Justification of the mapping approach for finite element modelling of ductile tearing

Ductile tearing plays a major role in the failure behaviour of flawed pipeline girth welds under plastic deformation. Different approaches exist to describe tearing in finite element analysis, each of which has specific advantages and disadvantages. This paper focuses on the highly pragmatic mapping approach, which interpolates between results of simulations with different but fixed flaw depths. The main advantage of mapping is its straightforward connection with experimentally determined crack growth resistance curves, by application of the tangency approach. Since mapping is unique in that it does not incorporate ductile tearing within a single simulation, its physical relevance may be questioned. This paper addresses a justification of the mapping approach from a fundamental point of view. First, an analytical proof of the concept is given based upon the mathematical background of the J integral. Then, a numerical validation gives confidence in the justification. Finally, attention is drawn to possible practical implementations of the mapping method.