Calculation of stress intensity factors corresponding to standard residual stress profiles for common weld joint geometries

ASME-PVP
ASME Pressure Vessel and Piping Conference Symposium on Weld Residual Stresses and Fracture 23-27 July 2000

Abstract

The new procedures for obtaining the RSP and K _RSP provide a practical alternative to the traditional assumption that 'residual stresses at welds are equal to yield'. The excessive conservatism which may be associated with that assumption can be reduced or eliminated. However, these new capabilities bring with them the danger of a 'black-box' syndrome. There are many different RSPs for different joint geometries and defect orientations, and the associated stress intensity factor solutions are complex. The fracture analyst may not be aware of the nature of the assumed residual stress distribution, or of the sensitivity of the assessment to the assumed residual stresses.

Examples are given in this paper of the variation of K _RSP as a function of crack size for a range of defect and weld configurations including long and short surface defects at butt and T-butt welds in plates and circumferential butt welds in cylinders. In order to demonstrate the benefits of using the standard residual stress profiles, the K _RSP values are compared with the stress intensity factor for the same defect subject to uniform yield magnitude residual stresses. A new solution is given for the K _RSP at a through-wall transverse crack subject to residual stresses having the trapezoidal shape given in the SINTAP and API 579 compendia for profiles of surface residual stresses.

Introduction

This paper starts with a summary and comparison of the RSPs in the three documents listed above ^[1-3] . Examples are given of stress intensity factors for a range of common defect and weld combinations, mostly calculated using the profiles and stress intensity solutions given in reports ^[2,4] from the SINTAP project. These examples illustrate the variation of stress intensity with crack depth, and the benefits to be obtained by assuming a non-linear RSP, as opposed to the traditional assumption of uniform residual stresses equal to the yield strength. Further examples are given in another SINTAP report ^[5] .

Comparison of published residual stress profiles

Table 1. Comparison of residual stress profiles in BS 7910, SINTAP and API 579

Q.1.4 Pipe axial seam welds (same as Q.1.2)

E6 Welds in storage tanks.
Single-V (E.6.3) and double-V (E.6.4) longitudinal welds

E5 Welds in spheres and pressure vessel heads
Single-V (E5.1) and double-V (E5.2) circumferential welds.
Single-V (E5.3) and double-V (E5.4) meridional welds

E6 Welds in storage tanks.
Single-V (E6.1) and double-V (E6.2) circumferential welds

E8.1 Main plate

E8.2 Stay plate

Fig.6 Set-on nozzle

E7.1 Corner joint

E7.2 Nozzle fillet weld

E7.3 Shell fillet weld at a reinforcing pad

E9.1 Seam welds

E9.2 Nozzle welds

BS 7910 and the SINTAP compendium are intended to be generally applicable for the assessment of flaws in welded structures. API 579 is concerned specifically with pressurised equipment used in the refinery and chemical industry. This difference of scope has led to some differences in the categorisation of weld types, as shown in Table 1. It should be noted that different terminologies are used for describing directions in API 579 compared with the other source documents, as summarised in Table 2. At circumferential welds, the term longitudinal refers to the cylinder axial direction in API 579, and to the circumferential direction (along the weld) in the other documents.

Table 2. Terminology for directions

Within the general categories of straight and curved full penetration butt welds in Table 1, BS 7910 and SINTAP give one set of RSPs for butt welds in flat plates and pipe axial seam welds, and one set of RSPs for circumferential butt welds in pipes. API 579 does not consider butt welds in flat plates, but gives separate sets of RSPs for welds in (i) piping and pressure vessel cylindrical shells, (ii) storage tanks and (iii) spheres and pressure vessel heads. It gives separate RSPs for longitudinal, circumferential and meridional welds, and for single-V and double-V welds.

For T-butt and T-fillet welds, BS 7910 and SINTAP give separate consideration to welds in plated construction and tubular construction. API 579 does not make this distinction, but does give profiles of stresses in the main plate and the stay plate.

With regard to the actual shapes of the profiles, the through-wall RSPs in BS 7910 and SINTAP include linear, bilinear, polynominal (up to 6 ^th order) and cosine profiles. Those in API 579 are more consistent in shape, all being linear, bilinear or 2 ^nd or 3 ^rd order polynominals. The surface RSPs in SINTAP and API 579 are trapezoidal, i.e. uniform inside the weld and decreasing linearly to zero in parent plate adjacent to the weld.

All the RSPs in API 579 and about half of those in BS 7910 and SINTAP are based on upperbound curves fitted to published residual stress data obtained by measurement or numerical modelling. The remainder of the RSPs in BS 7910 and SINTAP, including the surface profiles of longitudinal stresses and the bilinear through-wall profiles at the toes of T-butt and T-fillet welds, are based on a theoretical upper bound model of the extent of the plastically deformed zone adjacent to a weld developed by Leggatt ^[9,10] . The dimensions of the deformed zone are given as a function of material properties, weld heat input and plate thickness. The theoretically based profiles have been compared with relevant experimental and numerical solutions in the SINTAP project ^[2] , and found to be satisfactory. The theoretical model assumes a high restraint against thermal contraction after welding, which is an appropriate assumption for longitudinal stresses in nearly all cases, and for transverse stresses at T-joints in thicker materials (i.e. thicker than about 25mm). However, it may be less realistic in thinner materials, such that the RSPs become increasingly conservative as thickness decreases.

The empirically-based RSPs are strictly valid only within the range of plate thickness and welding conditions for which data were available. They have been non-dimensionalised with respect to plate thickness or weld width. This does not reflect the influence of welding and other parameters included in the theoretical model on the width of the plastically deformed zones adjacent to the welds. Hence the empirically-based RSPs may be over-conservative for thicknesses greater than those for which source data was available, and may be non-conservative for thicknesses below the range of the source data.

Longitudinal surface cracks at straight butt weld

Fig.1. Through-wall profiles of transverse residual stresses at butt weld

API 579 Eq.E.34 and E.79 are somewhat similar to the BS 7910 and SINTAP profiles, except in the region 0.4<z/t<0.9 where the API profiles are more tensile. API 579 Eq.E43 adopts the traditional conservative assumption of uniform yield magnitude stresses at double-V longitudinal welds in pipes and cylindrical pressure vessels, but Eq.E73 shows stresses decreasing linearly to zero at the root of single-V welds in storage tanks. The present authors would not be confident of always finding zero stress or less at this location: tensile transverse stresses can develop at the root of the weld as it is stretched by angular distortion during the deposition of the fill passes.

The 'normalised K _RSP', i.e. the stress intensity factor corresponding to the standard residual stresses profile divided by

Fig.2. Normalised K _RSP at longitudinal infinite surface crack at straight butt weld. Effect of residual stress profile

All the K _RSP values discussed above apply to long surface cracks at the side welded last (BS 7910), or at the outside (API 579). For cracks at the opposite face, the normalised K _RSP would tend to zero as the crack depth tends to zero for the RSP defined by API Eq.E.73 and to about 1.0 for the other profiles shown in Fig.1. This is clearly a significant difference, and further work to confirm the validity of Eq.E.73 in this region would be desirable.

The normalised K _RSP for the deepest and surface intersection points of semi-elliptical surface cracks of aspect ratio, 2c/a, equal to 3.33 and 10 are plotted in Fig.3. K _RSP was evaluated using a solution for a 5 ^th order polynominal stress profile ^[4] , and hence it was necessary to fit a 5 ^th order polynominal to the 6 ^th order BS 7910/SINTAP profile shown in Fig.1.

Fig.3. Normalised K _RSP at finite surface crack at butt weld in plate. Effect of crack aspect ratio at deepest point and surface intersection

In contrast to the K _RSP shown in Fig.2 for infinite surface cracks, the normalised K _RSP shown in Fig.3 for the deepest point of finite surface cracks falls continuously with crack depth. The stress intensity factor is always positive, despite the presence of compressive stresses in the range 0.5<z/t<0.8. The normalised K _RSP at the surface intersection points of finite surface cracks is approximately constant at about 0.8 for an aspect ratio of 2c/a = 3.33, and is initially lower but rises with crack depth for a crack of aspect ratio 2c/a = 10. The stress intensity at the surface intersection point is greater than that at the deepest point for a/t > 0.1 with 2c/a = 3.33, and for a/t > 0.5 with 2c/a = 10.

Transverse through-wall cracks at butt weld

Fig.4. Profile across weld of longitudinal surface residual stresses

A solution for a through-wall crack in an infinite flat plate subject to a trapezoidal RSP was given in Ref 5 and is reproduced here. The solution was obtained by integrating the weight function solution given on page 5.11a of Ref 11 for a symmetrical point load, p, at a distance, y, from the centre of a crack length, 2a, in an infinite plate. For a transverse crack subjected to longitudinal stresses,

The solution for the trapezoidal profile shown in Fig.4 is as follows:

For

For

For

The normalised K _RSP for through-wall cracks subject to trapezoidal profiles with different widths of tensile zone from W ₂/W ₁ = 3 to 9 are shown in Fig.5. For a/W ₁ ≤0.5, the crack is within the weld, and is subject to yield magnitude stresses, giving normalised K _RSP=1. For a/W ₁>0.5, the crack length is greater than the weld width, and the normalised K _RSP falls with crack length, at a rate dependent on the total width of the tensile zone. The use of the trapezoidal RSP removes the conservatism inherent in the traditional assumption of residual stresses equal to yield strength for cracks whose width is greater than the weld width.

Fig.5. Normalised K _RSP at transverse through thickness crack at butt weld in plate. Effect of residual stress profile

Longitudinal surface cracks at T-joints

Fig.6. Through-wall profiles of transverse residual stresses at toe of T-butt or T-fillet weld

Normalised K _RSP values for longitudinal surface cracks of aspect ratio 2c/a = 3.33, 10 and infinity at the toe of a T-butt weld are shown in Fig.7. These were evaluated assuming the bilinear profile shown in Fig.6 with z _o/t = 0.5. They were evaluated using a solution from the SINTAP stress intensity factor handbook ^[4] for a semi-elliptical surface crack in a plate subject to through-wall stress profile expressed as a 5 ^th order polynominal. Hence it was necessary to fit a 5 ^th order polynominal to the bilinear profile, which gave a very good fit. It can be seen that the normalised K _RSP rises with crack depth for an infinitely long surface crack, but falls for cracks of finite length.

Fig.7. Normalised K _RSP at deepest point of short surface crack at toe of T-butt weld for bilinear RSP with z _o/t = 0.5. Effect of aspect ratio

The normalised K _RSP for the deepest and surface intersection points of longitudinal surface cracks of aspect ratio 2c/a = 3.33 at the toes of T-butt welds subject to uniform residual stress,

Fig.8. Normalised K _RSP at short surface crack at T-butt weld. Effect of residual stress profiles

Circumferential surface cracks at circumferential butt welds

Fig.9. Through-wall profiles of transverse residual stresses at single-V circumferential butt welds with q/(vt) = 60J/mm ²

Drawings in API 579 and the SINTAP compendium imply that the single sided weld is made from the outside : the profiles would be different if the weld was made from the inside.

API 579 has, in general, adopted a more conservative approach than SINTAP, in as much as the former gives entirely tensile stresses while the latter gives compressive stresses at various locations. The two approaches show some agreement with respect to the stresses at the root of the weld (i.e. at z/t=1). Both methods agree that the stress is a function of heat input, q/v, and thickness, t. API gives yield tensile stresses for low thickness conditions, and SINTAP gives yield tensile stresses for high heat input per unit thickness (i.e. for low thickness). Both methods give reduced tensile stresses at the root for high thickness or low q/vt conditions.

Although the two profiles given by SINTAP have undoubtedly been observed in practice, it is difficult to reconcile the abrupt change in profile at the transitional value of q/vt=60J/mm ². It is also the case that some observations have been made of zero or low tensile stresses at the outside face, z/t=0. Hence, the API profiles may be considered more appropriate for surface defects located at the outside surface. On the other hand, the tensile peak shown in the SINTAP high heat input RSP at z/t=0.4 has also been observed in practice, and the API 579 profiles may be unconservative for buried defects at this location.

Normalised K _RSP values corresponding to the SINTAP high heat and low heat profiles and to uniform yield stresses acting on a full circumferential defect at the root of a circumferential butt weld are shown in Fig.10. These were calculated using a weight function solution. The normalised K _RSP for uniform yield residual stresses rises gradually from 1.2 at a/t=0 to 2.0 at a/t=0.6. The normalised K _RSP for the SINTAP high heat RSP falls gradually with crack depth from 1.2 at a/t=0, and hence would provide some benefit in terms of reduced K _RSP at crack depths a/t>0.2. The normalised K _RSP for API low thickness RSP (not shown) would lie between the uniform yield stress and SINTAP high heat curves and hence would be of limited benefit.

Fig.10. Normalised K _RSP at fully circumferential crack at outside surface of pipe. Effect of residual stress profile

The normalised K _RSP for the SINTAP low heat RSP falls rapidly with crack depth, and hence would show significant benefit, even for shallow cracks. The normalised K _RSP for the API 579 high thickness RSP (not shown) can be obtained by scaling down the uniform yield stress solution by 0.2, and hence would also show considerable benefit compared with the assumption of uniform yield stresses.

Summary and conclusions

• Three sets of standardised residual stress profiles for common weld joint types have recently become available.
  
  
• Many of the profiles given in BS 7910:1999 ^[1] Appendix Q and the SINTAP project residual stress compendium ^[2] are identical: those in API 579 ^[3] Appendix E show some similarities with the BS 7910 and SINTAP profiles, but have different equations.
  
  
• Areas where one or other of the published profiles may be unconservative or over-conservative have been discussed in this paper.
  
  
• A SINTAP project report ^[4] and API 579 ^[3] provide stress intensity factor solutions applicable to non-linear residual stress profiles.
  
  
• The reduction in stress intensity factor obtained by using the published profiles instead of the traditional assumption of uniform yield magnitude residual stresses has been quantified for a range of examples.
  
  
• A new solution for the stress intensity factor at a through-wall crack subject to a trapezoidal residual stress profile is presented.
  
  
• Further investigation of the transverse residual stresses at circumferential butt welds is needed.

Nomenclature

This paper was based in part on work done at TWI under sub-contract to the Health and Safety Executive, as part of SINTAP, a collaborative project supported by the European Commission. The authors acknowledge the support of their project partners and sponsors.

References