Fatigue assessment of welded and high frequency mechanical impact (HFMI) treated joints by master notch stress approach

Accepted Manuscript Fatigue assessment of welded and high frequency mechanical impact (HFMI) treated joints by master notch stress approach Martin Leitner, Michael Stoschka, Markus Ottersböck PII: DOI: Reference:

S0142-1123(17)30040-3 http://dx.doi.org/10.1016/j.ijfatigue.2017.01.032 JIJF 4222

To appear in:

International Journal of Fatigue

Received Date: Revised Date: Accepted Date:

15 September 2016 21 January 2017 23 January 2017

Please cite this article as: Leitner, M., Stoschka, M., Ottersböck, M., Fatigue assessment of welded and high frequency mechanical impact (HFMI) treated joints by master notch stress approach, International Journal of Fatigue (2017), doi: http://dx.doi.org/10.1016/j.ijfatigue.2017.01.032

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Title: Fatigue assessment of welded and high frequency mechanical impact (HFMI) treated joints by master notch stress approach Authors: Martin Leitner, Michael Stoschka, Markus Ottersböck Affiliation: Montanuniversität Leoben, Chair of Mechanical Engineering, Austria Abstract High frequency mechanical impact (HFMI) treatment is a reliable and utmost effective method for post-weld fatigue strength improvement of steel joints, especially in case of high-strength steel applications. In 2014, the HFMI master notch stress approach was firstly introduced as an alternative design concept. It features an engineering-feasible method to assess the notch fatigue strength of HFMI-treated joints based on weld toe notch stress concentration, base material yield strength and load stress ratio. This paper presents an essential update of the HFMI master notch stress approach by facilitating the notch factor KW, obtained as the ratio of effective notch stress k to structural stress s. This enables a thorough fatigue assessment of welded structures without the need of a nominal cross-section definition. To proof the applicability, a comprehensive validation of the HFMI master notch stress approach incorporating over 230 additional steel joint specimen results covering both constant and variable amplitude tests is conducted. The constant amplitude study reveals that the fatigue strength of the HFMI master notch stress approach, utilizing the notch factor KW, is well applicable for material strengths up to ultra highstrength steels with a nominal yield limit of 1,300 MPa. In addition, the notch stress based service strength evaluation of variable amplitude loaded HFMI-treated high-strength steel joints considering a specified damage sum of D=0.3 according to Sonsino can be also well utilized for HFMI-treated joints. Keywords: Welded joints, High frequency mechanical impact (HFMI) treatment, Fatigue assessment, Notch stress approach, Service strength.

Nomenclature D fy fy,0 FAT k1 k2 kk kR ky Kn KW N rf rr R s t TS  k,B k n S 



Specified damage sum Yield strength Reference yield strength Fatigue class at two million load-cycles Slope of the S/N-curve above the knee point Slope of the S/N-curve below the knee point Slope magnification factor of the HFMI master notch stress model Stress ratio factor of the HFMI master notch stress model Strength magnification factor of the HFMI master notch stress model Stress concentration factor of a weld defined as ratio of k/n Notch factor of a weld defined as ratio of k/S Number of load-cycles to failure Fictitious radius Real radius Stress ratio defined as ratio of min/max Multiaxiality constant Plate thickness Stress-based scatter index Micro-support distance Notch stress base point of the HFMI master notch stress model Effective notch stress Nominal stress Structural stress Standard deviation

1

Introduction

Local fatigue assessment methods such as the structural and the notch stress approach are nowadays widely used in industrial applications to assess the service strength of welded joints [1-4]. They support the fatigue strength evaluation of complexly shaped, welded assemblies by a single reference S/N-curve, thus enabling a rapid lightweight design cycle of welded structures [5-8]. A minor beneficial effect of high-strength steel in welded structures is only obtained if the weld quality is increased, i.e. by ensuring a smooth weld toe transition with shallow notches in case of fully penetrated joints [9, 10]. Generally, the fatigue strength of fully-penetrated welded joints can only significantly enhanced if posttreatment methods such as HFMI (high-frequency-mechanical-impact) are applied [11]. This features an improved lightweight design especially for welded structures made of high-strength steels [12-14]. But for HFMI-treated steel joints, the applicable stress-based design concepts are a bit more complex than the originally introduced local design concepts [1]. The HFMI-process affects the local weld toe geometry towards a shallower a notch, hardens the material locally and incorporates compressive residual stresses in the treated region. Thus, the beneficial gain in fatigue strength is strongly coupled with the material strength and the structural type of evaluated joint. An overview of common design concepts to assess the fatigue strength of welded structures is provided in [15, 16]. For structures exhibiting a comparably simple geometry, such as beams, the nominal stress approach is most feasible. In case of the nominal stress approach, the allowable fatigue strength as FATclass depends only on the structural detail of the joint. The nominal stress within the base plate acts as fatigue load. However, for more complexly shaped components a computation of nominal stresses is not always performable. Therefore, a fatigue assessment on the basis of the structural stress is more applicable. Besides the structural stress concept according to Haibach, which takes the maximum principal stress at a distance of about 2 mm to the weld toe into account, the hot-spot stress is one widespread and industrial feasible approach, see [2]. But the structural stress concept has also its limitations especially for hidden details, e.g. weld roots. In such cases, the effective notch stress approach featuring the fictitious notch radius of rf=1.0 mm is best applicable. As shown in [17] for aluminium joints, and also validated for steel joints, the theoretical background of this concept bases on Neuber’s micro-support theory [18] assuming

rf  rr   *  s

(1)

Herein, rf is the fictitious notch radius, rr the real radius, * the micro-support distance, and s the multiaxiality constant. Based on experimental studies in [18] it is recommended to use *=0.4 mm and s=2.5 for mild structural steels. For welded joints the worst case represents a sharp crack, which equals to a real radius of rr=0 mm, leading to a fatigue effective reference radius of rf=1.0 mm. The effective notch stress assessment utilizes a fatigue class of FAT225 as principal stress design basis [1]. This notch stress approach is also extended and verified for the fatigue assessment of magnesium joints, which are commonly used in automotive components, see [19]. In addition, a suggestion for mean-stress consideration is presented in [20]. For HFMI post-treated joints, the well-known effective notch stress approach is not directly applicable without further modifications. A recently published guideline [21] defines allowable stress ranges for HFMI posttreated steel welds in dependency of base material grade and load stress ratio. The therein given effective notch stress ranges depend both on the material and joint type and are utilized as discretised FAT-classes, ranging from FAT320 to FAT500. The stepping scheme equates as a geometric series similarly to the nominal stress approach. Additionally, for seams with a quite low stress concentration factor, such as butt joints, a nominal stress limit is given up to FAT180 for post-treated welds in the guideline. An alternative effective notch stress fatigue assessment tool for HFMI-treated welds was firstly introduced in [22]. It features a continuous assessment of fatigue strength for HFMI-treated joints without the need of discretised material classes. An update of this approach including thin-walled, high-strength steel joints is given in [23]. This HFMI master notch stress approach bases on the maximum principle notch stress concentration factor Kn, which is defined as the ratio of the effective notch stress k, by featuring the recommended one millimetre effective weld toe radius, to the nominal stress n in the base plate of the specimens, see [24]. However, it is often difficult to evaluate the notch stress concentration factor in real applications, because, as aforementioned, the nominal stresses are not easily defined for complex weld structures with varying cross sections. Hence, this paper contains an essential upgrading of the HFMI master notch stress approach additionally featuring the notch factor KW instead of the stress concentration factor Kn. The working principle of the extended HFMI master notch stress approach maintains basically unchanged, but an extended validation to constant and variable loaded steel specimens is subsequently given.

2

Methods

This contribution addresses the following topics regarding the application of the HFMI master notch stress approach, as introduced in [22]: 1. Enhance applicability of the method by use of the notch factor KW, see procedure in chapter 3 The notch factor KW of a weld is defined as the ratio of the effective notch stress k to the structural stress s leading to KW=k/s [25]. This notch factor corrects the notch stress concentration in welded joints if mild notches have to be accessed. A lower limit value of KW=1.6 is recommended for the notch stress approach of welded joints to ensure a fatigue class of FAT225 based on maximum principle stress evaluation. Besides, in [24] lower limit values for the notch stress concentration Kn,min are provided depending on the applied base material yield strength. However, the application of a comparably lower value of Kn,min=1.6 is conservatively well applicable as validated in [22] for shallow notched butt joints applying the HFMI master notch stress approach. Summarized, the use of KW instead of Kn enables an improved applicability of the method to engineering tasks as the need of nominal stress evaluation is no longer required. 2. Validate the HFMI master notch stress approach with independent datasets focussing on high stress ratios and material grades up to ultra-high-strength steel joints, compare to section 4.1 A quite huge amount of additional datasets basing on recently conducted work validates the introduced notch stress fatigue assessment method for HFMI post-treated steel joints. The dataset covers material grades up to S1300. The stress ratio ranges from alternating to tumescent level and it incorporates tension and bending load cases. 3. Proof of applicability as service strength design concept for HFMI-treated welded joints, see section 4.2 For service loads conducted by variable amplitude testing it is recommended to use a damage sum lower than one for conservative design of welded joints [26-28]. Beside the damage sum, the material’s ductility and deformation mode also affects the endurable number of load-cycles [29]. Recent investigations deduced an applicable damage sum of about one-third for variable-amplitudeloaded welded joints without post-treatment [30-32]. Previously conducted service block load investigations lead to a conservatively applicable damage sum for high-cycle service strength applications for HFMI post-treated high-strength steel joints [33]. Hence, focus is laid on variable amplitude test data to deduce the applicable damage sum within proper statistical bounds.

3

HFMI master notch stress approach

The concept of unifying HFMI-treated, notch stress based, mainly constant amplitude fatigue test results into a master S/N-curve was firstly introduced in [22]. A brief summary of the key steps during the development of the HFMI master notch stress approach is depicted in an abbreviated manner.

3.1

Basic principle

The endurable notch stress range k of HFMI-treated steel joints is based on a single reference HFMI master notch stress curve. This master S/N-curve is subsequently transformed by factors taking yield strength, stress ratio and stress concentration into account. The latter ones vary for each structural weld detail dependent on the joint type, wall thickness and load case. The underlying notch stress k is evaluated with an effective radius of one millimeter enabling the evaluation of the notch stress concentration factor Kn=k/n by a relation to the nominal stress n in the cross-section of the base plate. Beside, the notch factor KW=k/s can be applied instead of the stress concentration factor Kn, as discussed in the previous chapter. Therefore, the structural hot-spot stress s can be evaluated by different methods, see [34].

Fig. 1: Basic scheme of HFMI master notch stress model (according to [22]) The working principle to obtain a local notch stress S/N-curve for HFMI-treated joints is shown in Fig. 1. The HFMI master notch stress curve, plotted as solid black line, acts as reference S/N-curve for each fatigue assessment case. At first, the base point k,B is influenced only by the material strength fy. It should be noted that the material certificates yield strength value can be used instead of a discretised material class, for example S355 to S550, as suggested in [13, 35]. The base material strength is considered by a strength magnification factor ky, firstly introduced in [13], whereby an exponent of =0.277 is well applicable for the yield strength correction after HFMI treatment featuring a reference yield strength of fy,0=355 MPa. At second, the inverse slope k1 in the finite life region is affected both by material grade and stress concentration or notch factor. The evaluated slope is calculated from the initial slope value of the reference curve kref and multiplied by a unique slope magnification kk. The course of this magnification factor is plotted in Fig. 2. Thus, the inverse slope ranges from kmin = 4 up to kmax=7.5. This matches quite well to the recommended slope of k1=5 evaluated in the HFMI Round-Robin test series [12]. At third, the finite life region is limited up to five million cycles. As the presented approach has to be also applicable for variable loadings, the high-cycle fatigue region facilitates a second shallower inverse slope value of k2=2.k-1=9 according the Palmgren-Miner rule modified by Haibach [36], which is recommended in [21] for service load design too. This strategy is also applied for constant amplitude loading of HFMItreated joints, which is knowingly more conservative and contrary to [37] suggesting for as-welded steel joints a second inverse slope of k2=22 in the high-cycle fatigue region. This deviation can be reasoned that the presented HFMI master notch stress model should be able to act as conservative design guideline both for constant and variable loading, and the necessary amount of engineering feasible design factors have to be minimized. In addition, as the stability of introduced compressive residual stresses may vary at testing, e.g. due to exceedance of the local yield limit in the notch or environmental influences, a slope of about nine is conservatively more applicable especially if high- and ultra-high-strength steels are evaluated.

Fig. 2: Representation of slope magnification factor kk basing on the stress concentration factor Kn or notch factor KW (according to [22])

Finally, the effect of load ratio is taken into account by an additional stress ratio factor kR. It limits the maximum constant amplitude stress range for HFMI-treated joints. This is in alignment with the suggestions given in [38, 39].

k R  1.0345  0.345  R

 R  0.1

k R  1.075  0.75  R

 0.1  R  0.5

k R  0.7

 R  0.5

(2)

The underlying HFMI notch stress master S/N-curve was evaluated as FAT225 in [22]. A re-evaluation including additional thin-walled datasets, depicted in [23], proposed a more conservative fatigue strength stress range of FAT200. This updated reference HFMI notch stress master curve is shown in Fig. 3. In total, over three-hundred HFMI-treated specimen data points are included in this evaluation study incorporating different structural details; such as butt joints, transversal stiffeners, cruciform joints, and longitudinal attachments, base material yield strengths ranging from 355 MPa to 960 MPa, and base plate thicknesses from 5 mm to 30 mm. Fatigue testing is performed at stress ratios between 0.1 to 0.5 under uniaxial loading condition.

Fig. 3: Reference HFMI notch stress master S/N-curve The utilization of the HFMI notch stress model is further on exemplified for a stiffener possessing different uniaxial load directions. Hence, the depicted notch stress method is not limited within a certain load angle as the maximum principal stress course, applied both for notch and structural stress analysis, is always evaluated perpendicular to the weld seam path.

3.2

Application of model

This section shows the application of the HFMI notch stress master S/N-curve model for three different stiffener types. The specimens are made of mild construction steel S355, exhibit a sheet thickness of 6 mm, stiffener length of 25 mm, throat thickness of about 4 mm and nominal cross section of 50 mm in the testing area. The stiffeners are welded in three different vectors onto the base plate; therefore, the following designations are assigned:  Longitudinal stiffener (LS) - Stiffener is welded in the direction of the loading  Skewed stiffener (SS) - Stiffener is welded at an angle of 45° to the loading direction  Transversal stiffener (TS) - Stiffener is welded perpendicular to the loading vector HFMI-treatment is performed in accordance to the recently published quality guideline [11] utilizing the pneumatic impact treatment (PIT) technology [40] and applying a pin tip radius of 2 mm. In order to evaluate the notch stresses numerically, finite element models are set-up incorporating a reference radius of one millimetre at the weld toe. As the fatigue tests revealed that no crack initiated at the partial penetrated weld root, this section was not evaluated in the effective notch stress analysis. Mesh density and element type are defined in accordance to [41] utilizing four elements for a forty-five degree weld toe angle and quadratic shape functions with reduced integration scheme, see Fig. 4. The numerical effects of mesh density and element type are comprehensively studied in [42] revealing that the given recommendation is generally well suitable for the effective notch stress analysis of welded joints.

Fig. 4: Detail of mesh at weld toe region for longitudinal stiffener specimen (label LS) To reduce the amount of numerical computation effort, the longitudinal and transversal stiffeners are modelled quarter-symmetrically, only the skewed stiffener specimen is considered as full model. Fig. 5 pictures the notch stress evaluation of the longitudinal, skewed and transversal stiffener. The longitudinal stiffener exhibits a notch stress concentration factor of Kn=2.52, whereat the skewed stiffener features a slightly increased value of Kn=2.63. Tab. 1 depicts both the stress concentration factor Kn and the notch factor KW, whereby the structural stress s is evaluated on the basis of the hot-spot method presented in [2] applying a nominal reference load of 1 MPa in the adjacent cross-section. The three evaluated samples exhibit similar tendencies of stress concentration factor and notch factor, but the values are not identical because of slightly varying structural hot-spot stresses.

Fig. 5: Longitudinal (LS), skewed (SS) and transversal stiffener (TS) The evaluated Kn values as notch stress concentration factors indicate that the skewed and longitudinal stiffener specimens possess a significant higher stress concentration at the weld toe compared to the transversal stiffener geometry. Kn [-] KW [-] Identifier s [MPa] 2.52 1.34 1.88 Longitudinal stiffener (LS) 2.63 1.33 1.98 Skewed stiffener (SS) 2.03 1.14 1.78 Transversal stiffener (TS) Tab. 1: Numerically computed factors Kn and KW of the stiffener samples Additionally, the KW-factors, which incorporate the structural hot-spot stresses s, lead to a comparable trend. As already mentioned these factors are not depended on the nominal cross section and are therefore easily applicable to complexly shaped weld structures. Focus of the paper is laid on the application and validation of the HFMI master notch stress approach, wherefore the previously introduced influence factors; namely ky, kR, and kk, need to be calculated. As the yield strength with fy=355 MPa and the stress ratio with R=0.1 are equal to the initial settings of the HFMI notch stress master model, both factors are equal one, i.e. ky=1 and kR=1. On the contrary, the effective notch stress concentration factor Kn and notch factor KW are varying for the investigated weld joints. This leads to slightly differing slope magnification factors as shown in Tab. 2. In this study, both Kn and KW are used as input parameter for the evaluation of kk according to the course plotted in Fig. 2. The tendencies of Kn and KW are basically equal, but the ratio of these two parameters is not constant as the structural hotspot stress changes for each evaluated structural weld detail. kk [-] (based on Kn) (based on KW) Longitudinal stiffener (LS) 1.63 1.32 Skewed stiffener (SS) 1.67 1.39 Transversal stiffener (TS) 1.42 1.22 Tab. 2: Evaluated slope magnification factors kk for the stiffener samples Identifier

Comparing the investigated specimen types, namely longitudinal and skewed stiffener, to the transversal stiffener, the results of magnification factor kk indicate the lowest values for the latter one. Further on, this leads to a slightly shallower inverse slope of the estimated HFMI notch stress curve for the transversal stiffener. This is in alignment to the fact that mild notched geometrical details are less beneficial to HFMItreatment than sharp notched details, which is also investigated for the butt weld test data involved in [24]. These numerically estimated fatigue tendencies were proven by conducted constant amplitude fatigue tests, whereby the transversal stiffener showed a higher fatigue resistance compared to the other ones. Although the number of about three to five specimens is strongly limited within these test series, the results can be used to match the conducted experiments to the proposed number of fatigue cycles utilizing the HFMI notch stress master S/N-curve. Based on the evaluated influence factors, the HFMI master notch stress approach is applied and the calculated number of load-cycles by the model is compared to the experimentally assessed values.

Fig. 6: Calculated versus experimental fatigue life results for investigated stiffener joints evaluating kk on the basis of Kn At first, the estimated fatigue life using the notch stress concentration factor Kn to evaluate kk are depicted in Fig. 6. It is shown that all data points are conservative; implying that the calculated number of loadcycles Ncal undermatches the experimental values Nexp. At an experimental number of two million cycles Nexp=2.106, the evaluated upper scatter band reveals a calculated value of Ncal=1.16.106 load-cycles, leading to a good agreement and a conservative fatigue assessment.

Fig. 7: Calculated versus experimental fatigue life results for investigated stiffener joints evaluating kk on the basis of KW At second, the notch factor Kw is used to evaluate the slope magnification factor kk. Fig. 7 pictures the . 6 results, whereat again, all calculated data points are conservative. At Nexp=2 10 , the evaluated upper scatter . 6 band reveals a calculated value of Ncal=1.27 10 load-cycles. This features again a safe design, but the assessed load-cycle based standard deviation is slightly increased to a value of N=0.213. This proofs that the depicted notch fatigue strength assessment method is conservatively well applicable for the investigated HFMI-treated, mild steel stiffeners featuring varying load directions.

4

Validation of HFMI notch stress model

This chapter focuses on the validation of the proposed HFMI master notch stress approach by numerous recently conducted fatigue tests. In addition to the investigated longitudinal stiffener results, the HFMI test data points taken from literature include varying base material yield strengths, structural weld details, stress ratios, and loading types in order to ensure a widespread validation of the presented assessment concept. The appendix summarizes the included data and provides detailed information regarding specimen geometry, fatigue testing and material parameters as well as numerical analysis results providing both stress concentration factor Kn and notch factor KW. In the course of the numerical computations, the boundary conditions considering clamping of the specimens are taken from each incorporated reference. If no specific information is provided, the clamped sections at the ends of the specimen are defined based on own experience in order to not influence the notch stress condition at the weld toe. This chapter is split into two sections. Constant amplitude (CA) fatigue tests are evaluated first and variable amplitude (VA) loaded fatigue tests are studied subsequently. The following data sets are utilized for the validation, whereby detailed information in regard to each test series is provided in the appendix:  Berg, 2014 [43] (CA)  Bucak, 2011 [44] (CA)  Huo, 2005 [45] (VA)  Kuhlmann, 2006 [46] (CA)  Leitner, 2015 [33] (VA)  Marquis, 2008 [47] (VA)  Nykänen, 2015 [48] (CA)  Ottersböck, 2015 [49] (CA)  Shimaniku, 2015 [50] (CA)  Ummenofer, 2013 [51] (CA)  Yildirim, 2013 [12] (VA)

4.1

Constant amplitude loading

For the fatigue test results considering constant amplitude loading a total number of 172 data points are evaluated. It has to be pointed out that these additional datasets were not included for the evaluation of the reference HFMI master notch stress S/N-curve as shown in Fig. 3. Therefore, the depicted validation is performed using independent datasets without overlapping test data entries. In Fig. 8 a comparison of the calculated and experimental fatigue life, calculating the slope magnification factor kk on the basis of the stress concentration factor Kn, is depicted. Similar to the investigated stiffener joints the examination indicates that almost all data points are conservative implying that the calculated numbers of load-cycles Ncal undermatches the experimental values Nexp. As a huge amount of data points are considered, the standard deviation increases slightly to a value of N=0.357. However, for a fatigue-life based evaluation this value is comparable to N=0.344, which is obtained by evaluating the recommended stress-based scatter band of TS=1/1.5 [22] and applying an inverse slope of value k=5 that fits well to HFMI-treated joints [21]. At an experimental number of two million load. 6 . 6 cycles Nexp=2 10 , the evaluated upper scatter band reveals a calculated value of Ncal=1.76 10 load-cycles. This fits well and still enables a conservative fatigue assessment, whereby over ninety percent of the involved data points are estimated safely.

Fig. 8: Calculated versus experimental fatigue life results for constant amplitude loading test data evaluating kk on the basis of Kn

As described, in order to assess complexly shaped structures, a fatigue assessment on the basis of stress concentration factor Kn is not generally possible, as a nominal cross section may not be properly defined. Thus, the calculated and experimental fatigue life utilizing the notch factor KW for constant amplitude loading testing is shown in Fig. 9. Again, the statistically evaluated standard deviation N=0.383 is quite comparable to the IIW-recommended value. . 6 Nevertheless, at an experimental number of two million load-cycles Nexp=2 10 , the evaluated upper scatter . 6 band supports a calculated value of Ncal=2.08 10 load-cycles, which is close to the experimental result. A conservative fatigue assessment is still facilitated, because only slightly more than ten percent of the involved data points are estimated non-conservatively.

Fig. 9: Calculated versus experimental fatigue life results for constant amplitude loading test data evaluating kk on the basis of KW Concluding the application of the HFMI master notch stress approach to fatigue data tested under constant amplitude, it is shown that presented method is also well applicable. An evaluation of the slope magnification factor kk based on stress concentration factor Kn or notch factor KW leads to a conservative fatigue assessment, whereby about ninety percent of the included data points are safely estimated.

4.2

Variable amplitude loading

For the fatigue test results considering variable amplitude loading a total number of additional 60 data points are included. These are again not incorporated in the compilation of the reference HFMI master notch stress S/N-curve. According to Sonsino [31], a specified damage sum of D=0.3 ought to be used in the fatigue life assessment. The equivalent stress range is computed on the basis of the displayed equation in the subsequent figures in accordance to [28] and firstly proposed by Niemi in [52]. Preliminary investigations in [33] involving the applicability of specified damage sums of D=0.3, D=0.5, and D=1.0 for HFMI-treated T-joints lead to the conclusion that a value of D=0.3 as specified damage sum is most appropriate. For comparison, an additional evaluation utilizing a specified damage sum of D=0.5 is also conducted in this paper. At first, the calculated and experimental fatigue life utilizing kk on the basis of Kn is given in Fig. 10. As the involved variable amplitude data is obtained by testing under different load-spectra, the evaluated standard deviation with a value of N=0.366 is slightly above the ones in case of constant amplitude loading. However, . 6 . 5 the resulting upper scatter band at Nexp=2 10 load-cycles exhibits a calculated value of Ncal=7.19 10 loadcycles, applying a specified damage sum of D=0.3 for an evaluation based on Kn. The mean value of the relation between the logarithmic experimental and calculated load-cycles exhibits a conservative underestimation of about 19 % in case of D=0.3. On the contrary, for D=0.5 a non-conservative overestimation by approximately 25 % is observed, which proofs the proper feasibility of the specified damage sum D=0.3.

Fig. 10: Calculated versus experimental fatigue life results for variable amplitude loading test data evaluating kk on the basis of Kn (specified damage sum D=0.3) At second, the approach evaluating the slope magnification factor kk on the basis of the notch factor KW is also studied for the variable amplitude loading test data, compare to Fig. 11. Herein, the evaluated life-cycle standard deviation enhances up to a quite high value of N=0.475, but nevertheless, mostly all calculated fatigue life results are conservative. In particular, at an experimental number of two million loadcycles Nexp=2.106, the evaluated upper scatter band reveals a calculated value of Ncal=1.08.106 load-cycles, approving also a safe service strength assessment of the evaluated HFMI-treated, high-strength steel joints. Again, the mean value of the relation between the logarithmic experimental and calculated load-cycles shows a conservative underestimation of about 18 % applying D=0.3. In case of D=0.5 a non-conservative overestimation by roughly 19 % is evaluated indicating once more the proper use of the specified damage sum D=0.3.

Fig. 11: Calculated versus experimental fatigue life results for variable amplitude loading test data evaluating kk on the basis of KW (specified damage sum D=0.3) Summing up, the application study of the HFMI master notch stress approach shows that by utilizing a specified damage sum of D=0.3 for the equivalent notch stress range a thoroughly conservative fatigue assessment is enabled. As the included data points exhibit different load-spectra, stress ratios, material yield strengths, and structural details, this result indicates the widespread practicability of the engineering-feasible, enhanced notch stress approach for HFMI-treated steel joints.

Conclusions Based on the presented results covering both constant and variable amplitude tests of welded and HFMItreated steel joints, the following conclusions can be drawn applying the presented HFMI master notch stress approach in industry: 





The HFMI master notch stress approach can be conservatively implemented as a design tool if the notch factor KW is used. It requires a numerical assessment of both notch and structural hot-spot stress, but omits the need of nominal stress evaluation. Thus, the industrial applicability of this updated approach for HFMI-treated welded steel joints in complexly shaped structures is ensured. For constant amplitude loading both investigated evaluation procedures, based on either Kn or KW, lead to an good agreement with the experimental results. About ninety percent of the investigated one-hundred seventy-two specimen fatigue samples are assessed conservatively. This validates the conservative applicability of the presented HFMI master notch stress method for HFMI post-treated steel joints. In case of variable amplitude loading, a specified damage sum of D=0.3 [31] is applied to assess the equivalent stress range basing on the recommendation provided in [28]. An extended application study taking sixty variable amplitude loaded specimen results into account proofs the conservative service strength design of this notch-stress based concept for HFMI-treated steel joints.

References [1] Radaj, D.; Sonsino, C. M.; Fricke, W.: Fatigue assessment of welded joints by local approaches, Woodhead Publishing Ltd, 2006. [2] Niemi, E.; Fricke, W.; Maddox, S. J.: Fatigue Analysis of Welded Components - Designer´s guide to the structural hot-spot stress approach, Woodhead Publishing Ltd, Cambridge, 2006. [3] Radaj, D.; Sonsino, C. M.; Fricke, W.: Recent developments in local concepts of fatigue assessment of welded joints; International Journal of Fatigue 31 (2009) 1, pp. 2–11. [4] Sonsino, C. M.: A Consideration of Allowable Equivalent Stresses for Fatigue Design of Welded Joints According to the Notch Stress Concept with the Reference Radii rref = 1.00 and 0.05 mm; Welding in the World 53/3 (2009), pp. R64–R75. [5] Kassner, M.: Fatigue strength analysis of a welded railway vehicle structure by different methods; International Journal of Fatigue 34 (2012) 1, pp. 103–111. [6] Bruder, T.; Störzel, K.; Baumgartner, J.: Fatigue assessment of seam welds of automotive components by local stress approaches; Materialwissenschaft und Werkstofftechnik 39 (2008) 10, pp. 726–733. [7] Sonsino, C. M.; Bruder, T.; Baumgartner, J.: S-N Lines for Welded Thin Joints - Suggested Slopes and FAT Values for Applying the Notch Stress Concept with Various Reference Radii; Welding in the World 54 (2010) 11-12, pp. R375-R392. [8] Esderts, A.; Willen, J.; Kassner, M.: Fatigue strength analysis of welded joints in closed steel sections in rail vehicles; International Journal of Fatigue 34 (2012) 1, pp. 112–121. [9] Jonsson, B.; Dobmann, G.; Hobbacher, A. F.; Kassner, M.; Marquis, G.: IIW Guidelines on Weld Quality in Relationship to Fatigue Strength, Springer International Publishing, Cham, 2016. [10] Haagensen, P. J.; Maddox, S. J.: IIW Recommendations On Methods for Improving the Fatigue Strength of Welded Joints, Woodhead Publishing Ltd; Elsevier Science, Cambridge, 2013. [11] Marquis, G. B.; Barsoum, Z.: Fatigue strength improvement of steel structures by high-frequency mechanical impact: proposed procedures and quality assurance guidelines; Welding in the World 58 (2014) 1, pp. 19–28. [12] Yildirim, H. C.; Marquis, G. B.: A round robin study of high-frequency mechanical impact (HFMI)-treated welded joints subjected to variable amplitude loading; Welding in the World 57 (2013) 3, pp. 437–447. [13] Yildirim, H. C.; Marquis, G. B.: Fatigue strength improvement factors for high strength steel welded joints treated by high frequency mechanical impact; International Journal of Fatigue 44 (2012), pp. 168–176. [14] Leitner, M.; Barsoum, Z.; Schäfers, F.: Crack propagation analysis and rehabilitation by HFMI of prefatigued welded structures; Welding in the World, 60/3 (2016), pp. 581-592. [15] Sonsino, C. M.; Fricke, W.; Bruyne, F. de; Hoppe, A.; Ahmadi, A.; Zhang, G.: Notch stress concepts for the fatigue assessment of welded joints – Background and applications; International Journal of Fatigue 34 (2012) 1, pp. 2–16.

[16] Sonsino, C. M.; Hanselka, H.; Karakas, Ö.; Gülsöz, A.; Vogt, M.; Dilger, K: Fatigue Design Values for Welded Joints of the Wrought Magnesium Alloy AZ31 (ISO-MgAI3Zn1) According to the Nominal, Structural and Notch Stress Concepts in Comparison to Welded Steel and Aluminium Connections. Welding in the World, 52/5-6 (2008), pp. 79-94. [17] Morgenstern, C.; Sonsino, C. M.; Hobbacher, A.; Sorbo, F.: Fatigue design of aluminium welded joints by the local stress concept with the fictitious notch radius of rf= 1mm. International journal of fatigue, 28/8 (2006), pp. 881-890. [18] Neuber H.: Über die Berücksichtigung der Spannungskonzentration bei Festigkeitsberechnungen [About the consideration of the stress concentration for calculations of strength]. Konstruktion 20/7 (1968), pp. 245-251. [19] Karakas, Ö.; Morgenstern, C.; Sonsino, C. M.: Fatigue design of welded joints from the wrought magnesium alloy AZ31 by the local stress concept with the fictitious notch radii of rf= 1.0 and 0.05 mm; International Journal of Fatigue, 30/12 (2008), pp. 2210-2219. [20] Karakas, Ö.: Consideration of mean-stress effects on fatigue life of welded magnesium joints by the application of the Smith-Watson-Topper and reference radius concepts; International Journal of Fatigue 49 (2013), pp. 1-17. [21] Marquis, G. B.; Barsoum, Z.: IIW Recommendations for the HFMI Treatment - For Improving the Fatigue Strength of Welded Joints, ISBN 978-981-10-2503-7, Springer, 2016. [22] Leitner, M.; Stoschka, M.; Eichlseder, W.: Fatigue enhancement of thin-walled, high-strength steel joints by high-frequency mechanical impact treatment; Welding in the World 58 (2014) 1, pp. 29–39. [23] Stoschka, M.; Leitner, M.; Barsoum, Z.: Study of the local notch stress HFMI master S/N-curve approach nd on high-strength steel joints; in Proceedings of 2 Swedish Conference on Design and Fabrication of Welded Structures (Barsoum, Z. Ed.), 2013, pp. 76–90. [24] Yildirim, H.C.: Fatigue strength assessment of HFMI treated butt welds using the effective notch stress method, Welding in the World 58/3 (2014), pp. 279-288. [25] Fricke, W.: Guideline for the Fatigue Assessment by Notch Stress Analysis for Welded Structures; IIWDoc. XIII-2240r1-08/XV-1289r1-08, 2008. [26] Sonsino, C. M.: Fatigue testing under variable amplitude loading; International Journal of Fatigue 29 (2007) 6, pp. 1080–1089. [27] Sonsino, C. M.: Multiaxial fatigue assessment of welded joints – Recommendations for design codes; International Journal of Fatigue 31 (2009) 1, pp. 173–187. [28] Hobbacher, A. F.: Recommendations for Fatigue Design of Welded Joints and Components, Springer International Publishing, Cham, 2016. [29] Sonsino, C. M.: Influence of material’s ductility and local deformation mode on multiaxial fatigue response; International Journal of Fatigue 33 (2011) 8, pp. 930–947. [30] Sonsino, C. M.; Kueppers, M.: Multiaxial fatigue of welded joints under constant and variable amplitude loadings; Fatigue & Fracture of Engineering Materials and Structures 24 (2001) 5, pp. 309–327. [31] Sonsino, C. M.; Lagoda, T.; Demofonti, G.: Damage accumulation under variable amplitude loading of welded medium- and high-strength steels; International Journal of Fatigue 26 (2004) 5, pp. 487–495. [32] Marquis, G. B.: Fatigue assessment methods for variable amplitude loading of welded structures; in Fracture and Fatigue of Welded Joints and Structures (MacDonald, K. Ed.), Elsevier Science, Burlington, 2011, pp. 208–238. [33] Leitner, M.; Gerstbrein, S.; Ottersböck, M. J.; Stoschka, M.: Fatigue Strength of HFMI-treated Highstrength Steel Joints under Constant and Variable Amplitude Block Loading; Procedia Engineering 101 (2015), pp. 251–258. [34] Doerk, O.; Fricke, W.; Weissenborn, C.: Comparison of different calculation methods for structural stresses at welded joints; International Journal of Fatigue 25 (2003) 5, pp. 359–369. [35] Marquis, G. B.; Barsoum, Z.: A Guideline for Fatigue Strength Improvement of High Strength Steel Welded Structures Using High Frequency Mechanical Impact Treatment; Procedia Engineering 66 (2013), pp. 98–107. [36] Haibach E.: Betriebsfestigkeit - Verfahren und Daten zur Berechnung (Structural durability – Methods and data for calculation). 2nd ed. Düsseldorf, VDI-Verlag, 2003. [37] Sonsino, C.M.: Effect of residual stresses on the fatigue behaviour of welded joints depending on loading conditions and weld geometry, International Journal of Fatigue, 31 (2009), pp. 88-101. [38] Weich, I.: Edge Layer Condition and Fatigue Strength of welds improved by mechanical post-weld treatment; Welding in the World 55 (2011) 1-2, pp. 3–12. [39] Mikkola, E.; Doré, M. J.; Khurshid, M.: Fatigue Strength of HFMI Treated Structures Under High R-ratio and Variable Amplitude Loading; Procedia Engineering 66 (2013), pp. 161–170. [40] Gerster, P.: Praktische Anwendungen der PIT-Technologie; Stahlbau 78 (2009) 9, pp. 680–683. [41] Fricke, W.: IIW Recommendations for the Fatigue Assessment of Welded Structures by Notch Stress Analysis, Woodhead Publishing Ltd, Cambridge, 2012.

[42] Bruder, T.; Störzel, K.; Baumgartner, J.; Hanselka, H.: Evaluation of nominal and local stress based approaches for the fatigue assessment of seam welds; International Journal of Fatigue 34 (2012) 1, pp. 86–102. [43] Berg, J.; Stranghöner, N.: Fatigue Strength of Welded Ultra High Strength Steels Improved by High Frequency Hammer Peening; Procedia Materials Science 3 (2014), pp. 71–76. [44] Bucak, Ö.; Weich, I.; Lorenz, J.; Buschner, J.: Numersiche und experimentelle Untersuchungen zum Spannungszustand (Hot Spot Stress) und zum Ermüdungsverhalten beim Einsatz von Schweißnahtnachbehandlungsverfahren an geschweißten Längs- und Quersteifen aus Blechen aus S690; in Festschrift Gerhard Hanswille (Institut für Konstruktiven Ingenieurbau Ed.), Wuppertal, 2011, pp. 59–72. [45] Huo, L.: Investigation of the fatigue behaviour of the welded joints treated by TIG dressing and ultrasonic peening under variable-amplitude load; International Journal of Fatigue 27 (2005) 1, pp. 95–101. [46] Kuhlmann, U.; Dürr, A.; Günther, H.-P.: Verbesserung der Ermüdungsfestigkeit höherfester Baustähle durch Anwendung der UIT-Nachbehandlung; Stahlbau 75 (2006) 11, pp. 930–938. [47] Marquis, G. B.; Björk, T.: Variable amplitude fatigue strength of improved HSS welds; IIW-Doc. XIII2224-08, 2008. [48] Nykänen, T.; Björk, T.: Assessment of fatigue strength of steel butt-welded joints in as-welded condition – Alternative approaches for curve fitting and mean stress effect analysis; Marine Structures 44 (2015), pp. 288–310. [49] Ottersböck, M. J.; Leitner, M.; Stoschka, M.: Effect of loading type on welded and HFMI-treated T-joints; IIW-Doc. XIII-2584-15, 2015. [50] Shimanuki, H.; Yonezawa, T.: Estimation method of fatigue strength based on the residual stress for the welded joint improved by Ultrasonic Impact Treatment (UIT); IIW-Doc. XIII-2603-15, 2015. [51] Ummenhofer, T.; Weidner, P.: Improvement factors for the design of welded joints subjected to high frequency mechanical impact treatment; Steel Construction 6 (2013) 3, pp. 191–199. [52] Niemi, E.: Random loading behavior of welded components. In: SJ Maddox and M. Prager (eds). Proc. of the IIW International Conference on Performance of Dynamically Loaded Welded Structures, San Francisco, Welding Research Council, New York, 1997.

Appendix Reference

Fatigue test conditions Cover plate Joint type

R-ratio

S960, S1100, S1300 7.5 mm 6 mm, 4 mm 0.1

Cyclic load

Tension

Nomenclature in figure

Ber2014-6, Ber2014-7 Ber2014-8

Joint type

Base plate thickness R-ratio

Longitudinal stiffener S1100, S1300 4 mm, 6 mm 0.1

Cyclic load

Tension

Nomenclature in figure

Ber2014-9, Ber2014-10

Joint type

Base plate thickness R-ratio

Transversal attachment S1100, S1300 6 mm 4 mm 0.1

Cyclic load

Tension

Nomenclature in figure

Ber2014-3, Ber2014-5

Material

Base plate thickness

Berg, 2014 [43]

Material

Berg, 2014 [43]

Material

Berg, 2014 [43]

Results of numerical analysis

Joint type Material

Berg, 2014 [43]

Berg, 2014 [43]

Base plate thickness R-ratio

6 mm

Cyclic load

Tension

Nomenclature in figure Joint type

Ber2014-4

Material Base plate thickness R-ratio

S960, S1100 7.5 mm, 6 to 8 mm 0.1

Cyclic load

Tension

Nomenclature in figure

Ber2014-1, Ber2014-2

Joint type

Longitudinal stiffener S690

Material

Bucak, 2011 [44]

0.1

Butt-joint

Base plate thickness R-ratio

20 mm

Cyclic load

Bending

Nomenclature in figure Joint type

Buc2011-1

Material

Bucak, 2011 [44]

Transversal attachment S1100

0.25

Transversal attachment S690

Base plate thickness R-ratio

40 mm

Cyclic load

Bending

Nomenclature in figure

Buc2011-2

0.25

Joint type Material

Huo, 2005 [45]

Base plate thickness R-ratio

8 mm

Cyclic load

Tension

Nomenclature in figure Joint type

Huo2005

Material

Kuhlmann, 2006 [46]

Transversal attachment S690 12 mm

Cyclic load

Tension

Nomenclature in figure Joint type

Kuh2006

Base plate thickness R-ratio

-1

Transversal attachment S355, S690, S960 5 mm 0.1

Cyclic load

Tension

Nomenclature in figure

Lei2015-1, Lei2015-2, Lei2015-3

Joint type

Longitudinal stiffener S960

Material

Marquis, 2008 [47]

0.1

Base plate thickness R-ratio

Material

Leitner, 2015 [33]

Longitudinal stiffener S390

Base plate thickness R-ratio

6 mm

Cyclic load

Tension

Nomenclature in figure

Mar2008

-1

Nykänen, 2015 [48]

Joint type

Butt joint

Material

S1100

Base plate thickness R-ratio

6 mm

Cyclic load

Tension

Nomenclature in figure

Nyk2015

Joint type

Transversal attachment S355, S690 5 mm

Material

Ottersböck, 2015 [49]

Base plate thickness R-ratio

Bending

Nomenclature in figure

Ott2015-1, Ott2015-2

Joint type

Longitudinal stiffener S572

Base plate thickness R-ratio

12 mm

Cyclic load

Tension

Nomenclature in figure Joint type

Shi2015

Material

Ummenofer, 2013 [51]

0.1

Cyclic load

Material

Shimaniku, 2015 [50]

0.1

0.5

Transversal attachment S460

Base plate thickness R-ratio

30 mm

Cyclic load

Tension

Nomenclature in figure

Umm2013-1

0.1

Joint type Material

Ummenofer, 2013 [51]

Base plate thickness R-ratio

30 mm

Cyclic load

Tension

Nomenclature in figure Joint type

Umm2013-2

Material

S460, S690 30 mm

Base plate thickness R-ratio Ummenofer, 2013 [51]

0.1

Butt-joint

0.1

Cyclic load

Tension

Nomenclature in figure

Umm2013-3, Umm2013-4

Joint type

Longitudinal stiffener S700

Material

Yildirim, 2013 [12]

Longitudinal stiffener S690

Base plate thickness R-ratio

8 mm

Cyclic load

Tension

Nomenclature in figure

Yil2013

-1

  

Highlights Presentation of HFMI master notch stress approach taking base material yield strength, stress ratio, and notch stress condition into account Model bases on effective notch and structural stress thus enabling a local fatigue assessment of complex welded structures A comprehensive validation including over 230 constant and variable amplitude fatigue test results proofs the feasibility of the concept