PSI - Issue 13

Moritz Lessmann et al. / Procedia Structural Integrity 13 (2018) 1232–1237 Author name / Structural Integrity Procedia 00 (2018) 000–000

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Figure 5 – An example of a 3D cracked-body mesh for a semi-elliptical surface breaking defect in a toroidal pipe generated with mixed element types and nodal transformation 3. Failure Assessment Diagram vs. Elasto-Plastic Modelling 3.1. Failure Assessment Diagram Approach CBFEA conducted to determine a limiting defect size often consists of an elastic analysis to find the J-Integral / SIF values, combined with an elasto-perfectly-plastic limit load analysis. Assessment points for a range of defect lengths are derived and plotted on a FAD, with the limiting defect size defined when the failure assessment curve (FAC) is crossed, Figure 6. However, the problem with this lies in how to interpolate between the assessed defect lengths to determine what the limiting defect size would be (i.e. the defect length at which the FAC is crossed), as K r and L r do not linearly interpolate/extrapolate with defect length. The solution to this problem lies in understanding the meaning of the FAC. Regardless of how it is derived, the FAC is an approximation to the value:√(J e /J), based on the value of L r [Anderson]. That is to say, how much higher would J be if the calculation included an elasto-plastic material model rather than the elastic assumptions made (J e ). From this knowledge we can recast our problem by making an estimate of what J is based on the value of J e and L r . In this case: ���� � � � � � � We also know that K r is calculated as � � � ��� So, if we recast using the elastic relation between J and K we can calculate ���� � � � ��� � � � � � � � The material allowable if not already defined in terms of the energy release rate (J mat ) can also be calculated from K mat . ��� � � � ��� It is then possible to re-plot the value of J opt1 verse crack length. Figure 7 provides a clearer illustration of the response of the defect with increasing defect size when compared to the FAD, assessing J opt1 and J ep against the material allowable. The elasto-plastic assessment is shown to release conservatisms in the analysis as evidenced by a shift in the limiting defect size The limiting defect size (i.e. the point at which the material allowable is exceeded) may then be determined directly through a chosen interpolation scheme. This is in contrast to the FAD approach, where justification of a defect length at which the FAC is crossed is less clearly supported.