Compilation of stress intensity factor and load limit solutions for the Fitnet procedure

Isabel Hadley, TWI
Szabolcs Szavai, Bay Zoltán Foundation for Applied Research

Paper presented at FITNET 2006. International Conference on Fitness-for-Service, 17-19 May 2006, Amsterdam, The Netherlands. FITNET 06-022.

Abstract

In compiling the FITNET compendia for stress intensity factor and limit load solutions (Annexes A and B), the aim was to compile a comprehensive set of solutions that are accurate, user-friendly, consistently presented andmaintainable. Ultimately, the decision was made to incorporate the K-solutions from both BS 7910 and R6 procedures (with selected solutions from other sources), and L_r solutions mainly from R6/SINTAP.

Introduction

The estimation of applied stress intensity factor, K_I, and limit load, L_r, for a given crack/component geometry are critical inputs to a fitness-for-service calculation. One of the tasksin FITNET was therefore to review the available sources on K-solutions and limit loads, to recommend the most suitable for inclusion in Annexes A (K-solutions) and B (Limit Loads), and to present the solutions in a format consistentwith the rest of the procedure. This paper presents an outline of the approach used in compiling the Annexes. It also highlights selected cases where significant differences between existing procedures were found, and gives examples ofsolutions unique to FITNET.

Nomenclature

• B: section thickness

• f_W: finite width factor; a factor that magnifies the stress intensity when the crack is relatively large compared with the body in which it is located.

• k_m: stress magnification factor due to misalignment

• k_tb: stress concentration factor applied to bending stress

• k_tm: stress concentration factor applied to membrane stress

• M: bulging factor (applied to certain solutions for internally pressurised cylinders containing an axial flaw)

• M_km, M_kb: stress intensity magnification factors associated with cracks located close to a weld toe

• M_m, M_b: stress intensity magnification factors for a particular cracked geometry

• P_b: primary bending stress

• P_m: primary membrane stress

• Q_b: secondary bending stress

• Q_m: secondary membrane stress

• r_i: internal radius of pipe

• r_m: mean radius of pipe

• Y: normalised stress intensity, ie K_I/(πa).λ. For the inner surface under membrane loading, the simplified solution follows the same trends as the geometry-specific. Geometry-specific solutions are therefore preferred when the geometry of the component falls withinthe specified range.

   

  Fig. 2. K-solution for axial through-thickness crack in a cylinder a) Membrane stress, outer surface b) Membrane stress, inner surface

c) Bending stress, outer surfaced) Bending stress, inner surface

Finally, Figure 3a and b compare the BS7910, R6 and API 579 solutions for an extended axial flaw in a pipe (external and internal flaws respectively). The R6 and API solutions show a higher K-solution for externalthan for internal flaws, whereas the BS 7910 solutions are identical for internal and external flaws, and should be treated with caution.

Fig.3. K-solution for extended axial crack in a cylinder a) Membrane stress, external crackb) Membrane stress, internal crack

A simplified solution based on a flat plate solution multiplied by a bulging factor is also shown for comparison. It overestimates the geometry-specific solutions across the range of a/B, but can be used for geometries outside therange covered by the geometry-specific solutions.

Compilation of limit load solutions

Annex B of FITNET contains a wide range of limit load solutions, based largely on the R6/SINTAP solutions. Most of the geometries are similar to those of Annex A, although there are exceptions. For example, Annex B contains someunique solutions (e.g. limit load solutions for tubular joints), but has fewer solutions for bolts, bars, cylinders and plates than Annex A. Annex B also contains solutions for strength-mismatched materials, 'bi-materials' (adjacentmaterials of different strength) and clad materials, as summarised in Table 1.

In contrast with the situation observed when collating the K-solutions, the available L_r-solutions do not show many differences between them. There are fewer sources of solutions available, and the maindifference between them is in the method of presentation. The most extensive solutions were found in R6^[5] and SINTAP^[8]. Although SINTAP solutions forL_r have already been incorporated into R6 procedures, the latter contains several additional solutions.

For the case of bending loads, solutions from the SINTAP procedure sometimes express the limit load in terms of an equivalent outer-fibre bending stress, σb^L. In most cases, however, the solution for a given case is presented as a limit force value, F^N, pressure, P_e, bending moment, Me^b, or - in the case of axi-symmetric through wall bending - bending moment per unit angle of wall subtended at the centre of the section, m_L and in terms of the parameterL_r.

The solutions are based on a constant membrane and/or through-wall bending stress, and can be readily solved with a calculator or spreadsheet. All available models, e.g. global/local collapse, plane strain/plane stress. Mises/Trescaare collated in Annex B, with the responsibility placed on the user to select the appropriate solution.

Special features of Annex B

There are additional useful L_r-solutions in Annex B to take account of inhomogeneous components, thereby allowing the use of the more advanced levels of fracture analysis. Three different examples ofinhomogeneity are considered:

• mismatch: two materials with similar tensile properties are joined by a weld, the tensile properties of which may either be higher than that of the parent material (overmatching) or lower (undermatching). A crack is assumed to be present, either at the weld centreline, or at the weld/parent interface (see Figure 4a).
• bi-material joint: two materials with different tensile properties are joined, and a crack is assumed to be present at the interface between the two (see Figure 4b).
• clad component: here, the crack is assumed to be perpendicular to the clad/parent interface (see Figure 4c).

Fig. 4. Examples of material inhomogeneity in FITNET Annex B a) Mismatched weld geometries;
FITNET Lr solutions are available for a flaw at the weld centreline (left) or the fusion line (right)b) Example of a bi-material joint;
FITNET Lr solutions are available for a flaw at the interface between the components, which have dissimilar tensile properties

 c) Example of a clad material;
FITNET Lr solutions are available for a through-thickness flaw (left) and for a through-thickness flaw situated at the centre of a repair in the cladding (right)

The solutions for cladding are unique to FITNET; neither R6 nor SINTAP currently contains these solutions. However, bi-material components in the form of clad plates are in practice often used to improve the corrosion resistance ofthe substrate metal. Cracks developed during service in clad steel plates of pressure vessels can be divided into two major categories: surface cracks in the corrosion-resistant clad layer, and under-clad (sub-clad) cracks. Sincesurface cracks in the clad layer may grow into the substrate, limiting the service life of these components. Both types of cracks pose potential dangers for the structure, requiring careful inspection and structural assessment againstfracture. Furthermore, given that such defective areas may be repaired by welding, the structural significance of repair weld defects of the bi-material components may need to be assessed. Annex B therefore includes solutions developedby Alexandrov^[20], and Koçak and Motarjemi ^[21,22] for the treatment of cracked bi-material plates under tension, with and without repairwelds.

Concluding comments

A wide-ranging set of solutions for stress intensity and limit loads is presented in Annexes A and B, based largely on existing FFS procedures (especially R6/SINTAP and BS 7910). Whilst there may be occasions where the user needs tolook outside FITNET for an appropriate solution, it is envisaged that most practical cases can be solved from the array of plates, pipes, bars and other geometries offered in FITNET.

Acknowledgments

This work was jointly funded by the European Commission's FITNET Thematic Network (5th Framework Programme, Contract No. G1RT-CT-2001-05071) and the Industrial Members of TWI (as part of the Core Research Programme).

Thanks are also due to Martin Goldthorpe and Liwu Wei for their contributions to the K-solution compilation, and to BSI and British Energy for their co-operation in making available the BS 7910 and R6 documents and backgroundinformation.

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