Establishing the probability of failure
BS 7910 (“Guide to methods for assessing the acceptability of flaws in metallic structures”) has long been used to assess the structural integrity of welded joints in safety-critical structures. The fracture mechanics equations given in the standard are numerous and complex, so TWI developed special software – CrackWISE – to automate the process.
BS 7910 and CrackWISE assume deterministic inputs, ie single values of the important variables such as applied stress, fracture toughness and flaw size. In reality, these variables are statistically distributed and should be treated using probabilistic fracture mechanics (PFM). In principle, the probability of failure (Pf) can be calculated and used as part of a quantitative risk assessment (QRA) of safety-critical structures.
Annex K of BS 7910 contains a simplified method of quantifying Pf, using partial safety factors (PSFs) derived from PFM calculations, but in practice it is rarely used.
TWI has now developed a probabilistic module for CrackWISE, to expand its functionality. The new module is currently undergoing alpha testing to assess its robustness and user-friendliness, and to validate it against results from earlier PFM work.
Project objective
In this project TWI applied the CrackWISE probabilistic module to a known problem, with a view to validating the software.
Verifying the new approach
Whereas the deterministic version of CrackWISE can be validated by comparison against hand calculations (the answer for a given set of inputs is unique), the same considerations do not apply to PFM calculations, which produce a different set of input data each time the software is run. Consequently, the programme consisted of two tasks:
- Reproducing the PFM calculations (based on simple cracked plate models) that were used to develop the PSFs in Annex K of BS 7910:2013 and comparing the CrackWISE results with those of the earlier work.
- Replicating an earlier probabilistic assessment of a more complex welded joint that better represents a welded structure.
Encouraging results
This project demonstrated the ability of the new software to reproduce selected models used in the derivation of the PSFs in Annex K of BS 7910:2013 (see Figure 1). However, it also revealed that the agreement between Annex K and a direct PFM approach is weak, except for certain specific cases against which the model was originally calibrated. A direct PFM approach is therefore preferable to the use of PSFs to achieve a particular target Pf.
There are a number of outstanding challenges in the application of PFM (including the availability of high-quality data and the skill required of the analyst) to real engineering structures. Nevertheless, this work showed the ability of the software to calculate the relative effects of important variables, such as the scatter in tensile properties and fracture toughness, or the precision of the non-destructive testing technique (see Figures 2 and 3, overleaf).
The next step will be for TWI to investigate further the application of PFM to real engineering structures, such as pressure vessels and offshore structures, including wind turbine support towers.
See over for Figures 2 and 3.