Crack tips

The nature of the stress field around crack tips is somewhat controversial: it is known that over-loaded cracks grow more slowly than expected but it is not clear why. There are several proposed models but little experimental data due to the difficulties in measuring with sufficient spatial resolution to reveal the tensile lobes ahead of a loaded crack. All fatigue life prediction models currently in engineering use are phenomenological rather than physically-based. One of the main reasons for this has been the lack of direct quantitative data describing the actual complete crack-tip stress/strain field accompanying fatigue crack growth.

Crack growth rates generally increase as a crack lengthens; thus the majority of the lifetime of a crack in a structural component is spent when the crack is short. Uncertainties in short crack-propagation behavior therefore have the greatest influence on lifetime prediction. Unfortunately this is also the regime within which the study of crack behavior is most difficult. Furthermore, it is well known that near the surface crack behavior is very different from the bulk necessitating the study of relatively thick samples.

High resolution EDD promises a significant breakthrough in the study of cracks. Since the characteristic stress field around the crack tip is estimated to decay within a few tens to hundreds of micrometers, outside the range of what is achievable with neutrons, EDD is currently the only candidate for the non-destructive characterization of strain fields in bulk engineering materials with such spatial resolution.

The elastic strain measured in the vicinity of the crack tip for specimen CT1. The apparent vertical feature in the centre of the sample (at 6 mm) is due to missed data points when spectra were lost during a beam refill.

The elastic opening strain ε22 as predicted by the three-dimensional finite-element analysis for a crack specimen (CT1).

Strain field in the proximity of a crack in austenitic steel.

The figure above shows the experimental elastic opening strain (left) of a 25 mm thick austenitic steel compact tension specimen in the vicinity of the crack tip which can be directly compared with the prediction of a finite element analysis (right) for approximately the same volume element. This example clearly demonstrates the ability of the EDD technique to reveal fine details of the crack strain fields with sufficient accuracy. Recently with a fine grained aluminum alloy 5091 sample a spatial resolution of 20 µm was achieved. Measurements even in the plastic region surrounding the crack tip were possible. The simultaneous use of two germanium detectors provided two independent and perpendicular stain measurements guaranteeing the required precision.

The achieved unique information will be invaluable both in validating present finite element simulations of fatigue crack growth and in developing the high accuracy simulations necessary for physically realistic fatigue life prediction models.

Marrow T.J., Steuwer A., Mohammed F., Engelberg D., Sarwar M. - Measurement of crack bridging stresses in environment-assisted cracking of duplex stainless by synchrotron diffraction - Fatigue and Fracture of Engineering Materials and Structures 29, 464-471 (2006).