- Email: [email protected]
Fatigue assessment of high frequency mechanical impact (HFMI)-improved fillet welds by local approaches
International Journal of Fatigue 52 (2013) 57–67
Contents lists available at SciVerse ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Fatigue assessment of high frequency mechanical impact (HFMI)-improved fillet welds by local approaches Halid Can Yildirim a,⇑, Gary B. Marquis a,b, Zuheir Barsoum b a b
Department of Applied Mechanics, Aalto University, P.O. Box 14300, FI-00076 Aalto, Finland KTH – Royal Institute of Technology, Department of Aeronautical & Vehicle Engineering, Division of Lightweight Structures, Teknikringen 8, 100 44 Stockholm, Sweden
a r t i c l e
i n f o
Article history: Received 6 December 2012 Received in revised form 14 February 2013 Accepted 18 February 2013 Available online 27 February 2013 Keywords: High frequency mechanical impact (HFMI) Fatigue strength improvement High strength steels Structural hot spot stress Effective notch stress
a b s t r a c t Local fatigue assessment methods like the structural hot spot stress and effective notch stress methods as defined by the International Institute of Welding are widely used by design engineers and researchers to assess the fatigue strength of welded components. This paper provides a comprehensive evaluation of published data for welded joints which had been improved using high frequency mechanical impact (HFMI) treatment. All of the published data for HFMI-treated welds are presented in terms of nominal stress. The goal of the current paper is to establish local fatigue assessment procedures for improved fillet welds. In total, 160 published experimental results for longitudinal and cruciform welds subjected to R = 0.1 axial loading are evaluated. Local stress quantities for each joint were assessed based on the finite element analyses and reported nominal stress values. A correction procedure for yield strength that was previously verified for nominal stress-based fatigue assessment is also applied to the local stress methods studied in this paper. For both the structural hot spot stress and effective notch stress methods, sets of characteristic fatigue strength curves as functions of yield strength are proposed and verified. The structural hot spot stress method includes one set of fatigue strength curves for load-carrying welds and a second set for non-load carrying welds. The effective notch stress method includes a single set of curves for all welds. All of the design curves proposed in this study are conservative with respect to available fatigue test data. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction In 2007, after an extensive literature survey and an international round robin exercise, Commission XIII: Fatigue of Welded Components and Structures of the International Institute of Welding (IIW) completed a best-practice recommendation for implementing four common post-weld fatigue strength improvement methods for welded steel and aluminium structures [1]. The guideline includes procedures for applying treatment methods and quality assurance measures, and also provides recommendations for implementing these techniques in the fatigue design of structures. Two weld profile modification methods, burr-grinding and TIG remelting (i.e. TIG dressing), and two residual stress modification methods, hammer peening and needle peening, are covered by the guideline. In parallel to the development of this guideline, there has been an increasing number of publications dealing with high frequency mechanical impact treatment (HFMI) technologies. The innovation of locally modifying the residual stress state in welded components
⇑ Corresponding author. Tel.: +358 445 666 556. E-mail address: halid.yildirim@aalto.fi (H.C. Yildirim). 0142-1123/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijfatigue.2013.02.014
by the use of ultrasonic technology is widely attributed to Statnikov, a development scientist at the Sevmash Shipping Enterprise in Russia [2]. Subsequent fatigue studies were performed in cooperation with E.O. Paton Welding Institute in the Ukraine [3]. Additionally, further contributions by Feng and Graff [4], Prokopenko et al. [5] and Prokopenko and Lyatun [6] should also be highlighted for the development of ultrasonic technologies. Today, there are numerous HFMI peening tool manufacturers and service providers and the numbers are steadily increasing as the technique has proven to be reliable, effective and user-friendly. While details of the tools differ, the operating principle is identical: cylindrical indenters are accelerated against a component or structure with high frequency (>90 Hz). The impacted material is highly plastically-deformed, causing changes in the material microstructure and the local geometry, as well as the residual stress state in the region of impact. In comparison to hammer peening, the HFMI operation is more user-friendly and the spacing between alternate impacts on the work piece is very small, thus resulting in a finer surface finish. HFMI devices are known by the following names: ultrasonic impact treatment (UIT) [7], ultrasonic peening (UP) [8], ultrasonic peening treatment (UPT) [9,10], high frequency impact treatment (HiFiT) [11], pneumatic impact treatment (PIT) [12] and ultrasonic needle peening (UNP) [13,14].
58
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67
Nomenclature fy fy,o FAT
K m1 m2 Nf S DS t
q r
yield strength reference yield strength IIW fatigue class, i.e., the stress range in MPa corresponding to 95% survival probability at 2 106 cycles to failure (a discrete variable with 10–15% increase in stress between steps) stress concentration slope of the line for stress cycles above the knee point slope of the line for stress cycles below the knee point cycles to failure nominal stress nominal stress range plate thickness of the specimen radius stress
Yildirim and Marquis recently completed a study of all available experimental data on the fatigue strength of welded joints improved by HFMI [15]. Most of the 414 reported data points have been performed using constant amplitude R = 0.1 axial tension fatigue, but some data for other R-ratios, variable amplitude testing and bending fatigue are also reported. The axially-loaded HFMItreated joints used were longitudinal stiffeners, cruciform joints and butt joints. Bending loading was performed using T-joints. The studies considered a variety of different steel grades but no data for HFMI-treated aluminium welds was available. The study showed that an S–N slope m1 = 5 adequately described the data. This is in contrast to the slope m1 = 3 used, for example, in the IIW best practice guideline for welded structures improved by hammer peening or needle peening [1]. Welded specimens treated by HFMI methods also tended to have slightly greater fatigue strength than did specimens treated with traditional hammer peening. In order to assess the influence of steel yield strength on the observed fatigue improvement of HFMI-treated welds, Yildirim and Marquis [16] evaluated several proposed equations for considering material yield strength. Published data for axially-loaded HFMItreated welds subjected to constant amplitude R = 0.1 were considered. The steel yield strengths varied from 260 to 969 MPa and specimen thicknesses varied from 5 to 30 mm. A yield strength correction method was proposed and verified. The recommendation for design includes a five (5) fatigue class increase in strength for joints fabricated from fy = 355 MPa steel, with respect to the nominal fatigue class in the as-welded condition. One additional fatigue class increase in fatigue strength (about 12.5%) for every 200 MPa increase in static yield strength was proposed. The specific fatigue class increase is defined for N = 2 106 cycles and assumes an S–N slope m1 = 5 for HFMI-treated welds and m1 = 3 for welds in the as-welded state. A recently-completed round robin study of welded high strength steel joints treated using four different HFMI treatment technologies was promising with respect to the development of a future guideline [17]. Nominally-identical, longitudinal, non-load carrying attachments in S700 MC high strength steel, fy = 700 MPa, were manufactured at a single location, then randomly distributed to four HFMI equipment manufacturers for treatment. All HFMI-treated welds were subjected to identical variable amplitude fatigue loading on a single test machine. Experimental results indicated that all of the HFMI-improved welds from the four different HFMI equipment manufacturers satisfied the previously-proposed characteristic line, based on both the material yield strength and the specimen geometry.
rN
standard deviation in Log (Nf)
Subscripts K characteristic value corresponding to 95% survival probability at 2 106 cycles to failure (a continuous variable) f effective s hot spot stress i value for specimen i m mean value corresponding to 50% survival probability at 2 106 cycles to failure w notch stress
The aim of the current paper has been to develop appropriate guidelines for the fatigue assessment of HFMI-improved fillet welds based on local approaches, namely, the effective notch stress (ENS) approach and the structural hot spot stress (SHSS) approach. These are studied using the available constant amplitude fatigue test data for HFMI-improved welds subjected to stress ratio R = 0.1. Only axially-loaded test data from longitudinal and cruciform fillet welds are considered. Data are evaluated both with and without the previously-proposed correction for material yield strength [16].
2. Fatigue assessment of welded structures by local approaches A variety of local fatigue assessment procedures for welded structures has been developed. A comprehensive survey of these methods has been prepared by Radaj et al. [18]. Thus far, the IIW has developed and published detailed guidelines concerning two local fatigue design approaches for welded components: the SHSS method [19] and the ENS method [20]. In 2006, the IIW published fatigue design recommendations based on the use of the SHSS which include proposals for design curves expressed in terms of the hot-spot stress range [19]. In a welded plate structure, the structural stress at the hot spot includes all stress-increasing effects of a structure, with the exception of the non-linear peak stress occurring at the local notch, i.e. at the weld toe. Determination of the SHSS (excluding the non-linear peak stress) can be performed by extrapolation, choosing proper extrapolation distances from the weld toe. For plates with t P 5 mm, these distances vary from 0.4 t to 2.5 t, where t is the plate thickness. In the case of steel in the as-welded condition, two SHSS characteristic curves are proposed for as-welded fillet-welded joints. These are FAT 90 for load-carrying or FAT 100 for non-load carrying welds. This method is included in the existing IIW recommendations for improved welded joints [1]. For welds improved by hammer or needle peening, the appropriate SHSS characteristic curve for non-load carrying joints is FAT 125 for mild steel (fy < 355 MPa) and FAT 140 for higher strength steel (fy P 355 MPa) with an S–N slope of m1 = 3. For load-carrying joints, the respective characteristic curves are FAT 112 for mild steel and FAT 125 for higher strength steel. In 2008, the IIW approved a guideline concerning fatigue design of welded components based on the ENS approach to fatigue assessment [20]. In this method, the maximum principal stress or von Mises stress at the notch, e.g. weld toe or root, can be
59
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67
Table 1 Experimental R = 0.1 constant amplitude axial fatigue data for HFMI-treated longitudinal welds with stress concentration values obtained from finite element calculations based on structural and notch stresses.
a b
Ref.
Steel type
fy (MPa)
Treatment method
Plate thickness (mm)
Number of specimens in series
Ks
Kw (qf = 1 mm)
[30] [31] [31] [32] [33] [33] [33] [34] [34] [34] [35,36] [37]
S700 S690QL S690QL 16Mn S350 S700 S900 SS800 16Mn Q235B S355 S960
700b 786a 786a 390b 398a 780a 900a 700a 390a 267a 355b 960a
UP/ UIT UIT HiFiT UP/UPT UP/UPT UP/UPT TIG + UP UP/UPT UP/UPT UP/UPT UIT PIT
8 16 16 8 12 12 12 8 8 8 8 5
16 16 15 6 5 7 10 8 6 7 10 11
1.22 1.25 1.25 1.22 1.30 1.30 1.30 1.22 1.22 1.22 1.30 1.44
2.72 2.99 2.99 2.72 2.69 2.69 2.69 2.72 2.72 2.72 2.31 1.81
Measured fy. Nominal fy.
Table 2 Experimental R = 0.1 constant amplitude axial fatigue data for HFMI-treated cruciform welds with stress concentration values obtained from finite element calculations based on structural and notch stresses.
a b
Ref.
Steel type
fy (MPa)
Treatment method
Plate thickness (mm)
Number of specimens in series
Ks
Kw (qf = 1 mm)
[38] [38] [38] [38] [39] [39] [40] [41]
S355J2 S355J2 S460ML S460ML S355J2 S690QL AH36 350 W
398a 398a 504a 504a 477a 781a 392a 350b
UIT UIT UIT UIT PIT PIT UIT UIT
12 12 12 12 12 12 20 9.5
7 4 5 5 8 7 3 5
1.30 1.30 1.30 1.30 1.30 1.30 1.42 1.18
1.53 1.53 1.53 1.53 1.53 1.53 1.57 1.66
Measured fy. Nominal fy.
idealized by assuming a linear-elastic material behaviour using the finite element method. The actual weld profile at the toe or root that includes all variations of weld shapes is replaced and rounded by a fictitious notch radius in order to avoid arbitrary or infinite stress results. For welds having a plate thickness of over 5 mm, it is proposed that
qf ¼ q þ 1 mm
ð1Þ
where q is the actual radius of the weld toe and qf is the effective radius which is implemented to the finite element modelling. For a worst case scenario and for practical applications, the actual radius is usually assumed to be close to zero. Therefore, the ENS approach for the fatigue assessment of welded structures is reduced to qf = 1 mm at the weld toe or root. When the stress assessment method is based on the maximum principal stress and using qf = 1 mm, FAT 225 is normally considered for all types of as-welded specimens. For von Mises stress, FAT 200 is used. However, some recent studies have shown that with the notch stress approach for welded structures, the FAT 225 S–N line represents less than 95% survival probability, particularly for cruciform and butt welds [21–23]. 3. Analysis methods 3.1. Fatigue data In the current study, fatigue test data previously studied by Yildirim and Marquis were further evaluated [16]. Only test results obtained at R = 0.1 were considered, since a definitive relationship concerning the influence of stress ratio for HFMI-treated welds has not yet been finalized. The original data can be found in references listed in Tables 1 and 2.
3.2. Assessment of the structural hot spot stress For each of the specimen geometries considered, stress analysis procedures as described by Niemi et al. were used to evaluate the SHSS [19]. Finite element models of each specimen were modelled using second-order solid brick elements. Maximum element size close to the weld toe was limited to t/4, whereas it was limited to 1 t overall in the model for all analyses. Weld toe angle was idealized to 45° as recommended by Fricke [20]. For longitudinal welds, linear extrapolation perpendicular to the weld toe was considered using the evaluation points 0.4 t and 1.0 t [24]. In addition, a modified structural stress method as proposed by Poutiainen and Marquis was applied, in order to accurately capture the local effect of weld size and weld stress for cruciform joints [25]. Due to symmetry, quarter models were used for single-sided attachments and 1/8 models were used for double-sided attachments, see Fig. 1. A unit stress was applied to the ends of models in order to obtain longitudinal stresses at extrapolation points, 0.4 t and 1.0 t away from the weld toe, and a structural stress concentration factor could be determined for each specimen geometry evaluated by using Eq. (2). Quadratic extrapolation using the evaluation points 0.4 t, 0.9 t and 1.4 t was considered and found to give slightly greater values of Ks. However, all computations were based on the more conservative linear extrapolation results.
K s ¼ rs =r
ð2Þ
3.3. Assessment of the effective notch stresses With respect to the ENS method and HFMI, Eq. (1) would result in relatively large qf because q in the case of HFMI-treated welds can be from 1.5 to more than 7 mm. For example, Fig. 2 shows weld
60
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67
Fig. 1. Sample finite element models for (a) longitudinal and (b) cruciform welds.
Fig. 2. Measured HFMI weld toe radii and HFMI groove depth for several HFMI technologies (A, B, C and D are different HFMI technologies). Test specimens are from a recently-completed round robin study [17].
toe geometry measurements for the HFMI specimens treated by several technologies (A, B, C and D) reported in the round robin study [17]. In theory, the treated welds with larger radii should perform better in fatigue. However, there is a complex interaction between treatment parameters, toe radius, microstructure of the treated zone and residual stresses which is not fully understood. The extra benefit of modelling a weld toe notch with a radius equal to the actual radius of the HFMI-treated zone is therefore difficult to establish. Additionally, the exact weld toe geometry following HFMI has not been fully reported in all studies. In the current study, it has been decided to perform the notch stress analysis using an artificial notch radius qf = 1 mm, using procedures as described by Fricke [20]. The ENS concentration factors, Kw, at the weld toe and weld root were evaluated using finite element models having a weld toe radius qf = 1 mm for each specimen geometry. Second-order solid elements were considered and maximum element size close to the weld toe and/or root and overall in the model was limited to R/10 and 1 t in all of the analyses. Weld toe angle was idealized to 45° in the case of longitudinal and cruciform welds, as recommended by Fricke [20]. As with the SHSS analyses, symmetry was used and a unit stress was applied to the ends of models in order to obtain maximum principal stresses at the weld toe or root. The ENS concentration factor is defined with respect to the structural stress using the following equation:
K w ¼ rw =rs
ð3Þ
3.4. Statistical analysis of the data Hobbacher [24] has pointed out the difficulty of performing statistical analysis of data arising from numerous studies. This can be especially problematic for fatigue test data of welds improved by technologies like HFMI. Most fatigue test results are statistically evaluated using an assumed log-normal distribution of fatigue strength. For post-weld-improved data from numerous independent studies, all data may not exist as a single population. When evaluated as a single log-normally-distributed population, the addition of a small number of exceptionally strong test specimens will increase both the computed mean fatigue strength and variance, such that the resulting computed characteristic value is actually less than the computed characteristic strength without the exceptionally strong test specimens. In the current study, the three-parameter Weibull distribution was used to assess the statistical distribution of fatigue data [26]. See for example Schjive [27]. 4. Results Results of the stress analysis for SHSS and ENS, as well as other important details of the test specimens, are presented in Tables 1
61
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67 Table 3 Structural hot spot stress analyses of published data from Tables 1 and 2. Slope m1 = 5 was assumed.
a
Specimen type
Total data points
Longitudinal attachment Cruciform joint
116 44
Including fy correctiona
Not including fy correction
DSm (MPa)
DSk (MPa)
rN
DSm (MPa)
DSk (MPa)
rN
295 282
220 231
0.47 0.29
256 268
207 229
0.30 0.23
fy correction to reference yield strength fy,o = 355 MPa.
Table 4 Notch stress analyses of published data from Tables 1 and 2. Slope m1 = 5 and qf = 1 mm were assumed.
a
Specimen type
Total data points
Longitudinal attachment Cruciform joint All joints
116 44 160
Including fy correctiona
Not including fy correction
DSm (MPa)
DSk (MPa)
rN
DSm (MPa)
DSk (MPa)
rN
661 478 600
475 388 418
0.38 0.30 0.47
571 456 519
450 385 406
0.25 0.25 0.32
fy correction to reference yield strength fy,o = 355 MPa.
and 2 for longitudinal attachments and cruciform welds, respectively. Table 3 presents results of the Weibull three-parameter regression analysis for the SHSS method based on data from Tables 1 and 2. Table 4 presents results of the three-parameter regression analysis for the ENS method. In both tables, there are separate columns representing the regression analyses performed both with and without the previously mentioned material yield strength correction proposal [16]. The yield strength correction procedure requires the selection of a so-called reference yield strength. In the current study, fy,o = 355 MPa is selected. In all cases, the best fit regression mean lines and characteristic lines are based on a forced S–N slope m1 = 5.
Figs. 3 and 4 show the available fatigue data for HFMI-treated welds in terms of SHSS and ENS, respectively. These are based on the nominal stresses reported in the individual studies and the values of Kw and Ks computed in this study and shown in Tables 1 and 2. Separate graphs show the data with and without fy correction. Experimental data for each of the joint types are shown separately. The best fit regression mean lines and characteristic lines from Tables 3 and 4 are also shown. Based on the previous study by Yildirim and Marquis [16], a welded detail in fy = 355 MPa steel improved by HFMI is expected to have a five fatigue class improvement with respect to the same detail in the as-welded condition. If the same logic is applied to the SHSS method, the resulting S–N line for load-carrying details
Fig. 3. Available fatigue data for HFMI-treated welds presented in terms of SHSS both without (left) and with (right) fy correction. Ks values are shown in Tables 1 and 2 for (a) longitudinal non-load carrying attachments and (b) cruciform joints. fy correction is to a reference yield strength fy,o = 355 MPa.
62
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67
Fig. 4. Available fatigue data for HFMI-treated welds based on effective notch stress without (left) and with (right) fy correction presented for qf = 1 mm. Kw values are shown in Tables 1 and 2 for (a) longitudinal non-load carrying attachments, (b) cruciform joints and (c) both joint geometries. fy correction is to a reference yield strength fy,o = 355 MPa.
would be FAT 160 and FAT 180 for non-load carrying details. As previously mentioned, the specific fatigue class increase is defined for N = 2 106 cycles and assumes an S–N slope of m1 = 5 for HFMI-treated welds and m1 = 3 for welds in the as-welded state. Table 5 gives the existing IIW classes for SHSS approach for as-welded and improved joints and the proposed FAT classes for HFMI-treated joints as a function of fy. This is shown graphically in Fig. 5. The available SHSS test data for different ranges of fy for non-load carrying and load-carrying specimens are shown in Figs. 6 and 7. The proposed characteristic S–N lines are also shown. Table 6 gives the existing IIW characteristic FAT class for the ENS approach for as-welded joints and the respective proposed FAT classes for HFMI-treated welds. These are shown graphically in Fig. 8. In light of the afore-mentioned recent studies that have shown that the FAT 225 S–N line may not represent 95% survival probability for joints in the as-welded condition [21–23], it was decided that a fatigue class improvement of four (4) would be added for welded details in fy = 355 MPa steel. Classes for other fy are similarly adjusted. The ENS method S–N curve for an HFMI-im-
proved detail in fy = 355 MPa steel would be FAT 360. Available experimental data for HFMI-improved welds evaluated according to the ENS method and arranged according to fy are shown in
Table 5 Existing IIW FAT classes for SHSS approach for as-welded and improved joints and the proposed FAT classes for HFMI-treated joints as a function of fy. fy (MPa)
Load-carrying fillet welds
As-welded, m = 3 [24] All fy 90
Non-load carrying fillet welds 100
Improved by hammer or needle peening, m = 3 [1] fy 6 355 112 125 355 < fy 125 140 Improved by HFMI, m = 5 235 < fy 6 355 140 355 < fy 6 550 160 550 < fy 6 750 180 750 < fy 6 950 200 950 < fy 225
160 180 200 225 250
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67
63
respect to the same weld detail in the as-welded condition. Moreover, it can be further extended to represent a step-wise increase up to an eight (8) fatigue class improvement for fy > 950 MPa. This increase is represented in Fig. 5a as a solid line which indicates one additional fatigue class increase in fatigue strength (about 12.5%) for every 200 MPa increase in static yield strength. Fig. 5b represents the comparable proposal for load-carrying attachments. The proposal of one additional fatigue class increase in fatigue strength for every 200 MPa increase in static yield strength remains, but the characteristic fatigue strength for load-carrying joints is one (1) FAT class lower than those proposed for non-load carrying joints for all yield strengths. This is consistent with existing IIW guidelines for welds improved by hammer and needle peening which are shown as dashed lines in Fig. 5a and b. It is also consistent with IIW guidelines for welds in the as-welded condition. 5.3. Effective notch stress (ENS) approach method
Fig. 5. Proposed FAT values for SHSS approach as a function of fy for (a) for non-load carrying and (b) for load-carrying welds.
Fig. 9. Proposed characteristic curves from Table 6 are also given in this figure. 5. Discussion 5.1. The effects of yield strength correction method The use of fy correction results in decreased rN and lower DSk and DSm for each specimen type. This is shown in Figs. 3 and 4 and Tables 3 and 4. Lower values of DSk and DSm are to be expected, since these values represent the lines for HFMI-treated specimens at the reference yield strength fy,o = 355 MPa. Without the fy correction method, the curves are higher, since the lines represent a mix of test specimens with a wide variety of yield strengths (260 MPa < fy < 960 MPa), the vast majority of existing data referring to steels with fy > 355 MPa. 5.2. Structural hot spot stress (SHSS) method With respect to the SHSS method, proposed FAT values in Table 5 for both non-load and load-carrying specimens are consistent and conservative with respect to yield strength corrected characteristic values at fy,o = 355 MPa in Table 3. For example, the SHSS characteristic fatigue strength of a non-load carrying fillet weld (longitudinal attachment) based on statistical assessment of the experimental data and yield strength corrected to fy = 355 MPa was found to be 207 MPa, see Table 3. The corresponding proposed maximum possible FAT class for non-load carrying welds from steel with fy = 355 MPa is FAT 180. The consistency of these values indicates that the experimental results based on SHSS confirm the maximum FAT class increase of five (5) with
With respect to the ENS approach, proposed FAT values in Table 6 are consistent and conservative with respect to yield strength corrected characteristic values at fy,o = 355 MPa given in Table 4. For example, the ENS characteristic fatigue strength of all fillet welds, based on statistical assessment of the experimental data and yield strength corrected to fy = 355 MPa, was found to be 406 MPa, see Table 4. The corresponding proposed maximum possible FAT class in Table 6 for fillet welds from steel with fy = 355 MPa is FAT 360. The consistency of these values indicates that the experimental results based on ENS confirm the maximum FAT class increase of four (4) with respect to the same weld detail in the as-welded condition. It is interesting to note that in an earlier investigation on both as-welded and HFMI-improved specimens, the effective notch radius qf = 1 mm has been applied to axially-loaded specimens and a FAT class of 360 has been fitted for HFMI-treated joints with a slope of m1 = 5 [28]. This study did not make any distinction with respect to yield strength. Instead, a single FAT class was suggested for all steel grades. This value is identical to the S–N line for fy = 355 MPa in the current study. 5.4. FAT proposals versus fy corrected fatigue data For both local approaches, there are several data points below the calculated characteristic lines in Figs. 3 and 4. This is expected since the characteristic lines which were derived using Weibull distribution are computed to represent 95% survival probability of the fatigue population. In the case of the ENS approach, for example, Fig. 4c shows the joint results for both specimen types. A survival probability of 95% would mean that approximately eight data points out of 160 would fall below the computed characteristic FAT line (solid line). In total, six (6) points are below the line and several others lie just at or above the line. Experimental data represented as SHSS for non-load carrying and load-carrying specimens are shown in Figs. 6 and 7, respectively. Data are grouped according to fy of the base material and are shown together with the respective proposed FAT class S–N curves. With the exception of only one data point that appears in Fig. 6c, the proposed S–N curves are conservative with respect to the experimental results. Similarly, Fig. 9 shows the experimental data represented as ENS and grouped according to fy, the proposed characteristic S–N lines from Table 6 for HFMI-improved welds and the IIW characteristic curve for as-welded joints. No points in Fig. 9 fall below the proposed S–N lines. Thus, the target survival probability for the characteristic lines is achieved considering that FAT classes represent discrete steps. For both local assessment
64
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67
Fig. 6. Experimental data for non-load carrying HFMI-treated welds based on SHSS. Proposed characteristic curves from Table 5 are also shown for: (a) 235 < fy 6 355, (b) 355 < fy 6 550, (c) 550 < fy 6 750, (d) 750 < fy 6 950 and (e) 950 < fy.
Fig. 7. Experimental data for load-carrying HFMI-treated welds (cruciform joints) based on SHSS. Proposed characteristic curves from Table 5 are also shown for: (a) 355 < fy 6 550 and (b) 550 < fy 6 750.
methods, the use of yield strength correction representing one fatigue class (approximately 12.5%) increase in strength for every 200 MPa increase in fy has been verified.
Dashed lines in Figs. 6 and 7 represent the existing IIW characteristic curves for joints improved by hammer or needle peening. It is easy to see that the proposed S–N curves for HFMI-improved
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67 Table 6 Existing IIW characteristic curve based on the effective notch stress (ENS) approach for as-welded joints and proposed characteristic curves based on the ENS approach for HFMI-improved joints as a function of fy. fy (MPa)
a
Effective notch stress characteristic curve modelled using qf = 1 mm
All fy
As-welded, m1 = 3 [20] 225a
Improved by HFMI, m1 = 5 235 < fy 6 355 355 < fy 6 550 550 < fy 6 750 750 < fy 6 950 950 < fy
320 360 400 450 500
Some studies suggest that FAT 200 is a better fit for the experimental data.
65
which were assessed based on nominal stress [16]. Those cautions are also valid in the case of local stress approaches. For design cases where R > 0.1, the proposed FAT class may need to be reduced. This topic is beyond the scope of this document, but proposals for R > 0.1 constant amplitude loading and variable amplitude loading have been developed by Marquis et al. [29]. In literature, the benefits of HFMI treatment technologies are considered to be derived from the introduction of beneficial compressive residual stresses near the weld toe, as well as the achievement of a smooth transition from parent material to weld metal via the establishment of a defined weld groove shape. Since this study is based on available experimental test results, all features which contribute to increased fatigue strength have already been included. With regard to the ENS method, it is clear from Fig. 2 that various HFMI technologies produce different toe radii and depths. Based on the available experimental evidence, it is not possible to isolate a single factor which contributes to the added fatigue strength, e.g., the effect of the reduced stress concentration at the weld toe. Instead of measuring each HFMI weld profile and applying distinct radii for each application, the use of qf = 1 mm even for HFMI-improved weld models has been considered to be a more practical and easier-to-implement solution. End users who regularly resort to the ENS approach frequently have automatic meshing routines which can then be used for an entire structure, including both HFMI-treated welds and non-treated welds.
6. Conclusions
Fig. 8. Proposed FAT values for ENS approach as a function of fy.
welds follow the data better than the lines for hammer or needle peening. The proposed HFMI lines allow significantly more applied stress in the high cycle region as compared to the lines for hammer or needle peening. In the low cycle region, however, the proposals in this study can result in lower allowable stresses, especially for lower strength materials. For the ENS approach, characteristic curves for improved joints have not been previously defined, thus the dashed lines in Fig. 9 show the characteristic S–N lines for joints in the as-welded condition. As can be seen in Fig. 9, there is some region of the S–N curve for which the HFMI-improved line actually falls below the line for as-welded joints. For fy < 355 MPa steels, the intersection occurs at about N = 200,000. For 355 < fy 6 550 and 550 < fy 6 750 steels, this occurs at N = 60,000 cycles and N = 30,000 cycles, respectively. Similar observations based on the SHSS can be made from Figs. 6 and 7. Figs. 6d and e, and 9d and e represent experimental data for high strength steels (fy > 750 MPa), with the stress represented by SHSS or ENS. In all cases, the experimental data lie above the proposed characteristic S–N curve. However, the data are only just barely conservative with respect to the proposed S–N line. These should be confirmed by additional tests.
5.5. Applicability and validity The data in this study consisted of test results obtained from a stress ratio R = 0.1 and 1 104 6 Nf < 1 107 cycles. All of the S–N curves for HFMI proposed in this document are assumed to have slopes of m1 = 5 in the region of 1 104 6 N < 1 107 cycles and m2 = 9 for 1 107 6 N. This represents the more general design case of variable amplitude loading. Special caution about R-ratios and variable amplitude was previously advised for HFMI welds
This paper provides a comprehensive evaluation of published data for high frequency mechanical impact (HFMI)-treated welds subjected to R = 0.1 constant amplitude loading. In total, 160 experimental fatigue test results for longitudinal and cruciform welds subjected to axial loading have been evaluated, based on established local approach concepts for welded joints. The structural hot spot stress (SHSS) and the effective notch stress (ENS) methods have been considered. In each case, stress analysis was performed in accordance with guidelines developed by the International Institute of Welding. For each of the weld geometries reported in literature, the finite element method was used to determine the respective stress concentration factors for SHSS and ENS. A previously-developed fy correction method for nominal stress was also implemented for local fatigue strength approaches. Characteristic values for SHSS and ENS have been calculated using the fy correction method. According to the findings, the following conclusions can be drawn: For both local assessment methods, the use of fy correction representing one fatigue class (approximately 12.5%) increase in strength for every 200 MPa increase in fy has been verified. Fatigue classes for the SHSS and the ENS which represent the fatigue strength of HFMI-improved joints at 2 106 cycles and assume an S–N slope of m1 = 5 have been proposed and verified with the available corrected fatigue data. For the SHSS method, a five (5) fatigue class improvement with respect to the same weld detail in the as-welded condition has been proposed and verified for both non-load and load-carrying welded joints. For the ENS approach, a four (4) fatigue class improvement has been proposed and verified. The proposed characteristic curves are found to be conservative with respect to more than 95% of the available fatigue test data. Only limited experimental data for high strength steels (fy > 750 MPa) are reported. The proposed characteristic curves
66
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67
Fig. 9. Experimental data for HFMI-treated welds based on ENS. Proposed characteristic curves from Table 6 are also shown for (a) 235 < fy 6 355, (b) 355 < fy 6 550, (c) 550 < fy 6 750, (d) 750 < fy 6 950 and (e) 950 < fy.
are conservative with respect to this data, but more studies are encouraged. Studies concerning R-ratios other than 0.1 and variable amplitude studies are also recommended.
Acknowledgements Support for this work has been partially provided by the LIGHT research programme of the Finnish Metals and Engineering Competence Cluster (FIMECC), the Finnish Funding Agency for Technology and Innovation (TEKES), the Research Foundation of Helsinki University of Technology, and the EU Research Fund for Coal and Steel under grant agreement RFSR-CT-2010-00032 ‘‘Improving the fatigue life of high strength steel welded structures by post weld treatments and specific filler material’’.
References [1] Haagensen PJ, Maddox SJ. IIW Recommendations on methods for improving the fatigue lives of welded joints. Cambridge/Paris: Woodhead Publishing Ltd./ International Institute of Welding; 2013. [2] Statnikov E, Shevtsov U, Kulikov V. Ultrasonic impact tool for welds strengthening and reduction of residual stresses, Publications Scientific Works Metallurgy, SEVMASH, USSR, No. 92; 1977. p. 107–12 [in Russian].
[3] Statnikov E, Trufyakov V, Mikheev P, Kudryavtsev Y. Specification for weld toe improvement by ultrasonic impact treatment. Paris: International Institute of Welding; 1996 [IIW Document XIII-1617-96]. [4] Feng C, Graff K. Impact of spherical tool against a sonic transmission line. J Acoust Soc Am 1972;52(1):254–62. [5] Polotskiy I, Nedoseka A, Prokopenko G, Trefilov V, Firstov S. Relieving of residual welding stresses by ultrasonic treatment. Autom Weld 1974;5:74–5 [in Russian]. [6] Prokopenko G, Lyatun T. Investigation of parameters of surface hardening with the help of ultrasound, Physics and chemistry of materials treatment. J Sound Vib 1997;3:91–5 [in Russian]. [7] Applied Ultrasonics.
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67 [18] Radaj D, Sonsino C, Fricke W. Fatigue assessment of welded joints by local approaches. Cambridge: Woodhead Publishing Ltd.; 2006. [19] Niemi E, Fricke W, Maddox S. Fatigue analysis of welded joints – designer’s guide to the structural hot-spot stress approach. Cambridge: Woodhead; 2006. [20] Fricke W. IIW recommendations for the fatigue assessment of welded structures by notch stress analysis. Cambridge: Woodhead Publishing Ltd.; 2012. [21] Kranz B, Sonsino C. Verification of the FAT values for the application of the notch stress concept with reference radii rref = 1.00 and rref = 0.05. Welding in the World 2010;54(7/8): R218–24. [22] Pedersen M, Mouritsen O, Hansen M, Andersen J, Wenderby J. Re-analysis of fatigue data for welded joints using the notch stress approach. Int J Fatigue 2010;32:1620–6. [23] Barsoum Z, Jonsson B. Fatigue assessment and LEFM analysis of cruciform joints fabricated with different welding processes. Weld World 2008;52(7/ 8):93–105. [24] A Hobbacher, IIW recommendations for fatigue design of welded joints and components, WRC bulletin 520. New York: The Welding Research Council; 2009. [25] Poutiainen I, Marquis G. A fatigue assessment method based on weld stress. Int J Fatigue 2006;28:1037–46. [26] Weibull W. A statistical distribution function of wide applicability. J Appl Mech 1951;18:293–7. [27] Schijve J. A normal distribution or a Weibull distribution for fatigue lives. Report LR-689 Delft University of Technology; 1992. [28] Pedersen M, Mouritsen O, Hansen M, Andersen J. Experience with the notch stress approach for fatigue assessment of welded joints. In: Proceedings of Swedish conference on light weight optimized welded structures Borlänge, Sweden; 2010. [29] Marquis G, Mikkola E, Yildirim H, Barsoum Z. Fatigue strength improvement of steel structures by HFMI: proposed fatigue assessment guidelines. Paris: International Institute of Welding; 2013 [IIW Document XIII-2452-13]. [30] Haagensen PJ, Alnes Ø, Progress report on IIW WG2 round robin fatigue testing program on 700 MPa and 350 MPa YS Steels. Paris: International Institute of Welding; 2005 [IIW Document XIII-2081-05]. [31] Weich I. Fatigue behaviour of mechanical post weld treated welds depending on the edge layer condition (Ermüdungsverhalten mechanisch
[32]
[33]
[34]
[35]
[36] [37]
[38]
[39]
[40]
[41]
67
nachbehandelter Schweißverbindungen in Abhängigkeit des Randschichtzustands). Doctorate thesis Technischen Universität CaroloWilhelmina; 2008. Huo L, Wang D, Zhang Y. Investigation of the fatigue behaviour of the welded joints treated by TIG dressing and ultrasonic peening under variableamplitude load. Int J Fatigue 2005;27:95–101. Martinez L, Blom AF, Trogen H, Dahle T. Fatigue behavior of steels with strength levels between 350 MPa and 900 MPa the influence of post weld treatment under spectrum loading. In: Blom A, editor. Proceedings of the North European engineering and science conference (NESCO) welded highstrength steel structures, Stockholm; 1997. Wang T, Wang D, Huo L, Zhang Y. Discussion on fatigue design of welded joints enhanced by ultrasonic peening treatment (UPT). Int J Fatigue 2009;31:644–50. Lihavainen V, Marquis G, Statnikov E. Fatigue strength of a longitudinal attachment improved by ultrasonic impact treatment. Weld World 2004;48(5/ 6). Lihavainen V, Marquis G. Fatigue life estimation of ultrasonic impact treated welds using a local strain approach. Steel Res Int 2006;77(12):896–900. Leitner M, Stoschka M, Schörghuber M, Eichlseder W. Fatigue behavior of highstrength steels using an optimized welding process and high frequency peening technology. In: IIW international conference, Chennai; 2011. Kuhlmann U, Dürr A, Bergmann J, Thumser R. Fatigue strength improvement for welded high strength steel connections due to the application of post-weld treatment methods (Effizienter Stahlbau aus höherfesten Stählen unter Ermüdungsbeanspruchung). Forschungsvorhaben P620 FOSTA, Düsseldorf: Verlag und Vertriebsgesellschaft GmbH; 2006. Kuhlmann U, Gunther H. Experimentelle untersuchungen zur ermüdungssteigernden wirkung des PIT-verfahrens. Versuchsbericht: Universität Stuttgart, Institut für Konstruktion und Entwurf, September; 2009. Okawa T, Shimanuki H, Funatsu Y, Nose T, Sumi Y. Effect of preload and stress ratio on fatigue strength of welded joints improved by ultrasonic impact treatment. Welding in the world 2013;(2):235–41. Yekta R. Walbridge S. Acceptance criteria for ultrasonic impact treatment (UIT), Ontario Ministry of Transportation, Report HIIFP-110, Ontario (Canada): St. Catherines; 2012.
Contents lists available at SciVerse ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Fatigue assessment of high frequency mechanical impact (HFMI)-improved fillet welds by local approaches Halid Can Yildirim a,⇑, Gary B. Marquis a,b, Zuheir Barsoum b a b
Department of Applied Mechanics, Aalto University, P.O. Box 14300, FI-00076 Aalto, Finland KTH – Royal Institute of Technology, Department of Aeronautical & Vehicle Engineering, Division of Lightweight Structures, Teknikringen 8, 100 44 Stockholm, Sweden
a r t i c l e
i n f o
Article history: Received 6 December 2012 Received in revised form 14 February 2013 Accepted 18 February 2013 Available online 27 February 2013 Keywords: High frequency mechanical impact (HFMI) Fatigue strength improvement High strength steels Structural hot spot stress Effective notch stress
a b s t r a c t Local fatigue assessment methods like the structural hot spot stress and effective notch stress methods as defined by the International Institute of Welding are widely used by design engineers and researchers to assess the fatigue strength of welded components. This paper provides a comprehensive evaluation of published data for welded joints which had been improved using high frequency mechanical impact (HFMI) treatment. All of the published data for HFMI-treated welds are presented in terms of nominal stress. The goal of the current paper is to establish local fatigue assessment procedures for improved fillet welds. In total, 160 published experimental results for longitudinal and cruciform welds subjected to R = 0.1 axial loading are evaluated. Local stress quantities for each joint were assessed based on the finite element analyses and reported nominal stress values. A correction procedure for yield strength that was previously verified for nominal stress-based fatigue assessment is also applied to the local stress methods studied in this paper. For both the structural hot spot stress and effective notch stress methods, sets of characteristic fatigue strength curves as functions of yield strength are proposed and verified. The structural hot spot stress method includes one set of fatigue strength curves for load-carrying welds and a second set for non-load carrying welds. The effective notch stress method includes a single set of curves for all welds. All of the design curves proposed in this study are conservative with respect to available fatigue test data. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction In 2007, after an extensive literature survey and an international round robin exercise, Commission XIII: Fatigue of Welded Components and Structures of the International Institute of Welding (IIW) completed a best-practice recommendation for implementing four common post-weld fatigue strength improvement methods for welded steel and aluminium structures [1]. The guideline includes procedures for applying treatment methods and quality assurance measures, and also provides recommendations for implementing these techniques in the fatigue design of structures. Two weld profile modification methods, burr-grinding and TIG remelting (i.e. TIG dressing), and two residual stress modification methods, hammer peening and needle peening, are covered by the guideline. In parallel to the development of this guideline, there has been an increasing number of publications dealing with high frequency mechanical impact treatment (HFMI) technologies. The innovation of locally modifying the residual stress state in welded components
⇑ Corresponding author. Tel.: +358 445 666 556. E-mail address: halid.yildirim@aalto.fi (H.C. Yildirim). 0142-1123/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijfatigue.2013.02.014
by the use of ultrasonic technology is widely attributed to Statnikov, a development scientist at the Sevmash Shipping Enterprise in Russia [2]. Subsequent fatigue studies were performed in cooperation with E.O. Paton Welding Institute in the Ukraine [3]. Additionally, further contributions by Feng and Graff [4], Prokopenko et al. [5] and Prokopenko and Lyatun [6] should also be highlighted for the development of ultrasonic technologies. Today, there are numerous HFMI peening tool manufacturers and service providers and the numbers are steadily increasing as the technique has proven to be reliable, effective and user-friendly. While details of the tools differ, the operating principle is identical: cylindrical indenters are accelerated against a component or structure with high frequency (>90 Hz). The impacted material is highly plastically-deformed, causing changes in the material microstructure and the local geometry, as well as the residual stress state in the region of impact. In comparison to hammer peening, the HFMI operation is more user-friendly and the spacing between alternate impacts on the work piece is very small, thus resulting in a finer surface finish. HFMI devices are known by the following names: ultrasonic impact treatment (UIT) [7], ultrasonic peening (UP) [8], ultrasonic peening treatment (UPT) [9,10], high frequency impact treatment (HiFiT) [11], pneumatic impact treatment (PIT) [12] and ultrasonic needle peening (UNP) [13,14].
58
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67
Nomenclature fy fy,o FAT
K m1 m2 Nf S DS t
q r
yield strength reference yield strength IIW fatigue class, i.e., the stress range in MPa corresponding to 95% survival probability at 2 106 cycles to failure (a discrete variable with 10–15% increase in stress between steps) stress concentration slope of the line for stress cycles above the knee point slope of the line for stress cycles below the knee point cycles to failure nominal stress nominal stress range plate thickness of the specimen radius stress
Yildirim and Marquis recently completed a study of all available experimental data on the fatigue strength of welded joints improved by HFMI [15]. Most of the 414 reported data points have been performed using constant amplitude R = 0.1 axial tension fatigue, but some data for other R-ratios, variable amplitude testing and bending fatigue are also reported. The axially-loaded HFMItreated joints used were longitudinal stiffeners, cruciform joints and butt joints. Bending loading was performed using T-joints. The studies considered a variety of different steel grades but no data for HFMI-treated aluminium welds was available. The study showed that an S–N slope m1 = 5 adequately described the data. This is in contrast to the slope m1 = 3 used, for example, in the IIW best practice guideline for welded structures improved by hammer peening or needle peening [1]. Welded specimens treated by HFMI methods also tended to have slightly greater fatigue strength than did specimens treated with traditional hammer peening. In order to assess the influence of steel yield strength on the observed fatigue improvement of HFMI-treated welds, Yildirim and Marquis [16] evaluated several proposed equations for considering material yield strength. Published data for axially-loaded HFMItreated welds subjected to constant amplitude R = 0.1 were considered. The steel yield strengths varied from 260 to 969 MPa and specimen thicknesses varied from 5 to 30 mm. A yield strength correction method was proposed and verified. The recommendation for design includes a five (5) fatigue class increase in strength for joints fabricated from fy = 355 MPa steel, with respect to the nominal fatigue class in the as-welded condition. One additional fatigue class increase in fatigue strength (about 12.5%) for every 200 MPa increase in static yield strength was proposed. The specific fatigue class increase is defined for N = 2 106 cycles and assumes an S–N slope m1 = 5 for HFMI-treated welds and m1 = 3 for welds in the as-welded state. A recently-completed round robin study of welded high strength steel joints treated using four different HFMI treatment technologies was promising with respect to the development of a future guideline [17]. Nominally-identical, longitudinal, non-load carrying attachments in S700 MC high strength steel, fy = 700 MPa, were manufactured at a single location, then randomly distributed to four HFMI equipment manufacturers for treatment. All HFMI-treated welds were subjected to identical variable amplitude fatigue loading on a single test machine. Experimental results indicated that all of the HFMI-improved welds from the four different HFMI equipment manufacturers satisfied the previously-proposed characteristic line, based on both the material yield strength and the specimen geometry.
rN
standard deviation in Log (Nf)
Subscripts K characteristic value corresponding to 95% survival probability at 2 106 cycles to failure (a continuous variable) f effective s hot spot stress i value for specimen i m mean value corresponding to 50% survival probability at 2 106 cycles to failure w notch stress
The aim of the current paper has been to develop appropriate guidelines for the fatigue assessment of HFMI-improved fillet welds based on local approaches, namely, the effective notch stress (ENS) approach and the structural hot spot stress (SHSS) approach. These are studied using the available constant amplitude fatigue test data for HFMI-improved welds subjected to stress ratio R = 0.1. Only axially-loaded test data from longitudinal and cruciform fillet welds are considered. Data are evaluated both with and without the previously-proposed correction for material yield strength [16].
2. Fatigue assessment of welded structures by local approaches A variety of local fatigue assessment procedures for welded structures has been developed. A comprehensive survey of these methods has been prepared by Radaj et al. [18]. Thus far, the IIW has developed and published detailed guidelines concerning two local fatigue design approaches for welded components: the SHSS method [19] and the ENS method [20]. In 2006, the IIW published fatigue design recommendations based on the use of the SHSS which include proposals for design curves expressed in terms of the hot-spot stress range [19]. In a welded plate structure, the structural stress at the hot spot includes all stress-increasing effects of a structure, with the exception of the non-linear peak stress occurring at the local notch, i.e. at the weld toe. Determination of the SHSS (excluding the non-linear peak stress) can be performed by extrapolation, choosing proper extrapolation distances from the weld toe. For plates with t P 5 mm, these distances vary from 0.4 t to 2.5 t, where t is the plate thickness. In the case of steel in the as-welded condition, two SHSS characteristic curves are proposed for as-welded fillet-welded joints. These are FAT 90 for load-carrying or FAT 100 for non-load carrying welds. This method is included in the existing IIW recommendations for improved welded joints [1]. For welds improved by hammer or needle peening, the appropriate SHSS characteristic curve for non-load carrying joints is FAT 125 for mild steel (fy < 355 MPa) and FAT 140 for higher strength steel (fy P 355 MPa) with an S–N slope of m1 = 3. For load-carrying joints, the respective characteristic curves are FAT 112 for mild steel and FAT 125 for higher strength steel. In 2008, the IIW approved a guideline concerning fatigue design of welded components based on the ENS approach to fatigue assessment [20]. In this method, the maximum principal stress or von Mises stress at the notch, e.g. weld toe or root, can be
59
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67
Table 1 Experimental R = 0.1 constant amplitude axial fatigue data for HFMI-treated longitudinal welds with stress concentration values obtained from finite element calculations based on structural and notch stresses.
a b
Ref.
Steel type
fy (MPa)
Treatment method
Plate thickness (mm)
Number of specimens in series
Ks
Kw (qf = 1 mm)
[30] [31] [31] [32] [33] [33] [33] [34] [34] [34] [35,36] [37]
S700 S690QL S690QL 16Mn S350 S700 S900 SS800 16Mn Q235B S355 S960
700b 786a 786a 390b 398a 780a 900a 700a 390a 267a 355b 960a
UP/ UIT UIT HiFiT UP/UPT UP/UPT UP/UPT TIG + UP UP/UPT UP/UPT UP/UPT UIT PIT
8 16 16 8 12 12 12 8 8 8 8 5
16 16 15 6 5 7 10 8 6 7 10 11
1.22 1.25 1.25 1.22 1.30 1.30 1.30 1.22 1.22 1.22 1.30 1.44
2.72 2.99 2.99 2.72 2.69 2.69 2.69 2.72 2.72 2.72 2.31 1.81
Measured fy. Nominal fy.
Table 2 Experimental R = 0.1 constant amplitude axial fatigue data for HFMI-treated cruciform welds with stress concentration values obtained from finite element calculations based on structural and notch stresses.
a b
Ref.
Steel type
fy (MPa)
Treatment method
Plate thickness (mm)
Number of specimens in series
Ks
Kw (qf = 1 mm)
[38] [38] [38] [38] [39] [39] [40] [41]
S355J2 S355J2 S460ML S460ML S355J2 S690QL AH36 350 W
398a 398a 504a 504a 477a 781a 392a 350b
UIT UIT UIT UIT PIT PIT UIT UIT
12 12 12 12 12 12 20 9.5
7 4 5 5 8 7 3 5
1.30 1.30 1.30 1.30 1.30 1.30 1.42 1.18
1.53 1.53 1.53 1.53 1.53 1.53 1.57 1.66
Measured fy. Nominal fy.
idealized by assuming a linear-elastic material behaviour using the finite element method. The actual weld profile at the toe or root that includes all variations of weld shapes is replaced and rounded by a fictitious notch radius in order to avoid arbitrary or infinite stress results. For welds having a plate thickness of over 5 mm, it is proposed that
qf ¼ q þ 1 mm
ð1Þ
where q is the actual radius of the weld toe and qf is the effective radius which is implemented to the finite element modelling. For a worst case scenario and for practical applications, the actual radius is usually assumed to be close to zero. Therefore, the ENS approach for the fatigue assessment of welded structures is reduced to qf = 1 mm at the weld toe or root. When the stress assessment method is based on the maximum principal stress and using qf = 1 mm, FAT 225 is normally considered for all types of as-welded specimens. For von Mises stress, FAT 200 is used. However, some recent studies have shown that with the notch stress approach for welded structures, the FAT 225 S–N line represents less than 95% survival probability, particularly for cruciform and butt welds [21–23]. 3. Analysis methods 3.1. Fatigue data In the current study, fatigue test data previously studied by Yildirim and Marquis were further evaluated [16]. Only test results obtained at R = 0.1 were considered, since a definitive relationship concerning the influence of stress ratio for HFMI-treated welds has not yet been finalized. The original data can be found in references listed in Tables 1 and 2.
3.2. Assessment of the structural hot spot stress For each of the specimen geometries considered, stress analysis procedures as described by Niemi et al. were used to evaluate the SHSS [19]. Finite element models of each specimen were modelled using second-order solid brick elements. Maximum element size close to the weld toe was limited to t/4, whereas it was limited to 1 t overall in the model for all analyses. Weld toe angle was idealized to 45° as recommended by Fricke [20]. For longitudinal welds, linear extrapolation perpendicular to the weld toe was considered using the evaluation points 0.4 t and 1.0 t [24]. In addition, a modified structural stress method as proposed by Poutiainen and Marquis was applied, in order to accurately capture the local effect of weld size and weld stress for cruciform joints [25]. Due to symmetry, quarter models were used for single-sided attachments and 1/8 models were used for double-sided attachments, see Fig. 1. A unit stress was applied to the ends of models in order to obtain longitudinal stresses at extrapolation points, 0.4 t and 1.0 t away from the weld toe, and a structural stress concentration factor could be determined for each specimen geometry evaluated by using Eq. (2). Quadratic extrapolation using the evaluation points 0.4 t, 0.9 t and 1.4 t was considered and found to give slightly greater values of Ks. However, all computations were based on the more conservative linear extrapolation results.
K s ¼ rs =r
ð2Þ
3.3. Assessment of the effective notch stresses With respect to the ENS method and HFMI, Eq. (1) would result in relatively large qf because q in the case of HFMI-treated welds can be from 1.5 to more than 7 mm. For example, Fig. 2 shows weld
60
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67
Fig. 1. Sample finite element models for (a) longitudinal and (b) cruciform welds.
Fig. 2. Measured HFMI weld toe radii and HFMI groove depth for several HFMI technologies (A, B, C and D are different HFMI technologies). Test specimens are from a recently-completed round robin study [17].
toe geometry measurements for the HFMI specimens treated by several technologies (A, B, C and D) reported in the round robin study [17]. In theory, the treated welds with larger radii should perform better in fatigue. However, there is a complex interaction between treatment parameters, toe radius, microstructure of the treated zone and residual stresses which is not fully understood. The extra benefit of modelling a weld toe notch with a radius equal to the actual radius of the HFMI-treated zone is therefore difficult to establish. Additionally, the exact weld toe geometry following HFMI has not been fully reported in all studies. In the current study, it has been decided to perform the notch stress analysis using an artificial notch radius qf = 1 mm, using procedures as described by Fricke [20]. The ENS concentration factors, Kw, at the weld toe and weld root were evaluated using finite element models having a weld toe radius qf = 1 mm for each specimen geometry. Second-order solid elements were considered and maximum element size close to the weld toe and/or root and overall in the model was limited to R/10 and 1 t in all of the analyses. Weld toe angle was idealized to 45° in the case of longitudinal and cruciform welds, as recommended by Fricke [20]. As with the SHSS analyses, symmetry was used and a unit stress was applied to the ends of models in order to obtain maximum principal stresses at the weld toe or root. The ENS concentration factor is defined with respect to the structural stress using the following equation:
K w ¼ rw =rs
ð3Þ
3.4. Statistical analysis of the data Hobbacher [24] has pointed out the difficulty of performing statistical analysis of data arising from numerous studies. This can be especially problematic for fatigue test data of welds improved by technologies like HFMI. Most fatigue test results are statistically evaluated using an assumed log-normal distribution of fatigue strength. For post-weld-improved data from numerous independent studies, all data may not exist as a single population. When evaluated as a single log-normally-distributed population, the addition of a small number of exceptionally strong test specimens will increase both the computed mean fatigue strength and variance, such that the resulting computed characteristic value is actually less than the computed characteristic strength without the exceptionally strong test specimens. In the current study, the three-parameter Weibull distribution was used to assess the statistical distribution of fatigue data [26]. See for example Schjive [27]. 4. Results Results of the stress analysis for SHSS and ENS, as well as other important details of the test specimens, are presented in Tables 1
61
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67 Table 3 Structural hot spot stress analyses of published data from Tables 1 and 2. Slope m1 = 5 was assumed.
a
Specimen type
Total data points
Longitudinal attachment Cruciform joint
116 44
Including fy correctiona
Not including fy correction
DSm (MPa)
DSk (MPa)
rN
DSm (MPa)
DSk (MPa)
rN
295 282
220 231
0.47 0.29
256 268
207 229
0.30 0.23
fy correction to reference yield strength fy,o = 355 MPa.
Table 4 Notch stress analyses of published data from Tables 1 and 2. Slope m1 = 5 and qf = 1 mm were assumed.
a
Specimen type
Total data points
Longitudinal attachment Cruciform joint All joints
116 44 160
Including fy correctiona
Not including fy correction
DSm (MPa)
DSk (MPa)
rN
DSm (MPa)
DSk (MPa)
rN
661 478 600
475 388 418
0.38 0.30 0.47
571 456 519
450 385 406
0.25 0.25 0.32
fy correction to reference yield strength fy,o = 355 MPa.
and 2 for longitudinal attachments and cruciform welds, respectively. Table 3 presents results of the Weibull three-parameter regression analysis for the SHSS method based on data from Tables 1 and 2. Table 4 presents results of the three-parameter regression analysis for the ENS method. In both tables, there are separate columns representing the regression analyses performed both with and without the previously mentioned material yield strength correction proposal [16]. The yield strength correction procedure requires the selection of a so-called reference yield strength. In the current study, fy,o = 355 MPa is selected. In all cases, the best fit regression mean lines and characteristic lines are based on a forced S–N slope m1 = 5.
Figs. 3 and 4 show the available fatigue data for HFMI-treated welds in terms of SHSS and ENS, respectively. These are based on the nominal stresses reported in the individual studies and the values of Kw and Ks computed in this study and shown in Tables 1 and 2. Separate graphs show the data with and without fy correction. Experimental data for each of the joint types are shown separately. The best fit regression mean lines and characteristic lines from Tables 3 and 4 are also shown. Based on the previous study by Yildirim and Marquis [16], a welded detail in fy = 355 MPa steel improved by HFMI is expected to have a five fatigue class improvement with respect to the same detail in the as-welded condition. If the same logic is applied to the SHSS method, the resulting S–N line for load-carrying details
Fig. 3. Available fatigue data for HFMI-treated welds presented in terms of SHSS both without (left) and with (right) fy correction. Ks values are shown in Tables 1 and 2 for (a) longitudinal non-load carrying attachments and (b) cruciform joints. fy correction is to a reference yield strength fy,o = 355 MPa.
62
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67
Fig. 4. Available fatigue data for HFMI-treated welds based on effective notch stress without (left) and with (right) fy correction presented for qf = 1 mm. Kw values are shown in Tables 1 and 2 for (a) longitudinal non-load carrying attachments, (b) cruciform joints and (c) both joint geometries. fy correction is to a reference yield strength fy,o = 355 MPa.
would be FAT 160 and FAT 180 for non-load carrying details. As previously mentioned, the specific fatigue class increase is defined for N = 2 106 cycles and assumes an S–N slope of m1 = 5 for HFMI-treated welds and m1 = 3 for welds in the as-welded state. Table 5 gives the existing IIW classes for SHSS approach for as-welded and improved joints and the proposed FAT classes for HFMI-treated joints as a function of fy. This is shown graphically in Fig. 5. The available SHSS test data for different ranges of fy for non-load carrying and load-carrying specimens are shown in Figs. 6 and 7. The proposed characteristic S–N lines are also shown. Table 6 gives the existing IIW characteristic FAT class for the ENS approach for as-welded joints and the respective proposed FAT classes for HFMI-treated welds. These are shown graphically in Fig. 8. In light of the afore-mentioned recent studies that have shown that the FAT 225 S–N line may not represent 95% survival probability for joints in the as-welded condition [21–23], it was decided that a fatigue class improvement of four (4) would be added for welded details in fy = 355 MPa steel. Classes for other fy are similarly adjusted. The ENS method S–N curve for an HFMI-im-
proved detail in fy = 355 MPa steel would be FAT 360. Available experimental data for HFMI-improved welds evaluated according to the ENS method and arranged according to fy are shown in
Table 5 Existing IIW FAT classes for SHSS approach for as-welded and improved joints and the proposed FAT classes for HFMI-treated joints as a function of fy. fy (MPa)
Load-carrying fillet welds
As-welded, m = 3 [24] All fy 90
Non-load carrying fillet welds 100
Improved by hammer or needle peening, m = 3 [1] fy 6 355 112 125 355 < fy 125 140 Improved by HFMI, m = 5 235 < fy 6 355 140 355 < fy 6 550 160 550 < fy 6 750 180 750 < fy 6 950 200 950 < fy 225
160 180 200 225 250
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67
63
respect to the same weld detail in the as-welded condition. Moreover, it can be further extended to represent a step-wise increase up to an eight (8) fatigue class improvement for fy > 950 MPa. This increase is represented in Fig. 5a as a solid line which indicates one additional fatigue class increase in fatigue strength (about 12.5%) for every 200 MPa increase in static yield strength. Fig. 5b represents the comparable proposal for load-carrying attachments. The proposal of one additional fatigue class increase in fatigue strength for every 200 MPa increase in static yield strength remains, but the characteristic fatigue strength for load-carrying joints is one (1) FAT class lower than those proposed for non-load carrying joints for all yield strengths. This is consistent with existing IIW guidelines for welds improved by hammer and needle peening which are shown as dashed lines in Fig. 5a and b. It is also consistent with IIW guidelines for welds in the as-welded condition. 5.3. Effective notch stress (ENS) approach method
Fig. 5. Proposed FAT values for SHSS approach as a function of fy for (a) for non-load carrying and (b) for load-carrying welds.
Fig. 9. Proposed characteristic curves from Table 6 are also given in this figure. 5. Discussion 5.1. The effects of yield strength correction method The use of fy correction results in decreased rN and lower DSk and DSm for each specimen type. This is shown in Figs. 3 and 4 and Tables 3 and 4. Lower values of DSk and DSm are to be expected, since these values represent the lines for HFMI-treated specimens at the reference yield strength fy,o = 355 MPa. Without the fy correction method, the curves are higher, since the lines represent a mix of test specimens with a wide variety of yield strengths (260 MPa < fy < 960 MPa), the vast majority of existing data referring to steels with fy > 355 MPa. 5.2. Structural hot spot stress (SHSS) method With respect to the SHSS method, proposed FAT values in Table 5 for both non-load and load-carrying specimens are consistent and conservative with respect to yield strength corrected characteristic values at fy,o = 355 MPa in Table 3. For example, the SHSS characteristic fatigue strength of a non-load carrying fillet weld (longitudinal attachment) based on statistical assessment of the experimental data and yield strength corrected to fy = 355 MPa was found to be 207 MPa, see Table 3. The corresponding proposed maximum possible FAT class for non-load carrying welds from steel with fy = 355 MPa is FAT 180. The consistency of these values indicates that the experimental results based on SHSS confirm the maximum FAT class increase of five (5) with
With respect to the ENS approach, proposed FAT values in Table 6 are consistent and conservative with respect to yield strength corrected characteristic values at fy,o = 355 MPa given in Table 4. For example, the ENS characteristic fatigue strength of all fillet welds, based on statistical assessment of the experimental data and yield strength corrected to fy = 355 MPa, was found to be 406 MPa, see Table 4. The corresponding proposed maximum possible FAT class in Table 6 for fillet welds from steel with fy = 355 MPa is FAT 360. The consistency of these values indicates that the experimental results based on ENS confirm the maximum FAT class increase of four (4) with respect to the same weld detail in the as-welded condition. It is interesting to note that in an earlier investigation on both as-welded and HFMI-improved specimens, the effective notch radius qf = 1 mm has been applied to axially-loaded specimens and a FAT class of 360 has been fitted for HFMI-treated joints with a slope of m1 = 5 [28]. This study did not make any distinction with respect to yield strength. Instead, a single FAT class was suggested for all steel grades. This value is identical to the S–N line for fy = 355 MPa in the current study. 5.4. FAT proposals versus fy corrected fatigue data For both local approaches, there are several data points below the calculated characteristic lines in Figs. 3 and 4. This is expected since the characteristic lines which were derived using Weibull distribution are computed to represent 95% survival probability of the fatigue population. In the case of the ENS approach, for example, Fig. 4c shows the joint results for both specimen types. A survival probability of 95% would mean that approximately eight data points out of 160 would fall below the computed characteristic FAT line (solid line). In total, six (6) points are below the line and several others lie just at or above the line. Experimental data represented as SHSS for non-load carrying and load-carrying specimens are shown in Figs. 6 and 7, respectively. Data are grouped according to fy of the base material and are shown together with the respective proposed FAT class S–N curves. With the exception of only one data point that appears in Fig. 6c, the proposed S–N curves are conservative with respect to the experimental results. Similarly, Fig. 9 shows the experimental data represented as ENS and grouped according to fy, the proposed characteristic S–N lines from Table 6 for HFMI-improved welds and the IIW characteristic curve for as-welded joints. No points in Fig. 9 fall below the proposed S–N lines. Thus, the target survival probability for the characteristic lines is achieved considering that FAT classes represent discrete steps. For both local assessment
64
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67
Fig. 6. Experimental data for non-load carrying HFMI-treated welds based on SHSS. Proposed characteristic curves from Table 5 are also shown for: (a) 235 < fy 6 355, (b) 355 < fy 6 550, (c) 550 < fy 6 750, (d) 750 < fy 6 950 and (e) 950 < fy.
Fig. 7. Experimental data for load-carrying HFMI-treated welds (cruciform joints) based on SHSS. Proposed characteristic curves from Table 5 are also shown for: (a) 355 < fy 6 550 and (b) 550 < fy 6 750.
methods, the use of yield strength correction representing one fatigue class (approximately 12.5%) increase in strength for every 200 MPa increase in fy has been verified.
Dashed lines in Figs. 6 and 7 represent the existing IIW characteristic curves for joints improved by hammer or needle peening. It is easy to see that the proposed S–N curves for HFMI-improved
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67 Table 6 Existing IIW characteristic curve based on the effective notch stress (ENS) approach for as-welded joints and proposed characteristic curves based on the ENS approach for HFMI-improved joints as a function of fy. fy (MPa)
a
Effective notch stress characteristic curve modelled using qf = 1 mm
All fy
As-welded, m1 = 3 [20] 225a
Improved by HFMI, m1 = 5 235 < fy 6 355 355 < fy 6 550 550 < fy 6 750 750 < fy 6 950 950 < fy
320 360 400 450 500
Some studies suggest that FAT 200 is a better fit for the experimental data.
65
which were assessed based on nominal stress [16]. Those cautions are also valid in the case of local stress approaches. For design cases where R > 0.1, the proposed FAT class may need to be reduced. This topic is beyond the scope of this document, but proposals for R > 0.1 constant amplitude loading and variable amplitude loading have been developed by Marquis et al. [29]. In literature, the benefits of HFMI treatment technologies are considered to be derived from the introduction of beneficial compressive residual stresses near the weld toe, as well as the achievement of a smooth transition from parent material to weld metal via the establishment of a defined weld groove shape. Since this study is based on available experimental test results, all features which contribute to increased fatigue strength have already been included. With regard to the ENS method, it is clear from Fig. 2 that various HFMI technologies produce different toe radii and depths. Based on the available experimental evidence, it is not possible to isolate a single factor which contributes to the added fatigue strength, e.g., the effect of the reduced stress concentration at the weld toe. Instead of measuring each HFMI weld profile and applying distinct radii for each application, the use of qf = 1 mm even for HFMI-improved weld models has been considered to be a more practical and easier-to-implement solution. End users who regularly resort to the ENS approach frequently have automatic meshing routines which can then be used for an entire structure, including both HFMI-treated welds and non-treated welds.
6. Conclusions
Fig. 8. Proposed FAT values for ENS approach as a function of fy.
welds follow the data better than the lines for hammer or needle peening. The proposed HFMI lines allow significantly more applied stress in the high cycle region as compared to the lines for hammer or needle peening. In the low cycle region, however, the proposals in this study can result in lower allowable stresses, especially for lower strength materials. For the ENS approach, characteristic curves for improved joints have not been previously defined, thus the dashed lines in Fig. 9 show the characteristic S–N lines for joints in the as-welded condition. As can be seen in Fig. 9, there is some region of the S–N curve for which the HFMI-improved line actually falls below the line for as-welded joints. For fy < 355 MPa steels, the intersection occurs at about N = 200,000. For 355 < fy 6 550 and 550 < fy 6 750 steels, this occurs at N = 60,000 cycles and N = 30,000 cycles, respectively. Similar observations based on the SHSS can be made from Figs. 6 and 7. Figs. 6d and e, and 9d and e represent experimental data for high strength steels (fy > 750 MPa), with the stress represented by SHSS or ENS. In all cases, the experimental data lie above the proposed characteristic S–N curve. However, the data are only just barely conservative with respect to the proposed S–N line. These should be confirmed by additional tests.
5.5. Applicability and validity The data in this study consisted of test results obtained from a stress ratio R = 0.1 and 1 104 6 Nf < 1 107 cycles. All of the S–N curves for HFMI proposed in this document are assumed to have slopes of m1 = 5 in the region of 1 104 6 N < 1 107 cycles and m2 = 9 for 1 107 6 N. This represents the more general design case of variable amplitude loading. Special caution about R-ratios and variable amplitude was previously advised for HFMI welds
This paper provides a comprehensive evaluation of published data for high frequency mechanical impact (HFMI)-treated welds subjected to R = 0.1 constant amplitude loading. In total, 160 experimental fatigue test results for longitudinal and cruciform welds subjected to axial loading have been evaluated, based on established local approach concepts for welded joints. The structural hot spot stress (SHSS) and the effective notch stress (ENS) methods have been considered. In each case, stress analysis was performed in accordance with guidelines developed by the International Institute of Welding. For each of the weld geometries reported in literature, the finite element method was used to determine the respective stress concentration factors for SHSS and ENS. A previously-developed fy correction method for nominal stress was also implemented for local fatigue strength approaches. Characteristic values for SHSS and ENS have been calculated using the fy correction method. According to the findings, the following conclusions can be drawn: For both local assessment methods, the use of fy correction representing one fatigue class (approximately 12.5%) increase in strength for every 200 MPa increase in fy has been verified. Fatigue classes for the SHSS and the ENS which represent the fatigue strength of HFMI-improved joints at 2 106 cycles and assume an S–N slope of m1 = 5 have been proposed and verified with the available corrected fatigue data. For the SHSS method, a five (5) fatigue class improvement with respect to the same weld detail in the as-welded condition has been proposed and verified for both non-load and load-carrying welded joints. For the ENS approach, a four (4) fatigue class improvement has been proposed and verified. The proposed characteristic curves are found to be conservative with respect to more than 95% of the available fatigue test data. Only limited experimental data for high strength steels (fy > 750 MPa) are reported. The proposed characteristic curves
66
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67
Fig. 9. Experimental data for HFMI-treated welds based on ENS. Proposed characteristic curves from Table 6 are also shown for (a) 235 < fy 6 355, (b) 355 < fy 6 550, (c) 550 < fy 6 750, (d) 750 < fy 6 950 and (e) 950 < fy.
are conservative with respect to this data, but more studies are encouraged. Studies concerning R-ratios other than 0.1 and variable amplitude studies are also recommended.
Acknowledgements Support for this work has been partially provided by the LIGHT research programme of the Finnish Metals and Engineering Competence Cluster (FIMECC), the Finnish Funding Agency for Technology and Innovation (TEKES), the Research Foundation of Helsinki University of Technology, and the EU Research Fund for Coal and Steel under grant agreement RFSR-CT-2010-00032 ‘‘Improving the fatigue life of high strength steel welded structures by post weld treatments and specific filler material’’.
References [1] Haagensen PJ, Maddox SJ. IIW Recommendations on methods for improving the fatigue lives of welded joints. Cambridge/Paris: Woodhead Publishing Ltd./ International Institute of Welding; 2013. [2] Statnikov E, Shevtsov U, Kulikov V. Ultrasonic impact tool for welds strengthening and reduction of residual stresses, Publications Scientific Works Metallurgy, SEVMASH, USSR, No. 92; 1977. p. 107–12 [in Russian].
[3] Statnikov E, Trufyakov V, Mikheev P, Kudryavtsev Y. Specification for weld toe improvement by ultrasonic impact treatment. Paris: International Institute of Welding; 1996 [IIW Document XIII-1617-96]. [4] Feng C, Graff K. Impact of spherical tool against a sonic transmission line. J Acoust Soc Am 1972;52(1):254–62. [5] Polotskiy I, Nedoseka A, Prokopenko G, Trefilov V, Firstov S. Relieving of residual welding stresses by ultrasonic treatment. Autom Weld 1974;5:74–5 [in Russian]. [6] Prokopenko G, Lyatun T. Investigation of parameters of surface hardening with the help of ultrasound, Physics and chemistry of materials treatment. J Sound Vib 1997;3:91–5 [in Russian]. [7] Applied Ultrasonics.
H.C. Yildirim et al. / International Journal of Fatigue 52 (2013) 57–67 [18] Radaj D, Sonsino C, Fricke W. Fatigue assessment of welded joints by local approaches. Cambridge: Woodhead Publishing Ltd.; 2006. [19] Niemi E, Fricke W, Maddox S. Fatigue analysis of welded joints – designer’s guide to the structural hot-spot stress approach. Cambridge: Woodhead; 2006. [20] Fricke W. IIW recommendations for the fatigue assessment of welded structures by notch stress analysis. Cambridge: Woodhead Publishing Ltd.; 2012. [21] Kranz B, Sonsino C. Verification of the FAT values for the application of the notch stress concept with reference radii rref = 1.00 and rref = 0.05. Welding in the World 2010;54(7/8): R218–24. [22] Pedersen M, Mouritsen O, Hansen M, Andersen J, Wenderby J. Re-analysis of fatigue data for welded joints using the notch stress approach. Int J Fatigue 2010;32:1620–6. [23] Barsoum Z, Jonsson B. Fatigue assessment and LEFM analysis of cruciform joints fabricated with different welding processes. Weld World 2008;52(7/ 8):93–105. [24] A Hobbacher, IIW recommendations for fatigue design of welded joints and components, WRC bulletin 520. New York: The Welding Research Council; 2009. [25] Poutiainen I, Marquis G. A fatigue assessment method based on weld stress. Int J Fatigue 2006;28:1037–46. [26] Weibull W. A statistical distribution function of wide applicability. J Appl Mech 1951;18:293–7. [27] Schijve J. A normal distribution or a Weibull distribution for fatigue lives. Report LR-689 Delft University of Technology; 1992. [28] Pedersen M, Mouritsen O, Hansen M, Andersen J. Experience with the notch stress approach for fatigue assessment of welded joints. In: Proceedings of Swedish conference on light weight optimized welded structures Borlänge, Sweden; 2010. [29] Marquis G, Mikkola E, Yildirim H, Barsoum Z. Fatigue strength improvement of steel structures by HFMI: proposed fatigue assessment guidelines. Paris: International Institute of Welding; 2013 [IIW Document XIII-2452-13]. [30] Haagensen PJ, Alnes Ø, Progress report on IIW WG2 round robin fatigue testing program on 700 MPa and 350 MPa YS Steels. Paris: International Institute of Welding; 2005 [IIW Document XIII-2081-05]. [31] Weich I. Fatigue behaviour of mechanical post weld treated welds depending on the edge layer condition (Ermüdungsverhalten mechanisch
[32]
[33]
[34]
[35]
[36] [37]
[38]
[39]
[40]
[41]
67
nachbehandelter Schweißverbindungen in Abhängigkeit des Randschichtzustands). Doctorate thesis Technischen Universität CaroloWilhelmina; 2008. Huo L, Wang D, Zhang Y. Investigation of the fatigue behaviour of the welded joints treated by TIG dressing and ultrasonic peening under variableamplitude load. Int J Fatigue 2005;27:95–101. Martinez L, Blom AF, Trogen H, Dahle T. Fatigue behavior of steels with strength levels between 350 MPa and 900 MPa the influence of post weld treatment under spectrum loading. In: Blom A, editor. Proceedings of the North European engineering and science conference (NESCO) welded highstrength steel structures, Stockholm; 1997. Wang T, Wang D, Huo L, Zhang Y. Discussion on fatigue design of welded joints enhanced by ultrasonic peening treatment (UPT). Int J Fatigue 2009;31:644–50. Lihavainen V, Marquis G, Statnikov E. Fatigue strength of a longitudinal attachment improved by ultrasonic impact treatment. Weld World 2004;48(5/ 6). Lihavainen V, Marquis G. Fatigue life estimation of ultrasonic impact treated welds using a local strain approach. Steel Res Int 2006;77(12):896–900. Leitner M, Stoschka M, Schörghuber M, Eichlseder W. Fatigue behavior of highstrength steels using an optimized welding process and high frequency peening technology. In: IIW international conference, Chennai; 2011. Kuhlmann U, Dürr A, Bergmann J, Thumser R. Fatigue strength improvement for welded high strength steel connections due to the application of post-weld treatment methods (Effizienter Stahlbau aus höherfesten Stählen unter Ermüdungsbeanspruchung). Forschungsvorhaben P620 FOSTA, Düsseldorf: Verlag und Vertriebsgesellschaft GmbH; 2006. Kuhlmann U, Gunther H. Experimentelle untersuchungen zur ermüdungssteigernden wirkung des PIT-verfahrens. Versuchsbericht: Universität Stuttgart, Institut für Konstruktion und Entwurf, September; 2009. Okawa T, Shimanuki H, Funatsu Y, Nose T, Sumi Y. Effect of preload and stress ratio on fatigue strength of welded joints improved by ultrasonic impact treatment. Welding in the world 2013;(2):235–41. Yekta R. Walbridge S. Acceptance criteria for ultrasonic impact treatment (UIT), Ontario Ministry of Transportation, Report HIIFP-110, Ontario (Canada): St. Catherines; 2012.