Fatigue Strength Experiment and S-N Curve Fitting Method of Ship Typical Joints

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(1.Marine Design&Research Institute of China,Shanghai 200011,China;2.College of Shipbuilding Engineering,Harbin Engineering University,Harbin 150001,China)

Abstract:The selection of S-N curves has always been a key issue in fatigue assessment for ship structures.For some specific structural forms of large ships,no suitable S-N curves in the existing classification society rules can be applied to structural fatigue assessment.In this paper,a large ship with a complex structure was selected as an example.The S-N curve characteristics of typical joints were studied through real scale model fatigue experiments.Through finite element calculation of the fatigue strength of the whole ship based on spectrum analysis,the key areas with serious fatigue problems were identified for determination of the test locations in the model.The real scale fatigue experiment models were designed and built according to the real ship structure of the selected typical joints.Fatigue strength experiments of each typical joint under multiple load conditions were conducted to obtain fatigue life values of typical joints under each load condition.S-N and P-S-N curves for each typical joint were fitted on the basis of the experimental results.The fitted P-S-N curves obtained by the experimental results were applied to the fatigue strength assessment of typical joints,the results were compared with those obtained by the S-N curves of existing classification society rules,and the differences were presented.

Key words:typical joint;real scale model;fatigue experiment;spectrum analysis;S-N curve fitting

0 Introduction

Fatigue failure is one of the main failure forms of marine structures[1].For many years,the fatigue fracture of ship structures has been considered as one of the most significant problems in shipbuilding industry[2].One of the key issues in fatigue assessment is the selection of suitableS-Ncurves.For some specific structural forms of large ships,the absence of suitedS-Ncurves in the existing classification society rules has greatly reduced the accuracy of fatigue strength assessment.In order to solve this problem,it is necessary to determine theS-Ncurve characteristics for particular structural forms by model experiments.Also through fatigue experiments under simulated real load and environment,the fatigue characteristics of structural components could be correctly evaluated,and the expected effect of the fatigue analysis could be verified.

In this study,real-scale model fatigue experiments were carried out on selected special structural joints of ships,and the stress ranges and load cycle numbers of hot-spots were measured under different ranges of alternating loads,and then theS-Ncurves suitable for the special structural forms were fitted.By comparing the fittedS-Ncurves with the CCS RuleS-Ncurves,we could intuitively determine which was more conservative for the calculation result of fatigue life from the relative position relationship of each curve in theS-Ncurve figure.

1 Selection of fatigue experiment joints

The direct calculation method of fatigue assessment based on spectrum analysis is a widelyaccepted method which can truly reflect the fatigue performance of a ship hull[3].The wave loads of fatigue strength assessment are computed by wave load calculation software and applied to the finite element structure to obtain the fatigue stress response and stress range,and then the fatigue life of the checked structure can be acquired through the calculation of cumulative damage degree[4].

In this study,a certain type of warship was selected as the research object.The main dimensions and related parameters of the ship are shown in Tab.1.The finite element model of the whole ship was established(See Fig.1).A total of 2 788 nodes related to fatigue strength assessment were selected in the model according to structural strength rules,which covered all types of typical nodes of the whole ship,and all nodes were classified according to their structure types.The spectrum analysis method was adopted to calculate the fatigue strength of the whole ship.Four typical loading conditions of the example ship(normal displacement,full load displacement,displacement of returning to the port,and maximum displacement)were selected as the working conditions of this calculation study.It was assumed that the probability of occurrence of each loading condition is the same in the whole life of the ship,namely time distribution coefficientα=0.25.The wave loads were calculated by Compass-Walcs-Basic,a wave load calculation software based on three dimensional potential flow theory,which was developed by Institute of Mechanics of Harbin Engineering University.The stress response transfer functions and stress response spectra of the hull structure in each regular wave were calculated by applying the wave loads to the finite element model of the ship hull,and the cumulative fatigue damage degrees and fatigue lives in the 20-year fatigue recovery period were finally obtained.The nodes with the shortest fatigue life among all the node types were sorted out to be the focused areas for fatigue assessment.The calculation conditions and parameters of the wave loads are shown in Tab.2.The types of nodes with serious fatigue problems and the calculation results of fatigue life are shown in Tab.3.

Tab.1 Hull main dimensions and related parameters

Tab.2 Wave load response parameters

Tab.3 Results of fatigue life calculation

Fig.1 Whole ship Patran finite element model

Based on the calculation results of the spectrum analysis method for fatigue strength assessment of the whole ship,considering the structural particularity of experimental research joints,three typical joints(intersection of main deck girder and transverse bulkhead,large opening elliptic arc corner of main deck,and circular arc joint of superstructure end and main hull)were selected as the research objects of this fatigue experiment.Tab.4 shows the real ship finite element structure and the stress distribution of the three experimental joints.

Tab.4 Finite element structures and stress nephograms

2 Fatigue experiment model design

The experimental models were designed according to the principle that the stress distribution at the hot spot of the model was consistent with that of the real ship.Also during the experiment fatigue failure should initiate at the fatigue hot spot.MTS multi-point loading test system and DH3817F dynamic and static strain test and analysis system were used in the test.Considering the limitation of test conditions,due to the complex test loading form and boundary conditions,it was also necessary to design the supporting devices.The detailed structure and size information of the specimens are shown in Figs.2-4,according to which the finite element model of each experimental joint was established.By simulating the real loading modes of the actuator cylinder in Tab.5,different ranges of alternating loads were applied on the finite element models of each joint,and groups of alternating load values for each joint in this experiment were determined according to the stress calculation results of the hot spot[5].The finite element structure,stress nephogram and loading model are shown in Tab.5.

Fig.2 Specimen machining drawing of Joint 1

Fig.3 Specimen machining drawing of Joint 2

Fig.4 Specimen machining drawing of Joint 3

Tab.5 Finite element structures,stress nephograms and loading modes of experimental models

3 Measurement content of fatigue experiment

3.1 Stress distribution measurement

The stress state of model fatigue experiment was measured by a resistance strain gauge.Before the fatigue experiment,the static stress distribution near the welding toe was tested,and the number of strain gauges was increased in the static test so as to find out the hot spot location and the corresponding hot spot stress concentration coefficient.In the fatigue experiment,some points are extracted from the strain sheet of static test for dynamic strain measurement.Specifically,according to the results of finite element calculation and analysis,strain gauges were arranged every 30 mm or so at the hot spot of the structural part,and a fixed load was applied to determine the stress distribution state near the hot spot of the structural part.

3.2 Determination of load conditions

The fatigue experiments of the three typical joints were carried out under multiple load conditions.At the same time,in order to investigate the discreteness of experimental data,one more model was added under each load condition.The experimental load ranges of the total 15 specimens are shown in Tab.6.

Tab.6 Experimental load ranges and number of specimens

3.3 Fatigue failure criteria

During the fatigue experiment,as the fatigue load cyclic loading,N1andN2required constant observation.N1represents the cycle number of visible surface cracks with a length of 30 mm whileN2represents the number of cycles when the crack penetrates the plate thickness.

3.4 Method of experimental data processing[6]

The measuring spots were arranged with a three-way right angled strain rosette,as shown in Fig.5 below.

Fig.5 Three-way right angled strain rosette

The principal strainε,the principal stressσ,and the intersection angleφbetweenσ1and 0°lines could be calculated by the following formulas(ε0,ε45,ε90were the strains of measuring spots):

According to Guidelines for Fatigue Strength of Ship Structure 2015 of CCS,the main stress within 45° perpendicular to the fatigue crack growth direction was selected in the calculation of the stress range.

The hot spot stressσhwas obtained by interpolation with the formula below,as shown in Fig.6.

Fig.6 Hot spot stress interpolation diagram

whereσt/2andσ3t/2were the maximum principal stresses,t/2 mm and 3t/2 mm respectively from the welding,twas the thickness of the plate.

4 Fatigue experiment results

4.1 Joint 1

Fatigue experiment on 6 specimens of Joint 1 was carried out under alternating loads of 1～10 t,1.4～14 t,and 1.5～15 t.The experimental results demonstrate,as expected,that the locations of fatigue cracks of the 6 specimens are all at the intersection of bracket and longitudinal girder or the intersection of bracket and transverse bulkhead.Each stress component of fatigue failure locations under different loading conditions was monitored and the results of stress range were calculated.The monitored value of stress components and the calculated results of stress ranges are shown in Tab.7.According to the calculated hot spot stress range,theDcurve of CCS RuleS-Ncurves was selected to calculate the theoretical cycle times of fatigue loading,and the results were compared with the actual cycle times,as shown in Tab.8.The experiment model and failure location are shown in Fig.7 and Fig.8.

Fig.7 Experiment model of Joint 1

Fig.8 Stress monitoring position of Joint 1

Tab.7 Stress compositions and stress ranges(Joint 1)

Tab.8 Stress ranges,predicted cycle numbers and actual cycle numbers(Joint 1)

Tab.8(Continued)

4.2 Joint 2

Fatigue experiment on 3 specimens of Joint 2 was carried out under alternating loads of-4～4 t(-4 t represented 4 t in compression state while 4 t represented 4 t in tensile state)and 0.9～9 t.The experimental results exhibit,as expected,that the locations of fatigue cracks of the specimens are all located near the center of the large opening corner.Same as Joint 1,the monitored value of stress components and the calculated results of stress ranges are shown in Tab.9.The comparison of theDcurve theoretical cycle times and actual cycle times are shown in Tab.10.The experiment model and failure location are shown in Figs.9-10.

Tab.9 Stress compositions and stress ranges(Joint 2)

Tab.10 Stress ranges,predicted cycle numbers and actual cycle numbers(Joint 2)

Fig.9 Experiment model of Joint 2

Fig.10 Stress monitoring position of Joint 2

4.3 Joint 3

Fatigue experiment on 6 specimens of Joint 3 was carried out under alternating loads of 1～10 t,1.4～14 t and 1.5～15 t.The experimental results show,as expected,that the locations of fatigue cracks of the specimens are all at the intersection of superstructure bulkhead and the main deck(The test of Specimen 2 was terminated as no fatigue failure was detected in Specimen 2 after 712 000 cycles of alternating loading.).The monitored value of stress components and the calculated results of stress ranges are shown in Tab.11.The comparison of theDcurve theoretical cycle times and actual cycle times are shown in Tab.12.The boundary condition of the model was a simple support,as shown in Fig.11.The location of strain gauges is shown in Fig.12,and the experiment model and failure location are shown in Fig.13 and Fig.14.

Tab.11 Stress compositions and stress ranges(Joint 3)

Tab.12 Stress ranges,predicted cycle numbers and actual cycle numbers(Joint 3)

Fig.11 Boundary condition(simply supported)

Fig.12 Strain gauges

Fig.13 Experiment model of Joint 3

Fig.14 Stress monitoring position of Joint 3

5 S-N curves fitting[7-8]

Nrepresents the number of cycles required for the structure to reach fatigue failure under a single cyclic load with a stress range ofS.The relationship betweenSandNis generally reflected by the medianS-Ncurve obtained by fitting the results of several fatigue tests,which can be expressed as

wheremrepresents the slope of the medianS-Ncurve whileArepresents the parameter obtained in fatigue test.

Due to the discretization of fatigue experimental data,the curve between fatigue stress(S)and fatigue life(N)is not a one-to-one corresponding single value relationship curve,but closely related to survival rateP.In the structural design and analysis based on fatigue strength,when the survival ratePis appropriately selected according to the structural importance,more reliable results of fatigue life can obviously be obtained with the adoption ofP-S-Ncurve.In the field of shipbuilding and marine engineering,P=97.72%( )μP=-2.0 is often used for general structural components.The standard deviation is uniformly set as a fixed value by DNV and ABS[9-10].For this test,due to the limited number of specimens,the standard deviationSlgAwas set as 0.2 according to DNV rules.Then theP-S-Ncurve is expressed as

5.1 Fitting and comparison of S-N curves for Joint 1

The hot spot stress values at the welding seam of the 6 experimental specimens of Joint 1 were taken as the data points for curve fitting.The medianS-Ncurve andP-S-Ncurve were plotted based on a log-log linear model and compared with theS-Ncurves of CCS rules.The parameters of theP-S-Ncurve are shown in Tab.13.The comparisons between the fitted curves,based on least square method and constant slope maximum likelihood method,and theS-Ncurves of CCS rules are shown in Fig.15 and Fig.16 respectively.

Tab.13 Parameters of P-S-N curves(Joint 1)

Fig.15 Comparison between least square fitting curves and CCS rule curves

Fig.16 Comparison between constant slope maximum likelihood method fitting curves and CCS rule curves

5.2 Fitting and comparison of S-N curves for Joint 2

As can be seen from the distribution of the three data points of Joint 2 in Fig.17,two of them are almost identical.The lack of data points could result in more difficulty inS-Ncurve fitting.In this study,the relatively lower data point was selected to obtain the corresponding constant slope maximum likelihood curve.It is obvious that the fatigue assessment of this typical structure by using this fitted curve is conservative.

The hot spot stress values at the welding seam of the 3 experimental specimens of Joint 2 were taken as the data point for curve fitting.The medianS-Ncurve andPS-Ncurve were plotted based on a log-log linear model and compared with theS-Ncurves of CCS rules.The parameters of theP-S-Ncurve are shown in Tab.14.The comparison between the fitted curve,based on constant slope maximum likelihood method and the CCS RuleS-Ncurves is shown in Fig.17.

Fig.17 Comparison between constant slope maximum likelihood method fitting curves and CCS Rule curves

Tab.14 Parameters of P-S-N curves(Joint 2)

5.3 Fitting and comparison of S-N curves for Joint 3

The hot spot stress values at the welding seam of the 5 experimental specimens of Joint 3 were taken as the data point for curve fitting(No.2 specimen was not damaged and was not used as the data point for fitting).The medianS-Ncurve andP-S-Ncurve were plotted based on a log-log linear model and compared with theS-Ncurves of CCS rules.The parameters of theP-S-Ncurve are shown in Tab.15.The comparison between the fitted curves,based on least square method and constant slope maximum likelihood method,and theS-Ncurves of CCS rules are shown in Fig.18 and Fig.19 respectively.

Tab.15 Parameters of P-S-N curves(Joint 3)

Fig.18 Comparison between least square fitting curves and CCS Rule curves

Fig.19 Comparison between constant slope maximum likelihood method fitting curves and CCS Rule curves

6 Fatigue life revision

The experimental fittedP-S-Ncurves were taken in the fatigue life revision of the three experimental joints.With theP-S-Ncurves fitted by the constant slope maximum likelihood method as shown in Fig.16,Fig.17 and Fig.19 as benchmarks,theS-Ncurve of CCS rules below each benchmark was selected to revise the fatigue lives by direct calculation method based on spectrum analysis,and the results are shown in Tab.16.

Tab.16 Revision of fatigue assessment results

7 Conclusions

The following conclusions are drawn from this experimental study:

(1)The fitted fatigueP-S-Ncurves of the three typical joints of ship structures can serve as a guide for the design and strength assessment of ship structure in the future.

(2)As can be seen from the comparison between the fittedP-S-Ncurves and the CCS Rule curves,there exists a large difference between the slope of least square method curve and that of the CCS curve(m=3).As the slope of regularS-Ncurves was close to 3 according to the statistical analysis of relevant data,theP-S-Ncurves fitted by constant slope(m=3)maximum likelihood method were finally adopted for the revision of fatigue life calculation results.

(3)In the experimental design stage,the tested stress components can be determined through the arrangement of strain gauges.In this experiment,the interpolation method,by which different stress components were calculated to obtain the hot spot stress,was consistent with the interpolation method of spectrum analysis.Therefore,the stress value indicated in the experiment was the hot spot stress,which could be directly compared with the result calculated by spectrum analysis method to improve the research efficiency.

(4)As can be seen from the calculation results,the revised fatigue life value of each typical joint is generally less than that before fatigue life revision,which indicates that the experimental fittedS-Ncurves are relatively more conservative than the CCS Rule curves,and suggests that the experimental study of fatigue characteristics of ship specific structural forms is quite essential.

(5)As can be seen from the corresponding relationship between experimental loading condition and stress response,specimens of the same typical joint under same loading condition can generate different stress responses,which reflect the great influence of welding quality on fatigue life.Therefore,it is suggested that the specimens in fatigue experimental research should be conducted by the same shipyard as the real shipbuilding to ensure the consistency of welding technology and make the experiment more reasonable.

Due to the limitation of experimental conditions,the number of data points used forS-Ncurves fitting in this study is limited.In the future research,both the loading conditions of each typical joint and the number of specimens under each loading condition should be increased to make the experiment more rigorous and the results more accurate.