Experimental Procedures

Experimental procedures to determine the stress intensity factor were often used with some intensity in the past, when numerical calculations were of limited availability. All the methods relied on measuring some features of the displacement fields of clastic specimens, and relating them to the energy release rate or to the stress intensity factor.

The simplest method, which is generally used in laboratory environments, uses the experimental version of the differential stiffness method. It is implemented by measuring the compliance of a specimen for various crack depths and determining Q from Q — (P2/2b)dC/da. In principle, two tests with two slightly different crack lengths are enough to get a result lor a given crack length. However, experimental accuracies being always very limited, it is usually better to make a larger number of tests over a finite range, fit a smooth curve to these results, and then perform the differentiation. Because the experimental accuracy in obtaining the compliance is rarely better than 1%, this method is not very reliable unless the compliance variation due to the growth of the crack is a sufficiently large fraction of the total compliance. This excludes large specimens or structures with tiny cracks (or, generally speaking, small relative crack depths). In some test setups, a further source of error is that, in order to have a good control of the geometry, cracks are substituted by cut slits (notches). In this case, the notch width must be much less than any relevant dimension of the specimen (crack length, remaining ligament length, distance of applied loads from the crack tip, etc.).

Other methods rely on the analysis of the properties of the strain or displacement fields dose to the crack tip. These include: strain gauge techniques, photoelastic techniques, interferometric techniques, and the caustics method.

The strain gauge technique measures the strain and stress at a set of points around the crack tip by means of bonded electrical strain gauges. In the photoelastic technique, the shear strain field around the crack is measured in a specimen made of a photoelastic polymer. In the interferometric techniques, the displacement field (usually the component normal to the crack plane) is mapped by interferometry. From the experimental results of stress, shear-strain, or displacement vs. the distance to the crack tip, near-tip fitting techniques similar to those sketched for numerical methods are used to infer the value of the stress intensity factor.

The principle of the caustics method is different of the former in that it uses the out-of-plane displace­ments to find the stress intensity factor. Due to Poisson effect, a depression of the surface of the specimen is produced around the crack tip. If the surface is polished, a mirror with a profile determined by the elastic
field is produced. When a beam of light impinges normally over this mirror, the reflected rays produce a bright kidney-shaped spot whose size is related to the stress intensity factor. If transparent specimens are used, transmitted light can be used and then the specimen acts as a lens with a profile determined by the elastic field.

In all these techniques, it is essential to guarantee that the plastic zone is small compared to the size of the region over which the stresses, strains, or displacements are measured. If notches, instead of cracks, are used (which is usual in photoelastic techniques), corrections are required to take into account the finite radius at the tip.

For details of the experimental techniques, see Smith and Kobayashi 1993.