Experimental Investigation of Stress Concentration and Fatigue Behavior in 9% Ni Steel Welded Joints under Cryogenic Conditions

: This experimental study delves into the intricate mechanics of stress concentration and fatigue behavior exhibited by 9% Ni steel welded joints under cryogenic conditions. The study specifically examines butt-welded, fillet longitudinal, and fillet transverse specimens, comparing their fatigue properties under room and cryogenic temperatures. Notably, determining hot-spot stress presents a challenge, as it cannot be directly obtained through traditional means. To overcome this limitation, a method for predicting hot-spot stress is introduced, which considers the effects of mis-alignments and weld bead characteristics. The study also highlights the impact of grip-clamping-induced specimen deformation and the reduced middle section on stress concentration resulting from misalignments. Furthermore, it proposes separate consideration of the effects of the weld bead on the axial nominal stress and on the bending stress of the specimen. The accuracy of strain gauge measurements in cryogenic environments is addressed by suggesting a method to correct the output of 2-wire strain gauges using a fixed ratio derived from 2-wire and 3-wire strain gauges. By comparing predicted hot-spot stress with actual measurements, the study validates the reliability of the proposed predictive method. These findings contribute to a deeper understanding of the behavior of 9% Ni steel welded joints under cryogenic conditions and provide valuable insights for design and engineering in similar applications


Introduction
Due to the expansion of the global population and economy, there is a concurrent increase in energy demand.This increase in energy needs, combined with the desire to reduce CO2 emissions, leads to a continuously increasing demand for Liquefied Natural Gas (LNG), which is a clean energy source [1].As IMO environmental regulations [2], such as CO2 emission restrictions, have been strengthened, the demand for LNG fuel ships that can replace conventional ships has been increasing.LNG tanks present a potential risk of leakage and explosion accidents, and many researchers have evaluated their safety during cryogenic service [3,4].The Self-supporting Prismatic shape IMO type B (SPB) LNG tank can reduce the sloshing effect, making it commonly used in LNG fuel ships [5].The SPB-type tank is mainly made using 9% Ni steel, since 9% Ni steel has excellent mechanical properties under cryogenic temperature [5].For 9% Ni steel, various monotonic tensile tests and fatigue tests have been conducted recently [6][7][8][9].Shielded metal arc welding (SMAW) and submerged arc welding (SAW) are mainly applied to the welding method for 9% nickel steel.In the case of flux-cored arc welding (FCAW), welding consumables for 9% nickel steel were developed [9].Lee et al. found that when the temperature decreased, for 9% Ni steel, no visible improvement in the true tensile strain of the base metal was observed, but a significant increase in the true tensile strain of the weld metal was observed [6].According to the crack growth and CTOD evaluation, 9% Ni steel did not show any significant change in its mechanical behavior with respect to the temperature drop [6].In the study by Kim et al., it was noted that as the temperature decreased, the fatigue limits of the base metal, weld metal, and corner weld of 7% nickel steel all increased [7].The fatigue crack propagation properties of 9% Ni steel were summarized by Shiratsuchi and Osawa [8].
Estimating the fatigue life according to the S-N curve has always attracted attention.There are different approaches for the fatigue life analysis of a welded joint.These methods are distinguished mainly by the parameters used to describe fatigue life "N" or fatigue strength [10].When performing a series of fatigue tests, the nominal stress can be simply calculated from the dimensions of the specimen and the applied force.The fatigue strength is determined by comparing the nominal stress range with the S-N curves classified according to the weld joint types [11].The residual stress will affect fatigue properties as well.Xin, H. reported that the full range of S-N curves based on hardness measurements without considering residual stress effects overestimates the fatigue life of buttwelded joints [12].For the evaluation of stresses in welded joints, hot-spot stresses have been widely used [13].On the other hand, once the hot-spot stress is considered, the test data would show a significantly improved correlation with the mean S-N curve scatter band [14].To determine hot-spot stress, strain gauges are typically employed for measurement.Hot-spot stress is estimated by extrapolating values measured from these strain gauges.However, issues such as strain gauge detachment during testing and errors due to improper installation may arise.When working with thin specimens, the short distance between strain gauges and the weld bead complicates accurate installation.Especially in the case of cryogenic temperature experiments, the accuracy of the strain gauge would be degraded.This study aims to overcome these challenges by developing precise and efficient methods for detecting hot-spot stress in cryogenic environments.
The stress concentration factor () is defined as the ratio of the maximum stress to the nominal stress of a target section.In the case of butt-welded joints, to address the practical issues, the stress concentration factor is used as the ratio between the hot-spot stress and the nominal stress.The stress concentration of the butt-welded specimen is mainly blamed on the existence of misalignment and the weld bead.Berge and Myhre [15] proposed a method to calculate the  due to axial misalignment [15].By employing explainable machine learning, Braun et al. [16] found that macro-geometric axial and angular misalignment was the most influential parameter on the failure location of small-scale butt-welded joints.Chen et al. [17] reported that the failure location of butt joints with backing plates in fatigue tests could be accurately predicted with the traction structural stress method with considerations of angular joint misalignments.Qiu et al. [18] indicated that the plate thickness greatly influenced the fatigue reliability index of typical welded joints.The effect of the location of the weld and aspect ratio on the  was studied by Cui et al. [19].
However, for the specimen used in this study, the weld position is in the middle, so both the weld position and the aspect ratio have a negligible effect on the  calculation.Xing and Dong [14] found that the load-carrying fillet-welded specimens would deform during the grip-clamping process, which also affects the .This study suggests that specimen deformation should also be considered when predicting the  of buttwelded specimens.In the meantime, the above-summarized  prediction methods for butt welds are the methods applied to structures, which cannot be directly applied to specimens because they do not consider the effect of the reduced section in the middle of the specimen on the hot-spot stress.In this study, the effect of the reduced midsection of the specimen on the stress concentration is taken into account and compared with the constant width model.
Meanwhile, these studies did not consider the effect of the bead on the , so these methods are insufficient in predicting the .The stress concentration caused by the weld bead could be estimated using finite element analysis from a misalignment-free model, as reported by Kang et al. [20].Lillemäe et al. [21] obtained the  by building a finite element model in which both the bead and misalignment were present.They indicated that the relationship between the hot-spot stress and the nominal stress is highly non-linear for the thin specimen.However, when multiple specimens with different misalignments need to be studied, the FE model needs to be re-established, resulting in lower efficiency.By introducing one additional stress concentration factor, Dong et al. [11] studied the effect of the weld bead on stress concentration.Instead, this study argues that the specimen experiences both axial and bending stresses during the experiment.So the effect of the bead on axial stress and bending stress should be considered separately.Finite element analysis is employed to individually investigate the stress concentrations caused by the bead on the tensile and bending specimens.
This study enhances existing methods by considering the combined effects of misalignment, bead, clamped grips, and reduced middle sections.The effect of the bead on axial and bending stresses is also studied separately.A comparison of this study with previous works is presented in Table 1.The prediction method is more suitable for predicting the hot-spot stress and the  of butt-welded specimens.To verify the feasibility of the proposed method, the predicted  is compared with the measured .The results show that the experimentally obtained  is in good agreement with the predicted .By using the method proposed in this study, it is possible to solve the disadvantages that may occur during strain measurement, such as incorrect installation and strain gauge detachment.It can also be used to check the validity of the  values obtained from the test if the actual test results deviate too much from expectations.
In the case of fillet specimens, Mashiri et al. [22] showed the differences in stress concentrations that occur from the different weld shapes.Hong et al. [23] used the peridynamic to simulate the fatigue process in a fillet weld.Chen et al. [24] investigated the fatigue performance of full-size fillet-welded specimens with incomplete penetration and misalignment of the weld root based on experimental tests and finite element analysis.A unified master S-N curve covering different plate thicknesses, materials, and weld profiles was also proposed [24].The fatigue failure mode transition behavior of aluminum filletwelded connections was analyzed systematically by Xing et al. [25].Ahola and Björk [26] investigated the effect of specimen attachment misalignment on stress concentration and calculated the  using finite element analysis.Meanwhile, the effective notch stress method and 4R method could be used in fillet-welded joint fatigue [27].However, a method to predict the  by considering multiple weld dimensions does not exist yet.Meanwhile, measuring the profile with the 3D scanner would be laborious and could induce errors.Therefore, using the strain gauge to measure the hot-spot strain is more efficient for the fillet specimen.
The 2-wire strain gauge is commonly used at room temperature.However, using the 2-wire strain gauge directly in a cryogenic environment will reduce the accuracy of the experimental results.At cryogenic temperature, the 3-wire strain gauge is frequently used, but the cost of the experiment will increase.This study compares the output differences of the two strain gauges in the cryogenic environment.Based on the comparison results, a method of correcting the values obtained from the 2-wire strain gauge is proposed.The hot-spot stress of the fillet specimen can be measured more economically using the proposed calibration method.
In the present study, fatigue tests are conducted on three types of specimens: buttwelded, fillet longitudinal, and fillet transverse specimens at both room and cryogenic temperatures.The main objectives of this study are as follows: (1) to compare the fatigue characteristics of the three welded specimens at different temperatures and summarize the crack initiation position; (2) to optimize the method of studying the effect of misalignment on stress concentration; (3) to investigate the effect of the bead on stress concentration in specimens; and (4) to propose a strain gauge calibration method for cryogenic temperature testing.

Orientation and Measurement
Butt welding is a common connection in welded structures.There are four weld roots near the welding part.The welding direction of the specimen can be distinguished by checking the stacking sequence of the fish-scale-like pattern on the welded part.As shown in Figure 1a, the earlier welded part is on the lower layer, and the subsequent welded part is on the upper layer.Then, the front and back of the specimen can be distinguished according to the size of the bead, as shown in Figure 1b.The base material (BM), heat-affected zone (HAZ), and weld metal (WM) in the specimen have been marked in Figure 1b.In this way, the orientation of each specimen can be defined, where  is the width of the specimen, and  is the thickness of the specimen.For a better understanding, E (Earlier welding), S (Subsequent welding), F (Front), B (Back), U (Upper), and L (Lower) are employed, as shown in Figure 1c.Furthermore, the weld root could be named using FU, FL, BU, and BL corresponding to the position shown in Figure 1d.Eight strain gauges are installed on both sides of the specimen to measure the strain, and the numbers from 1 to 8 denote the eight strain gauges, respectively, as shown in Figure 1d.The specimen thickness () is 12 mm.By measuring the strain at 0.5 (6 mm) and 1.5 (18 mm) from the weld root, the hot-spot strain can be obtained by the linear extension method.
The profiles on both sides of each specimen are measured to study the misalignment effect.The average value on both sides is taken as the misalignment of the specimen.Importing the profiles into AutoCAD for measurement is shown in Figure 2a.Since the specimen direction has already been distinguished, the direction of the axial misalignment and angular distortion can be defined, as shown in Figure 2b.The bead appearance is obtained by 3D scanning, as shown in Figure 2c and translated to the FE model for further analysis, as presented in Figure 2d.

𝑆𝐶𝐹 Prediction Method Review
The  is the ratio between the hot-spot stress ( ℎ ) and nominal stress (  ), as in Equation (1): The classical  calculation method considers the effects due to the specimen's initial axial misalignment (ⅇ) and angular distortion (), and the analytical equations are applied based on the simple beam theory as in Equation (2) [15].
where the following apply:   : the stress magnification factor due to axial misalignment (dimensionless);   : the stress magnification factor due to angular distortion (dimensionless); : 3 for clamped; 6 for pinned condition; : the total length of the specimen (mm); : the thickness of the specimen (mm).
As for standards, like BS 7910 [28], IIW [29], and DNV [30], they consider the nominal stress effect.However, this effect is negligible for the specimens which are tested in this study.DNV also considers misalignment tolerance,   =  − 0.1.The misalignment used to calculate (  ) is the actual misalignment () minus 0.1.

Stress Components
Due to misalignment, bending stress is induced in the specimen during the gripping procedure before the fatigue test.At this moment, though the nominal stress (  ) is zero, the hot-spot stress is non-zero.So in the subsequent fatigue experiments, the total hot-spot stress ( ℎ ) has two components: (1) hot-spot stress initiated by gripping ( ℎ, ) and ( 2) hot-spot stress initiated by nominal stress ( ℎ, ), as in Equation (3).
In the fatigue test, the loading amplitude is valuable to study, defining the  ∆ as in Equation ( 4).The   and   correspond to the maximum and minimum values during the loading process.
Combine Equations ( 3) and ( 4), and the relationship between  ℎ and   is given by Equation (5).
As shown in Figure 3, the slope represents  ∆ , while the intercept represents  ℎ, .Shen et al. [31] stated that the stress magnification factor could decrease as the nominal stress increases.However, Figure 3a shows that the slope of the   −  ℎ curve is invariant.In this way, the  ∆ of the specimen in this study is not a function of   .During the fatigue test, the specimen is subjected to periodic tensile load, and its stress distribution can be divided into two parts: axial nominal stress and bending stress.By adopting the superposition principle, the bending stresses due to axial misalignment and angular distortion could be discussed separately.For instance, the stress distribution can be presented in Figure 4 when considering the axial misalignment.The   represents the stress magnification factor due to axial misalignment.
The total stress has two components: (a) nominal stress for balancing the axial load ( Δ  ); and (b) bending stress for balancing the moment due to misalignment (Δ , ).The axial nominal stress remains constant in the thickness direction, but the bending stress varies linearly through the thickness and becomes zero at the neutral line.The axial nominal stress is equal to the load applied to the specimen.The bending stress is proportional to the nominal stress and also depends on the magnitude of misalignment.
Thus, the total stress could be written as in Equation (6).
Considering the angular distortion existing case, the stress could be written as in Equation (7).The   is the stress magnification factor due to angular distortion.
When both axial misalignment and angular distortion exist, using the principle of superposition, Equation ( 8) can be obtained: The first term represents axial nominal stress, while the second and the third term represent bending stress due to the misalignment.The magnitude of the   or   should be the same for different roots.However, the direction of the bending stress is opposite on both sides.Table 2 gives the sign of the stress for each root, where "+" indicates tension and "−" indicates compression.

The Bead Effect
At the welding position, the weld bead is present.Unlike the base material specimen, this results in an inhomogeneous stress distribution, regardless of whether the specimen is subjected to axial tension or bending load.In order to study the impact of the bead,   is employed.The   is defined as the ratio of hot-spot stress to nominal stress when the specimen with a bead receives tensile stress or bending stress.Also, this study suggests that the effect of beads on axial tensile stress ( , ) and bending stresses ( , ) should be considered separately.
This part focuses exclusively on the effect of the bead.Therefore, the FE model is constructed without incorporating axial misalignment or angular distortion.Although each specimen has a unique contour at the bead part, scanning is laborious, and there is minimal variation between specimens.Consequently, only one specimen's contour is scanned, and the finite element model is based on these scanning results.
The model is created using Patran 2011, and the finite element analysis is conducted using MSC-Nastran 2011.The entire specimen utilizes 8-node Hex8 elements with a minimum mesh size of 1 mm.Larger mesh sizes are used in the clamped portion of the specimen at both ends, which improves the simulation efficiency, while smaller mesh sizes are used in the bead region of the model.The mesh details are illustrated in Figure 5.The mesh division method is referenced from Kang's study [20].
The elastic modulus of 9% Ni steel is set to 196.3 MPa, and Poisson's ratio is set as 0.3.For the boundary conditions, the nodes on one side are fixed.With reference to Kang's study [20], apply the axial tensile stress ( ,, ) or bending stress ( ,, ) on the other side as the loading condition.The results are shown in Figure 6.Selecting the stress located at 0.5 (, thickness) and 1.5 from the weld bead, the hot-spot stress ( ℎ,, or  ℎ,, ) could be calculated using linear extrapolation.The bead effect parameter for the tensile load case ( , ) and bending load case ( , ) can be obtained by computing the ratio of the hot-spot stress to the nominal stress, as presented in Equations ( 9) and ( 10): , =  ℎ,, / ,, (10)

The Clamped and Reduced Mid-Section Effect
Since the specimen is not flat, when the grip is clamped, not only will the bending stress (  ) appear, but the specimen will also deform, which would affect the subsequent fatigue tests [14].The so-called clamped effect refers to the influence of this deformation, as shown in Figure 7.
Due to the lack of considering the influence of the clamped effect, the classical   and   calculation methods are insufficient.In reference [14], the authors introduced a method for predicting the  ∆ that takes into account the clamped effect in load-carrying fillet specimens, as shown in Figure 8a.
The butt-welded specimen is welded by two base materials; adding the welding part in the middle, the specimen can be divided into three parts, as shown in Figure 8b.Although the bead sizes on both sides of the specimen are different (16 mm and 18 mm), the difference is narrow and could be ignored.Assuming the welded portion forms a thin rectangle, the butt-welded specimen would exhibit a configuration similar to that of the load-bearing fillet specimen, as shown in Figure 8c.In this way, it is found that the model predicting the fillet specimen's  ∆ can also be used for butt-welded specimens.The specimen used in this study has a narrow width in the middle section.The narrow mid-section is widely used in experimental studies, and the reduced mid-section is also recommended in the ASTM standard E466 [32].The narrow middle section ensures that failure occurs at the welded part during the experiment.Therefore, the reduction in the mid-section should be taken into account.
Therefore, this study improves this model and finds that considering or not considering the reduction in the mid-section has a non-negligible effect on the  ∆ prediction.In the reference, the model is only divided into left and right parts, as shown in Figure 9a.To consider the impact of the reduced mid-section, we divided the specimen into six parts, which have different widths, as  1 ,  2 ,  3 , …,  6 , as shown in Figure 9, and  1 = 5 mm,  2 = 85 m,  3 = 45 mm in Figure 9b.
For example, for the Num. 1 specimen, the comparison between the specimen with considering or without considering the narrow mid-section after clamping the specimen is shown in Figure 10.By using the method reported in the reference [14], the bending stress due to the axial misalignment (Δ , ) and angular distortion (Δ , ) could be calculated.Then the   and   are given by Equations ( 11) and (12).
The   and   of the Num. 1 specimen are given in Figure 11.
By considering the effect of the bead on axial nominal stress and bending stress separately, the  ∆ for the butt specimen could be obtained as in Equation (13).

Calibrating the 2-Wire Strain Gauge Output
For cryogenic temperature tests, the accuracy of the general 2-wire strain gauge could be reduced.Therefore, the cryogenic 3-wire strain gauge should be employed to maintain accuracy.As a consequence, the cost would increase.A correcting method is introduced in this section to improve the accuracy of the 2-wire strain gauge in a cryogenic environment.
The strain measurement system has two components: strain gauge and data acquisition system (DAQ) devices.The strain gauge can investigate the attached object deformed by measuring the resistance change.After the gauge is deformed, the strain () could be obtained, given in Equation (14), where   is the gauge resistance (Ω), and  is the gauge factor at the corresponding temperature.
The gauge resistance and gauge factor are supplied by the gauge manufacturer.The circuit diagram in the DAQ device is shown in Figure 12a.Any change in resistance   can be reflected as a change in  0 , given in Equation (15), where  1 ,  2 ,  3 , and   are fixed values in the DAQ device.
The strain gauge can be divided into two parts, which are the grid of the gauge and the wires of the gauge, as shown in Figure 12b.Both the grid and the wires have resistance, which are   ,   .In fact, when experimenting in a fixed-temperature environment,   is a constant value.So the gauge resistance change ∆  is equivalent to the gauge grid resistance change ∆  .The circuit diagrams of the 2-wire strain gauge and the 3-wire strain gauge are illustrated in Figure 13.
The wires are made of copper, so the resistance is sensitive to temperature changes.If the experiment is executed at varying temperatures, the resistance of the wire (  ) will change with the temperature.The resistance change in the wires will affect the accuracy of measuring the resistance change due to gauge grid deformation (∆  ).Therefore, the strain of the attached object cannot be measured correctly.As for the 3-wire strain gauge, as shown in Figure 13b, the resistance of the wire  ,1 is in a series with the gauge grid and the resistance of the wire   is in a series with the  3 .Since equal resistance changes which occur simultaneously in the adjacent arms of a bridge circuit produce no bridge imbalance, temperature changes which affect   together are effectively cancelled [33].This is the temperature compensation for the 3-wire strain gauge.For fixed-temperature cryogenic experiments, the 3-wire strain gauge can be used directly since the manufacturer provides the value of the gauge factor under the cryogenic temperature ( 3,.).The strain measured at cryogenic temperature by the 3-wire strain gauge is  3, , given in Equation (16). 3, is the 3-wire strain gauge grid resistance. 3, = ∆ 3, ( 3, ×  3,.) ⁄ For the 2-wire strain gauge, when the experiment is carried out in a constant-temperature cryogenic environment, the   would change during the cooling process from normal temperature to low temperature.However, in the subsequent experiments,   is a constant value since the temperature is fixed.The value used to calculate the strain is the change in resistance during the test, so changes in   during the cooling process will not affect subsequent test results measurement.The accurate strain ( 2,, ) could be obtained by Equation (17). 2, is the 2-wire strain gauge's gauge factor at cryogenic temperature and  2, is 2-wire strain gauge grid resistance.
However, since the 2-wire strain gauge is not designed for cryogenic temperature experiments, the gauge factor ( 2, ) at cryogenic temperature may not be provided by the manufacturer.Directly using the gauge factor of 2-wire strain gauges at room temperature ( 2, ) as in Equation ( 18) would make the strain result ( 2,, ) inaccurate. 2,, = ∆ 2, ( 2, ×  2, ) ⁄ Theoretically, under the same loading condition, if the correct gauge factor ( 2, ) is used, the strain measured by the 2-wire strain gauge ( 2,, ) and the strain measured by the 3-wire strain gauge ( 3, ) should be the same, as summarized in Equation (19) where  2,,  2,, ⁄ represents the ratio of the inaccurate strain to the correct strain.It can be seen that the invariant  2,,  2,, ⁄ is not a function of ∆ 2, or ∆ 3, , indicating that this value is not affected by the elongation of the specimen.It means that this value is invariable under different stress conditions.
To obtain this value, the plate specimen is made as shown in Figure 14.The specimen was designed with reference to ASTM E8/E8M [34].The 2-wire strain gauge and the 3wire strain gauge are attached to the specimen.By stretching the specimen, strain gauges will show different outputs at cryogenic temperatures as  3, and  2,, .At the same time, a comparative experiment is performed at room temperature.The strain measured at room temperature by the 3-wire strain gauge is  3, and the strain measured by the 2-wire strain gauge is  2, .It can be seen from Figure 15 that at room temperature,  3,  2, ⁄ = 1.It indicates that under room temperature, the outputs from the different gauges are the same.However, at cryogenic temperature, the output of the 2-wire strain gauge is smaller, and ε 3w,cryo ε 2w,cryo,inac ⁄ is a stress-independent constant value which is 1.048.Through Equation (20), it can be seen that the  2,,  2,, ⁄ is 1.048.Then, the inaccurate output measured by the 2-wire strain gauge at cryogenic temperatures can be corrected by using this value.In this way, the 2-wire strain gauge can be used more accurately for cryogenic experiments.

Test Introduction
Three kinds of specimens are tested, including the butt-welded, fillet transverse, and fillet longitudinal specimens.The 9% Ni steel is supplied by POSCO located in Pohang, Republic of Korea.The material properties are given in Appendix A. The universal testing machine and its operating system are provided by MTS, with a maximum load capacity of ±50 tons.The cryogenic test chamber is manufactured by R&B with an operating temperature range of −180 to 80 °C.The apparatus is shown in Figure 16.The calibration of the machines was conducted within the six months prior to the test.The tests are carried out at room (20 °C) and cryogenic (163 °C) temperatures.The specimen dimensions and the welding information are shown in Figure 17 and Table 3, respectively.The specimens are welded using flux-cored arc welding (FCAW).For the butt-welded specimens, 1G welding is employed, while the fillet-welded specimens use 2F welding, as shown in the following figures.The specimen design refers to the ASTM E466 [32].The force ratio () is 0.1 (kN/kN), and the test frequency is 6 to 15 Hz.During the cryogenic temperature test, the specimens are kept in the chamber for 1.5 h before the experiment to allow the specimen to cool completely, and experiments are carried out without interruption.During the cryogenic temperature test, the temperature of the specimens is maintained within ±1 degree of the target temperature.For strain measurement, the data acquisition system (DAQ) devices are from National Instruments, and the strain gauges are from KYOWA.In the area where the strain gauge is installed, the specimen is first ground using an angle grinder, followed by polishing with sandpaper, and then wiped with acetone.

S-N Curve
To describe the relationship between stress amplitude (Δ) and fatigue life (), the S-N curve is employed as in Equation ( 21).The  and  are fatigue life curve parameters.
The S-N design curve is determined with 97.7% of survivability, as shown in Equation (22), where  is the standard deviation.
For the cryogenic temperature test, the corrected ratio  2,,  2,, ⁄ is used to calibrate the results measured by the 2-wire strain gauge.The S-N curves of three specimens are illustrated in Figures 16-18.The S-N curve parameter is given in Table 4.The FAT value refers to the corresponding stress on the curve when fatigue life  = 2 × 10 6 (cycles) and this value can be called fatigue strength.FAT(M) stands for the mean curve, and FAT(M-2STD) stands for the design curve.Figures 18-20 also show that specimens at cryogenic temperature could provide higher fatigue resistance than at room temperature.Table 4 shows that the S-N curve based on nominal stress has a smaller correlation coefficient ( 2 ) than the S-N curve based on hot-spot stress.

Fracture Point
According to the direction of the specimen, the four hot spots could be named as "FU, FL, BU, BL".For the butt-welded specimens, as shown in Figure 21, most of the cracks tend to appear where the  ∆ is the largest.For the fillet longitudinal specimen, the orientation is set randomly because the specimen's orientation cannot be distinguished.For the fillet transverse specimen, the orientation of specimens can be distinguished according to the attachment, and the orientations of the fillet transverse specimens are shown in Figure 22.It can be seen from Figures 23 and 24, which are for the fillet specimen, that the cracks do not appear where the hot-spot stress is the largest.Figure 3b,c show that the intercept of each curve is exceedingly small, indicating that in the process of grip closing, compared with the butt-welded specimen, only a tiny bending stress is generated in the fillet specimen.Therefore, the initial bending stress does not affect the location of crack generation.For some specimens, cracks could appear at the weld root where the  ∆ is less than 1.0.In addition to the  ∆ , the appearance of the weld root also affects the appearance of the crack.

Comparison of the S-N Curve
As for fatigue tests of 9% Ni steel, butt-welded and fillet longitudinal specimens had been reported in many studies [6][7][8][9].Although the base metal is the same, the nominal stress-based S-N curve of the specimen will be different under different welding conditions, thicknesses, or stress ratios, as illustrated in Figure 25

Hot-Spot Stress Prediction
The  ∆ can be predicted according to Equation (13).In this section, the predicted  ∆ will be compared with the experimentally measured  ∆ .To evaluate the accuracy of predicting the  ∆ , the prediction error is defined as in Equation (23).
In this part, only the room temperature test specimens are used for comparison.To obtain the   and   , four methods can be selected, which are summarized in Table 6.

Author
Contents BS 7910 Adapted from Ref. [29] and IIW
As for considering the bead effect, three methods can be selected, which are summarized in Table 7. Method I represents the case which does not consider the bead effect.Method II assumes that  , =  , =  , , which means that the influence of the bead on the axial stress and on the bending stress is the same.Method III considers the influence of the bead on the axial stress and on the bending stress, respectively, which is recommended in this study.First, compare the accuracy of predicting the  ∆ when different   and   prediction methods are applied.At this time, Method III is selected to consider the bead effect.When different prediction methods are employed, the prediction errors   of each specimen at the different weld root positions are shown in Figure 26.  = 0% means that the predicted  ∆ is exactly the same as the measured  ∆ .The positive value indicates an overestimation of the  ∆ , and the negative value indicates an underestimation.To show the accuracy of the prediction more intuitively, take the average of |  | for all specimens, defined as   .As shown in Table 8, the method proposed in this study has higher accuracy than other methods.For the root FL with the highest probability of crack occurrence, the value of   is only 5.8%.Next, the accuracy is compared when different methods are used to account for the bead effect.At this time, select the method proposed in this study to calculate   and   .The prediction errors   for each specimen are given in Figure 27.
Table 9 indicates that the accuracy considering the bead effect is higher than that without considering the effect.If the effect of the bead on the axial stress and on the bending stress is investigated separately, the accuracy could be slightly improved.In addition to the physical meaning, according to the definition of  , , it could be known from Equation ( 13) that  , could be used to describe the sensitivity of the specimen to the misalignment.So simply assuming that  , and  , are equal, like in Method II, is not rigorous.Due to the slight misalignment of the specimen used in this study, the prediction accuracy is not significantly improved when Method III is adopted.Four ways could be used to calculate the   and   , and three ways could be selected when considering the bead effect.Therefore, there are a total of 4 × 3 = 12 methods to predict  ∆ .For each method, the mean   for each root can be calculated as  ,4  = ( , +  ,4  +  , +  , )/4, summarized in Table 10.Table 10 indicates that using the proposed method in this study to calculate   and   , and considering the influence of the bead on the tensile and bending stress separately, the accuracy of predicting the  ∆ could be improved.The method proposed in this study to predict the stress concentration factor is depicted in Figure 28.

Predicted Hot-Spot Stress-Based S-N Curve
Using the predicted  ∆ , the S-N curve can be plotted based on the predicted hotspot stress.The comparison results are shown in Figure 29.
The predicted hot-spot stress-based S-N curve has a higher correlation coefficient than the nominal stress-based S-N curve, as shown in Table 11.The predicted hot-spot stress-based S-N curve is similar to the measured hot-spot stress-based S-N curve.

Conclusions
The present study provides the S-N curves for three kinds of welded specimens.To overcome the problems that may arise during the strain gauge measurement, this study proposes a hot-spot stress prediction method that considers multiple factors affecting hotspot stress.The reliability of the prediction method is proved by comparing the predicted hot-spot stress with the experimentally measured hot-spot stress.The obtained outcomes can be summarized as follows: 1. To address potential issues during strain gauge measurements, the study proposes a hot-spot stress prediction method.This method considers multiple factors influenc-ing hot-spot stress, enhancing the reliability of stress predictions.Experimental verification confirms the accuracy of predicted hot-spot stresses compared to measured values.2. This study proposes an innovative approach focusing on the influence of the midsection of the specimen on stress concentration factor (SCF) prediction.Taking into account the clamped effect and the reduced mid-section allows the obtained   ,   values to more accurately predict the hot-spot stress.3. The bead is found to have different effects on the axial tensile stress and on the bending stress concentration.By considering the effect of the bead on axial nominal stress and on bending stress separately, the prediction accuracy can also be improved.4. The research discovers that the ratio of output strain between 3-wire and 2-wire strain gauges remains constant.This finding allows for the correction of 2-wire strain gauge outputs in cryogenic environments, thereby improving the accuracy of experimental results.
The limitation of this study is that the effect of residual stress on fatigue life is not considered.Whether   is affected by the thickness, and whether it can be applied to more specimens, remains to be investigated.Future studies could address these limitations to enhance understanding and application.The stress-strain curves are shown in Figure A2, and material properties are given in Table A1.
The Young's modulus (E) of 9%Ni steel increases with decreasing temperature.The yield strength, tensile strength, and fracture strength are significantly increased, and the corresponding strain increased slightly.

Figure 1 .
Figure 1.Butt-welded specimens' orientation.(a) E and S distinction; (b) F and B distinction and specific areas for the materials; (c) total orientation; (d) gauge and hot-spot naming.

Figure 5 .Figure 6 .
Figure 5.The model of the butt specimen.

Figure 9 .Figure 10 .
Figure 9. Dividing the specimen into several parts according to the width.(a) Two parts; (b) six parts.

Figure 15 .
Figure 15.The ratio between strain measured by 3-wire gauge and strain measured by 2-wire gauge.(a) At cryogenic temperature; (b) at room temperature.

Figure 18 .
Figure 18.The butt-welded specimen test results and S-N curves.(a) Room temperature test; (b) cryogenic temperature test.(The arrow indicates that the fatigue limit is reached and the test is stopped manually.)

Figure 19 .Figure 20 .
Figure 19.The fillet longitudinal specimen test results and S-N curves.(a) Room temperature test; (b) cryogenic temperature test.(The arrow indicates that the fatigue limit is reached and the test is stopped manually.) Δ ℎ = hot-spot stress range, Δ ℎ, = hot-spot stress range after calibration, N = fatigue life, FAT(M) = the corresponding stress on the mean curve when fatigue life  = 2 × 10 6 (cycles), FAT(M-2STD) = the corresponding stress on the design curve when fatigue life  = 2 × 10 6 (cycles).

Figure 21 .
Figure 21.Butt-welded specimens' fracture point information from room temperature tests.(a) Hotspot stress at each root; (b)  ∆ at each root.

Figure 22 .
Figure 22.Fillet longitudinal specimen orientation.(a) U and L distinction; (b) F and B distinction; (c) total orientation.

Figure 23 .Figure 24 .
Figure 23.Fillet longitudinal specimens' fracture point information from room temperature tests.(a) Hot-spot stress at each root; (b)  ∆ at each root.

Figure 25 .
Figure 25.Comparing the nominal stress-based S-N curve in references at room temperature (R.T.) with that at cryogenic temperature (C.T.).(a) Butt-welded specimens; (b) fillet longitudinal specimens.

Figure 26 .
Figure 26.Comparison of accuracy when predicting misalignment effects using different methods.(a) Front upper roots; (b) front lower roots; (c) back upper roots; (d) back lower roots.

Figure 27 .
Figure 27.Comparison of accuracy when predicting bead effects using different methods.(a) Front upper roots; (b) front lower roots; (c) back upper roots; (d) back lower roots.

Figure 28 .
Figure 28.Method to predict the stress concentration factor for the butt specimen.

Figure 29 .
Figure 29.Comparison between the butt-welded specimen S-N curves.(a) Room temperature tests; (b) cryogenic temperature tests.
Author Contributions: Conceptualization, Y.-Y.L. and Y.-H.P.; methodology, Y.-Y.L. and D.K.K.; software, S.-W.H. and Y.-Y.L.; validation, Y.-Y.L. and D.K.K.; formal analysis, Y.-Y.L. and D.K.K.; investigation, S.-W.H. and Y.-Y.L.; resources, Y.-H.P.; data curation, Y.-Y.L. and D.K.K.; writingoriginal draft preparation, Y.-Y.L. and D.K.K.; writing-review and editing, Y.-Y.L. and D.K.K.; visualization, Y.-Y.L. and D.K.K.; supervision, D.K.K.; project administration, Y.-H.P.; funding acquisition, Y.-H.P.All authors have read and agreed to the published version of the manuscript.Funding: The present research was made possible by the project "Experimental study on material and fatigue for 9% Ni Steel at cryogenic temperature" (project no.0457-20200025) supported by POSCO.This work was also supported by a research project (P0018490, Development of Performance Evaluation Technics for LNG Cryogenic Cargo Containment Material and Structure System) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea).The APC was funded by Metals journal.Stressconcentration factor  ∆Stress concentration factor when focusing on the loading range  ∆,  ∆ from prediction  ∆,  ∆ from the test / Fatigue life curve parameters  Axial misalignment   The axial misalignment used to calculate  in DNV   Stress magnification factor due to angular distortion  /, Stress magnification factor due to the bead from axial tensile/bending FE model   Stress magnification factor due to the bead  , Stress magnification factor due to the bead from bending FE model   Stress magnification factor due to axial misalignment  2 Correlation coefficient  Standard deviation  Thickness /  Width of the specimen/width of each part of the specimen ( = 1~6)   Change in resistance of the gauge grid due to deformation of attached object  ℎ Hot-spot stress range  ℎ, Hot-spot stress range from the test after calibration  ℎ, Hot-spot stress range from prediction  ℎ, Hot-spot stress range from the test   Nominal stress for balanced axial load in specimen   Bending stress range due to misalignment  , Bending stresses for balanced moment in angular distortion existed specimen  , Bending stresses for balanced moment in axial misalignment existed specimen   Nominal stress range  Angular distortion  Strain  2,,/ Strain measured at cryogenic temperature by the 2-wire strain gauge, if accurate/inaccurate gauge factor is used  2/3,/ Strain measured by the 2-/3-wire strain gauge at room/cryogenic temperature  ℎ Hot-spot stress  ℎ,/, Hot-spot stress obtained from the FE model when axial tensile/bending stress is applied  ℎ, Hot-spot stress initiated by gripping  ℎ, Hot-spot stress initiated by nominal stress   Nominal bending stress induced by gripping   Nominal stress  ,/, The applied nominal axial tensile/bending stress when studying the bead effectAppendix A Specimens are made along the transverse and longitudinal direction of the base metal.Both longitudinal and transverse specimens are tested at room temperature and cryogenic temperature.The dimensions are shown in Figure A1.The specimen dimensions and test procedures follow the ASTM standard [34].(a) (b)

Table 1 .
Comparison of previous works and present study.

Table 2 .
Stress direction at four roots. .

Table 4 .
The S-N curve parameter.

Table 5 .
The S-N curve parameter summary and comparison.

Table 6 .
Four methods to calculate the misalignment-induced SCF.

Table 7 .
Different ways to consider the bead effect. , = parameters of the bead effect under axial tension conditions obtained by FEM,  , = parameters of the bead effect under bending conditions obtained by FEM,   = stress Note:  `  `  `

Table 8 .
Comparison of accuracy when predicting misalignment effects using different methods.  = the average of the errors in the predicted results of all specimens at each root, FU = front upper root, FL = front lower root, BU = back upper root, BL = back lower root. Note:

Table 9 .
Comparison of accuracy when predicting bead effects using different methods.  = the average of the errors in the predicted results of all specimens at each root, FU = front upper root, FL = front lower root, BU = back upper root, BL = back lower root. Note:

Table 10 .
Comparing the accuracy of twelve different methods. ,4  = the average of the errors in the predicted results of all specimens from four roots.

Table 11 .
Information about three S-N curves.
Note:  = fatigue life curve parameter,