Analytical and experimental study on the thickness effect to fatigue strength

Analytical and Experimental Study on the Thicloiess Effect to

Fatigue Strength

Norio Yamamoto*^, Masashi Moiiri*^, Tetsiio Okada*^, Takeshi Mori*'^

A B S T R A C T

Thicloiess effect is lawwn as a weakening factor in fatigue strength. However, sufficient lamwiedge is still unavailable with regard to what factors dominate the tivckness effect and how different structural or joint types as well as different loading patterns influence said thickness effect.

To investigate the factors which affect the thickness effect on fatigue strength, fundamental experiments using geometrically imitated specimens cut out fi-om a steel plate were carried out. As results, not only local stress concentrations hut also the stress gradient at weld toes was confirmed to be the dominant factors relevant to the thickness effect on fatigue strength. Then, fatigue tests of cruciform welded joints and gusset welded joints were carried out and analyzed and the conclusions obtained by the fundamental experiments were verified. Regarding cruciform welded joints, fatigue tests using as-welded specimens and PWHT specimens were carried out and it was confirmed that weld residual stress had little effect on the thickness effect.

Keywords

Fatigue strength; Thickness effect; Stress concentration; Stress gradient; Fatigue stress reduction factor

1. I N T R O D U C T I O N

h is commonly known that an increase in plate thickness causes a decrease in fatigue strength. This is called the "thickness effect" and some design standards"'^''^* take this thickness effect mto account for fatigue assessment. However, sufficient knowledge is still unavailable with regard to what factors dominate the thickness effect and how different structural or joint types as well as different loading patterns influence said thickness effect. As a result, there is concern that the existing fatigue rules and codes mcoiporate this thickness effect in a rather conservative way because o f these many unknown factors.

Some analytical or experimental studies'"' have been recently canied out to cope with this problem. However, more comprehensive study is necessary to establish more reasonable and reliable methods for evaluating thickness effect, applicable to variations o f details o f actual ship structures. To this end, a Joint Research Project, whose secretariat is ClassNK, was undertaken by the Shipbuilders' Association o f Japan (SAJ) and the Nippon Kaiji Kyokai (ClassNK).

In this project, thi-ee types o f experimental studies were planned:

'' Research Institute, Nippon Kaiji Kyokai (ClassNK) I H I Corporation

ClassNK T E C H N I C A L B U L L E T I N 2013

(1) Fundamental experiment to reveal the differences in stress concentrations and stress gradients in the thickness direction around weld toes depending on the thickness difference. Small specimens which imitate the shape o f a fillet weld joint section for a series o f different thicknesses were cut out from a steel plate, and were prepared for a fatigue strength experiment.

(2) Basic welded joint experiment to confirm the outcome o f the fundamental experiments. In this experiment, the effect o f weld residual stress in the cruciform welded joint was also evaluated.

(3) Stnictural model experunent to reveal the thickness effect in the actual ship structiu-al details depending on the load transfer mechanism.

In this paper, some o f the results o f these fimdamental experiments and basic welded joint experiments are shown in combination with associated fmite element analysis.

2. Fatigue tests

2.1 Fundamental experiment

To restrict the discussion, test specimens which imitate the shape o f welded-joint section were made by cutting out from a steel plate o f 20 mm thickness (KA32) as schematically

' Japan Marine United Corporation ' Hosei University

illustrated in Fig. 1. Photo 1 shows the test specimen of TP5. In order to restrict the point of crack initiation, 3 of 4 toe radii were processed as dull radius. Table 1 shows the mechanical properties and chemical compositions of the steel.

Test patterns in the fundamental experiments are " A " change in main plate thickness, " B " change in attached plate thickness, "C" change in both thicknesses with same ratio and " D " change in toe radius. Table 2 summarizes the combinations of plate thicknesses. In this study, weld length is determined based on the rule specifications of the lACS CSR-BC^l

250

(depth; 20mm)

Figure 1 Example of test specimen in fimdamental experiment (test specmien of TP2)

Photo 1 Example of test specunen in fundamental experiment (test specimen of TP5)

Table 1 Major chemical composition and mechanical properties o f t h e material Chemical Composition (%) Mechanical Properties

C Si M n P Yield stress (MPa) Tensile strength (MPa) Elongation (%) 0.17 0.37-0.39 1.34-1.36 0.016 - 0.018 347 - 352 519-523 2 7 - 3 0

Table 2 Combinations of plate thicknesses in fimdamental experiment (unit: mm, width of specimen=20mm)

Test pattern TP No. Main plate Attached plate Weld length; £ Toe radius; p Test pattern TP No.

thickness; tp Thickness; ta Height; ha Weld length; £

Toe radius; p 1 12 A 2 22 12 60 6.4 1 A 3 40 12 60 6.4 1 4 80 3 12 60 6.4 B 5 40 22 60 8.4 1 B 6 40 40 80 12 1 7 80 160 20 1 12 12 60 6.4 C 8 22 22 60 8.4 I C 6 40 40 80 12 I 9 80 80 160 20 10 0.5 2 22 12 60 6.4 1 D 11 3 D 12 0.5 5 40 22 60 8.4 1 13 3 34 ClassNK T E C H N I C A L B U L L E T I N 2013

2.2 Basic welded joint experiment

To comprehend the effect of weld residual stress on the thickness effect, fatigue tests for craciform fillet welded joints o f as-welded specimens and o f PWHT (post weld heat treatment) specimens were carried out. In addition, to comprehend the thickness effect on welded joints, fatigue tests for out-of-plane gusset welded joints were carried out. Test specunens were made of TMCP YP32 steel (rule

500

specified yield stress and tensile strength are 315 MPa and 440-590 MPa).

Table 3 summarizes the combinations of plate thicknesses. Fig. 2 shows illustrations of the test specimen. As shown in Fig. 2, the length between the points cramped by the test machine of cruciform fillet welded joint specimen and out-of-plane gusset welded joint specimen is about 500 mm and 600 mm respectively. Width of gusset plate is 120 mm.

120 w

Figure 2 Test specimen m basic welded jomt experunents

Table 3 Combinations of plate thicknesses in basic welded joint experunent (units: mm, width of specunen=100 mm)

Joint type Test No. Main plate thickness

Attached plate Target weld length

Target toe radius Joint type Test No. Main plate

thickness _{Thickness Height}

Target weld length Target toe radius Cruciform fillet welded joint 2-AW 40 22 60 8.4 1 Cruciform fillet welded joint 2-SR 40 22 60 8.4 1 Cruciform fillet welded joint 3-AW 40 80 160 12 1 Cruciform fillet welded joint 3-SR 40 80 160 12 1 Out-of-plane gusset welded joint 5-AW 12 12 60 6.4 1 Out-of-plane gusset welded joint 6-AW 22 12 60 6.4 1 Out-of-plane gusset welded joint 7-AW 40 12 60 6.4 1 Out-of-plane gusset welded joint 8-AW 80 12 60 6.4 1 Out-of-plane gusset welded joint 9-AW 40 24 60 8.4 1

AW: as welded, SR: stress relieved by PWHT

2.3 Fatigue test

Fatigue tests were carried out under load-conti-oUed axial loading with a pulsating constant amplitude (stress ratio R=0.05) at room temperature in air. Test loads were determined so that the fatigue lives fi-om lO' to lO' could be obtained effectively Fatigue tests were stopped by load cycles of approximately 5x10* unless a fatigue crack was initiated.

In this study, failure life, N f is defined as the number o f load cycles until the specimen has totally failed. Crack initiation life, Nc, in the fimdamental experiment is defmed as the number o f load cycles when crack depth becomes 1 mm. Crack depth was monitored by strain measurements using an analytically obtained relationship between crack depth and strain reduction. In addition, crack initiation life, Nc, in basic welded joint experiment is defmed as the number of load cycles when the stram amplitude drops to 95%. I n both experiments, strain was

measured by a stram gauge which was instaUed at a point 5 mm fi-om the weld toe.

Simultaneously, fatigue tests of base material were carried out to obtain the S-N relation of the material used in the fundamental experunent. Fig. 3 shows the test specunen used in the fatigue test of the base material. Based on these fatigue tests, the S-N relation o f the base material was obtained as follows. Fatigue strength at a 2x10'' fatigue fife was estimated as 393.32 MPa. B40 - - . ^ V V V U ! ^ 1 (1)12 1 0 2 0 JO ^ 20O

Figure 3 Test specimen used in the fatigue test of the base material

= 9 . 3 x 1 0 " ' - A ^ ^ ' - ' (1)

3. Finite element analysis

3.1 Analysis model

Finite element elastic analyses using MSC/Nastran were carried out. A plane strain element FE model (1/2 model) was used for the specimen o f the fimdamental experiments, and a solid FE element model (1/8 model) was used for the specimen of the basic welded joints experiments (see Fig. 4). Young's modulus o f £ ' = £'/(l - ) and i i were applied for the plane strain elements and solid elements respectively, where £=206GPa and i^0.3.

An identical element size o f minimum 0.05 mm was applied at the weld toes o f all the specimens o f the fundamental experiments in order to ehminate differences due to element size. The length o f each side o f the elements was made

identical as far as practical for accuracy o f analysis. In an actual fillet welded cruciform joint, a root face exists between main plates and attached plates. However, this root face was not modeled in the finite element model o f the fimdamental experiments. Dummy rod elements were attached on the surface along the weld toe contoiu' shape to obtain the boundary stresses along the weld toe surface.

Weld toes o f the specimens o f the basic welded joint experiments were modeled based upon toe radius. 10 elements were arranged along the curvature. The root face between the main plate and attached plate was modeled by a slit o f 0.4 mm. In order to evaluate the nodal load on the surface o f the main plate, membrane elements o f 10"' mm thickness were attached on the surface around the weld toe.

Half thickness o f attached plate

_».. 250(500/2)

Figure 4 FE models for the specimens o f fundamental experiments (upper) and basic welded joint experiments (lower)

As illustrated in Fig, 5, principal stress direction <^ was calculated in the surface element where the highest stress is exerted, and the stresses in this dii-ection were obtained in the elements along the radial dhection to the weld toe contour (i.e., along the thi-ough-thickness direction). Stress distribu-tion down to the 1 mm depth fi-om the surface was calculated by fitting the stresses in each element to 6th order polyno-mial.

Highest stress point

Bar element for surface stress

Figures Detail of FEA

3.2 Results of the analysis

The results o f the evaluated stress concentration factor and stress gradient at the location where the highest stress is exerted for each specimen are shown in Table 4, In this study, stress gradient is calculated based on the stresses at surface and at depth o f 1 mm. According to the results for the

specimens o f a basic welded joint, strain reduction o f 5% at the point 5 mm fi'om the weld toe almost corresponds to the condition that the crack propagates to 1 mm depth.

Fig. 6(a) shows the relationship between plate thickness and stress concentration factor and Fig. 6(b) shows the relationship between plate thickness and stress gradient. According to the results, changes in the stress concentration factor and also stress gradient are remarkable when both main plate thickness and attached plate thickness are changed (series C), In cases where attached plate thickness is not changitig in spite o f a change in mam plate thickness (series A ) , changes in the stress concentration factor and also the stress gradient become stable when main plate thickness become thicker than 22 mm. The same tendency can be observed in the case o f gusset welded joints when main plate thickness becomes thicker than 40 mm. I n general, both the stress concentration factor and stress gradient depend upon attached plate thickness more than main plate tliickness. In this study, weld length of the specimen was determined based upon attached plate thickness'*.

Fig. 7 shows the relationship between the stress concen-tration factor and stress gradient. As shown in this figure, the stress concentration factor and stress gradient have a linear relationship. This relationship seems to depend upon weld toe radius.

Table 4 Evaluated stress concentration factor and stress gradient for each specimen

Type Test No,

Plate thickness (mm) Weld length (mm) Toe radius (mm) Stress concentration factor Stress gradient Type Test No,

Main Attached Weld length (mm) Toe radius (mm) Stress concentration factor Stress gradient Series A TPl 12 12 6.4 1 2.56 2.05 Series A TP2 22 12 6.4 1 2.78 2.21 Series A TP3 40 12 6.4 1 2.82 2.24 Series A TP4 80 12 6.4 1 2.81 2,23 Series B TPS 40 22 8.4 1 3.23 2.52 Series B TP6 40 40 12 1 3.62 2.79 Series B TP7 40 80 20 1 3,88 2.96 Series C TP8 22 22 8.4 1 3,04 2.39 Series C TP9 80 80 20 1 4,48 3,36 Series D TPIO 22 12 6,4 O.S 3.44 2,63 Series D TPU 22 12 6,4 3 2.01 1,70 Series D TP12 40 22 8.4 0.5 4.01 3,00 Series D TP13 40 22 8.4 3 2,31 1,93 Cruciform welded joint 2-AW, -SR 40 22 8.4 1 3,23 1,84 Cruciform

welded joint 3-AW, -SR 40 80 12 1 3,88 2,24

Gusset welded joint 5-AW 12 12 6,4 1 3.33 1.75 Gusset welded joint 6-AW 22 12 6,4 1 3,68 1,97 Gusset welded joint 7-AW 40 12 6,4 1 3,93 2.11 Gusset welded joint 8-AW 80 12 6,4 1 4.1 2.2 ClassNK T E C H N I C A L B U L L E T I N 2013 37

3.0 2.S c ,<n 2.0 "G 2 1.5 1.5 1.0 0.", 0.0 0.0 1.0 2,n 5 0 4.0

Stress concentration factor 5.0 • series A • series B A series C series D cruciform gusset

Figure 7 Relationship between stress concentration factor and stress gradient

4. Fatigue test results

Figs. 8 to 11 show fhe results o f the fatigue tests for fimdamental experiments. In these figures, the left figure shows the relationship between nominal stress range and crack initiation hfe, and the right figure shows the relationship between notch stress range and crack initiation life. Notch stress ranges were calculated by multiplying the nominal stress range by a stress concentration factor which was evaluated by the FE analysis.

According to the test resuhs coiTelated by the nominal stress range, the effect o f plate thickness on fatigue strength was observed when the attached plate thickness changed, when both the plate thicknesses o f the main plate and the attached plate were increased, a decrease in fatigue strength was especially observed. However, the thickness effect on fatigue

strength was not remarkable when the thickness o f the attached plate was not changed. These observations are in agreement with previous reports^'' ^\

On the other hand, according to the test results correlated by the notch stress range, the effect of plate thickness on fatigue strength was not observed even in the case where both the plate thickness o f the main plate and attached plate were increased.

Based upon these fatigue test results, S-N relationship ( = l o g C • AiS"'" ) for each test pattern was obtained. Since the number o f fatigue tests for each test pattern was limited, the slope o f S-N relation was affected by the scatter of data. Therefore, the slope o f S-N relation was determined by all o f the data o f the fimdamental experiments. Table 5 summarizes the S-N relationship for each test pattern.

z

• TPl

• TP2 *TP3 VTP4

Crack initiation life, Nc

Figure 8 Fatigue test results for pattern A

(increase in main plate thickness with fixed attached plate thickness (ta=12): T P l ; tp=12, TP2; tp=22, TP3; tp=40, TP4; tp=80)

Figure 9 Fatigue test results for pattern B

(increase in attached plate thickness with fixed main plate thickness (tp=40): TP3; ta=12, TP5; ta=22, TP6; ta=40, TP7; ta=80)

IIXMI a. • TPl • TPS A TPS TP9

Cracl< initiation life, Nc

Figure 10 Fatigue test results for pattern C

(increase in attached plate thickness together with main plate thickness with same ratio: T P l ; tp=ta=12, TP8; tp=ta=22, TP6; tp=ta=40, TP9; tp=ta=80)

0. £ o • TPIO • TP2 AT P l l TP12 TPS TP13

Crack initiation life, Ne

2

5.E105

Crack initiation life, Nc

Figure 11 Fatigue test results for pattern D

(mcrease m toe radius: TPIO; p=0.5, TP2; p = l , T P l l ; p=3 (tp=22, ta=12), TP12; p=0.5, TP5; p = l , TP13; p=3 (tp=40, ta=22))

Table 5 S-N relationship and fatigue strength at a 2x10' fatigue life for each test pattern Nominal stress range Notch stress range

Pattern TP No. Nc N f Nc N f

Pattern TP No.

/;;= i.80 ;;;=7.66 m= ^80 ;»=7.66

i o g [ q FAT* _{i o g [ q} FAT* i o g [ q FAT* i o g [ q FAT* 1 27.04 227.98 24.28 222.26 30.62 582.49 27.41 567.88 A 2 26.67 206.76 24.01 204.43 30.57 575.22 27.41 568.74 A 3 26.39 192.33 23.72 187.49 30.35 542.95 27.17 529.29 4 26.55 200.45 23.93 199.71 30.49 562.68 27.36 560.59 3 26.39 192.33 23.72 187.49 30.35 542.95 27.17 529.29 B 5 25.94 171.13 23.38 169.27 30.42 552.59 27.28 546.59 B 6 25.65 158.53 23.12 156.86 30.56 573.74 27.41 567.68 7 25.16 139.35 22.72 138.85 30.33 539.84 27.23 537.89 1 27.04 227.98 24.28 222.26 30.62 582.49 27.41 567.88 C 8 25.86 167.47 23,31 166.07 30.10 508.45 27.01 504.20 C 6 25.65 158.53 23.12 156.86 30.56 573.58 27.40 567.52 9 24.69 123.35 22.37 125.06 30.42 552.23 27.36 559.88 10 25.98 172.84 23.43 171.86 30.70 594.75 27.54 591.39 2 26.67 206.76 24.01 204.43 30.57 575.22 27.41 568.74 D 11 27.29 243.47 24.53 239.51 29.96 489.38 26.86 481.42 D 12 25.39 148.09 22.95 148.63 30.69 592.51 27.56 594.67 5 25.94 171.13 23.38 169.27 30.42 552.59 27.28 546.59 13 26.90 220.08 24.22 217.88 30.10 507.95 27.00 502.87 *FAT denotes fatigue strength (MPa) at 2x10" fatigue life calculated by the S-N relation

4.2 Basic welded joint experiments

Figs. 12 to 15 show the resuhs o f fatigue tests o f basic welded jomt experiments. In these figures, the left figure shows the relationship between nominal stress range and fatigue hfe, and the right figure shows the relationship between notch stress range and fatigue life. Notch stress ranges were calculated by multiplying the nominal stress range by a stress concentration factor which was evaluated by FE analysis.

According to the results shown m Figs. 12 and 13, a difference m fatigue strength due to the difference in attached plate thickness could be observed, but the effect o f weld residual stress on the thickness effect was not observed. However, in the case o f a cruciform fillet welded joint, weld residual stress is considered to be relatively small. Actually, measured maximum weld residual stresses were 50 to 120

MPa. Further investigation would be required regarding the effect of weld residual stress on the thickness effect.

According to the resuhs shown in Figs. 14 and 15, although the test data showed relative scatter, the effect o f the thickness effect on fatigue strength could not be observed. Regarding gusset welded joints, the resuhs correlated by the notch stress range showed scatter when compared to the resuhs o f cmciform welded joints.

Based upon these fatigue test results, the S-N relationship ( A'^ = l o g C • AiS"'" ) for each test pattern was obtained. Since the number o f fatigue tests was limited, the slope o f the S-N relationship was affected by the scatter o f data. Therefore, the slope o f the S-N relationship was determined by all o f the data o f the welded joint experiments. Table 6 summarizes the S-N relationship for each test pattern.

2 50 i • 2-AV.' • 2-SR A 3-AW • 3-SR 3.E<0!,

Crack initiation life, Nc

1 2 • 2 100 3.E.0.1 • 2-AV.' 2.SB, A 3-AW • 3-SR 3 . E . 0 5

Crack initiation life, Nc

Figure 12 Fatigue test resuhs for cruciform welded joint according to crack initiation life

(2-AW; as-welded, tp=40, ta=22, 2-SR; PWHT tp=40, ta=22, 3-AW; as-welded, tp=40, ta=80, 3-SR; PWHT, tp=40, ta=80)

• 2-AW 2- 5B A 3-AW

3- SR

Figure 13 Fatigue test results for cmciform welded joint according to failure life

(2-AW; as-welded, tp=40, ta=22, 2-SR; PWHT, tp=40, ta=22, 3-AW; as-welded, tp=40, ta=80, 3-SR; PWHT, tp=40, ta=80)

9. E • 5-AW • 6-AW A 7-AW ;•: 8-AW

Crack initiation life,Nc

t ,(XK) 2 • 5-AW • 6-AW A 7-AW •:a-AW

Crack Initiation life, Nc

3.E4Ü6

Figure 14 Fatigue test results for gusset welded joint according to crack initiation life (5-AW; tp=12, 6-AW; tp=22, 7-AW; tp=40, 8-AW; tp=80)

5.E105 Failure life, Nf 5.E.0G S S e> • 5-AW C E • 6-AW £! A 7-AW -. n 5 t >; 8-AW Not < • 5-AW 6-AW A 7-AW •S-AW 5.E.05 Failure life,Nf

Figure 15 Fatigue test results for gusset welded joint according to failure life (5-AW; tp=12, 6-AW; tp=22, 7-AW; tp=40, 8-AW; tp=80)

Table 6 S-N relation and fatigue strength at 2x10'' fatigue hfe of each welded jomt

Joint type Test No.

Nominal Notch

Joint type Test No. Nc N f Nc N f

Joint type Test No.

;;;=5.14 ;);=4.41 OT=5.12 ;;;=4.61

Joint type Test No.

i o g [ q FAT* i o g [ q FAT* i o g [ q FAT* i o g [ q FAT*

Cmcifonn welded jomt 2-AW 16.91 116.33 15.54 124.38 19.47 374.99 18.35 407.88 Cmcifonn welded jomt 2-SR 16.91 116.31 15.55 125.05 19.47 374.91 18.36 410.00 Cmcifonn welded jomt 3-AW 16.09 80.58 15.02 94.55 19.06 311.55 18.16 371.34 Cmcifonn welded jomt 3-SR 16.29 88.25 15.14 100.95 19.26 341.34 18.28 395.29 Gusset welded jomt m=4.53 ;;)=4.10 /H=4.38 »)=4.30 Gusset welded jomt 5-AW 15.02 84.33 14.49 99.58 17.00 276.16 17.18 336.61 Gusset welded jomt 6-AW 15.15 90.03 14.58 104.94 17.32 326.24 17.46 391.95 Gusset welded jomt 7-AW 14.88 78.57 14.60 105.74 17.18 302.62 17.60 422.03 Gusset welded jomt 8-AW 14.91 79.67 14.70 112.30 17.29 321.15 17,77 463.32 *FAT denotes fatigue strength (MPa) at 2x10* fatigue life calculated by the S-N relationship

5. Thickness effect

5.1 Tliiclmess effect according to the results of fatigue tests

Conventionally, thickness effect on fatigue strength was incorporated in the design standards. For example, coirection factor for thickness effect which is defined as follows is to be applied to the stress range to take thickness effect into account. 2), 3)

flhick ~

Where

t

(2)

t,.^f: reference plate thickness in which stress is evaluated

( / , , ƒ = 22 mm^)-'))

n : thickness coirection exponent.

Fig. 16 shows the ratio o f t h e fatigue strength agamst the fatigue strength of reference thickness for Series A , B and C of the fundamental experiments and gusset welded joints. I n

each figure, evaluated correction factors for thickness effect are indicated by a dotted line. I n the case o f fimdamental experiments, a correction factor is evaluated for the fatigue strength in nominal stress which corresponds to crack initiation life; in the case of welded joints, h is evaluated for the fatigue strength in nominal stress which corresponds to failure life.

According to the resuhs shown in Fig. 16, the thickness effect is not observed when fatigue strength is assessed based upon notch stress. Although the defmition of notch stress is different, I I W suggests that consideration o f the thickness effect is not requii'cd in the case o f assessment based upon effective notch stress''.

The thickness effect is negligible m the case of gusset welded joints and Series A fundamental experiments (the case where attached plate thickness does not change). The thickness effect can be observed in the Series B and C fundamental experiments. It should be noted that in both cases, the thickness effect depends upon attached plate thickness. In other words, h may be said that the thickness effect depends upon the size of the weld.

!? .2 1.2 t; 3 " 0.8

0

main plate thickness

— • —N f Nominal

- - Nc Noiriin,-!!

n- 0.05 IIW

(a) Series A fimdamental experiment

; ,.-1

>2 0 .6

\

\

30 40 60 80 attactied plate thickness

— • —N f Nominal

—.: Nc Nominal

I V 0.1& IIW

(b) Series B fundamental experunent

,0 C O

s

I

main & attached plate thickness

« Nf ItoiliiiijH •(s'£ Nciminai — - - n - 0 . 2 IIW 0

i

i

i

I

S

S

main plate thickness

AW

(c) Series C fimdamental experiment (d) Out-of-plane gusset welded joint

Figure 16 Fatigue strength reduction due to thickness effect

5.2 Effect of stress concentration and stress

gradient on fatigue strengtli

According to tlie results shown in Fig. 6 and Fig. 16, it is considered that the thickness effect on fatigue strength is closely related to the stress concentration and stress gradient at the weld toe. Regarding this matter, Siebel" showed the correlation between the stress gradient ( ; ) f ) and the ratio o f stress concentration factor to fatigue strength reduction factor

{ a j (5 ) for various mechanically notched materials. Based

upon the Siebel's diagram o f steels whose yield stresses are 196 MPa and 392 MPa, the correlation between x and aj P for the material used in the fundamental experiments whose yield stress is 350 MPa can be obtained as shown in Fig. 17.

The fatigue strength of the fundamental experiments can be numerically estimated based upon the Siebel's diagram shown in Fig. 17 i f the stress concentration factor and the stress gradient are calculated by FE analysis. Fig. 18 indicates the relationship between the fatigue strength estimated by Siebel's diagram and the fatigue strength calculated by the S-N curve, which is derived from fatigue tests.

Ahhough this tends to under-estmiate by about 10% when compared to the experimental results, scatter in estimation is quite small. According to this resuh, it is considered that fatigue strength is dominated by not only the stress concentration factor, but also the stress gradient at the weld toe which changes according to the form of the joint.

Figure 17 CoiTclation between the stress gradient ( X ) and the ratio of stress concentration factor to fatigue strength

reduction factor {aj f i ) for the material used in the fimdamental experiments derived from Siebel's diagram

ti 250 100 50 ..•••••">^ • • • • ' Y - ' ' .yi'' ^ series A series B A series C X series D 0 50 100 150 200 250 300

fatigue strengtli by the experiments

Figure 18 Relationship between the fatigue strength estunated by Siebel's diagram and the fatigue strength calculated

by the S-N curve derived from the fatigue tests.

6. CONCLUSIONS

The main conclusions of the present study are as follows: (1) According to fimdamental experiments, the thickness effect

on fatigue strength depends upon the change in attached plate thickness rather more than the change in main plate thickness.

(2) The reason of above mentioned tendency is considered to be that fatigue strength is dommated by stress concentration and the stress gradient at weld toes which depend upon weld size. In addhion, m the case of ship structural design, weld size is usually determined based upon attached plate thickness.

(3) According to the fatigue test resuhs o f out-of plane gusset welded joints and previously reported fatigue test resuhs o f cruciform welded joints'' in which attached plate thickness did not change, the thickness effect was quite small. The reason for this is considered to be that stress concentration and stress gradient are not so senshive to an increase in main plate thickness.

(4) The effect of weld residual stress on the fatigue strength of cruciform welded jomt was negligible. However, firrther investigation is requked about this matter

Acknowledgements

This work was earned out by the Joint Research Project between the Sliipbuilders' Association of Japan (SAJ) and the Nippon Kaiji Kyokai (ClassNK). The authors would like to thank all the coinmrttee members o f the JRP, who carried out the various experiments, analyses and discussions.

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International Symposium on Practical Design of Ships and Other Floating Structures, Houston, 2007

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