Interaction of Multiple Surface Cracks

The purpose of this example is to demonstrate the capability in Zencrack to allow modelling of interaction of two defects. The analysis is based on experimental data published by Bostjan Bezensek and John Hancock. Their paper investigates the re-characterisation of complex defects according to codes such as BS7910 and R6 and assesses possible conservatism within the re-characterisation methodology.

The crack configuration is based on three-point-bend tests of specimens measuring 230mm x 150mm x 25mm, as shown in Figure 1. A number of different sizes of initial defect were tested and the analysis represented here uses typical initial defect dimensions. In this particular case the two defects have different initial sizes.

The experimental tests were conducted at a stress ratio of 0.1, keeping the applied stress intensity factor less than 30MPa sqrt(m). This required the adjustment of the load level as the test proceeded, thus generating a spectrum consisting of blocks of constant amplitude loading at lowering load levels. The crack growth data is modelled as a Paris line and therefore there is no account of possible near-threshold effects at the start of the analysis.

The Zencrack analysis is conducted in two phases:

• growth of the separate surface defects
• growth of a single joined defect

In both parts of the analysis the initial crack shape is defined by the user-defined crack front option in Zencrack. A typical mesh part way through the first phase of the analysis is shown in Figure 2.

The profiles for the whole analysis are shown in Figure 3 with a growth animation in Figure 4. The profiles of the right hand defect (i.e. the left side of this image is adjacent to the second crack) are compared with a typical test result in the top image of Figure 5. The analysis has shown slightly more growth at the surface than in the test, but the trend is correct. The reason for the surface discrepancy is not clear. A number of possibilities exist including: different crack growth data at the surface due to issues of rolling direction and material orientation; possible small effects of residual stress due the way the specimens were manufactured; insufficient element density. The latter option was checked by using a more refined model which gave essentially the same results. The effect of different Paris data was considered by reducing the calculated stress intensity factors at the surface. This can be demonstrated to give better agreement with the test data as shown in the bottom image of Figure 5 in which the surface values of K were reduced by 20% before crack growth integration took place. This type of change can readily be accomplished in Zencrack through user subroutine options.

The number of cycles predicted by the analysis was slightly lower than the test. There are several contributing factors including the issue of Paris data without any specific near-threshold effects taken into account. Also, it was observed during the tests that there was scatter of around 10000-15000 cycles in the number of cycles required to achieve a given crack length. This represents about 10% cycles up to coalescence.