrication may cause surface flaws to be present in them, which can be considered as semi-elliptic in shape with a maximum depth of 0.1 mm. He is also aware of the fact
that a moist air environment may cause stress corrosion cracking to occur in stressed glass. He has therefore approached you, as a fracture mechanics/failure consultant to advise him whether he should offer a one year guarantee on these bookcases.
Calculate the lifetime of a typical shelf under these conditions,
assuming no incubation period is required before the crack extends. You have access to the following information:
1. The maximum bending stress in a simply supported beam subject to a distributed load is given by:
2. The shelves are to be made from
soda glass with a modulus of elasticity E = 70 GPa and a work to fracture R = 0.01 kJ/m2. A crack velocity (v-K) curve for soda glass in a moist air environment is given below.
3. The stress intensity factor for a semi-elliptic surface defect can be calculated from: