A. Stacey, Offshore Safety Division, Health & Safety Executive, London, United Kingdom
J.-Y. Barthelemy, Institut de Soudure, Ennery, France
R. A. Ainsworth, Nuclear Electric Ltd, Barnwood, United Kingdom
R. H. Leggatt, The Welding Institute, Cambridge, United Kingdom
S. K. Bate, AEA Technology, Risley, United Kingdom
Proceedings of OMAE99, 18 th International Conference on Offshore Mechanics and Arctic Engineering
July 11-16, 1999, St. Johns, Newfoundland, Canada
Procedures for the structural integrity assessment of welded components have provided limited guidance on the treatment of residual stresses due to insufficient information on residual stress distributions in welded joints and uncertainties in the behaviour of residual stress distributions under applied loading. However, the assumptions made about the residual stresses can have a very significant effect on the structural integrity assessment and improved guidance on this subject is required.
The EC funded project Structural Integrity Assessment Procedures for European industry, SINTAP, has provided the opportunity to perform an extensive investigation on residual stresses and develop further the BS 7910 and Nuclear Electric R6 procedures. It has entailed an extensive literature review of residual stresses in the principal weld geometries (including plate butt, pipe butt, pipe to plate, T-butt and tubular welded joints), experimental and numerical investigations and the development and validation of procedures.
Experimental studies have shown that secondary stresses introduced by welding or by temperature gradients can have a significant effect on the load carrying capacity of a component containing a flaw. For this reason, the SINTAP project  has included a specific task on residual stresses with the overall aim of determining and validating the most appropriate methods of accounting for residual stresses in as-welded, weld repaired and post-weld heat treated welded joints for use in structural integrity assessment. Background information and an interim report on the task on residual stresses was presented in  . In summary, the SINTAP task on residual stresses comprised a number of sub-tasks:
- Status review: Review of existing information on the treatment of residual stresses in fracture prediction, including code-defined secondary stress profiles.
- Collation of Residual Stress Profiles: Collation of existing experimental and numerically predicted residual stress profiles; comparison with distributions recommended in codes, namely the draft BS 7910 document  and R6  .
- Experimental and Numerical Studies: Experimental and numerical investigations of residual stress distributions in welded joints. The numerical analysis work addressed the need for post-weld heat treatment (PWHT), the determination of its effectiveness and the derivation of criteria for PWHT of as-welded and repair-welded structures. Studies of through-wall defects were performed with reference to available experimental data and included further experimental work on thick, welded A533B steel plates. In addition, a study was performed of the estimation of J-integral when dominant residual stresses are present using centre-cracked panels, thus providing an insight into the influence of residual stresses on the fracture behaviour.
- Standardised Residual Stress Profiles: Derivation of standardised residual stress profiles for transverse and longitudinal through thickness residual stress distributions in a range of geometries of welded joints manufactured from ferritic and austenitic steels; definition of a framework for incorporation of residual stresses into fracture assessment procedures based on the Failure Assessment Diagram (FAD).
- Residual Stress Intensity Factors: Derivation of residual stress intensity factors for surface cracks in a range of geometries of welded joints, i.e.
- plate butt welds
- T-butt and fillet welded joints
- pipe butt welds
- pipe seam welds
- pipe to plate joints
- tubular joints
- repair welds
- Procedure Development & Validation: Development and validation of guidelines for the assessment of residual stress effects; incorporation into the SINTAP procedure.
An overview of the results from the residual stresses task are presented in this paper.
Residual stress distributions in welded joints
Generic residual stress distributions were derived in the SINTAP study for
- plate butt welds
- pipe seam welds
- circumferential butt joints
- T-butt joints
- pipe-to-plate and tubular joints
- repair welds
The residual stress distributions in R6  were used as the basis of the review and were supplemented by more recent data from the literature. The data are valid for the parameter ranges shown in Table 1. Further details on the through-thickness distributions are given in  . Residual stress distributions were also generated by numerical analysis for plate and pipe butt welded joints, PWHT ferritic steel joints and dissimilar metal welds  .
Table 1 Overview of residual stress data
|Plate butt joints
||24 - 300
||1.6 - 4.9
||310 - 740
|Pipe butt joints
||9 - 84
||0.35 - 1.9
||225 - 780
|Pipe seam welds
||50 - 85
||345 - 780
||25 - 100
||376 - 421
|Tubular & pipe to plate joints
||22 - 50
||0.6 - 2.0
||360 - 490
||75 - 152
||1.2 - 1.6
||500 - 590
The review was subsequently extended to include additional geometries, i.e. set in and set on nozzles, information generated in SINTAP and surface residual stresses. Generic upper bound distributions were then derived for the through-thickness and surface distributions in both the longitudinal and transverse directions in ferritic and austenitic steel.
The through-thickness distributions are presented below. They are normalised with respect to the wall thickness and the 0.2% proof stress or yield strength, σ Y . For transverse residual stresses σ Y should be taken to be the lesser of the yield stresses of the parent and weld material. The greater value of the two yield stresses should be used for longitudinal residual stresses and for repair welds.
The distributions are expressed either as a function of the welding conditions and of the mechanical properties of the materials or as a polynomial function. Two sets of distributions are available:
(a) for joints where the welding conditions are known
(b) for joints where the welding conditions are not known.
The distributions for (b) are more conservative than those for (a).
The surface distributions are reported in  and are not included in this paper.
Plate butt joints & pipe seam welds
The same distributions apply to both plate butt joints and pipe seam welds.
(a) For ferritic steels,
(b) For austenitic steels,
This distribution is applicable to welds with no restraint or with bending restraint, but not to welds with membrane restraint (i.e. restraint against transverse shrinkage). Where members are welded at each end to existing rigid parts of a structure, long range restraint residual stresses will be developed by the shrinkage of the closing weld. These stresses should be treated as primary stresses to be added to applied stresses parallel to the length of the member.
Circumferential butt joints
A conservative estimate of the longitudinal residual stress distribution for ferritic and austenitic steel pipe butt welds is given by a linear profile which is defined by a stress equal to σ Y at the outer surface and Equation.1. at the bore, i.e.
and z is measured from the outer surface.
For a pipe thickness of less than 15mm, a through-thickness tensile yield stress is obtained. The tensile stress at the bore decreases with increasing pipe thickness to a value of zero for a thickness of 85mm and then becomes compressive.
Transverse stresses [Austenitic steels]
The transverse residual stress profile for austenitic pipe butt joints is dependent on the thickness.
(a) if T ≥ 25mm,
σ Bore is defined thus:
for (R/T) ≤ 8.5,
Transverse stresses [Ferritic steels, Low heat input]
The transverse residual stress profile for ferritic pipe butt joints welded with heat inputs per unit thickness, [ q/V)/T
], of up to 60J/mm 2
are given below:
z is measured from the outer surface and σ Outer is obtained from the expression:
Transverse stresses [Ferritic steels, High heat input]
For ferritic pipe butt joints for which the heat input per unit thickness exceeds 60J/mm 2
where z is measured from the outer surface. The residual stress at the outer surface of the pipe is always in compression for all heat input values.
There is limited information on residual stress distributions in T-butt joints.
Where the welding conditions are known, provided r o < T,
if z ≤ r o ,
r o is the radius of the yield zone in mm
σ YP is the yield or 0.2% proof strength of the parent metal in MPa
( q/V) is the heat input rate in J/mm
h is the process efficiency (fraction of arc power entering plate as heat)
K is a material constant:
α is the coefficient of thermal expansion in °C -1
E is Young's modulus in MPa
ρ is the density in kg/mm 3
c is the specific heat capacity in J/kg°C
( ρ c) is the volumetric specific heat.
Typical material properties are presented in Table 2.
Table 2: Typical material properties of steels
|Properties||Ferritic steels||Austenitic stainless steels||Aluminium alloys|
||1.2 x 10 -5
||1.6 x 10 -5
||2.4 x 10 -5
|ρ c (Jmm 3/°C)
For thin joints, the width of the yield zone is given by the following expression:
For butt welds, T is the plate thickness. For T-joints, T is equal to ( T b + 0.5 T 8 ) where T b and T a are the base plate and attachment thicknesses, respectively.
The polynomial distributions are
for z/T ≤ 1/3,
Where the welding conditions are known,
if z ≤ r o,
The polynomial distributions for the transverse residual stress in the main plate of ferritic joints is given by the following expressions:
for z/T ≤ 1/2,
Pipe to plate and tubular joints
The same distributions are applicable to pipe-to-plate and tubular joints. The tubular joint data were obtained from ferritic specimens with brace to chord thickness ratios, τ , in the range 0.50 to 0.73. For τ >0.73, a uniform tensile residual stress of yield magnitude should be assumed. For τ <0.5, the profiles for T-butt welds are recommended. It should be noted that the brace to chord diameter ratio, β, was in the range 0.50 - 0.67 and caution is required for geometries outside this range. For low β values (i.e. β<0.2) the distributions for T-butt welds should be considered instead.
where z is the distance from the weld toe.
The transverse and longitudinal residual stress distributions in repair welds should be considered to be of yield magnitude throughout the depth of the repair. For part-depth repairs of depth z r , the residual stresses may be assumed to decrease from yield magnitude at the bottom of the repair to zero at depth z o below the repair weld, where z o is defined by equation (19):
for z r ≤ z ≤ (z r + z o),
where z is measured from the face of the component from which the repair was made.
The residual distributions for repair welds are derived from measurements on ferritic steels and therefore may not be applicable to austenitic steels.
Post-weld heat treated joints
The effect of post weld heat treatment (PWHT) on the residual stress distribution in welded joints was investigated using pipeline butt welds. The distribution was evaluated numerically using the software package SYSWELD 
. The parent material was assumed to have yield and ultimate strengths of 342MPa and 567 MPa, respectively, whilst the corresponding values for the weld metal were 511 MPa and 591 MPa. The pipe had a diameter of 1000 mm and a wall thickness of 30 mm. An asymmetric double vee weld geometry was simulated, with the first two passes deposited from the internal surface of the pipe and six subsequent passes from the outside. An axisymmetric two-dimensional finite element model was used with 702 elements and 2089 nodes.
SYSWELD simulates stress relief using a viscoplasticity model which can be used to represent the elasto-plastic isotropic work hardening response associated with materials during welding. Primary and secondary creep were modelled using a Norton-type creep law with coefficients relevant to time-dependent strain values for appropriate nominal static loads at 550°C. The following treatment was simulated:
- temperature increase from 20°C to 550°C in 9 seconds
- constant temperature of 550°C for 3 hours
- controlled cooling to 20°C at a rate of 20°C/hour.
The predicted through-thickness residual stresses after PWHT were very low, with a maximum value of approximately 10% of the weld metal yield strength. These results are within the bounds of the PWHT residual stress levels recommended in BS 7910, i.e. 15% of the yield strength in the transverse direction and 30% of the yield strength in the longitudinal direction.
Residual stress intensity factors
The residual stress profiles and the results of the numerical and experimental investigations have been used to develop and validate recommendations on the treatment of residual stresses being incorporated into the SINTAP defect assessment procedure. This has included the evaluation of stress intensity factors for the recommended residual stress profiles, subsequently referred to as residual stress intensity factors
The recommended profiles are mostly non-linear, so the methods for obtaining stress intensity factors are more complex than for linear stress distributions such as membrane or bending stresses. The objectives of this work were to explore the practicalities of applying the available solution techniques to the recommended residual stress profiles, to provide example solutions for typical joint and defect geometries, and to investigate the sensitivity of the calculated residual stress intensities to the assumed residual stress profile and solution method.
Solutions were obtained for a range of joint geometries, defect types and residual stress distributions.
Joint geometries and defect types
The following geometry and defect combinations were assessed:
- butt welds in plates: long longitudinal surface defects, short longitudinal surface defects, transverse through-thickness defects.
- T-butt welds: long and short longitudinal defects.
- circumferential butt welds in pipe, R/T = 10: long and short surface defects at outside and inside surfaces, through-thickness defects.
The following short surface defects were analysed:
- plate butt welds and T-butt welds, with aspect ratios, 2 c/a, of 3.33, 10 and infinity. Stress intensity factors have been calculated at the deepest point of the crack and at the surface intersection.
- circumferential butt welds, with aspect ratios, 2 c/a, of 4. Stress intensity factors have been calculated at the deepest point of the crack.
Residual stress distributions
All cases were analysed using the recommended SINTAP residual stress distributions. The following additional cases were analysed:
- effect of assuming residual stress equals parent yield strength - all cases except short surface defects with aspect ratio greater than 4.
- effect of BS 7910 residual stress reduction formula, i.e.
- as an example, the effect of reducing the residual stresses to 60% of the weld metal yield strength was analysed for a transverse through-thickness defect in a plate butt weld.
effect of using fitted polynomial functions for residual stresses at toe cracks in T-butt welds was analysed for long and short surface defects. Effect of heat input per unit thickness at circumferential butt welds - both the high and low heat input SlNTAP formulae were analysed.
All cases except through thickness cracks were analysed using the stress intensity solutions summarised in the SINTAP compendium of stress intensity solutions  . Some cases with uniform residual stresses were also analysed using solutions from Tada, Paris and Irwin  for comparison with the SAQ solutions.
The transverse through thickness cracks in butt welded plates were analysed using closed form expressions derived from weight function solutions given in  .
Stress intensity factors at short surface defects at the toes of T-butt welds were calculated by resolving them into membrane and bending components and using the Newman and Raju equations  . These were then compared with the compendium solutions for an aspect ratio, 2 c/a, of 3.33.
Stress intensity factors at through thickness cracks in circumferential butt welds were evaluated using solutions from the R6 Code software  , presented in  .
The residual stress distributions recommended in the SlNTAP compendium of residual stress profiles  have different shapes for different weld geometries and orientations, including fourth and sixth order polynomials, cosine functions, and piece- wise linear distributions including bilinear and trapezoidal shapes.
The calculations were performed using Mathcad software. The solutions for infinite surface cracks were in the form of weight functions which were multiplied by the local residual stress and integrated over the crack depth. The solutions for semi-elliptical surface cracks were closed form solutions for third or fifth order polynomial residual stress distributions. The residual stress profiles had to be fitted to these shapes, which introduced the possibility of error due to poor fit. Standard published solutions were used for through thickness defects and for validation analyses for surface defects.
It is not possible within this paper to describe the results of all the cases analysed. The results for longitudinal surface defects at butt welds in plate are given below as an example of the results obtained.
Residual stress intensity factors for longitudinal surface defect at plate butt weld
The stress intensity due to residual stress was calculated for infinite surface defects and for semi-elliptical surface defects of aspect ratio, 2 c/a, of 10 and 3.33. The through-thickness distribution of transverse residual stress acting on the longitudinal defect was the recommended SINTAP profile in which the normalised residual stress σ R T/ σ Y is expressed as a sixth order polynomial function of normalised depth from the surface, z/T. Additional cases were run assuming a uniform residual stress equal to the yield strength, σ Y . The stress intensities for infinite surface defects were calculated using the weight function solution given in the SINTAP stress intensity handbook  . Those for semi-elliptical defects were calculated using the closed form solution given in the handbook. This solution is applicable to a stress distribution expressed as a fifth order polynomial function of depth divided by crack depth, z/a. Hence it was necessary to fit a fifth order polynomial in z/T to the sixth order SINTAP profile (see Figure 1), and then for each crack depth, a/T, to transform the polynomial from a function of z/T to z/a.
Fig.1. Through-thickness transverse residual stress distribution in plate butt joint
The SINTAP handbook solution for semi-elliptical defects includes a solution for infinite aspect ratio, i.e. an infinite surface defect (equation A1.1). Stress intensities for infinite surface defects were calculated using this solution and the infinite crack solution in the handbook (equation A1.3) and found to agree within 10% at a/T= 0 and 0.8, and within 1% at intermediate values. This was considered to provide confirmation of the self-consistency of the handbook solutions and to validate the implementation of the solutions in Mathcad and the use of the fitted fifth order polynomial for all but the extreme crack depths. The 10% discrepancy at zero crack depth can be attributed to the poor fit at zero depth (see Figure 1).
Calculated stress intensity factors, normalised with respect to K o = σ √( Πa), are plotted for infinite surface defects subject to the SINTAP polynomial profile and for residual stresses equal to the yield strength in Figure 2. The solutions are identical as crack depth tends to zero (where the residual stress equals yield in both cases), but the solution for uniform stress becomes increasingly conservative with crack depth. This demonstrates the benefits to be obtained using the SlNTAP profile, especially for deeper cracks. The solution for uniform stresses was also calculated using a closed form solution from Tada, Paris and Irwin  , which gave virtually identical results.
Fig.2. Normalised residual stress intensity factors for infinite surface defect in plate butt joint
The stress intensity factor solutions for infinite surface defects subject to the SINTAP polynomial residual stress profile and for the deepest point and surface intersection point of semi-elliptical cracks of aspect ratios, 2c/a, of 10 and 3.33 are shown in Figure 3. The stress intensity rises for a/T > 0.2 for the infinite surface crack, but falls continuously with crack depth for the deepest point of the semi-elliptical cracks. The stress intensity is always positive, despite the fact that the residual stress is negative for crack depths between 0.5 and 0.8 of the plate thickness. The stress intensity at the surface intersection point is greater than that at the deepest point for a/T > 0.5 for a crack aspect ratio of 10, and for a/T > 0.1 for aspect ratio 3.33. Hence, fracture may initiate at or near the surface intersection, particularly for the crack of aspect ratio 3.33, for which the stress intensity at the surface point is greater than that for a crack of the same depth with an aspect ratio of 10.
Fig.3. Normalised residual stress intensity factors for deepest and surface points of surface defects in plate butt joint
Treatment of residual stresses in SINTAP defect assessment procedure
The principal features of the BS 7910 procedure relating to the assessment of residual stresses were presented in 
. The relaxation of secondary stresses due to plasticity is accounted for by equation (21) taken from R6 and BS 7910, i.e.
where ρ is a plasticity correction factor.
An alternative approach for the assessment of plasticity effects on the residual stress distribution has been proposed in SINTAP: a factor, V, is applied to K s to account for plasticity effects. K r is then defined thus:
Equations relating V and ρ have been developed using previously calculated numerical values of ρ to generate values of V/V o as a function of increasing load for a number of values of secondary stress, where
and corresponds to the value of V at zero primary stress, i.e. due to secondary stresses alone. It should be noted that the value of V becomes less than one for large L r values corresponding to mechanical stress relief of the secondary stresses.
(23a) is the effective elastic-plastic stress intensity factor for the secondary loading and is related to the J-integral associated with the secondary stress, i.e.
ψ and Φ are functions of L r and the ratio [ K p s / (K l p / L r )]. Important points to note are as follows:
- for zero primary loads, ψ = 0 and Φ = 1, so that failure occurs when K p s = K mat and V = V o .
- w is negative for large L r values, i.e. L r > 1.05, and this can lead to negative values of ρ when K l s/K p s is not significantly less than 1. Also, V < V o. This corresponds to mechanical stress relief of the secondary stresses.
- negative values of ρ can occur even at low mechanical loads if K p s < K l s . This generally corresponds to plastic relaxation of secondary stresses which are elastically greater than the yield stress.
- K p s can be calculated by various methods, listed below in decreasing order of complexity:
Numerical predictions of V/V o v. L r were obtained using equation (27) and values of Φ and ψ from R6  , derived from work by Ainsworth  , and are based on the R6 Option 1 FAD. The results are presented in Figure 4. They show that V/V o , increases moderately with increasing L r , for L r values up to approximately 0.9 and decreases at higher L r values. Ainsworth found that V/V o is very insensitive to the magnitude of the secondary stress, particularly for L r > 0.9, and he therefore proposed a simple approximate approach, as an alternative to equation (27). Two options are included in Figure 4:
- from equation (24) with J s evaluated from an elastic-plastic FE analysis;
- from elastic-plastic analysis of the uncracked body;
- from a plastic zone size correction to K l s
- K p s can be replaced by K l s when secondary stresses are low compared to the yield stress and elastic follow-up is not considered to be significant.
L r ≤ 0.9,
Fig.4. Numerical predictions of V/V o v. L r
Equations (28) bound the solutions for [ K p s / (K l p / L r)] ≤ 2 and use a constant value for low L r, similar to the approximate method in the current version of R6 which uses a constant value of ρ in this region. The plateau value could be made a function of the magnitude of the secondary stress. Equations (29) use a linear fit at low L r and bounds the solutions for [ K p s / (K l p / L r)] ≤ 5. At values of L r > 0.9, equations (28) and (29) are identical and correspond to the use of ρ = 0 for L r = 1.05 in R6. At higher values of L r, equations (27) (28) and (29) correspond to mechanical stress relief of the secondary stresses. V/V o has been set to 0.4 for L r > 1.4 as a bounding value to the numerical data but, in practice, full mechanical stress relief, i.e. V = 0, has been observed experimentally  .
Validation of SINTAP residual stress assessment procedure
Numerical and experimental studies were carried out to validate the assessment procedures presented above.
SINTAP Task 4 included a numerical study of the interaction of primary and secondary stresses. The study involved an evaluation of the contribution of thermal and weld-induced residual stresses in a welded pipe to the total CTOD and J-integral. The results showed that there is a rapid decrease in the contribution to J of residual stresses relative to the primary stresses at high values of L r . Comparisons with R6 predictions, expressed in terms of J, showed R6 to be conservative, although the extent of the conservatism is dependent on the value of the limit load used to evaluate L r . Since the R6 analyses were conservative, the V approach would also be expected to be conservative. However, the data have not been analysed in this way.
Additional FE analyses were performed on plates with under-, even- and over-matched welds  . The results for V are shown in Figure 5 which is similar to Figure 4, although V/V o assumes a value of less than 0.1 (compared with 0.4 in Figure 5) for L r > 1.05. The results confirm the suitability of equations (28) and (29). However, it should be noted that the results suggest that the proposed formulations are over-conservative for the overmatched case.
Fig.5. Comparison of equations (28) and (29) with numerical results from  for under-, even- and over-matched plates
Two series of experiments were performed on aluminium alloy and A5333B-1 steel plate specimens, respectively, to validate the formulations in equations (28) and (29) 
In the first series of tests, five pairs of centre-cracked plate specimens, where each pair consisted of one specimen containing residual stresses and one without residual stress, were fracture tested under axial loading. The residual stress distribution was in-plane self balancing, with a uniform tensile residual stress in the central region of the plate and compression in the outer regions. The maximum residual stress was 57% of the yield strength.
The second series of tests consisted of two pairs of welded specimens, each pair consisting of an as-welded and a post weld heat treated specimen, with a semi-elliptical surface crack in the weld. PWHT entailed heat treatment of 6-10 hours at 590±10°C with a heating rate of up to 200°C/hour and furnace cooling to 200°C. The welding residual stresses were self-balancing with tension at the surfaces and compression in the central region. The as-welded and post-weld heat treated transverse residual stress distributions in the low L r specimens are presented in Figure 6 which shows that, while the as-welded residual stresses are substantial, the residual stress levels in the post-weld heat treated specimens are relatively insignificant. The specimens were tested under four-point bending loading. One pair was tested in the low L r regime and the other in the high L r regime.
Fig.6. Transverse residual stress distributions in A533B-1 low L r plate butt joint specimens
The effects of residual stress on load carrying capacity with varying L r are presented in Figure 7. The aluminium alloy specimens demonstrated the large influence of residual stresses on the load carring capacity in the low L r region. The effect of residual stresses was found to decrease as L r increased and had no effect at L r and beyond, i.e. the elastic residual stress is dissipated at nett section yield. These results were confirmed by the second series of tests. The tests at low L r showed that the load carrying capacity of the as-welded specimens was approximately 60% of that of the post weld heat treated specimens. The high L r tests showed that the load carrying capacity was reduced in the as-welded specimen by approximately 5%.
Fig.7. Load carrying capacity ratio v. L r for aluminium test specimens
Both sets of test results are plotted against the R6 Option 1 failure assessment diagram (FAD) in Figure 8. The figure shows that, in general, conservative predictions were obtained for the aluminium alloy specimens. A small number of points fall below the curve and this was attributed to uncertainties in the experimental determination of the initiation event.
Fig.8. Comparison of aluminium residual stress test results with R6 Option 1 FAD
The predictions for the A533B-1 specimens were found to be very conservative, particularly for the as-welded specimens, even when the residual stresses were not included in the analysis. The differences were attributed to crack constraint effects, which are not considered in the R6 calculation, and to the limited number of K mat tests. The A533B-1 steel specimens were also compared with the R6 Option 2 FAD and it was found that, at low L r the Option 1 and Option 2 FAD predictions were very similar. However, the failure loads differed by a factor of 2 at high L r .
Two methods were used to evaluate V:
(a) from equation (22)
(b) from ρ: by combining equations (21) and (22),
ρ was evaluated from equation (25) with K p s determined by the simplified linear elastic calculation method defined in Appendix 4 of R6  . For the validation exercise, it was conisdered appropriate to set V o to a value of 1, resulting in ρ being equal to Ψ (see equation (26)). Values of Ψ were calculated using Table A4.1 in Appendix 4 of R6. These theoretical values of ρ were compared with the corresponding experimental ρ values calculated from equation (21).
K r was evaluated from equation (21) with L r defined by the R6 Option 1 FAD. K mat was evaluated from specimens which did not contain residual stresses, effectively using the R6 Option 1 FAD as a J-estimation scheme. The loads corresponding to initiation of tearing and subsequent amounts of crack growth for each specimen were converted to an L r value from which K r could be calculated, using the R6 Option 1 FAD. K mat was then calculated from the relationship
Values of V from equation (30) are compared with equations (28) in Figure 9. The majority of results lie below the proposed curves and suggest that the proposed formulations for V are acceptable. The results are consistent with the discrepancies between theoretical and experimental values of ρ which are shown in Figure 10.
Fig.9. Experimentally determined V v. L r
Fig.10. Experimental ρ v. theoretical ρ
Values of V from equation (31) are compared with equations (28) in Figure 11. Except for one point, all the points lie just below the proposed formulations and the results indicate that the proposed formulations for V are appropriate.
Fig.11. V (from equation (31)) v. L r
It was concluded that the proposed formulations for V are generally acceptable as an upper bound which is independent of the magnitude of K l s . Figure 11 confirms that, since ρ and V are determined from the same basis, expressing them as a multiple of rather than an additional term to ( K l s/K mat ) makes them only weakly dependent on ( K l s/K mat ).
The recommendations in BS 7910  on (a) residual stress relaxation due to applied loading, and (b) residual stress levels in post weld heat treated specimens were also evaluated and it was concluded that the recommendations are valid.
A substantial and extensive investigation of residual stresses has been performed in SINTAP:
- surface and through-thickness distributions have been derived for a wide range of welded plate and tubular joints
- numerical analysis has been used to predict welding residual stresses, the effects of post-weld heat treatment and the interaction of primary and secondary stresses.
- residual stress intensity factors have been evaluated for welded joints, thus providing direct quantification of residual stress effects to enable validation of assessment procedures.
- the influence of residual stresses on the fracture behaviour of welded joints has been validated experimentally.
- revised procedures for the analysis of residual stress effects in defect assessment have been developed.
Overall, SINTAP has resulted in significant advances in the characterisation and prediction of residual stress effects on the fracture behaviour of welded components. However, it has also highlighted the complex nature of residual stresses and has pointed to areas requiring further investigation. The following recommendations are made based on a review of the results generated by SINTAP:
- residual stress distributions are highly variable and there is a continuing need to obtain further information on distributions in welded joints.
- the V approach is included in SINTAP as an alternative developing method and enables V and V o to be readily evaluated from K p s , ψ and Φ which are defined in R6.
- there is a need to repeat the calculations of V/V o v. L r for different FADS and perform a comparison with the FE results generated in SINTAP.
- consideration should be given to reviewing the empirical relationship between VIV o and L r using the additional results referred to above, with a view to recommending a simple bounding curve or a table of data.
- there is a need for more extensive validation of the recommended procedure.
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