Analysis of residual stress relief mechanisms in post-weld heat treatment

International Journal of Pressure Vessels and Piping 122 (2014) 6e14

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Analysis of residual stress relief mechanisms in post-weld heat treatment Pingsha Dong*, Shaopin Song, Jinmiao Zhang Welded Structures Laboratory, Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 26 December 2013 Received in revised form 26 June 2014 Accepted 29 June 2014 Available online 15 July 2014

This paper presents a recent study on weld residual stress relief mechanisms associated with furnacebased uniform post-weld heat treatment (PWHT). Both finite element and analytical methods are used to quantitatively examine how plastic deformation and creep relaxation contribute to residual stress relief process at different stages of PWHT process. The key contribution of this work to an improved understanding of furnace based uniform PWHT can be summarized as follows:

Keywords: Weld residual stress Post-weld heat treatment (PWHT) Residual stress relief Stress relaxation Seam weld Residual stress modeling

(1) Plastic deformation induced stress relief during PWHT can be analytically expressed by the change in material elastic deformation capacity (or elastic deformation limit) measured in terms of material yield strength to Young's modulus ratio, which has a rather limited role in overall residual stress relief during furnace based uniform PWHT. (2) The most dominant stress relief mechanism is creep strain induced stress relaxation, as expected. However, a rapid creep strain development accompanied by a rapid residual stress reduction during heating stage before reaching PWHT temperature is shown to contribute to most of the stress relief seen in overall PWHT process, suggesting PWHT hold time can be significantly reduced as far as residual stress relief is concerned. (3) A simple engineering scheme for estimating residual stress reduction is proposed based on this study by relating material type, PWHT temperature, and component wall thickness. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Post-weld heat treatment (PWHT) is often required for pressure vessel and piping components for relieving residual stresses and/or improving weldment properties, as summarized in a comprehensive review by McEnerney and Dong [1]. Stipulations for performing PWHT are given in various design codes and standards such as ASME Division 2 [2], API 579 RP [3], EN 13445 [4], among others as discussed in Ref. [1]. All these codes share a set of rather similar PWHT requirements in terms of PWHT ramp-up heating rate, hold temperature, and hold time, depending upon the type of steel and wall thickness involved. However, there is little information available in the literature on how these stipulated PWHT conditions were determined, as illustrated by Fidler [5,6] and Smith and

* Corresponding author. E-mail address: [email protected] (P. Dong). http://dx.doi.org/10.1016/j.ijpvp.2014.06.002 0308-0161/© 2014 Elsevier Ltd. All rights reserved.

Garwood [7]. Experimental investigations like these on selected weldment geometries seem to support an estimate of residual stress reduction at about 30% of material yield strength, as adopted by various defect assessment procedures such as API 579 RP [3] and BS 7910 [8]. As far as residual stress relief is concerned, some recent investigations have shown that code-specified PWHT procedures could be excessively conservative, particularly in terms of hold time for thick vessels. For instance, MeEnerney and Dong [1] reviewed various national/international codes and standards including industrial reports such as the report by Sangdahl and Rebenack [9] on thick section vessel PWHT experiences. Dong and Hong [10] and Zhang et al. [11] reported a series of finite element residual stress and PWHT study using Omega creep model by Prager [12] on different PWHT hold temperature and hold time for vessel wall thickness up to 100 mm. They [1,10,11] found that for furnace based PWHT, the code required hold time can be significantly reduced for achieving an expected residual stress reduction as long as a

P. Dong et al. / International Journal of Pressure Vessels and Piping 122 (2014) 6e14

reasonable PWHT temperature is achieved, which can result in significant economic benefits. A very recent study by Takazawa and Yanagida [13] on a laboratory weld mockup specimen using both Norton and NortoneBailey creep models confirmed a rather similar trend as discussed above, particularly when PWHT temperature is close to or at coded-specified temperature level. It is worth noting that the aforementioned investigations involve three different types of creep models. Takazawa and Yanagida [13] considered both primary and steady-state creep behavior in the form of Norton Bailey model and pure steady-state creep behavior based on classical Norton model, while Dong and Hong [10] and Zhang et al. [11] used a tertiary creep model widely used by petroleum industry [3]. These previous investigations seem to suggest that as far as general residual stress relief behavior in PWHT of weldments is concerned, computational results are not that sensitive to which type of creep models used, as long as sufficient material properties for a given application are available. Although the aforementioned investigations provided an improved understanding on the mechanics of residual stress relief during PWHT, there exist a number of questions that are of both practical importance and fundamental in nature. For example, can PWHT hold time be prolonged to compensate the use of a lower PWHT temperature to achieve the same stress relief effects? A limited experimental study on a low carbon steel weldment by Olabi and Hashimi [14] seem to support this proposition, while the investigations both by Dong and Hong [10] and by Takazawa and Yanagida [13] seem to point out that hold time has no significant effect on residual stress relief. Therefore, a lower PWHT temperature may not be substituted with a longer hold time to achieve a similar residual stress relief effect. This finding seems to be supported by another recent study by Yaghi et al. [15] in which the authors reported that more than half of the residual stress reduction already occurred during the first 30 min after reaching PWHT temperature by considering a 100 hour of PWHT hold time. It should be noted that in the latter study [15] creep relaxation was assumed negligible during the temperature ramp up stage during which studies by Dong and Hong [10], Zhang et al. [11], and Takazawa and Yanagida [13] all showed that most of residual stresses are already relieved when PWHT temperature is reached. Another question is if residual stress relief occurs in any significant manner without even triggering creep relaxation mechanism when a component is heated up to a PWHT temperature? Stout [23] postulated that a residual stress reduction without creep relaxation can be measured by the ratio of material yield strength at PWHT temperature to its room temperature value, which could be significant, depending upon material yield strength dependency on temperature. Such a postulation has served as a basis for justifying some of codified PWHT procedures even to this day, e.g., in ASME Div 2 [2]. To the authors' best knowledge, a quantitative assessment on plastic deformation effects as a result of yield strength and Young's modulus change during PWHT is still not available in the literature except some preliminary results reported by the authors [10,11]. For instance, Yaghi et al. [15,17] stated that stress relaxation occur when yield stress and elastic modulus reduce to their values at PWHT temperature, but without qualifying how and to what an extent such a phenomena would contribute to plastic strain development in relieving residual stresses. The study by Takazawa and Yanagida [13] did not separate such effects from creep relaxation effects on residual stress relief in their computational analyses. With the above discussions, this paper is structured to address the following specific questions, after presenting a validation study on a girth welded component on which the computational modeling results using the procedures adopted in this work are compared with measurement results:

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(a) What is the dominant stress relief mechanism during furnace based PWHT (b) How does plasticity deformation caused by the change in yield strength and Young's modulus during heating play a role in stress relief, if any? (c) How to quantitatively inter-relate PWHT temperature, hold time, component wall thickness, and material type so that a more consistent “TimeeTemperature-Thickness” relationship can be develped for residaul stress relief purpose? It should be emphasized that this paper is focused upon residual stress relief. In addition to residual stress relief, material property improvement is another main objective for using PWHT in practice, which is currently being investigated in an on-going study, to be published separately in due time. 2. Analysis procedure Analysis of weld residual stress relief during PWHT involves modeling of both weld residual stress development process as a result of welding and residual stress relaxation process during PWHT when an as-welded component is subjected to a controlled heating, holding, and cooling cycle. 2.1. Weld residual stress modeling procedure A comprehensive discussion on requirements and effective methodologies for computational modeling of weld residual stresses for structural integrity assessment purposes are given in Dong and Hong [14], Dong [15], and most recently by Song et al. [16] to which the present study is a continuation of the same research program that is on-going at University of Michigan. As a result, detailed residual stress modeling procedures used in this study (see Ref. [16]) will not be repeated here due to space limitation. Instead, a validation example for demonstrating the validity of both residual stress modeling and creep relaxation modeling procedure will be presented here to provide a basis for supporting the discussions and observations to be presented in this paper. A P91 pipe girth weld mockup (see Fig. 1a) was taken from Yaghi et al. [17], on which both experimental residual stress measurements both under as-welded and after PWHT are also available. By using the welding conditions and materials properties given in Ref. [17], the same residual stress modeling procedure documented by the same authors in Ref. [16] is used to estimate the resulting residual stress state after welding. The finite element model (axisymmetric) details showing individual pass profiles are shown in Fig. 1b. The final through thickness residual stress distributions along weld centerline are shown in Fig. 1c and compared with Deep Hole Drilling (DHD) measurements given in Ref. [17]. It is evident that the agreement between the modeling results and measurement results is rather reasonable (see further discussions on such a comparison in Ref. [16]). The same modeling procedure is used throughout this paper for generating weld residual stress information for seam-welded pipes to be used for PWHT stress relief analyses. Note that analysis of PWHT stress relief with a focus on pipe girth welds as a part of this same study has already been reported by Zhang et al. [11]. 2.2. Creep relaxation modeling procedure With the weld residual stress state generated in the previous section (e.g., see Fig. 1c), PWHT procedure follows the following steps:

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180mm

290mm

(a)

400

DHD FEA

200 0 -200 -400 0

10

20 30 40 50 Distance from OD [mm]

Weld Centerline – Hoop Stresses

600

Weld Centerline – Axial Stresses Residual Stress [MPa]

Residual Stress [MPa]

600

(b)

60

400

DHD FEA

200 0 -200 -400 0

10

20 30 40 Distance from OD [mm]

50

60

(c) Fig. 1. P91 pipe girth weld geometry and finite element model details.

(1) The as-welded residual stress distribution is treated as an initial stress state for subsequent PWHT stress relaxation analysis, which is done by mapping the full-field residual stresses and corresponding effective plastic strain information onto the same model (2) A uniform temperature within the weldment is assumed to follow a specified PWHT heating and cooling cycle (see the one given in Fig. 2a for P91 pipe girth weld PWHT as given in Refs. [16,17]) in a quasi-static manner. This assumption can be justified for furnace-based PWHT stress relief treatment since a slow enough heating and cooling is stipulated in relevant Codes and Standards [e.g., 2-3] to avoid any

significant temperature gradients that may develop within weldment. (3) Elasto-viscoplastic analysis incorporating MPC Omega creep model [12] to be discussed in the section is then performed over the temperature cycled. The results after PWHT for the P91 pipe girth weld shown in Fig. 1 are plotted in Fig. 2b along with DHD residual stress measurement results after PWHT. The agreement between the modeling and measurement results seems very reasonable. Note that the magnitudes of both residual stress components after PWHT are very low, in the order of 20e30 MPa in peak values.

Fig. 2. Comparison of through-thickness residual stress distributions between modeling using Omega creep model and Deep Hole Drilling (DHD) measurement results: (a) PWHT thermal cycle; (b) Residual stress distributions along weld centerline after PWHT.

P. Dong et al. / International Journal of Pressure Vessels and Piping 122 (2014) 6e14

The incorporation of Materials Properties Council (MPC) Omega creep model in this study (see Ref. [12]) is based on the following considerations: (a) It has been adopted by ASME Div 2 [2] since 2007 and API 579 RP [3] over a decade ago and become widely accepted by US petroleum industry for performing creep related design and life assessments [19e21] (b) Its material constants for a large number of materials for pressure vessel and piping applications are available in the 2007 API 579 RP [3]. This is particularly important for this study in that both weld residual stress states and stress relief behaviors can be cross-compared over different classes of materials in order to establish a general relationship between PWHT parameters and material type (c) As discussed in the previous section, previous numerical and experimental studies [11e13,18,22] have showed that weld residual stress relief behaviors seem not sensitive to the use of any particular creep model among Norton [11,13,17], Norton Bailey [13], and Omega [10,11], in addition to the validation study shown in Fig. 2b.

9

50.8

Narrow Groove Weld: Groove Width = 9.5 I= 260 amp. , V=25 volts Speed =1000/min.

y 202

x Fig. 3. 2D cross-section model (generalized plane-strain) for a thick cylinder with a narrow gap seam weld (all length units in mm).

The Omega creep model is an engineering approach to account for steady state creep and strain-induced softening tertiary creep with a uniaxial form [12]:

ε_ c ¼ ε_ c0 exp½Um εc 

(1)

where ε_ c : current creep strain rate with an integrated form at time t as: εc ¼ 1=Um lnð1  Um εc0 tÞ ε_ c0 : reference or initial creep strain rate; Um: creep damage coefficient measuring a material's ability to tolerate creep strain as function of temperature and stress state, determined by the slope of the best fit line of natural logarithm of true strain rate versus creep strain test data. Eq. (1) can be written in its multi-axial stress/strain form sij as:

ε_ cij

c 3 sij ¼ $ ε_ c0 eUm ε 2 s

(2)

where sij,s, and εc are deviatoric stress tensor, von Mises effective stress and effective creep strain, respectively. Eq. (2) was coded as an ABAQUS creep user-subroutine for performing all PWHT analyses reported in this paper. A series of seam-welded thick-wall cylinders with different wall thicknesses are considered here. It should be noted that the findings to be discussed here are equally applicable to other weld configurations such as pipe girth welds as recently demonstrated in Ref. [11] by the same authors. A representative seam welded pipe and finite element model are illustrated in Fig. 3 with a wall thickness of 200 (50.8 mm). All relevant temperature-dependent material properties for residual stress modeling purposes were taken from Ref. [2]. As an example, Fig. 4 shows material yield stress and Young's modulus as a function of temperature for both 2-1/ 4CrMo and carbon steels [2] to be considered in this study. Note that Young's moduli for both materials are essentially same as shown in Fig. 4 according ASME Div 2 [3]. As demonstrated through parametric residual stress analyses given in Ref. [14], that beyond 700  C, material properties tend to have negligible effects on final residual stresses and that a linear extrapolation scheme to nil strength at melting temperature can be used without causing any significant differences in predicted residual stresses.

Fig. 4. Yield strength and Young's moduli as a function temperature for 2-1/4CrMo and carbon steel [2,3].

3. Analysis results 3.1. Stress relaxation mechanisms 3.1.1. Heating effects without creep To separate the contribution of plastic deformation to residual stress relief from that due to creep during PWHT, a seam welded component shown in Fig. 3 subjected to quasi-steady state heating and cooling PWHT cycle (see Fig. 5 with t1 ¼ 3 h, t2 ¼ 7 h, and

Fig. 5. PWHT cycle and parameters for uniform furnace-based stress relief PWHT.

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TPWHT ¼ 7000C) is evaluated first without activating creep response described by Eq. (2). The final residual stress state at the end of the heating and cooling cycle (solid lines without symbols) is compared with the as-welded residual stresses along weld centerline in Fig. 6. The resulting reduction in residual stresses after going through the given heating and cooling cycle is insignificant (only noticeable a localized area near OD surface) in both axial and hoop residual stress components. This seems to contradict an earlier hypothesis (e.g., [23]) that if a welded component is heated up to a sufficiently high temperature at which the material yield strength reduces to a fraction of that at room temperature (see Fig. 4), plastic strain development would result in a reduction of residual stresses by a similar fraction, even without considering material creep behavior. A detailed examination of the analysis results indicates that there are no noticeable plastic strains developed throughout the heating and cooling cycle, except at a few localized areas near OD, see Ref. [10] for detailed discussions. Fig. 4 indicates that 2-1/4CrMo has a yield strength of about 400 MPa at room temperature and about 100 MPa at 700  C. A heating up to 700  C would have resulted in a reduction of residual stress by 75%, according to [23]. A more rigorous treatment on this subject will be given in a later section.

Hoop Residual Stress, MPa

3.1.2. Creep relaxation If creep behavior is activated through Omega creep model given in Eq. (2) for the same case discussed in the previous section (see Fig. 6), the resulting stress and creep strain history results at two highly stressed positions are plotted in Fig. 7 for the entire PWHT cycle. As the weldment temperature is being ramping up, residual stress values at both positions reduce initially in an approximately linear manner which can be attributed to the approximately linear

300

reduction in yield strength shown in Fig. 4. At about two hours into heating (at a temperature range between 400  C and 500  C), a rapid reduction in residual stress can be seen in Fig. 7a, as a result of a rapid development of creep strain around the same time frame shown in Fig. 7b. During the holding part of the PWHT at 700Co, the reduction in residual stresses becomes insignificant, as a result of insignificant creep strain change during holding. Upon cooling down to room temperature, the final residual stresses are at about 100 MPa. Since there are no noticeable plastic strains developed during the PWHT cycle as discussed earlier and demonstrated in Ref. [10], the reduction of the residual stresses shown in Fig. 7a can be solely attributed to the development of creep strain or creepinduced stress relaxation shown in Fig. 7b. It is worth noting that creep strain becomes fully developed even before hold time starts. The creep relaxation behaviors during PWHT shown in Fig. 7 are not unique to the given residual stress distribution, material, and weld type. This can be illustrated by a further examination of the validation case on P91 girth weld PWHT analysis results presented earlier (see Figs. 1e2). Both hoop residual stress and creep strain histories at a point about 5 mm below OD surface is plotted in Fig. 8 over the entire PWHT cycle (see Fig. 2a). A similar behavior to that shown in Fig. 7 can be seen for the P91 pipe girth weld. Hoop creep strain becomes noticeable after just about one and half hours of heating and become stabilized when PWHT temperature (760  C) is reached. There is no noticeable change in either stress or creep strain during the entire hold time of 3 h shown in Fig. 2a.

200

3.2. Effects of PWHT parameters

500

As Welded

400

After Heating&Cooling w/o Creep

300 200 100 0 -100 -200

(a)

-300 0 Axial Residual Stress, MPa

Fig. 7. Effective stress and creep strain histories at Positions A and B during PWHT and associated effective stress and strain relationship (2-1/4CrMo): (a) von Mises effective stress; (b) effective creep strain.

10

20

30

40

50

60

700 As Welded

600

After Heating&Cooling w/o Creep

500 400

100

(b)

0 0

10

20

30

40

50

60

Distace from Inner Surface, mm Fig. 6. Comparison of residual stress distributions along weld centerline of 2-1/4CrMo seem weld between as-welded and after heating to 700C and cooling to room temperature without considering creep relaxation.

3.2.1. PWHT temperature By considering the same weldment shown in Fig. 3, effects of different PWHT temperatures on residual stress relief are examined as shown in Fig. 9 at a position in HAZ (5 mm below OD). Although the general trends in Fig. 9 are rather similar to those observed in Figs. 7 and 8, the differences in final residual stress values resulted from different PWHT temperatures are significant, particularly at a relative low PWHT temperature, e.g., at 4200C and 450  C, as shown

P. Dong et al. / International Journal of Pressure Vessels and Piping 122 (2014) 6e14

Fig. 8. Residual stress evolution at a highly stress position (5 mm below OD at weld centerline) during PWHT simulated using Omega creep model e P91 pipe girth weld.

500

Heating

Holding

Cooling

Hoop Stress, Mpa

400

420C

(a)

300

450C

420C

200

650C

500C

500C

100

600C 750C

0 0

2

4

6

Time, hrs

8

10

12

2.E-03

Hoop Creep Strain

Heating

Holding

Cooling

2.E-03

(b) 1.E-03 420C

500C

650C

8.E-04

500C 600C

4.E-04

750C

420C

0.E+00 0

2

4

6

8

10

12

Time, hrs Fig. 9. Stress relaxation and creep strain development at one location near HAZ (5 mm below OD) in 2-1/4CrMo seam weld with different PWHT temperatures (thold ¼ 4 h): (a) Hoop stress; (b) Hoop creep strain .

in Fig. 9a. With a PWHT temperature lower than about 500Co, the reduction of residual stresses become much less significant (Fig. 9a), as a result of insufficient creep strain development shown in Fig. 9b. 3.2.2. PWHT hold time and component thickness Fig. 10 shows the comparison of the residual stress evolution during PWHT with 4 h and 10 h of PWHT hold time for component thicknesses, 100 (25.4 mm) and 400 (101.6 mm), respectively. Note

11

that axial residual stress (parallel to weld in seam welded components) is normalized by base material yield strength in Fig. 10). As PWHT hold time increases from 4 h to 10 h, Fig. 10 shows that the benefit for using extended hold time is not noticeable as far as the residual stress reduction is concerned. This is consistent with the observations discussed in previous sections that most of the reduction in residual stresses occurs at the earlier stage of the PWHT, even before the PWHT temperature is reached during the last stage of temperature ramp up. With seam weld wall thickness changes from 1” (25.4 mm) to 400 (101.6 mm), the results in Fig. 9 show no noticeable difference in residual stress relaxation behaviors. Again, most of the stress relaxation can be seen occurring before the hold time begins. The 400 (101.6 mm) thick weldment gives a higher as-welded residual stress than the 100 (25.4 mm) weldment due to the higher restraint conditions. In view of Fig. 10, one might ask what specific thickness effects, if any, should be considered in determining PWHT parameters in practice. A series of transient finite element analyses were then performed to simulate the temperature response of the weldments with different thicknesses to the temperature ramp up and hold process during PWHT. Fig. 11 summarizes the analysis results. For a specified furnace temperature rise (solid line in Fig. 12) from room temperature to 650Co within a period of 3 h before hold starts, the 1” (25.4 mm) thick weldment follows the specified furnace temperature more closely than the 4” thick weldment. In addition, both the surface and mid-thickness temperatures are almost identical throughout, indicating transient effects of the heat conduction process within the weldment are negligible. Both findings suggest that if the convection heat transfer coefficient (h) is further increased (e.g., by increasing air circulation in the furnace), the temperature of the 400 (101.6 mm) weldment should follow more closely to that of the furnace. Alternatively, a decreased ramp up time can be used to achieve the same purpose. 3.2.3. Ramp-up rate versus thickness Both the stress relaxation results in Figs. 9, 10 and the heat transfer results shown in Fig. 11 suggest that thickness considerations in determining furnace-based PWHT parameters can be decoupled from creep relaxation problem and treated as a simple heat transfer problem [24] that can be solved analytically. As such, heat transfer problem definition given in Fig. 12a is solved analytically for a given ambient temperature (T∞) that is linearly rampingup with time up to a PWHT temperature, say at 650  C. Fig. 12b summarizes the solutions corresponding different plate thickness and ramp-up time, where temperature difference (T∞T) is defined as that between the mid-thickness temperature (T) and the ambient temperature (T∞). If assuming that a temperature gradient requirement of DT  25C anywhere within the plate during PWHT, Fig. 12b can then be re-plotted as the maximum ramp-up heating rate allowed as a function of plate thickness, shown in Fig. 13. Note that the heat convection coefficient (h) used in generating Figs. 12 and 13 is taken from a general reference [24], which can vary significantly depending upon actual furnace conditions. In practical applications, an appropriate h can be obtained from furnace specifications and/or by performing thermal couple measurements of both furnace and plate surface temperatures. 3.2.4. 2-1/4CrMo versus carbon steels A set of parametric analyses were also performed for carbon steel weldments using the same seam weld geometry as shown in Fig. 3. The corresponding carbon steel properties are taken from Ref. [2], some of which are documented in Fig. 4. As shown in Fig. 14, the overall trend in stress relaxation behaviors under various PWHT conditions is very similar to what has been discussed

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600

TPWHT= 650Co

1" Thick & 4hr Holding

Ramp up from 20 to 650C h = 3 X10^(-5) W/mm^2*C

4" Thick & 4hr Holding

1" Thick & 10hr Holding

1.5

4" Thick & 10hr Holding (Note: 1”=25.4mm)

1

Residual Stress after PWHT (4 hrs)

Residual Stress after PWHT (10 hrs)

0.5

Heating 0

0

4

8

12

Max Heating Rate (C/hr)

Axial Residual Stress/Sy

2

400

200

16

Time, Hrs. Fig. 10. Normalized axial residual stress development (Point A in Fig. 7) during PWHT: effects of wall thickness and PWHT holding time.

(Note: 1 inch =25.4mm)

0 0

2

4

6

8

Weldment Thickness (inch) 

Fig. 13. Maximum ramp-up heating rate (C /h) as a function of plate thickness in inches (1 inch ¼ 25.4 mm) to maintain a temperature gradient criterion of DT  25  C

with respect to 2-1/4CrMo steel weldments in previous sections. Some specific details vary, mainly due to the difference in yield strengths and resistances to creep between the two classes of steels. The final residual stress for the carbon steel after PWHT is lower than that in 2-1/4CrMo weldment, due to its lower initial aswelded residual stresses and its poor creep resistance, comparing with 2-1/4CrMo steel. It is worth noting that the ratio of the final residual stresses after PWHT between the two classes of material is similar to the ratio of their initial residual stresses (at Time ¼ 1hr in Fig. 14a), or the ratio of their initial yield strengths (Fig. 2a). The corresponding creep strain developments are given in Fig. 14b.

Fig. 11. Finite element conduction heat transfer analysis results of weldment surface and mid-thickness temperature during PWHT ramp-up and holding.

4. Discussions 4.1. Residual stress reduction estimation

Fig. 12. 2D analytical heat transfer analysis and temperature difference between midthickness and surface as a function of ramp-up time and plate thickness (2L).

One of key observations from the PWHT analysis results reported thus far is that the amount of the residual stress relaxation is dominated by the amount of creep strain generated. Furthermore, creep strain development does not show any significant dependency on PWHT hold time as long as a critical PWHT temperature is reached. Then, the question becomes if a relationship between the stress relaxation and creep strain can be established for a given class of materials with similar creep resistances. Fig. 15 shows the stress evolutions as a function of creep strain development at three PWHT temperatures. It is interesting to note that the results from PWHT at different temperatures fall into essentially the same straight line with a slope of Eave which approximately represents the average Young's modulus (E) of the material over a temperature range, further substantiating the finding that plastic strain is negligible during uniform PWHT. Upon a close examination, this temperature range seems to coincide with a temperature (T0) signifying the onset of creep strain development (see Fig. 9b) for a given PWHT temperature in a given material. The higher the PWHT temperature (TPWHT) becomes, the more reduction in residual stresses can be seen in Fig. 15, recognizing that for a given class of materials, there is an upper limit imposed on TPWHT based on metallurgical considerations, such as those in Refs. [2,3]. The same trend can be seen for carbon steel weldments, as discussed in Ref. [10]. For a given creep initiation temperature T0, the creep activation stress s0 can be determined from Fig. 15. Both T0 and s0 can be interpreted as the measurement of a material's

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13

Hoop Residual Stress, MPa

500 X2.25-CRQ Carbon Steel

400 300

200

Heating

100

Holding

Cooling

(a)

0 0

2

4

6

8

10

12

Time, hrs

Hoop Creep Strain

2.E-03 Fig. 16. Residual stress reduction fraction as a function of PWHT temperature fraction: 2-1/4CrMo versus carbon steel weldments.

1.E-03

8.E-04

Heating 4.E-04

Cooling

Holding

X2.25-CRQ

(b)

Carbon Steel

0.E+00 0

2

4

6

8

10

12

Time, hrs Fig. 14. Residual stress and creep strain evaluation during PWHT with Holding Temperature of 650  C e 2-1/4 CreMo versus carbon steel weldments.

Fig. 17. Elastic strain capacity as a function of temperature for three types of alloys.

reduction amount intended, Fig. 16 provides a simple method for determining the PWHT temperature to be used and Figs. 12 and 13 (once established for a given set of furnace conditions) can be used to determine a desirable ramp-up time in performing PWHT for residual stress relief purpose. It should be noted this study has been focused mostly on ferritic steel weldments. The discussions given above should be interpreted with caution when applying to stainless steel components, in which primary creep might play more important role in residual stress relaxation process. Fig. 15. Residual stress and creep strain relationship during PWHT and related parameters for generalizing stress relaxation e 2-1/4CrMo Weldments.

resistance to creep during PWHT and can be conveniently used for planning PWHT and quantifying its stress relief effects. As an example for practical applications, a dimensionless plot is provided in Fig. 16 for both 2-1/4CrMo and carbon steel weldments. The ordinate represents a normalized residual stress reduction srs0 from as-welded conditions by the creep activation stress s0, The abscissa represents a normalized temperature difference (TPWHTT0) by the creep initiation temperature T0. In doing so, each class of steel materials (in terms of their creep characteristics) can be represented by a single curve in the form of Fig. 16. If creep activation stress s0 is not known, an estimated residual stress value using API 579 Annex E [3] may be used. For a given residual stress

4.2. Effects of heating without creep As observed in Section 3.1.1, creep is the dominant mechanism for stress relaxation during PWHT. As temperature increases, both yield stress and Young's modulus decreases. For 2-1/4CrMo steel, the rate of yield stress reduction is slightly higher than that of Young's modulus reduction (Fig. 2). This resulted in a small amount (about 10e20%) of elastic strain capacity reduction during heating up to about 700  C, which leads to a maximum possible residual stress reduction in the order of 10e20% for this case. If creep strain development is not considered, the remaining elastic strain at a material point will cause the residual stress to spring back as the component returns to the ambient temperature. In general, the magnitude of stress relaxation due to material yield strength and Young's modulus reduction is directly related to the percentage of

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elastic strain that can be converted into plastic strain during heating. To quantitatively describe this phenomenon in the context of incremental metal plasticity, the following equation holds true:

Dε ¼ Dεe þ Dεp þ DεT þ Dεc

(3)

where total strain increment Dε is equal the summation of elastic strain (Dεe), plastic strain (Dεp), thermal strain (DεT), and creep strain (Dεc) increments. If creep strain development is not considered, i.e., Dεc ¼ 0 in Eq. (3), the total strain increment Dε must be equal to the thermal strain increment DεT since any material point in the component under uniform PWHT conditions is free to expand and contract. Therefore, the change in plastic strain increment (Dεp) is equal to the difference in elastic strain capacity, i.e., yield stress (sY) to Young's modulus (E) ratio, over a given temperature difference. Therefore, Eq. (3) can be re-written as:

Dεp ¼ Dεe ¼

s  Y

E

TRM



s  Y

E

TPWHT

(4)

The higher the difference, the more elastic strain is converted into plastic strain during heating and thus leads to more stress relaxation. For comparison purpose, Fig. 17 shows material elastic strain capacity as a function of temperature for three different alloys. It can be seen that 2-1/4CrMoV shows a variation of about 20% in elastic strain capacity while Inco 600 and 304 stainless steel show much less a variation, as temperature varies from room to about 800  C. Such elastic deformation capacity as a function of temperature provides a direct measurement of residual stress relief as a result of quasi-static heating to an elevated temperature, as analytically described by Eq. (4). 5. Concluding remarks The major findings from study on ferritic weldments may be summarized as follows: (a) Plastic strain effects on residual stress relaxation during furnace-based PWHT are rather small at least for the materials and PWHT conditions investigated in this paper, which can be quantitatively described as the difference between material elastic strain capacity (sY/E) change from room temperature to a given PWHT temperature for a given steel and alloy type according to Eq. (4) (b) The dominant residual stress relief mechanism in furnacebased uniform PWHT is creep strain development. Creep strain development or creep-induced stress relaxation occurs far earlier than recognized by current Codes and Standards, e.g., even before a component reaches a target PWHT temperature. Therefore, a significant economic benefit can be realized by reducing the currently required PWHT hold time if residual stress relief is the primary objective (c) For each class of steel materials, there exist two characteristic material-related parameters: creep initiation temperature T0 and creep activation stress s0. The former can be determined by performing a series of parametric creep analyses, while the letter can be inferred from material's yield strength dependency on temperature. With the two parameters, stress relaxation behavior in a welded component can be represented as a single curve between the normalized residual stress reduction by s0 and PWHT temperature difference by TPWHTT0 (see Fig. 16). (d) Weldment thickness effects can be de-coupled from the stress relaxation process and treated as a conduction heat transport problem by calculating the minimum ramp up

heating time required for achieving a uniform temperature anywhere within a welded component (see Fig. 13). Acknowledgments The publication is made possible by the financial support by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MEST) through GCRC-SOP at University of Michigan under Project 2-1: Reliability and Strength Assessment of Core Parts and Material System. The authors are grateful to the encouragement and oversight by Project PI Professor M. H. Kim during the preparation of this report. The authors also acknowledge the insight and valuable technical advices on the use of Omega creep model and material properties provided by Dr. Martin Prager of the Materials Research Council and Mr. David Osage of the Equity Engineering Group during the course of this investigation. References [1] McEnerney JW, Dong P. Recommended practices for local heating of welds in pressure vessels. Weld Res Counc Bull June 2000;452. [2] 2007 ASME boiler & pressure vessel code VIII Div 2e an international code. New York, New York: The American society of Mechanical Engineers; August 2007. [3] 2007 API 579-1/ASME FFS-1. Houston, Texas: American Petroleum Institute; August 2007. [4] EN 13445, unfired pressure vessels. European Committee for Standardization (CEN); 2002. [5] Fidler R. Residual stresses in a CrMoV-2CrMo pipe weld: part 1-the as-welded condition. Int J Press Vess Pip 1983;14:35e62. [6] Fidler R. Residual stresses in a CrMoV-2CrMo pipe Weld: Part 2-The heat treated condition. Int J Press Vess Pip 1983;14:181e95. [7] Smith DJ, Garwood SJ. Influence of postweld heat treatment on the variation of residual stresses in 50 mm Thick welded ferritic steel plates. Int J Press Vess Pip 1993;51:241e56. [8] BS7910:2013. Guide to methods of assessing the acceptability of flaws in metallic structures. The British Standards Institution; 2013. [9] Sangdahl GS, Rebenack ML. Effect of time and temperature for PWHT of heavy section weldments. CB&I Final Project Report; September, 1981. [10] Dong P, Hong JK. Residual stress relief in post-weld heat treatment. Paper No. PVP2008e61210. In: Proceedings of the ASME Pressure Vessel and Piping Conference; July 27e31, 2008 [Chicago, IL,USA]. [11] Zhang J, Dong P, Song S. Stress relaxation behavior in PWHT of welded components. Paper No. PVP2011e57826. In: Proceedings of the ASME Pressure Vessel and Piping Conference, July 17e21, Baltimore, MD, USA. [12] Prager M. The Omega method e an engineering approach to life assessment. ASME Trans J Press Vess Technol August, 2000;122:273e80. [13] Takazawa H, Yanagida N. Effect of creep constitutive equation on simulated stress mitigation behavior of alloy steel pipe during post-weld heat treatment. Int J Press Vess Pip 2014;117e118:42e8. [14] Dong P, Hong JK. Recommendations on residual stress estimate for fitness-forservice assessment. WRC Bull January, 2003;476. [15] Dong P. Length scale of secondary stresses in fracture and fatigue. Int J Press Vess Pip 2008;85:128e43. [16] Song S, Dong P, Zhang J. A full-field residual stress estimation scheme for fitness-for-service assessment of pipe girth welds: part I: identification of key parameters; part II: a full-field estimation scheme. Int Press Vess Pip 2014. Submitted for publication. [17] Yaghi AH, Hyde TH, Becker AA, Sun W, Williams JA. Comparison between measured and modeled residual stresses in a circumferentially butt-welded P91 steel pipe. J Press Vessel Technol 2010:132e41. [18] Yaghi AH, Hyde TH, Becker AA, Sun W. Finite element simulation of welded P91 steel pipe undergoing post-weld heat treatment. Sci Technol Weld Join 2011;16(3):232e8. [19] Jong-Taek Yeom, Jong-Yup Kim, Young-Sang Na, Nho-Kwang Park. Creep strain and creep-life prediction for Alloy 718 using the Omega method. Metals Mater Int 2003;9(6):555e60. [20] Kim Woo-Gon, Kim Sung-Ho, Lee Chan-Bock. Long-term creep characterization of Gr. 91 steel by modified creep constitutive equations. Met Mater Int 2011;17(3):497e504. [21] Manu CC, Birk AM, Kim IY. Uniaxial high-temperature creep property predictions made by CDM and MPC omega techniques for ASME SA 455 steel. Eng Fail Anal 2009;16:1303e13. [22] Alberg H, Berglund D. Comparison of plastic, viscoplastic, and creep models when modelling welding and stress relief heat treatment. Comput Methods Appl Mech Eng 2003;192:5189e208. [23] Stout RD. Postweld heat treatment of pressure vessels. WRC Bulletin 302. New York, New York: Welding Research Council; February 1985. [24] Kreith F, Black WZ. Basic heat transfer. New York: Harpper & Row; 1980.