Stability of high frequency mechanical impact (HFMI) post-treatment induced residual stress states under cyclic loading of welded steel joints

Engineering Structures 143 (2017) 589–602

Contents lists available at ScienceDirect

Engineering Structures journal homepage: www.elsevier.com/locate/engstruct

Stability of high frequency mechanical impact (HFMI) post-treatment induced residual stress states under cyclic loading of welded steel joints M. Leitner a,⇑, M. Khurshid b, Z. Barsoum b a b

Montanuniversität Leoben, Department Product Engineering, Chair of Mechanical Engineering, Austria KTH-Royal Institute of Technology, Department of Aeronautical and Vehicle Engineering, Division of Lightweight Structures, Sweden

a r t i c l e

i n f o

Article history: Received 16 November 2016 Revised 28 March 2017 Accepted 24 April 2017 Available online 2 May 2017 Keywords: Welded joints HFMI-treatment Cyclic residual stress stability X-ray measurement Numerical simulation Analytical residual stress relaxation models

a b s t r a c t This paper investigates the effect of cyclic loading on the stability of compressive residual stress fields induced by high frequency mechanical impact (HFMI) post-weld treatment. First, the effectiveness of the post-treatment technique is shown by fatigue tests incorporating mild steel S355 and highstrength steel S960 longitudinal stiffener specimens. Extensive X-ray residual stress measurements support the beneficial impact on the compressive residual stress state for mild and high-strength steel structures. They also illustrate that cyclic loading leads to a significant local relaxation of this condition. Second, a numerical simulation chain incorporating a structural weld simulation, numerical analysis of the HFMI-treatment, and a final cyclic loading step for the investigated mild steel specimen is set-up. The results show that the residual stresses at the surface of the weld toe are in agreement to the X-ray measurements for both the as-welded and HFMI-treated condition, which basically proofs the applicability of the manufacturing simulation. The numerical computation including the first five load-cycles demonstrates that the simulated residual stress relaxation again exhibits consistent results with the measurements. An additional utilization of an analytical relaxation model from literature reveals that the estimation of the residual stress state in the high-cycle fatigue region is well employable. Therefore, the scientific results in this paper proof the applicability of the presented consecutive numerical-analytical procedure to assess the local compressive residual stress stability of HFMI-treated welded steel joints in both the low- and high-cycle fatigue region. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction The beneficial effect of high frequency mechanical impact (HFMI)-treatment in order to enhance fatigue strength is primarily based on an improvement of the weld toe topography, a local hardening of the material and compressive residual stresses. Prior fatigue tests involving different kind of weld details and base material yield strengths in [1] reveal the positive effect of the HFMItreatment. In [2], the influence of grinding and hammer peening on crack propagation is investigated showing again that the posttreated conditions exhibit significantly advantageous fatigue properties. Due to the forming process in the course of the peening procedure, HFMI-treatment leads to a local change in microstructure. However, an analysis by [3] concludes that this effect is not mainly relevant for the increase in fatigue resistance. A recently published guideline [4] provides recommendations to the practical applica⇑ Corresponding author. E-mail address: [email protected] (M. Leitner). http://dx.doi.org/10.1016/j.engstruct.2017.04.046 0141-0296/Ó 2017 Elsevier Ltd. All rights reserved.

tion of the HFMI-treatment and includes benefit factors for nominal and local fatigue strength assessment. Especially in case of ultra-high strength steel joints, this technique seems to facilitate an essential increase in fatigue life [5], removing surface-near imperfections like undercuts at the weld toe, which are particularly harmful for high-strength materials [6]. Besides this geometrical impact, the local residual stress condition is of great importance for the fatigue strength of HFMI-treated joints. In [7], HFMI-treatment is applied as rehabilitation method, whereat it is found that the depth of the HFMI-induced compressive residual stress field is fundamental for the lifetime extension. HFMIprocess parameters and the corresponding final post-treated condition such as properly-, under- or over-treated affect this residual stress state and hence the fatigue behaviour [8]. Measurements by [9] indicate that the compressive residual stress is decreased just after the first load-cycle, whereby only a comparably small relaxation due to the further loading up to the high-cycle fatigue region takes place.

590

M. Leitner et al. / Engineering Structures 143 (2017) 589–602

These findings are of special interest in case of variable amplitude loading, which commonly occurs in real load applications. Fatigue tests in [10] using S700 high-strength steel longitudinal stiffeners in as-welded and HFMI-treated condition under constant and variable amplitude loading exhibit that the increase factor by the post-treatment is reduced in case of the latter loadscenario. This effect may be drawn to a local relaxation of the beneficial compressive residual stress state at higher load-levels, leading to a reduced fatigue life for variable amplitude loadspectra. An extensive literature survey focussing on the stability and significance of residual stresses during fatigue by [11] summarizes that many of the pronounced cyclic relaxation effects identified in the literature appear to be static effects, e.g. appearing at the first loading cycle or in the course of overloads. This statement is basically confirmed in [12] showing that the compressive residual stresses at the surface in the HFMI-treated weld toe region are relaxing from about
400 MPa to
250 MPa due to a single tensile load of 90% of the yield strength or alternatively, by a single compressive load of 60% of the yield strength. Additionally, experimental analysis in [13] with shot-peened round steel specimens concludes that just one single cyclic overload could decrease the fatigue life time by 25% to 60% compared to the situation with no overload. Similar results are presented in [14] for single overloads involving different temperature and notch conditions, and in [15] focusing on cyclic loading in the low cycle fatigue region. However, investigations by [16] reveal the occurrence of a certain residual stress relaxation in the high-cycle fatigue region, hence this effect should also not be neglected. Therefore, one efficient method to study the effect of residual stress stability during fatigue loading is based on numerical analysis. In [17], a coupled thermo-mechanical numerical simulation with a subsequent elastic-plastic analysis incorporating cyclic plasticity based on a nonlinear kinematic hardening rule is conducted. Furthermore, a finite element study in [18], which numerically investigates the residual stress stability and fatigue damage in HFMI-treated welded joints, concluded that the benefit from compressive residual stresses decreased with an increasing stress range, stress ratio and peak load magnitude due to increasing level of residual stress relaxation. However, this work is based on a simplified procedure considering the residual stress state by mapping an analytical field in the numerical model. An elaborated approach to incorporate the significant manufacturing process, such as welding and HFMI-treatment, within a numerical simulation is exemplified in [19]. In the course of own preliminary numerical studies this principal procedure, by setting-up a numerical simulation chain involving a structural weld simulation and a subsequent numerical analysis of the HFMI-process, is also scientifically researched with focus on a mild steel butt joint specimen, see [20]. On the basis of this work, the residual stress stability of a thin-walled mild steel S355 longitudinal stiffener specimen is analyzed in this paper, which contributes to the following scientific topics in detail:  Experimental investigation of the cyclic stability of HFMIinduced compressive residual stress states based on X-ray residual stress measurements for mild steel 355 and highstrength steel S960 joints.  Presentation of numerical simulation chain including structural weld simulation and numerical HFMI-treatment analysis for the investigated mild steel S355 longitudinal stiffener.  Numerical assessment of cyclic residual stress relaxation for the first five load-cycles and further estimation up to run-out level of fifty million load-cycles by an engineering feasible analytical model.

2. Review of analytical models for cyclic residual stress relaxation Besides the applicability of numerical approaches, several analytical procedures to estimate the residual stress relaxation under cyclic loading exist, which are reviewed in [21]. Herein, the models proposed for both residual stress relaxations due to thermal and mechanical loadings are reviewed. It is summarized that residual stresses do relax during the service life of a component, but it may not affect the fatigue life significantly. It is also concluded that the proposed residual stress relaxation models require further detailed study to examine their validity. One of the early models for residual stress relaxation is presented by Morrow and Sinclair [22]. They conducted strain-controlled fatigue tests to quantify the cyclic residual stress relaxation and recommend a basic relationship considering the yield strength, the amplitude and the mean stresses as well as the number of load-cycles, see Eq. (1).




rmN ry
ra ra ¼
rm1 rm1 ry

b  logðNÞ

ð1Þ

where rmN is the mean stress at the N-th cycle, rm1 is the mean stress at the first cycle, ra is the alternating stress amplitude, ry is the material yield strength, and b is a constant dependent on material softening and the applied strain range De. This model is only applicable for a load ratio of R =
1, because the surface residual stress is only analogous to the mean stress when the material is subjected to completely reversed loading. The model is experimentally verified for N > 106 and rmN < 20 MPa. Jhansale and Topper [23] suggest a power law relationship between the mean stress and the load-cycles to quantify cyclic residual stress relaxation. The relationship is given by Eq. (2), where rmN is the mean residual stress state after N-cycles, rml is the mean load stress state, and B is the relaxation exponent dependent on the material softening and applied strain range De.

rmN ¼ rml  NB

ð2Þ

rres N ¼ A þ m  logðNÞ

ð3Þ

Kodama [24] proposes a linear logarithmic relationship for residual stress relaxation, see Eq. (3). Thereby, rres N is the surface residual stress after N-cycles, A and m are material constants, which are depending on the stress amplitude ra. It is noted that the experimental data, which supports the linear logarithm, decreases the relationship between residual stress and the number of load-cycles only after the first cycle. Zhuang and Halford [25] recommend an analytical model for the relaxation of residual stresses. Their model incorporates the initial cold work and is based on finite element results. The model could predict the relaxation at R = 0 and R =
1 quite close to that obtained by numerical analysis. Their proposed relation is given in Eqs. (4) and (5) depicting the estimation without and with consideration of the effect by the load ratio R.

rres rmax  ra N ¼A 2 rres ðC 0 w  CyÞ

!m  ðN
1ÞB
1

rres 2  r2a N ¼A res jr0 j ð1
RÞ  ðC w  C y Þ2

ð4Þ

!m  ðN
1ÞB
1

ð5Þ

where Cw defines a parameter, which accounts for the degree of cold working. Material constants m and A are dependent on the cyclic stress and strain response, and need to be considered for each mean stress condition. Constant B controls the relaxation rate versus loading cycles and the initial residual stress is considered by

M. Leitner et al. / Engineering Structures 143 (2017) 589–602

rres 0 . Qian et al. [26] study the relaxation of residual stresses in welded joints in three steel types. All of the three material samples exhibit a different amount of stress relaxation. They propose a model for an estimation of residual stress relaxation, which treats dislocation motion during cyclic loading analogous to creep behaviour. Their introduced model is shown in Eq. (6). 
n m ra S¼ a þ b  ½logðN þ 1Þ

ry

ð6Þ

where S is residual stress relaxation, ra is the applied stress, ry is the yield stress, and N is the number of cycles. The factors a, b, m, and n are determined by non-linear fitting according to experimental data. Zaroog et al. [27] study residual stress relaxation in aluminum alloy specimens, which are shot-peened under three different process intensities. Within the work, cyclic tests for two load magnitudes are performed. Residual stresses and the cold work after each loading cycle are measured for the three shot-peening intensities utilizing X-ray diffraction at one, two, ten, thousand, and tenthousand load-cycles. It is investigated that the reduction in residual stress state, micro-hardness and cold work depends on the applied load-level. They also propose a model to estimate residual stress relaxation, see Eqs. (7) and (8).




rres 1 N ¼A C rres w 0

m  NB

C w ¼ K 1  H2v þ K 2  Hv þ K 3

ð7Þ ð8Þ

where constants m and A depend on the applied load and shotpeening intensity, B controls the relaxation rate, Hv is microhardness, Cw is cold work and K1, K2 and K3 are constants dependent on the applied load-level and shot-peening intensity. These can be found using regression fit for the experimental data. The presented model is a simple empirical one with less parameter than suggested by [25]. Han et al. [28] propose a linear relationship between the residual stress state and the number of load-cycles for the estimation of residual stress relaxation. The relationships are shown in the Eqs. (9) and (10).

ðrres Þrelax ¼ Nk ðrres Þ1cycle

the cyclic relaxation of the compressive residual stress state in the high-cycle fatigue region for the investigated mild steel S355 longitudinal stiffener specimen. The model acts as supplement to the numerical analysis, whereat only the first five load-cycles are considered and therefore, significantly extends the presented assessment procedure.

3. Experimental investigation 3.1. Specimen manufacturing In this work, a single-sided non-load carrying longitudinal stiffener specimen applying the same base and filler material is investigated, see Fig. 1. The specimens are automatically gas metal arc welded by the aid of a welding robot. An industrially well-established filler material G3Si1, applied as massive wire, in combination with a M21 shielding gas (82% Ar, 18% CO2), is used. Nominal mechanical properties of the investigated base (according to EN 10025) and filler metals (according to EN ISO 16834) are given for the mild steel S355 in Table 1 and for the high-strength steel S960 in Table 2. Basically, the same weld set-up and procedure is applied in case of the high-strength steel S960. On the contrary to the mild steel, a metal-cored wire G89 in combination with a three-component mixed gas (69% Ar, 30% He, 1% CO2) is utilized on the basis of preliminary studies [30,31] involving the effect of specific welding process parameters on the fatigue strength in as-welded condition. Welding process parameters for the longitudinal weld areas are a welding speed vweld of 0.6 m/min, wire feed rate vwire of 9 m/min, nominal welding current I of 240 A, and a nominal welding voltage U of 25 V. In case of the end-of-seam areas the same welding speed is applied, but to minimize heat-input and ensure proper welding conditions, a reduced vwire of 6 m/min with a nominal welding current I of 160 A, and a nominal welding voltage U of 21 V is operated.

ð9Þ

for ððrres Þini þ rapp Þ=ry < 1

ðrres Þrelax ¼ N
0:004 ðrres Þini

ð10Þ

for ððrres Þini þ rapp Þ=ry P 1 where (rres)relax is residual stress after N-cycles, (rres)1cycle is the residual stress after the first cycle, (rres)ini is initial residual stress, rapp is the applied stress, ry is the yield stress, and N the number of load-cycles. They observe that residual stress relaxation is comparably large in the first cycle and relatively small for the rest of the cycles. Li et al. [29] study residual stresses and their relaxation using finite element analysis in welded joints. They suggest a formula for estimating residual stress relaxation in hot spot stress system. Their formula is quite similar to the formula proposed by [28] but it is independent of the number of load-cycles. However, it should be more valid for the assessment of residual stress relaxation caused by static pre-loads. Summarized, there are numerous analytical models to assess residual stress relaxation each exhibiting specific boundary conditions and restrictions of application. In this work, the comparably engineering feasible model by Han et al. [28] is applied, because no further experimental effort in regard to evaluate material dependent constants is required. The model is utilized to estimate

591

Fig. 1. Geometry of longitudinal stiffener specimen (dimensions [mm]).

592

M. Leitner et al. / Engineering Structures 143 (2017) 589–602

Table 1 Nominal mechanical properties of mild steel S355 base and filler material. Type

Yield strength [MPa]

Ultimate tensile strength [MPa]

Elongation [%]

Base material Filler material

355 440

575 530

22 30

Table 2 Nominal mechanical properties of high-strength steel S960 base and filler material. Type

Yield strength [MPa]

Ultimate tensile strength [MPa]

Elongation [%]

Base material Filler material

960 930

1050 980

10 14

As aforementioned, welding of the longitudinal stiffener specimens is performed utilizing an automated robot, see Fig. 2a. During the welding process, the samples are fixed by two clamping elements at the end of the base plate. Due to an optimized calibration of the weld process in the course of previous studies [30,31], a minimized angular distortion in the range of one-tenth degrees is

finally observed, which also resulted in the course of the subsequently executed numerical analysis. In case of an increased angular distortion, the effect due to the clamping process on the effective stress ratio at the weld toe during testing can be fundamental and needs to be incorporated as shown by a recent study [32]. Fig. 2b depicts the application of the HFMI-treatment on the longitudinal stiffener specimen and a comparison of the resulting weld toe condition before and after performing the post-treatment. A detailed representation of the local weld toe topography improvement utilizing laser-confocal microscopy and macrographs of the cross-section is depicted in Fig. 3. The macrographs in the subfigures clearly show the three typical microstructural regions of a welded joint, such as the filler material (FM), heataffected-zone (HAZ), and unaffected base material (BM). Furthermore, they reveal a smoothening of the notch topography up to a weld toe radius of about R = 2 mm in accordance to the applied pin radius in the course of the HFMI-treatment. However, investigations in [32] concluded that the influence of the compressive residual stress state mainly exceeds the beneficial effect due to the weld topography improvement and therefore, special attention is laid on the cyclic residual stress stability in this paper. Additional Vicker’s hardness mappings are performed in order to validate the subsequently, numerically evaluated local material properties after welding and HFMI-treatment, see Fig. 4. A detailed analysis in [34] of the hardness state before and after HFMI-

Fig. 2. Automated welding process (a) and application of HFMI-treatment (b) for the investigated longitudinal stiffener specimens [33].

Fig. 3. Improvement of weld toe topography by HFMI-treatment [33].

M. Leitner et al. / Engineering Structures 143 (2017) 589–602

593

Fig. 4. Hardness (HV3) condition after welding and HFMI-treatment [34].

treatment indicates an increase of the local hardness in the surface-near region at the weld toe due to work hardening. 3.2. Fatigue test results To evaluate the effectiveness of the HFMI-treatment and in order to define a proper load-level for the subsequent investigation of the cyclic stability of the residual stress state, uniaxial fatigue tests at a tumescent load stress ratio of R = 0.1 are carried out. For comparison purpose, additional experiments with the base material plate, without exhibiting the welded stiffener, are executed. The fatigue test data points are statistically evaluated applying the procedure by [35] in the finite life region, and utilizing the method introduced in [36] for the high-cycle fatigue regime. Nominal S/N-curves are shown for a survival probability of PS = 97.7% in order to consider scattering of the results. The results for the base material, as-welded, and HFMI-treated condition in case of the mild steel S355 are depicted in Fig. 5. It is shown that the posttreatment leads to a significant increase by a factor of three in the high-cycle fatigue region, whereby the HFMI-treated condition almost reaches the base material fatigue strength. No beneficial effect is observed in the low-cycle fatigue region, which may be caused due to the comparably high local stress state at the weld toe leading to a relaxation of the compressive residual stress condition and hence, reducing the increase in fatigue life. The fatigue tests results for the high-strength steel S960 are presented in Fig. 6. Due to the application of the high-strength

Fig. 5. Nominal S/N-curve for base material, as-welded, and HFMI-treated condition (S355).

steel, the high-cycle fatigue strength of the as-welded condition indicates an increase by 39% compared to the mild steel behaviour. These experimental findings show that in case of utilizing optimized weld process parameters [30,31]; leading to an improvement of the weld toe topography, residual stress, and hardness condition, an application of high-strength steels can be beneficial also without any further post-treatment. In case of the HFMItreated condition the evaluated results reveal an enhancement by 34% of the high-strength compared to the mild steel as base material. A comparison of the as-welded and HFMI-treated condition for the high-strength steel maintains again an increase by a factor of nearly three in the high-cycle fatigue region, which proofs the benefit of the post-treatment technique. 3.3. Residual stress measurements The X-ray evaluation bases on CrKa radiation using the d(sin2W) cross-correlation method, a collimator size of 1 mm, a duration of exposure of 20 sec, and a Young’s modulus of 210 GPa. At the beginning, a basic measurement study investigating the effect of specific HFMI-treatment parameters is shown. All experiments are executed with the pneumatic impact treatment (PIT) device [37] defining nominal pin radius, actuator frequency, and pneumatic pressure as most relevant process parameters. These first findings are not primarily considered within the analysis of the cyclic residual stress stability, but the results of this sensitivity study act as valuable input for the numerical analysis of the HFMI-process. Thereby,

Fig. 6. Nominal S/N-curve for base material, as-welded, and HFMI-treated condition (S960).

594

M. Leitner et al. / Engineering Structures 143 (2017) 589–602

the measurements are performed at HFMI-treated base material plates without any preliminary welding. The further measurements, investigating the as-welded and HFMI-treated condition, are executed directly at the weld toe of the samples, compare to labelling of the measurement point (MP) in Fig. 1. Characterizations in depth are conducted by iteratively surface etching up to the defined measurement depths. Due to the comparably high effort of performing numerous X-ray measurements just one specimen for each incorporated condition is analyzed. The X-ray technique itself exhibits a scattering of the measured values by about ±10% depending on the X-ray measurement angle. However, these deviations are comparably small and therefore, no additional evaluation is conducted.

3.3.1. Study on the effect of HFMI-treatment parameters At first, the influence of the applied pin radius, as selected HFMI process parameter, on the final residual stress state after posttreatment is experimentally analyzed utilizing a base plate of the investigated mild steel S355. In the mid of each specimen a single HFMI-treatment line on the base material is executed and the residual stresses are measured by X-ray diffraction technique at the centre of the stripe. Fig. 7 pictures the measured residual stress state in the transverse direction to the HFMI-treated line in dependence of the applied nominal pin radius during post-treatment. The measurements are performed at a constant nominal pressure of 6105 Pa at a nominal actuator frequency of 80 Hz. It is shown that with an increasing nominal pin radius a higher level of HFMI-induced compressive residual stress is generated. An explanation may be that in case of greater nominal pin radii the mass of the pin increases leading to higher impact forces during the dynamic process creating higher indentation depths. However, the applied pin radius should fit to the geometry and size of the weld seam in order to ensure proper post-treatment and smooth weld toe topography, therefore, the choice of the nominal pin radius is mainly dependent on these geometric factors. Furthermore, the residual stress state in transverse direction to the HFMI-treated line in dependence of the applied nominal actuator frequency during post-treatment is analyzed. As no data is available for the investigated mild steel S355, this research is performed with a S700 high-strength steel plate. However, as the tendencies of the effect by the pin radius in the course of validation measurements with S700 are proven to be similar to the mild steel S355, the following results are additionally presented in this paper. The

measurements are conducted at a constant nominal pressure of 6105 Pa and a nominal pin radius of 2 mm. It is shown that due to an increase of the nominal actuator frequency a higher level of HFMI-induced compressive residual stress arises, see Table 3. For a constant pin mass, a higher actuator frequency leads to increased pin accelerations. Therefore, higher impact forces may emerge, which are leading to enhanced indentation depths and hence, the level of compressive residual stress state in the post-treated area expands. As the acceleration of the pin itself seems to have a significant effect on the final residual stress state, additional optical measurements of the pin movement are operated. With the aid of a highspeed camera involving one thousand frames per second the dynamic displacement of the pin is recorded and hence, the acceleration is calculated based on the second derivative. The optical measurement and the results for varying nominal actuator frequencies are depicted in Fig. 8. Thereby, an increase of the nominal actuator frequency results in higher accelerations of the pin leading to superior impact forces. Strain gauge measurements to assess the influence of the nominal pneumatic pressure on the impact force of the pin are investigated in [38]. Herein, an increasing of the pressure from 4105 Pa to 6105 Pa enhances the impact force of the pin from about 2 kN to 3 kN at a commonly applied actuator frequency of 90 Hz. Comparable values are experimentally determined in the course preliminary investigations of this work, see [20]. Summarized, the presented HFMI-process parameters do have a significant influence on final residual stress state after post-treatment. In practical application, their choice is mostly dependent on further boundary conditions, such as geometry and size of the weld seam in case of pin radius, base material yield strength considered for the pneumatic pressure, or amount of post-treatment area affecting the choice of actuator frequency in order to optimize the time and cost efficiency of the HFMI-process. 3.3.2. Influence of HFMI-treatment on welded joints At second, in depth X-ray measurements at the weld toe in aswelded and HFMI-treated condition of the investigated longitudinal stiffener specimen incorporating a mild steel S355 and a high-strength steel S960 are conducted before cyclic loading. The resulting residual stresses in transverse direction, which is the loading direction during fatigue testing, and the full width at half maximum (FWHM) value for the mild steel S355 specimen are depicted in Fig. 9. The resulting residual stress conditions reveal a distinctive difference between the as-welded and HFMI-treated condition, whereby a significant reduction of residual stress by the post-treatment is achieved even up to a depth of 1500 mm. Herein, the HFMI-treated specimen exhibits a compressive residual stress state in the first 50 mm of about
335 MPa almost equalling the nominal yield strength of the investigated base material. FWHM-values up to 2.3° in the as-welded and up to 3.5° in the HFMI-treated state are measured. These values indicate a local hardening of the material due to the post-treatment occurring up to a depth of about 800 mm to 1000 mm. This depth of HFMIeffectiveness is in accordance to experimental studies in [39]. The measured in depth residual stress in loading direction and FWHM-values for the high-strength S960 longitudinal stiffener specimen are shown in Fig. 10. As shown for the mild steel S355 specimen, again a fundamental effect of the HFMI-treatment on the residual stress state is observed. In the first 50 mm the postTable 3 Effect of actuator frequency on residual stress in transverse direction (S700).

Fig. 7. Residual stress in transverse direction in dependence of nominal pin radius (S355).

Frequency [Hz] (average negative acceleration of pin during post-treatment [mm/sec2]) Transverse residual stress value [MPa]

80 (
90)
212

90 (
100)
249

120 (
250)
350

M. Leitner et al. / Engineering Structures 143 (2017) 589–602

595

Fig. 8. Experimental evaluation of pin acceleration during HFMI-treatment.

Fig. 9. Longitudinal attachment with S355 as base material in as-welded and HFMI-treated condition at N = 0: Residual stress values in transversal (loading) direction and corresponding FWHM-values at weld toe.

Fig. 10. Longitudinal attachment with S960 as base material in as-welded and HFMI-treated condition at N = 0: Residual stress values in transversal (loading) direction and corresponding FWHM-values at weld toe.

treatment achieves a compressive residual stress condition of about
650 MPa. Further on, the effect of HFMI-treatment is recognizable up to a depth of about 1000 mm. In case of the high-

strength steel S960, FWHM-values reveal an increase from about 2.5° for the as-welded to approximately 4.5° for the HFMItreated state up to a minor depth of 200 mm. As the high-

596

M. Leitner et al. / Engineering Structures 143 (2017) 589–602

strength base material already exhibits a comparable high hardening condition, the potential of further hardening by the posttreatment in depth is therefore decreased. Summarized, HFMI-treatment leads to a beneficial reduction of the residual stress state in loading direction up to a depth of at least 1000 mm at the weld toe. Depending on the base material yield strength, the FWHM-values show a hardening effect from 200 mm up to about 1000 mm in depth. 3.3.3. Stability of HFMI-induced residual stress condition during cyclicloading At third, measurements on additional HFMI-treated mild steel S355 specimens, which are cyclically loaded up to 5107 loadcycles at the base material corresponding run-out load-level of Drn = 250 MPa, are investigated. The results of residual stress in loading and FHWM-values in depth of the post-treated weld toe in case of two mild steel S355 specimens are depicted in Fig. 11. At the surface near region up to 50 mm depth, the average residual stress state relaxes from about
335 MPa before loading to approximately
100 MPa after cyclic loading up to 5107 loadcycles. Actually, up to a depth of over 1500 mm a certain amount of relaxation takes place showing that the HFMI-induced residual stress condition is not stable even at comparably minor loadlevels at the run-out region. Measurements of the FWHM-values in depth point out that only a slightly decrease in the hardening condition arises due to the fatigue loading. Therefore, cyclic loading at the run-out load-level up to the high-cycle fatigue region leads only to a relaxation of the compressive residual stress state at the post-treated weld toe and not significantly reduces the local hardening condition for the investigated mild steel S355 specimen. Further analysis focuses on the same load-level of Drn = 250 MPa, but provides detailed measurement results for the first load-cycles, which may have a relevant influence on the cyclic stability of the local residual stress condition due to elasto-plastic redistribution at the HFMI-treated weld toe. Therefore, residual stress values are additionally measured at the weld toe surface after one and five load-cycles in case of the mild steel S355 specimen. The results are depicted in Fig. 12 additionally incorporating the average surface-layer values of the presented measurements before loading at N = 0 and after run-out at N = 5107 load-cycles. The experimentally assessed distribution reveals that a significant relaxation of the compressive residual stress state from about
335 MPa to approximately
200 MPa takes place due to first load-cycle. Further on, no distinctive relaxation between the first

Fig. 12. Surface residual stress values in transversal (loading) direction in dependence of number of load-cycles (S355).

and the fifth load-cycle is evaluated. However, a continuative cyclic relaxation from
200 MPa after the fifth load-cycle to around
100 MPa after run-out at fifty million load-cycles occurs as presented before. In addition, the measurement results for the HFMI-treated highstrength S960 longitudinal stiffener before and after fatigue loading at the run-out load-level of Drn = 275 MPa, are presented in Fig. 13. Hereby, again a substantial relaxation appears due to the fatigue loading in the high-cycle fatigue region. In the surface near region up to 50 mm, a relaxation from around
650 MPa before loading to roughly
200 MPa after cyclic loading up to 5107 load-cycles occurs. Nevertheless, the influence is measured up to a depth of just 600 mm, which is considerably less than for the mild steel S355. In case of the evaluated FWHM-values almost no change before and after fatigue loading is observed, which may be explained due to the use of the high-strength material. Summing up, an effect of cyclic loading on the HFMI-induced residual stress condition is observable based on the presented measurement results. In case of the mild steel S355, a significant relaxation occurs due to the first load-cycle even at minor loadlevels at the run-out region, which basically acts as quasi-static

Fig. 11. Longitudinal attachment with S355 as base material in HFMI-treated condition at N = 0 and N = 5107: Residual stress values in transversal (loading) direction and corresponding FWHM-values at weld toe.

M. Leitner et al. / Engineering Structures 143 (2017) 589–602

597

Fig. 13. Longitudinal attachment with S960 as base material in HFMI-treated condition at N = 0 and N = 5107: Residual stress values in transversal (loading) direction and corresponding FWHM-values at weld toe.

overload in this connection. Further cyclic residual stress relaxation is detected up to 5107 load-cycles. In order to analyse these findings in detail, analytical and numerical methods are applied on the mild steel S355 longitudinal stiffener specimen, which are presented in the following sections. The procedure is not utilized for the high-strength steel S960, as no material data in the course of the structural welding simulation is currently available. However, the principal of the method can be also facilitated for the highstrength steel S960 as well as other materials, if the material data base for the simulation task is available. 4. Numerical analysis In this section, a numerical simulation procedure is presented, which is applied on the investigated mild steel S355 single-sided non-load carrying longitudinal stiffener. The simulation tasks involve a structural weld simulation, numerical analysis of the HFMI-treatment, and a final simulation of the cyclic loading to investigate the residual stress stability numerically. 4.1. Structural weld simulation At first, a half-symmetrical structural thermo-mechanical coupled weld simulation is set-up, utilizing the software package Sys-

weld [40]. Herein, different hardening models, such as basic isotropic and kinematic hardening rule according to [41] are incorporated. A consideration of the kinematic portion [42], which involves the influence of dynamic recovery during cyclic loading [43] in addition to the backstress, is enabled. Details in regard to the applied simulation parameters and material models are provided in [7,44]. The default database in [40] provides extensive temperature-dependent thermal and mechanical properties for the applied mild steel S355, see Fig. 14. Among these data sets, two significant thermal properties, in particular the specific heat c and the thermal conductivity K, are presented in detail illustrating a distinctive phase-dependent difference up to approximately Ac1-temperature. In the course of the material properties, cooling rate-dependent phase transformation as time-temperaturetransformation behaviour (TTT) is incorporated in addition to temperature-dependent quasi-static values, such as yield stress, ultimate stress, Young’s modulus, Poisson’s ratio, and density. Further information involving comprehensive material data for the analyzed mild steel S355 is given within a preliminary study on a butt joint in [20]. For the structural weld simulation, the suggested heat-source model by [45] is utilized, whereby detailed information regarding calibration and finally applied parameters for the investigated longitudinal stiffener specimen is provided within a previous analysis [44].

Fig. 14. Thermal phase-dependent properties and TTT-diagram for mild steel S355 [40].

598

M. Leitner et al. / Engineering Structures 143 (2017) 589–602

Fig. 15 depicts the temperature distribution and the not-yet deposited filler material at a weld process time of t = 3.7 sec. The weld path is completed after a total weld time of t = 7.4 sec. Cool-down to ambient temperature is modelled by considering a total simulation time span of t = 1000 sec. The unclamping occurs during the last second of the cool-down stage. The resulting von Mises equivalent stress field and the amount of bainitic-martensitic microstructure after finishing of the structural weld simulation is presented in Fig. 16. The resulting residual stress values at the surface of the end-ofseam region of the longitudinal stiffener specimen are provided in Table 4 revealing a sound accordance. The evaluated residual stresses are shown as an average surface-layer value at the measurement point in the course of the X-ray measurements, see Fig. 1. As the focus of the residual stress relaxation is laid on the crack initiation point at the surface, only these values are presented in this study. Further details to the residual stress state are given in [44]. A comparison of the numerically computed values shows a good agreement to the X-ray measurements at the surface; therefore, this final condition acts as basis for the subsequent HFMItreatment simulation.

Table 4 Resulting residual stress results after welding process. X-ray measurement

Structural weld simulation

Residual stress in transversal (loading) direction at surface layer of weld toe [MPa]
110
111

4.2. Simulation of HFMI-treatment After the structural weld simulation, the numerical results including residual stress state, plastic strains and phasedependent material properties are transferred as mechanical cards into Abaqus [46]. Thereby, the elastic-plastic material behaviour of the investigated mild steel S355 is considered by a combined isotropic-kinematic hardening model for the implicit, displacement controlled HFMI-treatment simulation. In [20], a basic study regarding the effect of the hardening law on the stress-strain relationship based on a single element model is conducted. The results show that the combined hardening model includes the backstress after a change of the loading direction and sufficiently matches the

Fig. 15. Structural weld simulation: Temperature distribution during and not-yet deposited filler material at a process time of t = 3.7 sec [44].

Fig. 16. Structural weld simulation: Resulting von Mises equivalent stress field and amount of bainitic-martensitic microstructure after finishing of weld process [44].

599

M. Leitner et al. / Engineering Structures 143 (2017) 589–602

behaviour of the investigated mild steel S355. As similar conclusions are stated in [47], this model is applied in the subsequent simulation routine. Details regarding the incorporated process parameters are again included in [20]. Fig. 17 shows the HFMItreatment at the third stroke and the final residual stress condition after completion of the numerical HFMI-process simulation. Fig. 18 illustrates the final indentation depth at the end-of-seam weld toe area after simulating the HFMI-treatment. The resulting depth of about 0.19 mm is in agreement with microscopic measurements on metallographic cross-sections, which contributes to the applicability of the applied HFMI-process parameters in the course of the numerical simulation. In Table 5, a comparison of the numerically computed and X-ray measured results is provided, which shows that again, in consideration of the scattering due to X-ray measurements a generally good agreement with a maximum difference of just about five percent is achieved. The results reveal that the used material models are basically applicable for the simulation of the HFMI-process, whereat this finding is also confirmed by the analysis in [20] focussing on

Table 5 Resulting residual stress results after HFMI-treatment. X-ray measurement

HFMI simulation

Residual stress in transversal (loading) direction at surface layer of weld toe [MPa]
335
319

the influence of material modelling on the final residual stress condition. Summarized, both the numerical results after welding and HFMI-treatment are well comparable to the measurements. Therefore, the manufacturing process simulation chain is well suited to act as initial condition for a further study of the cyclic stability of the residual stress condition. 4.3. Computation of cyclic-loading Subsequent to the structural welding and HFMI-treatment simulation, the S355 specimen model is stressed with a nominal stress

Fig. 17. Simulation of HFMI-treatment: Resulting von Mises equivalent stress field at third stroke during post-treatment and after completion of HFMI-process.

Fig. 18. Final indentation depth at end-of-seam weld toe area after HFMI-treatment.

600

M. Leitner et al. / Engineering Structures 143 (2017) 589–602

Table 6 Nominal load stress history for simulation of five load-cycles (Drn = 250 MPa and R = 0.1). Step number

#1 (N = 1)

#2

Local load stress r in transversal (loading) direction at surface of weld toe [MPa] Load stress 278 27.8

range of Drn = 250 MPa at a stress ratio of R = 0.1 by five loadcycles. The load-history is numerically applied in accordance to the experiments and presented in Table 6. For the evaluation of the residual stress condition after just one load-cycle, the specimen is unloaded subsequent to the application of the nominal mean stress in the third step. The results for the Xray measurements and numerical simulation are summarized in Table 7. It is shown that the experimentally and numerically utilized values are in good accordance with a minor difference of up to only five percent, revealing that the applied manufacturing simulation chain including the material data and hardening models is well suitable to estimate the local residual stress relaxation due to cyclic stress at the first loadings. Similar work focussing on the cyclic stability of shot peening induced residual stresses in [48] showed that the amount of relaxation is significantly depending on the local plasticity expressed by the plastic Dep or total strain range Det. Therefore, the local elastoplastic material behaviour is one of the key factors influencing the cyclic residual stress redistribution, which is also identified in this paper in the course of the presented experimental and numerical investigations. Fig. 19 depicts the difference in plastic strain magnitude before and after the first load-cycle at the end-of-seam area of the HFMI-treated weld toe.

Table 7 Residual stress states after cyclic loading at Drn = 250 MPa and R = 0.1. N=0

N=1

N=5

Residual stress in transversal (loading) direction at surface of weld toe [MPa] X-ray Measurement
335
204
197 Numerical simulation
319
201
202

#3 to #10 (N = 2 to 5)

#11

#12

278 and 27.8

153

0

Herein, the local plastic strain magnitude exhibits a value of up to about Dep = 0.29%, which leads to a relaxation of the compressive residual stress state as presented. Furthermore, it is shown that the subsequent numerically analyzed loading steps up to a total number of five load-cycles do not significantly change the plastic strain behaviour anymore.

5. Discussion This chapter discusses the experimental, analytical and numerical results investigated in this work. In regard to the presented cyclic residual stress relaxation models, the proposal by [28] is a comparably feasible suggestion, because no specific material data needs to be evaluated at all. Therefore, this model is applied to estimate the cyclic residual stress stability of the HFMI-treated mild steel S355 longitudinal stiffener specimen in the high-cycle fatigue region up to a number of 5107 load-cycles. In addition, the numerical results act as estimation to cover the residual stress redistribution in the course of the first five load-cycles considering the local elasto-plastic material behaviour, which is simulated based on the manufacturing process and therefore incorporates the complex material history. The residual stress relaxation is analytically estimated on the basis of Eq. (9). Thereby, the locally applied load upper stress at the weld toe exhibits a numerically computed value of rapp = 695 MPa at a nominal stress range of Drn = 250 MPa and a load stress ratio of R = 0.1. A superposition of this local upper stress with the compressive residual stress condition of (rres)ini =
335 MPa leads to a value of 360 MPa. Utilizing the presented local hardness value of at least 180 HV3 at the HFMI-treated weld toe region in Fig. 4, this local stress is significantly below the local yield strength, which is estimated to be about 425 MPa on the basis of

Fig. 19. Plastic strain magnitude at end-of-seam weld toe area due to first load-cycle.

M. Leitner et al. / Engineering Structures 143 (2017) 589–602

601

are in sound agreement to the measurements with a maximum difference of only 5%. These results principally proof the applicability of the numerical method including the involved material and hardening models of the analyzed mild steel S355. For the estimation of the residual stress relaxation in the lowand high-cycle fatigue region, a consecutive numerical-analytical procedure is presented, which is well suitable in case of the investigated specimen type and mild steel material. The described method can be also applied to other specimen geometries as well as further base materials. Therefore, the work in this paper scientifically contributes to an improved fatigue assessment of welded and HFMI-treated structures and may act as basis for further studies regarding the residual stress stability of mild and high-strength steel joints under in-service conditions. References

Fig. 20. Cyclic stability of HFMI-treatment induced residual stress values in transversal (loading) direction: Comparison of numerical-analytical evaluation and X-ray measurement.

[49]. Applying the residual stress relaxation model by [28], the residual stress condition after the first load-cycle with a value of (rres)1cycle =
204 MPa and an empirically evaluated exponent of k =
0.038 lead to an estimated residual stress of (rres)relax =
191 MPa at a number of five, and of (rres)relax =
104 MPa at a number of 5107 load-cycles, which both equal a minor difference to the measurements of less than five percent. A comparison of the results by X-ray measurements, numerical as well as analytical analyses are provided in Fig. 20. Herein, a sound conformity is achieved showing that the presented consecutive numericalanalytical procedure is well exercisable to estimate the cyclic residual stress stability for both the low- and high-cycle fatigue region. However, it has to be noted that in service additional influences, such as variable amplitude loading [50] or multiaxial stress conditions [51], which may significantly affect the residual stress relaxation and the final fatigue life of welded and HFMI-treated structures. Thereby, this work acts as basis, which shows that for uniaxial load conditions the introduced consecutive numericalanalytical methodology is applicable, but in case of more complex operating conditions further analyses is still necessary.

6. Conclusions Based on the conducted experimental, analytical, and numerical work as well as the obtained results, the following conclusions can be drawn in regard to cyclic residual stress stability of the investigated HFMI-treated longitudinal stiffener specimens: A complementary study regarding the influence of HFMItreatment parameters shows that the nominal post-treatment frequency and the pin tip radius affect the induced residual stress state on base plate specimens. The magnitude of induced residual stresses increased with a rise in treatment frequency and pin tip radius. X-ray measurements for S355 and S960 longitudinal stiffener specimens reveal that due to cyclic loading a significant reduction of the beneficial compressive residual stress state at the HFMItreated end-of-seam weld toe area occurs. This relaxation process takes places in the low- and high-cycle fatigue region at comparably minor stress ranges near the run-out stress level. The presented numerical simulation chain incorporating both structural welding and HFMI-treatment simulation shows that the final residual stress states after each manufacturing process

[1] Leitner M, Stoschka M, Eichlseder W. Fatigue enhancement of thin-walled, high-strength steel joints by high-frequency mechanical impact treatment. Weld World 2014;58:29–39. [2] Tai M, Miki C. Fatigue strength improvement by hammer peening treatment— verification from plastic deformation, residual stress, and fatigue crack propagation rate. Weld World 2014;58:307–18. [3] Lefebvre F, Peyrac C, Elbel G, Revilla-Gomez C, Verdu C, Buffière J-Y. Understanding of fatigue strength improvement of steel structures by hammer peening treatment. Procedia Eng 2015;133:454–64. [4] Marquis G, Barsoum Z. IIW recommendations for the HFMI treatment. IIW collection. Springer; 2016. http://www.springer.com/de/book/ 9789811025037. [5] Berg J, Stranghoener N. Fatigue strength of welded ultra high strength steels improved by high frequency hammer peening. Procedia Mater Sci 2014;3:71–6. [6] Ottersböck M, Leitner M, Stoschka M, Maurer W. Procedia Eng 2016;160:214–22. [7] Leitner M, Barsoum Z, Schäfers F. Crack propagation analysis and rehabilitation by HFMI of pre-fatigued welded structures. Weld World 2016;60:581–92. [8] Yekta R, Ghahremani K, Walbridge S. Effect of quality control parameter variations on the fatigue performance of ultrasonic impact treated welds. Int J Fatigue 2013;55:245–56. [9] Tai M, Miki C. Improvement effects of fatigue strength by burr grinding and hammer peening under variable amplitude loading. Weld World 2012;56:109–17. [10] Yildirim HC, Marquis G, Sonsino CM. Lightweight design with welded highfrequency mechanical impact (HFMI) treated high-strength steel joints from S700 under constant and variable amplitude loadings. Int J Fatigue 2016;91:466–74. [11] McCLUNG RC. A literature survey on the stability and significance of residual stresses during fatigue. Fatigue Fract Eng Mater Struct 2007;30:173–205. [12] 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. Weld World 2013;57:235–41. [13] Dalaei K, Karlsson B. Influence of overloading on fatigue durability and stability of residual stresses in shot peened normalized steel. Mater Sci Eng A 2011;528:7323–30. [14] Buchanan DJ, John R. Residual stress redistribution in shot peened samples subject to mechanical loading. Mater Sci Eng A 2014;615:70–8. [15] Kim JC, Cheong SK, Noguchi H. Residual stress relaxation and low- and highcycle fatigue behavior of shot-peened medium-carbon steel. Int J Fatigue 2013;56:114–22. [16] Khurshid M, Barsoum Z, Marquis G. Behavior of compressive residual stresses in high strength steel welds induced by high frequency mechanical impact treatment. J Pressure Vessel Technol 2014;136. [17] Lee CH, Chang KH, Van Do VN. Finite element modeling of residual stress relaxation in steel butt welds under cyclic loading. Eng Struct 2015;103:63–71. [18] Mikkola E, Remes H, Marquis G. A finite element study on residual stress stability and fatigue damage in high-frequency mechanical impact (HFMI)treated welded joint. Int J Fatigue 2017;94:16–29. [19] Yuan K, Sumi Y. Simulation of residual stress and fatigue strength of welded joints under the effects of ultrasonic impact treatment [UIT]. Int J Fatigue 2016;92:321–32. [20] Leitner M., Simunek D., Shah F., Stoschka M. Numerical fatigue assessment of welded and HFMI-treated joints by notch stress/strain and fracture mechanical approaches. Adv Eng Software, 2016, in press. [21] Zaroog OS, Ali A, Sahari BB, Zahari R. Modelling of residual stress relaxation: a review, Pertanika. J Sci Technol 2009;17(2):211–8. [22] Morrow J, Sinclair GM. Cycle-dependent stress relaxation. In: Symposium on Basic Mechanisms of Fatigue, ASTM STP 237. American Society for Testing and Materials; 1958. [23] Jhansale HR, Topper TH. Engineering analysis of the inelastic stress response of a structural metal under variable cyclic strains. In: Cyclic stress-strain

602

[24]

[25] [26]

[27] [28] [29]

[30] [31] [32] [33]

[34]

[35]

[36]

M. Leitner et al. / Engineering Structures 143 (2017) 589–602 behavior-analysis, experimentation, and failure prediction ASTM STP 519. American Society for Testing and Materials. p. 246–70. Kodama S. The behaviour of residual stress during fatigue stress cycles. In: Proceedings of the international conference of mechanical behaviour of materials, vol. II; 1972, p. 111–118. Zhuang Wyman Z, Halford Gary R. Investigation of residual stress relaxation under cyclic load. Int J Fatigue 2001;23:31–7. Qian Z, Chumbley S, Karakulak T, Johnson E. The residual stress relaxation behavior of weldments during cyclic loading. Metal Mater Trans A 2013. http://dx.doi.org/10.1007/s11661-013-1688-9. Zaroog OS, Ali A, Sahari BB, Zahari R. Modeling of residual stress relaxation of fatigue in 2024-T351 aluminium alloy. Int J Fatigue 2011;33:279–85. Han S, Lee T, Shin B. Residual stress relaxation of welded steel components under cyclic load. Mater Technol (Steel Res) 2002;73(9):414–20. Li L, Wan Z, Wang Z, Ji C. Residual stress relaxation in typical weld joints and its effect on fatigue and crack growth. Acta Metall Sin (Engl Lett) 2009;22 (3):202–10. Stoschka M, Leitner M, Fössl T, Posch G. Effect of high-strength filler metals on fatigue. Weld World 2012;5(3/4):20–9. Stoschka M, Leitner M, Posch G, Eichlseder W. Effect of high-strength filler metals on the fatigue behaviour of butt joints. Weld World 2013;57:85–96. Leitner M. Influence of effective stress ratio on the fatigue strength of welded and HFMI-treated high-strength steel joints. Int J Fatigue 2017 [in press]. Leitner M., Stoschka M., Schörghuber M., Eichlseder W. Fatigue behaviour of high-strength steels using an optimized welding process and high frequency peening technology. In: Proceedings of the international conference of the international institute of welding, Chennai/India; 2011, p. 729–36. Leitner M, Stoschka M, Eichlseder W. Fatigue enhancement of thin-walled high-strength steel joints by high frequency mechanical impact treatment. Weld World 2014;58(1):29–39. ASTM International. Standard practice for statistical analysis of linear or linearized stress-life (S-N) and strain-life (e-N) fatigue data, designation: E739-91, reapproved 1998, 1998. Dengel D, Harig H. Estimation of the fatigue limit by progressively-increasing load tests. Fatigue Frac Eng Mater Struct 1980;3(2):113–28.

[37] Schäfers F, Gerster P, Leitner M. Overview of residual stress measurement and fatigue test data for pneumatic impact treated (PIT) joints, IIW-document XIIIWG2-146-15, 2015. [38] Foehrenbach J, Hardenacke V, Farajian M. High frequency mechanical impact treatment (HFMI) for the fatigue improvement: numerical and experimental investigations to describe the condition in the surface layer. Weld World 2016;60:749–55. [39] Branco CM, Infante V, Baptista R. Fatigue behaviour of welded joints with cracks, repaired by hammer peening. Fatigue Fract Eng Mater Struct 2004;27:785–98. [40] ESI Group. SYSWELD Toolbox, release 16; 2014. [41] Prager W. Recent development in the mathematical theory of plasticity. J Appl Phys 1949;235:7. [42] Armstrong P, Frederick C. A mathematical representation of the multiaxial bauschinger effect, CEGB Report RD/B/N731, 1966. [43] Chaboche J-L. A review of some plasticity and viscoplasticity constitutive theories. Int J Plast 2008;24:1642–93. [44] Stoschka M., Ottersböck M., Leitner M. Integration of phase-dependent workhardening into transient weld simulation. In: Proceedings of the ninth international conference on engineering computational technology; 2014. [45] Goldak J, Chakravarti A, Bibby M. A new finite element model for welding heat sources. Metall Trans B 1984;15(2):299–305. [46] Dassault Systemes, Abaqus 6.14; 2014. [47] Baptista R, Infante V, Branco C. Fully dynamic numerical simulation of the hammer peening fatigue life improvement technique. Procedia Eng 2011;10:1943–8. [48] Dalaei K, Karlsson B, Svensson L-E. Stability of shot peening induced residual stresses and their influence on fatigue lifetime. Mater Sci Eng A 2011;528:1008–15. [49] Pavlina E, Van Tyne C. Correlation of yield strength and tensile strength with hardness for steels. J Mater Eng Perform 2008;17(6):888–93. [50] Mikkola E, Remes H. Allowable stresses in high-frequency mechanical impact (HFMI)-treated joints subjected to variable amplitude loading. Weld World 2017;61:125–38. [51] Farajian M, Nitschke-Pagel T, Siegele D. Welding residual stress behavior in tubular steel joints. HTM J Heat Treat Mater 2014;69:1.