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Development of the BS 7910 failure assessment diagram for strain based design with application to pipelines

   
Simon Smith

TWI Ltd

Proceedings of the ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering OMAE 2012 July 1-6 2012, Rio de Janeiro, Brazil

Abstract

Engineering Critical Assessment (ECA) uses J estimation schemes to derive the crack tip loading of complex structures to determine their tolerance to crack-like flaws. The methods currently being used were derived in the 1980s for structures with primary stresses below the material yield strength. These are now being extensively used for loads beyond this level for what has been called Strain Based Design (SBD). Some papers have shown the standards BS7910:2005 and R6 Revision 4 can be unconservative when used for SBD. A possible reason has been identified and a suitable modification proposed. The proposed modification is briefly reviewed in the present paper together with a comparison of the method with suitable crack driving force data.

Introduction

Offshore oil production and transport facilities contain many welds. Welds may contain fabrication flaws or possibly develop in-service cracks by, for example, fatigue. The processes of Engineering Critical Assessment (ECA) were developed to provide safe methods for determining the criticality of defects in engineering structures. The methods were based upon the principles of post yield fracture mechanics (PYFM) which emerged in the 1960s. The Stress Intensity Factor (SIF) had already been developed. The SIF was able to determine the level of loading applied to the tip of a crack in a linear elastic material. Rice [1968] introduced the J contour integral to provide PYFM with a suitable parameter for expressing the crack tip loading for an elastic-plastic material. It was therefore possible to develop an ECA procedure for the comparison of the toughness of engineering materials and the applied loading for possible defects. A structure could be declared safe provided that its material toughness was greater than the highest crack tip loading of any crack in the structure under all possible service loadings. Methods for the measurement of material toughness, including constraint matching for pipeline welds have been and are still being developed (eg DNV-RP-F108, 2006 and more recently Paredes et al, 2010). It is therefore possible to determine the material toughness. The applied J was more difficult to calculate than the applied SIF because it is not proportional to load and cannot be determined using the relatively simple methods of linear elastic stress analysis. It was found, however, that the relationship between J and applied load could be accurately expressed if the plasticity was represented by power law hardening (Shih 1976). Numerous papers were therefore published which contained tables of the appropriate constants for two dimensional configurations (Shih and Hutchinson, 1976). These became known as J estimation schemes. For example, the EPRI scheme was based upon a power law material hardening assumption (Anderson, 1995).

Clearly, restricting material behaviour to power law hardening meant that some materials were not accurately represented by the EPRI scheme. The British Central Electricity Generating Board (CEGB) had been developing J estimation schemes during the 70s and early 80s. The evolution of their method was presented in a number of publications. In 1984, Ainsworth published an important paper in the development of J estimation for non-power law hardening materials (Ainsworth, 1984a). He showed that the basic methods of a power law hardening scheme could be generalised. He presented the new J estimation scheme in the form of a Failure Assessment Diagram (FAD). The FAD required engineers to determine the crack tip loading in terms of the SIF and the additional loading due to plasticity was accommodated through the shape of the FAD. It was therefore possible to perform PYFM ECA for non-power law hardening material based upon the elastically determined SIF combined with the collapse load of the cracked structure. The Ainsworth FAD was based upon the material stress-strain curve so it was classified as a material specific FAD to distinguish it from some more general, conservative expressions. The material specific FAD was adopted by the CEGB (later called British Energy) ECA code R6 (British Energy, 2010) and the British Standard BS 7910 (BSI, 2007). The material specific FAD is classified as Level 2B in BS 7910.

Recently, the Oil and Gas industry has applied the methods of ECA to cases where the nominal straining includes plasticity so that the nominal stresses are well over the material yield strength. Very high levels of strain are often developed during pipelay. The requirement for a safe assessment of in-service loadings may require the consideration of possible sources of significant straining such as frost heave and lateral buckling. Considerable research has therefore been directed towards the extension of ECA into what has been called Strain Based Design (SBD). Some of these studies have adopted Finite Element Analysis (FEA) to determine the actual crack driving force in terms of J up to typical pipeline loading levels of plastic strain. Comparisons with BS 7910 have found that there are some instances where the implied J derived from the FAD is less than the J predicted by FEA (eg Tkaczyk et al 2009 and Jayadevan et al 2004). This finding is of concern because it means that it might be possible to declare that a certain combination of crack size, material and loading is safe when this is not the case. This issue was discussed by Pisarski and Cheaitani (2008). They proposed that there were sufficient safeguards to prevent an unsafe assessment.

A recent paper (Smith, 2012) has investigated the Ainsworth material specific FAD and proposed a modification to remove its lack of conservatism in the SBD regime. It was shown that the modified material specific FAD was safe in a specific case where the existing BS 7910 FAD was shown to be unsafe. Further comparisons of the new FAD with the results of FEA predictions of J in the SBD regime are presented below to provide a more comprehensive assessment of the proposed modification. A recent publication (Chiodo and Ruggieri, 2010) has provided an EPRI-like scheme for three pipe diameter to thickness ratios in pure bending. The results are presented for hardening exponents of 5, 10 and 15 and for crack angles (subtended at the pipe centre) of up to 70° . The material specific FAD is applicable to a wide range of stress versus strain behaviours including the power law description. It is not therefore necessary to restrict it to power law behaviour. However, it is attractive to make a comparison of the new FAD with the results of Chiodo because it provides a means of expressing the performance of the modified FAD in terms of an easily recognisable hardening parameter.

Review of the BS 7910 material specific FAD

The early work by Ainsworth and his colleagues at the CEGB (Ainsworth, 1984b) concluded that it was possible to define a reference stress,σref, for a component containing a crack such that the applied J was given by the following expression.

eq1
[1]

The left hand numerator and denominator are the total applied J under conditions of plastic and elastic only deformation respectively. The material Youngs Modulus for elastic deformation is Ε and the stress versus strain curve is used to determine the reference strain (εref) at the calculated reference stress, σref. The expression will be trivial if linear hardening with a hardening modulus equal to Ε is assumed because the stress distribution will be the elastic solution. It is a powerful expression for non-linear hardening materials because it allows J to be determined from the elastic SIF.
Ainsworth (1984a) used expression 1 as the basis for the development of a J estimation scheme for elastic plastic materials where a transition from purely elastic deformation to dominantly plastic deformation during small scale yielding (SSY) was needed. The resulting scheme was expressed as a FAD as follows.

eq2
[2]

This is the material specific, level 2B FAD of BS 7910 defined in terms of the loading parameter, Lr (below), and the material yield strength, σy.

eq3
[3]

The fracture parameter, Kr, is the ratio of the elastically determined applied SIF to the material toughness defined in terms of a SIF. The elastic, plane stress conversion between J and SIF is given by expression 4.

eq4
[4]

It is clear, therefore, that the first term of the material specific FAD is derived from expression [1] and that the second term is a modification for SSY.

Review of the BS 7910 material specific FAD

It has recently been shown for a power law hardening material that the  following revision of expression [1] is needed for a specific case in which J  can be determined theoretically (Smith, 2012).

eq5
[5]

Clearly, the old and new equations are equivalent for linear strain hardening where n is unity. It is more important to state that, at very low levels of strain hardening (when n is large), the plastic J from expression (5) is twice the value given in equation [1]. This implies that the material specific FAD of expression (2) would significantly underestimate the crack tip loading at low levels of strain hardening when the loading is beyond SSY. The coefficient of the right hand side is therefore different for elastic and non-linear strain hardening materials. The material specific FAD of expression (2), however, relies on a material independent coefficient of unity as shown in expression (1).

An alternative FAD has been proposed which uses parameter X to change the effective coefficient from unity for low loads to two for higher loads. This is given by the expressions (6) and (7).

eq6
[6]
eq7
[7]

Expression (7) could be modified to make the FAD less conservative if a compromise value of the coefficient in expression (5) could be adopted. However, for the current paper the upper bound value is used. Constants  C1 and C2 provide a tuning facility for the modified FAD. The value of C1 determines the extent of the transition range and C2  determines the centre point of the transition. Values of 5 and 1 are used here.

EPRI-LIKE approach of CHIODO and RUGGIERI

Chiodo and Ruggieri (2010) have computed factors for an EPRI-like representation of the crack tip loading for an elastic-power law hardening pipe under pure bending (Figure 1). EPRI schemes assume that the total applied J for a crack in an elastic-plastic material is the sum of the J values determined from elasticity and plasticity alone as follows (Shih, 1976).

eq8
[8]

The material stress-strain behaviour is assumed to have elastic and power law hardening components as follows (where α is a material constant).

eq9
[9]

The J due to plasticity (Jp) arising from a mode of deformation defined by equation [9] can be estimated in the following form.

eq10
[10]

The applied moment is M and the collapse moment is Mo . The constant h1  is a function of the crack size and shape, the pipe dimensions and the hardening exponent. Dimension b is equal to the uncracked ligament depth ahead of the maximum depth of the crack or t - α. An expression for a nominal limit load, Mo , is given by Chiodo and Ruggieri. They also performed a wide range of Finite Element Analyses to determine h1  for a large set of geometries and levels of material hardening.

J from material specific FADs

A comparison of the FAD-based derived J curves with the results from Chiodo and Ruggieri was generated based upon a pipe of 400mm outside diameter and a material of yield strength 448MPa (65ksi). Results are presented for pipe wall thicknesses of 40mm, 26.7mm and 20mm (D/t ratios of 10, 15 and 20). Comparisons were made for work hardening exponents, n, of 5, 10 and 20. Crack depth to wall thickness (a/t) ratios in the range 0.075 to 0.45 were analysed. Chiodo and Ruggieri defined crack widths using an unconventional definition of angle as specified by their equation 13. The study investigated a range of actual total crack width, giving rise to a subtended angle at the pipe centre of 2θ. The half angles studied were in the range 0.05 to 0.25 expressed as the ratio θ/π.

The implied J from the existing BS 7910 level 2B material specific FAD (equation (2)) was compared with J derived from the Chiodo and Ruggieri (Equations [8] and [10]). The comparison is therefore being made with FEA results, albeit in the form of curve fits to the FEA results. The results also show J from the new FAD (expressions (6) and (7)).
A list of the results and their figures is given in Table 1.

Discussion and Conclusions

Smith (2012) and the current paper were motivated by concerns that BS 7910 was not conservative for SBD. However, the results show that BS 7910 is in fact conservative for most of the cases studied. Two cases of non-conservatism were found. The first case of unconservatism (Figure 7) was for low work hardening combined with a small crack width (2c). BS 7910 was also slightly unconservative for at a higher rate of work hardening (n equal to 5, Figure 6). The modified ‘Smith’ FAD was conservative in all cases, but its level of conservatism was always significant, so that it appears to be unattractive. BS 7910 was also found to be overly conservative for both long and deep cracks (Figures 8-10).

Acknowledgments

Dr Henryk Pisarski provided useful discussions of SBD during the preparation of this paper.

References

  • Ainsworth R A, 1984a: ‘The assessment of defects in structures of strain hardening material’, Engineering Fracture Mechanics 19 633-642.
  • Ainsworth R A, Chell G G and Milne I, 1984b: ‘Solution to the workshop problem using the CEGB fracture assessment procedure [R6]’, CSNI/NRC workshop on ductile piping fracture mechanics, San Antonio Texas, June 1984, 13-32.
  • Anderson T L, 1995: ‘Fracture Mechanics’, Second edition, CRC Press.
  • British Energy, 2010: ‘R6 Revision 4, Assessment of the integrity of structures containing defects’, 2001, with amendments to 2010.
  • BSI, 2007: ‘Guide to methods for assessing the acceptability of flaws in metallic structures’. BS 7910:2005, incorporating Amendment No.1.
  • Chiodo M S G and Ruggieri C, 2010: ‘J and CTOD estimation procedure for circumferential cracks in pipes under bending’, Engineering Fracture Mechanics, 77, 415-436.
  • DNV, 2006: ‘Fracture control of pipeline installation methods introducing cyclic plastic strain’, DNV-RP-F108.
  • Jayadevan K R, Ostby E and Thaulow C, 2004: ‘Fracture response of pipelines subjected to large plastic deformation under tension’, International Journal of Pressure Vessel and Piping, 81, 771-783.
  • Paredes L M, Carvalho H S S and Ruggieri C, 2010: ‘Applicability of J estimation procedures for overmatched SE(T) fracture specimens’, Proceedings of the ASME 2010 Pressure Vessels & Piping Division / K-PVP Conference, PVP2010, Bellevue, Washington, USA, Paper PVP2010-25121.
  • Pisarski H G and Cheaitani M, 2008: ‘Development of girth weld flaw assessment procedures for pipelines subjected to plastic straining’, International Journal of Offshore and Polar Engineering, 18, 3, 183-187.
  • Rice J R, 1968: ‘A path independent integral and approximate analysis of strain concentration by notches and cracks’, ASME Jnl App Mech 35, pp379-386.
  • Smith S D, 2012: ‘Notes on J Estimation in BS 7910 with comments on Strain Based Design’, Submitted to the International Journal of Pressure Vessel and Piping.
  • Shih C F, 1976: ‘J-integral estimates for strain hardening materials in antiplane shear using fully plastic solution’, Mechanics of Crack Growth, ASTM 590, 3-26.
  • Shih C F and Hutchinson J W, 1976: ‘Fully plastic solutions and large scale yielding estimates for plane stress crack problems’, Journal of Engineering Materials Technology, 98, October, 289-295.
  • Tkaczyk T, O’Dowd N P, Nikbin K and Howard B P, 2009, ‘A non-linear fracture assessment procedure for pipeline materials with a yield plateau’, Proceedings of the nineteenth International Offshore and Polar Engineering Conference, Osaka Japan.

Table 1 Figure numbers of plots of J versus nominal strain with the assumed pipe sizes and material behaviour.


Figure number

D/t

n

θ/π

a/t

2

10

20

0.15

0.075

3

15

20

0.15

0.112

4

20

20

0.15

0.15

5

20

10

0.15

0.15

6

20

5

0.15

0.15

7

20

20

0.05

0.15

8

20

20

0.25

0.15

9

20

20

0.15

0.3

10

20

20

0.15

0.45

Figure 1 Geometry of the cracked pipe under a pure bending moment, M.
Figure 1 Geometry of the cracked pipe under a pure bending moment, M.
Figure 2 J versus nominal applied strain for a pipe of 400mm diameter (D)
Figure 2 J versus nominal applied strain for a pipe of 400mm diameter (D), yield strength of 448MPa with D/t = 10, n = 20, θ/π = 0.15, a/t=0.075.
Figure 3 J versus nominal applied strain for a pipe of 400mm diameter (D)
Figure 3 J versus nominal applied strain for a pipe of 400mm diameter (D), yield strength of 448MPa with D/t = 15, n = 20, θ/π = 0.15, a/t=0.112.
Figure 4 J versus nominal applied strain for a pipe of 400mm dia (D), yield strength of 448MPa with D/t = 20, n = 20, θ/π = 0.15, a/t=0.15.
Figure 4 J versus nominal applied strain for a pipe of 400mm dia (D), yield strength of 448MPa with D/t = 20, n = 20, θ/π = 0.15, a/t=0.15.
Figure 5 J versus nominal applied strain for a pipe of 400mm diameter (D), yield strength of 448MPa with D/t = 20, n = 10, θ/π = 0.15, a/t=0.15.
Figure 5 J versus nominal applied strain for a pipe of 400mm diameter (D), yield strength of 448MPa with D/t = 20, n = 10, θ/π = 0.15, a/t=0.15.
Figure 6 J versus nominal applied strain for a pipe of 400mm diameter (D), yield strength of 448MPa with D/t = 20, n = 5, θ/π = 0.15, a/t=0.15.
Figure 6 J versus nominal applied strain for a pipe of 400mm diameter (D), yield strength of 448MPa with D/t = 20, n = 5, θ/π = 0.15, a/t=0.15.
Figure 7 J versus nominal applied strain for a pipe of 400mm diameter (D), yield strength of 448MPa with D/t = 20, n = 20, θ/π = 0.05, a/t=0.15.
Figure 7 J versus nominal applied strain for a pipe of 400mm diameter (D), yield strength of 448MPa with D/t = 20, n = 20, θ/π = 0.05, a/t=0.15.
Figure 8 J versus nominal applied strain for a pipe of 400mm diameter (D), yield strength of 448MPa with D/t = 20, n = 20, θ/π = 0.25, a/t=0.15.
Figure 8 J versus nominal applied strain for a pipe of 400mm diameter (D), yield strength of 448MPa with D/t = 20, n = 20, θ/π = 0.25, a/t=0.15.
Figure 9 J versus nominal applied strain for a pipe of 400mm diameter (D), yield strength of 448MPa with D/t = 20, n = 20, θ/π = 0.15, a/t=0.3.
Figure 9 J versus nominal applied strain for a pipe of 400mm diameter (D), yield strength of 448MPa with D/t = 20, n = 20, θ/π = 0.15, a/t=0.3.
Figure 10 J versus nominal applied strain for a pipe of 400mm diameter (D), yield strength of 448MPa with D/t = 20, n = 20, θ/π = 0.15, a/t=0.45.
Figure 10 J versus nominal applied strain for a pipe of 400mm diameter (D), yield strength of 448MPa with D/t = 20, n = 20, θ/π = 0.15, a/t=0.45.

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