Residual emphasis may hold a important consequence on the fatigue strength of welded articulations. As a non-fluctuating emphasis, it has an consequence similar to that of the average emphasis.
Recently the International Association of Ship Classification Societies ( IACS ) has issued Common Structural Rules ( CSR ) for severally oilers ( IACS 2006a ) and bulk bearers ( IACS 2006b ) . The consequence of average emphasis in weariness design is taken into history in both sets of regulations. However, the intervention is rather different, in peculiar with respect to residuary emphasis and shakedown effects.
In the present paper a comparative survey of fatigue design processs of the IACS regulations is reported, with accent on residuary emphasis effects. Testing was carried out with longitudinal fond regard dyer’s rockets in the as-welded status. The initial residuary emphasis was measured by a sectioning method utilizing strain pots. Hot topographic point emphasis was determined by experimentation by strain gages and numerically by finite component analysis utilizing different types of elements. Fatigue testing was carried out and SN-curves were plotted harmonizing to the relevant emphasis as specified by the regulations. In order to look into the shake-down consequence of residuary emphasis, proving was performed for several pre-load conditions which could be taken to stand for maximal burden degrees in a load history. The purpose of the survey is to lend towards better apprehension of the consequence of residuary emphasis and shakedown on fatigue strength of welded articulations.
Marine constructions like ship hulls and offshore oil platforms are in general designed for a finite fatigue life, typically 25 – 50 old ages of service, Ghose et Al. ( 1994 ) . In many instances the utile operational life is limited by weariness snap. This is peculiarly true for constructions made from high strength steel, due to the well known fact that the fatigue strength of welded steel articulations is basically unaffected by the output strength of the steel. Using high strength steel and thereby increasing the allowable emphasis degree therefore leads in general to a shorter fatigue life.
The consequence of welding residuary emphasis has traditionally been taken into history by the “ emphasis scope ” doctrine, i.e. by presuming the mean emphasis – due to residuary emphasis – to be big and tensile. The average emphasis of the external burden is therefore ignored in design. The emphasis scope attack was developed on the footing of informations from weariness trials utilizing changeless amplitude burden, Gurney ( 1976 ) . The inquiry has been raised whether this could be excessively conservative for constructions that are subjected to random burden and possible shakedown of residuary emphasis due to top out tonss.
This issue is reflected in the Common Structural Rules of IACS. In the oiler regulations, IACS ( 2006a ) there is no history of residuary emphasiss in the fatigue appraisal. In the majority bearer regulations, IACS ( 2006b ) , on the other manus, the consequence of residuary emphasis is explicitly incorporated in the computation of a average emphasis rectification factor.
A figure of surveies have been carried out to look into the consequence of residuary emphasis on weariness strength, e.g. Eide and Berge ( 1981 ) , Fricke ( 2005 ) , Lotsberg ( 2006 ) , McClung ( 2007 ) . Shakedown has similarly been studied, e.g. Iida and Takanashi ( 1999 ) , Takanashi et Al. ( 2001 ) .
: Equivalent hot topographic point emphasis scope
: Fatigue notch factor defined in.
: Correction factor for average emphasis
: Local hot topographic point average emphasis
: Structural hot topographic point average emphasis
: Residual emphasis
: mean emphasis plus half emphasis scope
: mean emphasis minus half emphasis scope
: mean emphasis due to inactive burden constituents in the full burden status or ballast status as appropriate
: predicted figure of rhythms to failure under emphasis scope S
: invariable relating to the average S-N curve, as given in
: criterion divergence of log ( N )
: opposite incline of the S-N curve, as given in
: figure of rhythms of emphasis scope
: figure of rhythms to failure at emphasis scope
: entire figure of emphasis scope blocks
Non-load transporting longitudinal filet welded specimens were made of structural steel EN10025. The thickness of the load-carrying home base was 12 millimeter. The output strength harmonizing to the factory certification was 424 MPa. In Figure 1 is shown the stress-strain curve from tensile proving.
The item geometry and the dimensions are shown in Figure 2. The dyer’s rockets were produced by manual welding ( SMAW ) utilizing rutile coated electrodes E7024-1 harmonizing AWS A5.1 specification. The dyer’s rockets were made in the horizontal place. No station weld intervention was applied.
Figure 1. Stress-strain curve from tensile trial.
Figure 2. Geometry and chief dimensions of the specimen.
Measurement of residuary emphasis
A sectioning method utilizing strain gages was used for measuring of residuary emphasis. Strip gages were applied in forepart of the dyer’s rocket, Figure 3. Each strip had five gages with gauge length 1 millimeter and with a spacing 2 millimeter, therefore covering a length of 8 millimeter. The strips could be positioned to mensurate strain from a distance of about 3 millimeter from the dyer’s rocket toe. Single gages were used for measuring of strain at locations farther off from the dyer’s rocket, californium. Figure 3.
Figure 3. Agreement of strain pots to mensurate the initial distribution of residuary emphasis ( program position )
The strain gages were connected to a multi-channel amplifier for signal processing, and recorded digitally, Figure 4. Residual emphasis relaxation was
Figure 4. Signal amplifier and informations acquisition system
measured by cutting the specimen in a plane matching to typical weariness snap, Figure 3. Film editing of the specimens was carried out manually with a hack saw to forestall inordinate warming and possible thermic strain. The alteration in strain due to the film editing was taken to be the residuary strain before the film editing. The recorded strain was assumed to be linear-elastic, and converted to emphasize utilizing Hooke ‘s jurisprudence.
Initially two dyer’s rockets were instrumented with biaxal gages, to mensurate strain in the longitudinal ( x- ) and cross ( y- ) way relation to the burden axis. Assuming x- and y- to be waies of chief emphasiss, the several constituents were calculated from:
( 1 )
( 2 )
The consequences are shown in Figure 5. Besides shown is emphasis in the x-direction, calculated on the footing of the uniaxial Hooke ‘s jurisprudence,
( 3 )
Figure 5. Residual emphasis distributions for two dyer’s rockets, calculate from biaxal and axial strain severally.
The consequence of biaxiality on the hot topographic point emphasis is seen to be instead little, compared to the built-in spread in residuary emphasis Fieldss. Hence, a simplified attack was adopted with measuring of residuary emphasis utilizing uniaxial strain gages and Equation 3.
By instrumentality of all four dyer’s rocket toes, four sets of informations were obtained for each specimen. A sum of 3 specimens were used to obtain the initial distribution of residuary emphasis.
Shakedown of residuary emphasis
If a welded articulation with big tensile residuary emphasis near to the dyer’s rocket is subjected to tensile burden, local plastic giving up will take topographic point, and the residuary emphasis field will go redistributed. With perennial lading with changeless amplitude the response will go elastic and additive, and in general, the residuary emphasis degree will be reduced. This procedure is termed shakedown.
To look into the consequence of shakedown residuary emphasis measurings were taken after a individual pre-load by 50 % , 75 % and 85 % of output emphasis. One specimen was subjected to a combination of a pre-load to 50 % of output emphasis followed by cyclic burden of 1000 rhythms with a nominal emphasis scope 100 MPa and a burden ratio R=0. The same sectioning process for measuring of residuary emphasis was applied in each instance.
Figure 6. 500 kN hydraulic actuator and the proving rig.
Constant-amplitude weariness testing was carried out in order to bring forth informations for appraisal of SN-curves. Testing was carried out with a A±500 kN capacity hydraulic actuator with hydraulic clasps as shown in Figure 6. Loading was in the elastic scope, with nominal emphasis scopes of 200 MPa and 100 MPa. Testing was carried out with two emphasis ratios, R=0 and R=-1.
Fatigue Assessment Procedures
The consequences of fatigue proving were analysed utilizing the two different processs of fatigue appraisal in IACS-CSR for bulk-carriers and for oilers severally.
The fatigue appraisal process is described in Section 8 of CSR for majority bearers, IACS ( 2006B ) . The process is based on the notch emphasis construct, Radaj et Al. ( 2006 ) , by computation of an “ tantamount notch emphasis scope. ”
For each burden status j the tantamount notch emphasis scope is calculated from:
( 4 )
where a?†I?equiv, J is the tantamount hot topographic point emphasis, calculated by FEA and utilizing the t/2-3t/2 additive extrapolation method and a set of fatigue notch factors Kf that are listed in Table 1.
Table Fatigue notch factors for the majority bearer process.
Butt welded articulation
Fillet welded articulation
Non welded articulation
The average emphasis, including effects of residuary emphasis and shakedown is taken into history by a instead luxuriant strategy. The average emphasis rectification is fundamentally:
( 5 )
where, for primary members and longitudinal stiffeners connexions, the average emphasis rectification factor, is equal to:
( 6 )
( 7 )
( 8 )
( 9 )
( 10 )
A simplified weariness appraisal process is described in Appendix C of CSR for dual hull oil oiler, IACS ( 2006a ) . The process is based on nominal emphasis calculated from beam theory, and a choice of design SN curves, Gurney ( 1976 ) .
Hot topographic point emphasis analysis may besides be applied. The hot topographic point emphasis is defined as the surface emphasis at 0.5t off from the dyer’s rocket toe location. This emphasis may be obtained by additive insertion utilizing the several emphasis at the 1st and 2nd component from the construction intersection. In this instance the Class D design SN curve shall be used.
The emphasis scope may be reduced depending on whether the average emphasis is tensile or compressive. If compressive emphasis exists and can be quantified, the consequence of average emphasis may be considered by presuming a emphasis scope equal to the tensile constituent plus 60 % of the compressive constituent. The entire emphasis scope sing the average emphasis consequence is to be taken as follows:
if and ( 11.a )
if ( 11.b )
if ( 11.c )
( 12 )
( 13 )
Stress ratio R can be determined as:
( 14 )
In footings of emphasis ratio, R, and emphasis scope, , Eq. ( 12 ) and ( 13 ) can be changed as follows:
( 15 )
( 16 )
Substitute Eq. ( 15 ) and ( 16 ) into Eq. ( 11.a ) ,
( 17 )
Eq. ( 11.a ) , ( 11.b ) and ( 11.c ) can be rewritten harmonizing to Eq. ( 5 ) and can be determined as follows:
( 19 )
Eq. ( 19 ) is in conformity with
Hot Spot Stress Analysis
Both processs described by IACS for weariness appraisal have demand to find hot topographic point emphasis. Finite element analysis utilizing commercial package ABAQUS was performed and confirmed by experiment.
Finite Element Method
Finite component modeling was carried out with several types of elements. Shell element theoretical account was the first pick because of its comparative simpleness. Due to geometrical symmetricalness of the specimen, merely one half of the specimen was modelled. The symmetrical boundary conditions were applied on the mid subdivision of the specimen in the way of planetary x-axis, and the distributed axial tonss were applied at the terminal of the home base, Figure 7. Both 4-node and 8-node shell elements were used.
Solid 20-node elements were besides used with two beds in the thickness way. A one-fourth theoretical account was developed to cut down calculation clip. The symmetrical boundary conditions were applied on the center of the specimen in the way of planetary x-axis and in the bottom surface of the specimen in the way of planetary y-axis. The distributed tonss were applied in the terminal of the load-carrying home base, Figure 8.
Figure 7. Shell element theoretical account.
Figure 8. Solid component theoretical account.
Finite component analysis is sensitive to engage size. . Some codifications, e.g. DNV ( 2008 ) hold recommended an optimal mesh size for computation of hot topographic point emphasis. When a coarse mesh is employed, t x T mesh size is recommended, where T is thickness of the member that is considered. The additive extrapolation method utilizing t/2 and 3t/2 as extrapolation points was applied to find the structural hot topographic point emphasis, as shown in Figure 9.
Figure 9. Structural hot topographic point emphasis by additive extrapolation method
Experimental emphasis analysis
Two strip gages were applied in forepart of the dyer’s rocket toe, each covering one extrapolation point at a distance t/2 and 3t/2 from the dyer’s rocket toe. For each specimen, four dyer’s rocket toes were instrumented, as shown in Figure 10.
Due to welding deformations, one surface of the load-carrying home base was convex and the other was concave, Figure 11. The deformations would give secondary constituents of flexing. Two constituents were considered. Clamping the specimens in the clasps would give a inactive bending constituent, lending to the average emphasis of the burden. Application of a nominal axial burden would give a dynamic bending constituent lending to the dynamic emphasis scope. The constituents were tensile on the concave side, and compressive on the bulging side of a specimen. These constituents were measured and taken into history in the analysis of the consequences.
Figure 10. Experimental method for mensurating hot topographic point emphasis
Consequences and Discussion
Initial residuary emphasis distribution
The initial distributions of axial residuary emphasis in the longitudinal and cross waies are plotted in Figure 11 and 12 severally. The emphasis is normalised to the output emphasis of the home base stuff. As a comparing the informations obtained by Berge and Eide ( 1982 ) is besides plotted. The two sets of informations presented in Figure 9 show the same tendency, with a steep gradient nearing the dyer’s rocket toe, and emphasis degrees at the dyer’s rocket toe of output magnitude. However, the information from the recent trials are about 20 % higher than the information from Berge and Eide. Possibly the variableness of welding methods and of output emphasis of dyer’s rocket metal could be the ground for this difference.
Figure 11. Normalised residuary emphasis distributions along the centreline in forepart of the dyer’s rocket toe.
Residual emphasis distribution across the specimen, Figure 12, show the same tendency. Close to the dyer’s rocket toe the residuary emphasis is big and tensile. The tensile emphasiss are balanced by compressive emphasiss at some distance from the dyer’s rocket. The cross-over from tensile to compressive took topographic point at a distance about 20 millimeter from the dyer’s rocket.
Figure 12. Normalised residuary emphasis distributions in cross subdivision.
Residual emphasis relaxation
In Figure 13 are shown residuary emphasis distributions in forepart of the dyer’s rocket toe after remarkable pre-loads. As shown, the residuary emphasis is strongly affected by the pre-load due to local plastic strain. The degree of residuary emphasis is reduced, and besides the gradient of residuary emphasis towards the hot topographic point. After a preload of 0.5 Sy the residuary emphasis at the hot topographic point was reduced by about 50 % . A preload of 0.85 Sy lead to finish shakedown.
The information indicate that shakedown takes topographic point during the first rhythm. The trial where 1000 rhythms were applied after the initial pre-load rhythm showed no farther consequence.
Figure 13. Residual emphasis distributions after pre-load.
Structural hot topographic point emphasis
Figure 14 demonstrates the consequences of stress analysis utilizing FEA with different types of elements. For solid elements the distance is measured to the dyer’s rocket toe. For shell elements the distance is measured to the shell intersection. Besides shown are experimental consequences. Calculations and measurings were compared at nominal emphasis of +100 MPa, -100 MPa, +50 MPa, and -50 MPa.
Figure 14. Stress distributions towards the dyer’s rocket toe, by FEA and by experimentation, at 100 MPa nominal emphasis.
The FEA consequences show a bit by bit increasing emphasis towards the dyer’s rocket with a changeless gradient to a distance of 8-10 millimeter from the dyer’s rocket toe. Closer to the dyer’s rocket the gradient increases dramatically and appears to diverge at the dyer’s rocket toe.
In footings of an extrapolated hot topographic point stress the 8-node elements gave the largest emphasis, the solid elements the lowest emphasis.
The mensural emphasis showed an overall less steep gradient towards the dyer’s rocket toe. The emphasis distributions are seen to be slightly different comparing the concave and the convex sides, californium. treatment of secondary bending emphasis, Figure 10.
It is evident that the 20-node solid elements gave the best tantrum to experimental consequences. The SCF values from the 20-node theoretical account is used in the subsequent weariness appraisal.
Table 2. SCF obtained by experimentation.
Table 3. SCF obtained from FEA
shows the weariness informations in footings of nominal emphasis scope. In Figure 16 the same informations are shown on the footing of hot topographic point emphasis, utilizing the SCF of 1,33, californium. Table 3. In both Figures the Class D design curve is besides shown.
The informations shown in Figure 15 and 16 appear to corroborate the attack of utilizing the hot topographic point emphasis towards the category D curve. It is moreover celebrated that proving at R = 0 and R = -1 gave about indistinguishable consequences, in line with the emphasis scope attack in fatigue design.
Figure 15. SN informations based on nominal emphasis
Figure 16. SN informations based on hot-spot emphasis
Fatigue appraisal processs
Bulk Carrier process
SN informations from the weariness trials were plotted in footings of the tantamount notch emphasis harmonizing to the bulk-carrier process with premise that the initial residuary emphasis after shake-down is 25 % of output emphasis, Figure 17. The green dotted line is the arrested development line of the Lotsberg ( 2006 ) information with log ( K1 ) = 15.639. Besides shown is the Class B design SN curve. The understanding with the Lotsberg information is really good.
The theoretical account was modified by presuming the residuary emphasis to be 63.5 % of output emphasis, based on the measuring of residuary emphasis after a preload of 200 MPa. The SN informations are plotted in Figure 18. With the modified theoretical account the SN informations tend to fall on the upper side of the arrested development line from Lotsberg ( 2006 ) . Even though the consequence is little, the difference between the R = 0 and R = -1 informations becomes less – in fact imbrication.
Figure 17. SN informations harmonizing to the original bulk-carrier process
Figure 18. SN curves harmonizing to the bulk-carrier process with alteration of residuary emphasis
Oil tanker process
Fatigue trial informations were plotted in footings of tantamount hot topographic point emphasis harmonizing to the oiler process, Figure 19. In this instance the informations autumn below the arrested development line from Lotsberg, and the difference between R = 0 and R = -1 increases. The information for R = -1 are about overlapping the Class D design curve, bespeaking the curve to be un-conservative in this instance.
Following a proposal made by Lotsberg ( 2006 ) the oiler process was modified by presuming a decrease factor for the compressive portion of the burden rhythm to be increased from 0.6 to 0.8. The ensuing SN informations are shown in Figure 20. It is observed that the information for R = -1 still appear to bespeak that the Class D curve is un-conservative. However, the sum of un-conservatism has decreased slightly.
Figure 19. SN curves harmonizing to oiler process with coefficient of compressive portion of 0.6
Figure 20. SN curves harmonizing to oiler process with coefficient of compressive portion modified into 0.8
Mean emphasis rectification factor
Mean emphasis rectification factors for the bulk-carrier process was calculated for the different instances that were assumed in the analysis. The consequences are shown in Table 4. It is interesting to observe that when the residuary emphasis was assumed to be 64 % of output strength, the average emphasis rectification for R = 0 and R = -1 became about equal.
Table 4. Mean stress rectification factor, fmean, bulk-carrier process.
In Table 5 the mean emphasis rectification factor harmonizing to the oiler process is shown, for the same scope of parametric quantities, in this instance for two different decrease factors for the compressive portion of the burden rhythm. In this instance the difference due to R-ratio is maintained.
Table 5. Mean stress rectification factor, fmean, tanker process.
Two different processs have been adopted for fatigue design of oilers and majority bearers. The processs were applied to tire trial informations utilizing welded specimens with big residuary emphasis. The undermentioned decisions were made:
In the as-welded status the residuary emphasis at the hot topographic point was at output magnitude.
Following a tensile pre-load, the residuary emphasis was significantly reduced, due to shake-down. The shake-down took topographic point during the first burden rhythm.
With a pre-load of 0.5Sy the residuary emphasis at the hot topographic point was reduced by about 50 % . With a preload of 0.85Sy complete shake-down was obtained.
Using the bulk-carrier process, the SN informations were in good understanding with the design standard. The understanding appeared to go even better, with less spread, when the process was applied with a residuary emphasis equal to the measured degree.
Using the oiler process, the SN informations gave consequences that could bespeak that the process is un-conservative. Increasing the decrease factor for the compressive portion of the burden rhythm from 0.6 to 0.8 gave better understanding.
The decisions are based on limited informations, and for two R-ratios merely. More informations is needed before concluding decision can be made.
This work was undertaken with a grant from Norse Research Foundation under the Strategic University Program Materials and Structural Integrity. Financial support is appreciatively acknowledged.
The staff of the Marine Structures Laboratory is appreciatively acknowledged for proficient aid and adept advice on the experimental parts of the work.