D J Abson ^{(a)} , Y Tkach ^{(a)} , I Hadley ^{(a)} and F M Burdekin ^{(b)}
^{(a)} TWI
^{(b)} Formerly Professor at University of Manchester Institute of Technology
Published in Welding Journal, vol.85, no.5, May 2006, pp.2935.
In Part 1 of this article, the similarities and differences between the exemptions from postweld heat treatment in several current codes were reviewed, and some rationalisations were considered. In this part, a fracture mechanics approach to the assessment of steel toughness requirements is demonstrated. The numbering of references and tables is continuous with Part 1.
Abstract
Fracture mechanics calculations have been carried out to determine the required level of toughness, as a function of material thickness, for CMn and low alloy steel which is not subjected to postweld heat treatment (PWHT), and these are compared with previous analyses used as the basis for codes.
Introduction
Postweld heat treatment is applied to welded steel assemblies primarily to reduce the likelihood of brittle fracture. This is achieved through a reduction in the level of tensile residual stresses and through tempering of hard, potentially brittle, microstructural regions. There are, of course, economic and logistical incentives to avoid PWHT wherever possible. This article reviews previous fracture mechanics methods used to form the basis of recommendations for fabrication codes, and outlines a generalised fracture mechanics approach to illustrate the implications, in terms of defect tolerance and toughness requirements, of not carrying out PWHT on welded steel structures. A series of curves is generated showing the relationship between materials strength, materials thickness, service temperature and required impact properties.
Objective
 To demonstrate the use of fracture mechanics procedures to define minimum toughness requirements for welded fabrications so that PWHT is not needed.
Approach
Fracture mechanics calculations used previously as a basis for code recommendations have been reviewed, and further independent calculations have been carried out, based on the methods described in BS 7910: 1999 (incorporating Amendment number 1) ^{[8]} . The assessment was implemented using TWI's Crackwise 3 software (Version 3.13).
Example calculations were carried out to determine the minimum required material fracture toughness for a variety of cases, in order to define limits for the avoidance of PWHT. However, it should be noted that the results of the calculations are intended to demonstrate the principle of analysis procedures such as BS 7910 for the justifying the avoidance of PWHT, and to illustrate the trends in toughness requirement with variables such as material strength and thickness. For a particular structure, the actual requirement may be higher or lower than that shown in this paper, depending on factors such as the actual stress applied to the component, the presence or otherwise of areas of stress concentration and the effectiveness of nondestructive examination (NDE). The results of this study should therefore not be applied directly to actual fabrications without expert consideration.
The use of fracture mechanics in assessing the need for PWHT
Justification for considering a fracture mechanics approach
While limiting thickness criteria beyond which PWHT is required have been in use for many years for pressure vessels and piping, and can be considered to have been validated by custom and practice, the scientific derivations of the criteria may not always be known. In the UK, the original requirements for low temperature applications of pressure vessels and storage tanks were based on an extensive series of notched and welded wide plate tests carried out at TWIin the 1960s ^{[42]} . However, it is likely that the criteria for many other codes were devised on the basis of engineering experience and best practice at the time. The basis on which the criteria were derived may not be so relevant today, owing to various factors. For example:
 Steelmaking technology and welding consumable manufacture have improved considerably in the last 25 to 30 years. As a consequence, the fracture toughness of parent steels and welds has improved.
 Improved understanding of welding defects has enabled the development of improved welding procedures and methods.
 Knowledge of welding residual stresses and the influence of these stresses and material thickness upon the fracture event (through fracture mechanics) has improved.
 Nondestructive testing methods have improved since the derivation of some of the codes. For example, ultrasonic inspection has been widely used as a regular inspection tool only in the past 25 to 30 years. Prior to this, radiography (a technique that is not wellsuited to the detection of planar flaws) would often have been the main technique used to identify embedded defects.
An alternative approach for deciding whether PWHT is necessary to avoid failure by fracture is by conducting a fracture mechanics assessment of the aswelded joint, using a recognised procedure such as that described in BS7910 ^{[8]} . It is obvious that a criterion for PWHT based on a fracture mechanics assessment is more complicated than a criterion based on material thickness alone. Nevertheless, the use of a fracture mechanics method is an attractive option to determine whether PWHT is necessary for the avoidance of failure by fracture.
A fracture mechanics analysis essentially provides a relationship between stress levels (applied and residual), flaw sizes and material properties (fracture toughness and yield strength). In determining whether PWHT is required,assumptions have to be made about stress levels and the size of flaw that might escape detection during inspection. The toughness level required to avoid failure can thus be determined.
Fracture mechanicsbased procedures have been used previously as the basis for determining maximum thicknesses for aswelded construction in the UK bridge and building codes ^{[4,5]} and also for the Eurocode 3 requirements. Details of these requirements are discussed in Part 1 of this paper.
The influence of increasing wall thickness on the measured fracture toughness of CMn steels
The basic assumption of fracture mechanics analyses is that fracture will occur in a material when the crack tip driving force, i.e. the applied stress intensity, exceeds the material's resistance to fracture initiation, i.e. the fracture toughness of the material.
So far as the crack tip driving force is concerned, the total applied stress intensity, K _{I,Total} , depends on both the applied stress intensity and the stress intensity due to residual stresses resulting from the welding process. Hence this factor can be expressed as:
K _{I,Total} = K _{I,Primary Stresses} + K _{I,Residual Stresses}
Higher levels of stress triaxiality in thicker sections render them more susceptible to fracture; see below. For these reasons, the reduction of residual stress levels in thicker components by PWHT may be necessary, in order to reduce the likelihood of brittle fracture.
Regarding materials resistance to fracture, it is generally observed that the measured fracture toughness of a ferritic steel tested in the lower transition region decreases with increased thickness of the specimen being tested. In the case of a throughthickness crack (for example, in the case of fracture mechanics test specimens), this phenomenon can be explained in terms of two factors:
 Weakest link theory.
The likelihood of a crack front sampling a region of low toughness increases with the amount of material it samples. That is, the average measured fracture toughness is expected to decrease with increased crack front length.
 Crack tip constraint.
The fracture process is also highly dependent on crack tip constraint (triaxiality), which in turn is a function of the geometry of the specimen being tested, including specimen thickness, loading mode, and crack depth. (The last two variables are usually standardised in fracture mechanics testing.) As the thickness of a SENB (single edge notched bend) specimen increases, so a greater proportion of the crack front experiences high crack tip constraint, and the fracture toughness decreases, until in the limit the plane strain fracture toughness, K_{Ic}, is reached.
Engineering critical assessment based on a fracture mechanics approach
Analyses used as the Basis for BS 5400:2000 and BS 5950:2000
The basis for the original requirements of BS 5400 ^{[31]} for bridges and the related requirements for BS 5950 ^{[30]} for buildings in the early 1980s is given in reference 4. The requirements were based on a combination of existing experience, the results of notched and welded wide plate tests, and a framework based on a fracture mechanics analysis using the then current edition of BSI Document PD 6493 [which subsequently became BS 7910 ^{[8]} ].
The assumptions about initial flaw sizes and applied and residual stress levels have a very strong influence on the resulting calculated requirements for fracture toughness. These then have to be related firstly to limiting thickness conditions and secondly to Charpy test requirements. For most practical applications of welded structures and pressurerelated components, fracture requirements are expressed in terms of the Charpy V notch impact test. Therefore, if fracture mechanics methods are to be used it is also necessary to have available a relationship between fracture mechanicsbased toughness and Charpy test energy absorption. As a result of the development of improved correlations between fracture mechanics toughness and Charpy energy absorption ^{[43]} , updated fracture mechanics treatments from PD 6493 to BS 7910 and the need to improve the treatment for typical stress concentration regions, a collaborative project was undertaken in the late 1990s between TWI and UMIST. The results from this project were used as a background for revised requirements for the avoidance of brittle fracture in BS 5400:2000 and BS 5950. Examples of the results from these previous analyses are compared with those derived in the present work in Fig.13, and discussed in the Fracture Mechanics section of the Discussion.
Fig.1. Results from fracture mechanics analyses for proportional and fixed flaws, and a comparison with BS 5400 requirements
Fig.2. Minimum toughness requirements for exemption from PWHT, plotted as (T min T 27J ); proportional flaw assumed
Fig.3. Minimum toughness requirements for exemption from PWHT, plotted as (T min T 27J ); fixed flaw size assumed
New calculations carried out in the present work
Introduction
Example calculations were carried out in the present project, independently of the work described in the previous section, to determine the minimum material fracture toughness for a variety of cases, in order to define limits for the avoidance of PWHT. The starting assumptions for the analysis were somewhat different from those described in the previous section, as summarised in Table 3. The model used to calculate the necessary material fracture toughness was based upon a semielliptical surfacebreaking flaw in a flat plate of thickness B. Note that the results of the calculations are intended to demonstrate the principle of analysis procedures such as in BS 7910 ^{[8]} for the avoidance of PWHT. The findings should not be applied directly to actual fabrications without expert consideration.
Table 3 A comparison of the assumptions underlying the fracture mechanics model used in this work, and that used in deriving the fracture avoidance rules of BS5400: 2000
Parameter  This study  Reference 5 (background to BS5400: 2000 
Flaw height, a 
 a=0.1B, but a ≥3mm ('proportional' flaw)
 3mm ('fixed' flaw)

 a=0.15B, but 3mm ≤a ≤12mm

Applied stress 
0.67R_{e} 
0.75R_{e} * 
P_{f} 
0.05 and 0.50 
0.40 
Flaw type, flaw aspect ratio, residual stress 
similar 
P_{f} = probability that toughness of a test specimen will exceed the toughness K_{mat} K_{mat} = required minimum fracture toughness B = plate thickness R_{e} = yield strength * refers to the socalled 'base case', k=1

Joint geometry
The welded joint was assumed to be a butt weld in flat plates of equal thickness (B). Plate thicknesses ranging from 10mm to 100mm were examined. Other geometries could have been readily accommodated in this approach, but the flat plate geometry was chosen for the purpose of illustration.
Flaw type and size
All flaws examined were of the semielliptical, surfacebreaking type, oriented parallel with respect to the welding direction, representing flaws which may be found within the weld metal or heataffected zone of a welded joint.
In terms of flaw size, two cases were studied. First, the flaw size was considered to be proportional to the thickness of the plate. The flaw height was chosen to be B/10, where B is the plate thickness (with the restriction that a minimum flaw height of 3mm was allowed). This flaw height, which is assumed to be the approximate height of a weld bead, is also assumed to be a credible size of flaw that might arise and remain undetected in a multiplepass fusion weld. In all cases, the flaw aspect ratio (a/2c) was set to 0.1, thus defining the flaw length.
In the second case, the flaw size was fixed, independent of plate thickness. A flaw height of 3mm was chosen, and a flaw length of 30mm, i.e. a/2c = 0.1.
Again, it must be emphasised that these flaw dimensions are used for illustrative purposes; the actual sizes to be used for assessment in a particular fabrication will depend on the type and quality of the NDE method used.
Material properties
Three materials with yield strength from 235 to 460 N/mm^{2} were considered, their room temperature tensile properties being listed in Table 4. The mechanical properties of the respective weld metals were assumed to be equal to those of the parent materials. The analyses were repeated for Material Design Minimum Temperatures (T _{min}) of 20°C and 50°C; assumed parent material properties at 20°C and 50°C are listed in Table 5.
Table 4 Parent material room temperature (20°C) mechanical properties
Material  Yield Strength (R_{e}), MPa  Tensile Strength (R_{m}), MPa 
A 
235 
360 
B 
340 
510 
C 
460 
680 
Table 5 Parent material mechanical properties at 50°C
Material  Yield Strength (R_{e}), MPa  Tensile Strength (R_{m}), MPa 
A 
295 
452 
B 
400 
600 
C 
520 
769 
Stresses
The primary stress was assumed to be a membrane stress of magnitude equal to twothirds of the room temperature yield strength of the parent material, i.e.:
P _{m} = (2/3) R _{e(RT)}
The secondary stress, i.e. the residual stress due to welding, was assumed to be a membrane stress of magnitude equal to the room temperature yield strength of the parent material, i.e.:
Q _{m} = R _{e (r.t.)}
Residual stress relaxation was enabled, as per BS 7910 ^{[8]} .
A stress intensity magnification factor (M _{km}) due to the presence of the weld toe was assumed, using the twodimensional solution specified by BS 7910 ^{[8]} . In addition, an arbitrary membrane stress concentration factor, k _{tm} , of 1.2 was assumed to apply, to take into account possible stressraising features such as joint misalignment. Note that gross stress concentrating features such as holes are not considered in this simple model, and that such features would considerably increase the required fracture toughness.
Fracture toughness
The minimum required fracture toughness, K _{mat} , was calculated from the information above, using TWI's Crackwise 3 software.
An estimate of the equivalent T
_{27J} , i.e. the temperature at which a fullsize Charpy Vnotch impact specimen absorbs 27J, was then calculated for two 'probabilities of failure', P
_{f} = 0.05 and P
_{f} = 0.5, using the correlation between fracture toughness and Charpy energy given in Annex J of BS7910
^{[8,43]} . This correlation (the socalled 'Master Curve' is based on a wellvalidated correlation between the temperature to achieve an absorbed Charpy energy of 27J and that to achieve a fracture toughness of 3,160 N/mm
^{3/2} (100MPa √m) in a 25mm thick section. The reason for considering two different values of P
_{f} lies in the different levels of reliability that may be required for a structure, which in turn will influence the value of P
_{f} chosen. [P
_{f} is actually the probability that the toughness of a specimen will exceed the toughness K
_{mat} ; note that it is not the probability of failure of the structure itself.] Note that the Master Curve is primarily a tool for estimating minimum expected fracture toughness from Charpy energy for the purpose of making decisions on the repair of welding flaws, in which case a value of P
_{f} = 0.05 is usually adopted. It is not intended to be used to estimate Charpy energy requirements from fracture toughness requirements, but if used in this way a value of P
_{f} = 0.50 might be appropriate, to avoid excessive conservatism in the Charpy energy requirement. The appropriate level of P
_{f} will probably lie somewhere between 0.05 and 0.5, and will depend on factors such as the consequences of failure of a structure, and whether the structure is redundant, i.e. whether an alternative load path is available. In this study, both P
_{f} = 0.05 and P
_{f} = 0.5 were used, since the main objective was to illustrate the trends in Charpy energy requirement associated with increasing materials strength and thickness, and decreasing T
_{min} .
Results of fracture mechanics assessment
The results of the analyses are shown in Fig.1 to 9.
The required toughness (K _{mat} ) for the three materials and the two types of flaw (proportional and fixed) is shown against thickness in Fig.1. The figure refers to the requirements at T _{min} =20°C, but the results for T _{min} =50°C were virtually coincident, assuming the value of K _{mat} to be that associated with the temperature T _{min} . The equivalent curves used to derive the BS5400: Part 3 rules are also shown for comparison with the results of the current study. It can be seen that, for the geometries and flaw sizes investigated in the present work, the required toughness actually decreases slightly with increasing section thickness from 10 to 25 mm. This is simply because BS7910 ^{[8]} uses two failure criteria: brittle fracture and plastic collapse of the uncracked ligament. For these thinner sections, plastic collapse tends to dominate, and the toughness requirement therefore initially decreases with thickness. As thickness increases beyond 25mm, fracture becomes the dominant failure mode.
The calculated minimum material fracture toughness values were then correlated with a required value of T _{27J} , using the Master Curve correlation. Since the Master Curve is based on K _{mat} values measured on a 25mm thick specimen, a correction is required to account for thickness effects. The Master Curve thickness correction is based on a 'weakest link' theory, i.e. the larger the specimen tested, the greater the likelihood of the flaw sampling an area of low toughness. Consequently, components of thickness greater than 25mm require increased fracture toughness (and hence decreased T _{27J} ) compared with 25mm thick components. Conversely, components less than 25mm thick would be expected to require less toughness (and hence increased T _{27J} ) compared with 25mm thick components. The precise shape of the T _{27J} vs thickness curve is then dependent upon both how the calculated values of K _{mat} vary with thickness and the Master Curve thickness correction.
Figure 2 shows the minimum Charpy requirements (in terms of a specified value of temperature difference between T _{min} and T _{27J} ) for the avoidance of postweld heat treatment as a function of thickness, t _{max} , for the case of initial flaw sizes assumed to be proportional to the thickness. Figure 3 shows the equivalent requirements assuming a fixed flaw height of 3mm. In the case of the fixed flaw size, the toughness requirement levels off for thickness above 70mm, whilst for the proportional flaw, the required material toughness increases with section thickness.
The required material fracture toughness at the design minimum temperature increases with material strength. Figures 2 and 3 show that for both proportional and fixed flaw size cases, the curves for different strength levels (R _{e} =235 and 340MPa) lie approximately parallel to one another, with higher toughness requirements (larger value of T _{min}  T _{27J} ) for higher strength steels. They also show that higher toughness levels are required for a lower probability factor in the Charpy energy absorption/fracture toughness correlation, and that higher Charpy energy requirements apply to the 'proportional flaw' than to the 'fixed flaw'.
Figure 4 provides the calculated T _{27J} values against thickness for service at T _{min} = 20°C for the proportional flaw size case and for all three materials considered, whilst Fig.5 shows the corresponding information for the fixed flaw size case. T _{27J} values were calculated for two probabilities of failure, namely: P _{f} = 0.05 and P _{f} = 0.5. The results show how material strength and section thickness, as well as the original assumptions made about flaw size and the value of P _{f} , influence the calculated T _{27J} requirement. As expected, the most onerous values of T _{27J} were obtained for the high strength material (material C, Re = 460MPa) of thickness 100mm. At T _{min} = 20°C and a probability of failure P _{f} = 0.05, the required T _{27J} temperature of the high strength material for the proportional flaw size case is 77°C. For the fixed flaw size case, the equivalent figure would be 37°C. For a probability level of 0.5, the corresponding figures are 41°C and 0°C.
Fig.4. Minimum toughness requirements for exemption from PWHT, plotted in terms of required value of T 27J ; T min =20°C and proportional flaw size assumed.
Fig.5. Minimum toughness requirements for exemption from PWHT, plotted in terms of required value of T 27J ; T min =20°C and fixed flaw size assumed
Since the height of the proportional flaw is assumed to be 0.1 times the thickness, the above 'proportional flaw size' calculation assumes the existence of a surface flaw of 10mm throughwall height and length 100mm. The 'fixed flaw size' case assumes that a surface flaw 3mm high and 30mm long could be present in the structure (and could be missed by nondestructive examination). In practice, whether or not PWHT is required would therefore depend in part on judgements about the size of flaw that could be reliably detected and the probability figure considered appropriate. For example, the figure P _{f} =0.4 for the BS5400: Part 3 rules was chosen largely on the basis of fitting existing service experience of the avoidance of fracture failures, with particular reference to bridge failures.
It should be noted that steels with strength R _{e} =460MPa can be supplied with excellent Charpy properties, and the use of 100mm thickness at 20°C in the aswelded condition is therefore possible, subject to the specification of appropriate Charpy energy and NDE.
Equivalent calculations can be carried out for T _{min} =50°C, using Figs 2 and 3. Since T _{min} T _{27J} is virtually independent of T _{min} , the T _{27J} requirements shown above for T _{min} =20°C simply shift by the change in minimum service temperature, ie by 70°C. Consequently, the requirements for a highstrength (R _{e} =460MPa) 100mm thick section steel shift to 147°C<T _{27J} <111°C (proportional flaw assumption) or 107°C<T _{27J} <70°C (fixed flaw assumption). Given such onerous requirements on Charpy energy, PWHT may be the only option for thicksection highstrength steels operated at low temperature (for example pressure equipment under blowdown conditions).
An additional analysis was carried out to investigate and illustrate the influence of PWHT on the estimated minimum requirements of the material toughness to avoid failure by fracture. The method used was similar to that used for the aswelded state, except that the magnitude of secondary (residual) stress was assumed to be 20% of the yield strength of the parent material, as recommended by BS7910 ^{[8]} .
The minimum required fracture toughness, temperature T _{27J} and values of (T _{min}  T _{27J} ) were calculated for material C (highstrength steel) in the aswelded condition (AW) and after PWHT. The results, given in Fig.69, reveal a large reduction in fracture toughness requirement for the material after PWHT. For example, the required minimum fracture toughness for a section thickness of 100mm (proportional flaw size) decreases from 5,500 N/mm ^{3/2} in the aswelded condition to 3,000 N/mm ^{3/2} after PWHT. In terms of Charpy requirement, the values of (T _{min}  T _{27J} ) shift by approximately 38°C (50°C for the fixed flaw assumption).
Fig.6. Minimum toughness requirements for a highstrength steel (R e =460MPa), plotted as (T min T 27J ); T min =50°C and proportional flaw size assumed
Fig.7. Minimum toughness requirements for a highstrength steel (R e =460MPa), plotted as (T min T 27J ); T min =50°C and fixed flaw size assumed
Fig.8. Minimum toughness requirements for a highstrength steel (R e =460MPa), plotted in terms of T 27J requirement; T min =50°C and proportional flaw size assumed
Fig.9. Minimum toughness requirements for a highstrength steel (R e =460MPa), plotted in terms of T 27J requirement; T min =50°C and fixed flaw size assumed
Discussion
Fracture mechanics assessment
As noted earlier, the required fracture toughness (K
_{mat} values) for a thicksection welded joint made from highstrength steel was found to approach 5,500N/mm
^{3/2} (173.8MPa √m) at the minimum operating temperature. This requirement may be somewhat difficult to satisfy in the weld and heataffected zones of many structural steels without very careful control of welding consumables and welding procedures, particularly as fracture toughness is generally observed to decrease with both section thickness and material strength.
As material yield strength increases, not only do specified toughness levels commonly increase, but it becomes increasingly difficult to meet toughness requirements without a PWHT, as noted earlier. For example, for steel C (R _{e} =460MPa) 25mm thick, intended for service at 50°C in the aswelded condition, the results of the fracture mechanics model calculations show that, for a failure probability P _{f} = 0.05, T _{27J} = 89°C is needed. This would probably be impossible to achieve in a parent and HAZ of a CMn steel of this strength. It may be noted that, for the example given, the PD 5500 ^{[26]} toughness requirement would be 40J at 176°C (T _{27J} ≈185°C), while the API 620 ^{[19]} requirement would be 40J at 67°C (T _{27J} ≈76°C). Thus, whilst the requirements of the codes have generally been found to be conservative, the degree of conservatism clearly varies, and may not always be present for the higher strength grades of steel. For finegrained CMn steels of this strength level that are intended for service at low temperatures, it may be therefore be appropriate to carry out a fracture mechanics analysis to see whether PWHT can be safely omitted.
The fracture mechanics calculations have generated graphs that give some pointers to areas where existing code requirements are too restrictive, and also some indication that PWHT would be appropriate where it is currently not required. It may be possible to assemble available compositional, toughness, residual stress and welding data from TWI and other data bases, in order to generate similar families of curves, based on measured data. Preliminary graphs could be used to identify significant gaps for which a programme of testing could be drawn up. By using such graphs, individual applications could then be considered, using material toughness and material thickness, carbon equivalent and minimum welding parameters to demonstrate the case for the omission of PWHT or for increases in the limiting thickness. It will, of course, be necessary to convince insurance companies and classification societies involved with theplant or structure of the viability of this approach, and it is therefore desirable that they are involved in any discussions from the outset of the work.
In the present investigation, it has been confirmed that a fracture mechanics assessment, with assumed values of defect size and material strength, provides a costeffective method of investigating whether PWHT is necessary in order to avoid failure by fracture. The cost of performing the analyses is relatively modest and, in some cases, the costs saved if PWHT can be avoided are large.
The strength of the welds considered in the calculations contained in this article were assumed to be matched to that of the parent materials. In practice, welds are usually designed to slightly overmatch the parent material properties. In this case, the residual stresses in the direction parallel to the weld bead are expected to be higher than the yield strength of the parent material. The adverse effects this has upon the critical toughness may be partially accounted for by the increased strength of the weld metal. The effects of weld overmatching (or undermatching) are worthy of more detailed consideration on a casebycase basis.
General discussion
Whilst fracture mechanics analyses such as in the present article and those carried out as a basis for BS 5400/BS5950 and by Mohr ^{[40]} can give an indication of what changes in the codes it may be possible to justify, the elimination of such anomalies can only be brought about if adequate toughness data become available. This is clearly one area where anirksome restriction exists, and where a programme of welding and mechanical testing would demonstrate whether any changes should be made in the relevant specifications. Another approach is, with the agreement of all interested parties,to carry out a fracture mechanics assessment on a case by case basis. As noted in Part 1 of this article, with this approach, Leggatt at al ^{[41]} showed that, in some of the examples that they considered, PWHT was not necessary.
Conclusions
BS 7910 level 2 assessments have been carried out for two values of material design minimum temperature, using assumed values of materials strength, flaw size and stress. The BS 7910: 1999 Annex J correlation between fracture toughness and Charpy impact energy was used to derive toughness requirement in terms of T _{27J} , and the results have been compared with previous fracture mechanicsbased analyses, including those underpinning the current BS5400: Part 3 rules for fracture prevention in steel bridges. From this study, the following conclusions have been drawn:
 If it is required to make a case for exemption from specific code requirements for PWHT, it may be possible to do so on the basis of a fracture mechanics analysis for a particular case. Such an approach will require consideration of the fracture toughness at the minimum service temperature, the quality of fabrication in terms of maximum sizes of flaw likely to be present, and the maximum stress levels (applied and residual) which will occur.
 Fracture mechanics analyses carried out in the present work have been compared with those used as a basis for the general structural code requirements, and have given comparable results.
 In a fracture mechanics assessment with assumed values of defect size and material strength, as expected, the toughness requirement can generally be expressed as a function of the difference in temperature between the material design minimum temperature (T _{min} ) and the temperature at which the Charpy energy is at least 27J. The toughness requirements become more onerous with increasing material strength and, more especially, with increasing thickness when the initial flaw size is assumed to be proportional to the thickness.
 As examples, for T _{min} = 20°C, the toughness requirements are not unduly onerous, given the quality of modern steels and weldments, and the calculations provide an example where there is some justification for increasing the thickness limit beyond which PWHT is required in current codes.
 For T _{min} = 50°C, the toughness requirements are sufficiently onerous that it might be appropriate to give a PWHT, even at the lower levels of thickness, for the higher strength grades. Possible examples are quenched and tempered steels, in certain applications, where the toughness may be inadequate at low design temperatures.
 The required fracture toughness (K _{mat} values) for a highstrength thicksection welded joint was found to approach 5,500N/mm ^{3/2} (173.8MPa √m). This requirement may be somewhat difficult to satisfy in the weld and heataffected zones of many structural steels without very careful control of welding consumables and welding procedures, particularly as fracture toughness is generally observed to decrease with both section thickness and material strength.
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Acknowledgements
Helpful discussions with C S Wiesner and other colleagues at TWI are gratefully acknowledged. The work was carried out within the Core Research programme of TWI, which was funded by Industrial Members of TWI.