Procedia Engineering 40 ( 2012 ) 148 – 153

1877-7058 © 2012 Published by Elsevier Ltd.doi: 10.1016/j.proeng.2012.07.071

Steel Structures and Bridges 2012

Assessment of Fatigue of Structural Steels J.Djubeka and V. Ilanovskýb*

aHomolova 11, 841 02, Bratislava, Slovakia bDepartment of Metal and Timber Structures, Slovak University of Technology, Radlinského 11, 813 68, Bratislava, Slovakia

Abstract

After the application of N cycles of stress range Δσ, the crack will grow from the initial to critical length according to the algebraic equation (4). The algebraic equation holds for any material, only if m>2. For structural ferritic steel, the critical length of crack is a=8mm (10), where the number of fatigue cycles is N=108 and cyclic stress range Δσ=27.5MPa. Under repeated shear loading the largest membrane and bending stresses are concentrated in the vicinity of corners of the web. The stress ranges for 106 cycles (steel and aluminium alloys) and the constants in equation of curve Δσ3.N=constant are given as follows in the fifth chapter. © 2012 Published by Elsevier Ltd. Selection and review under responsibility of University of Žilina, FCE, Slovakia.

Keywords: planar flaws; ferritic steels; non-ferrous metals; cyclic shear loading; crack in rectangular web

1. Crack growth analysis

The fatigue crack growth rate can be related to the stress intensity factor amplitude ΔK=Kmax- Kmin as

m

steel

msteel

m

steelm

EEK

EEKA

dNda ...10.3. 13 (1)

where da/dN is the rate of crack propagation, A and m are constants which depend on the material and the applied conditions, including environment. The stress intensity factor range, ΔK, is a function of the crack

* Tel.: +421-259-274-367

E-mail address: vladimir.ilanovsky@stuba.sk

Available online at www.sciencedirect.com

Open access under CC BY-NC-ND license.

Open access under CC BY-NC-ND license.

149 J.Djubek and V. Ilanovský / Procedia Engineering 40 ( 2012 ) 148 – 153

geometry factor depending on the orientation and size of the crack surface, cyclic stress range Δσ, E elastic modulus and critical length of the crack a, respectively

aYK ... (2)

Since

12

122

11.1

2

1mm

o

a

am

aam

a

da

o

(3)

we have

NAYaa

mm

mm

o

....11.1

2

11

21

2

(4)

where the initial length of the crack is considered as ao=10-3m. The algebraic equation (4) holds for any material, only if m>2.

2. Fatigue crack growth in ferritic steels and non-ferrous metals

2.1. Structured ferritic steels

For structural ferritic steels operating at temperatures up to 20°C, with assuming the absence of specific corrosion fatigue data, the upper bound of the parameter A and the parameter m, are recommended as

3m

1210.4.2A (5)

For ferritic steels with yielding or steels for which 0.2% proof strength is less 600 MPa and operating in air or other non-aggressive environments at temperatures up to 100°C one should use the parameters

3m

1310.3A (6)

2.2. Fatigue crack growth in non-ferrous metals

The fatigue crack growth rate and stress intensity factor range can be expressed approximately as functions of ΔK and elastic modulus E. Then, the crack growth constants m=3 and A=3.10-13, corresponding to ferritic steels, can be utilized for another material with elastic modulus E as m=3 and A=3.10-13.(Esteel/E)m= 3.10-13.(Esteel/E)3. The stress intensity factor range can be modified by ΔK= ΔKsteel.(E/Esteel).

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3. Critical length of crack

For structural ferritic steel, the parameter A=2.4.10-12 and the term (Δσ.√π)m.A.N is constant and equal to 27.5. Assuming the number of fatigue cycles N=108 and the threshold stress intensity factor amplitude ΔKth=5MPa.m1/2 we have

21025.0..5.27

5.. YYY

Ka th (7)

For structural ferritic steel the equation (4) becomes

35,03

.5.271025.010

1.5.0

1 YY (8)

or

0299.2.709.03 YY

(9)

Hence Y=1.142 The critical length of crack is

ma 00805.0142.11025.0 2

(10)

Assuming N=104 and a= 0.0011 (a>ao), for structural ferritic steel we obtain

NAYaao

....115.0

1 3 (11)

Hence

3.81.90011.01

001.01

5.01 Y (12)

We have Y=0.66 Comment: if a=ao , then Y=0

4. Cracking of web under cycling shear loading

In the case of crack propagation the stresses are given as follows

22 cossin..y (13)

151 J.Djubek and V. Ilanovský / Procedia Engineering 40 ( 2012 ) 148 – 153

cos.sin.1.xy (14)

Hence we obtain

1..1

2tgtg

y

xy (15)

For pulsating repeated loading

tgtgxyy

21 (16)

where γ=-tg2β It should be said, that for the web under shear loading, we have γ≤0. The equivalent stresses on the crack surface given by

Byn

Axm

Twnm

BATzE

mnmn

xy

..cos...cos.....1

... 2

(17)

2

2

xy (18)

express the membrane and bending stresses of simply supported web, with z being the perpendicular distance from the middle surface xy. The expressions for the stresses σy and τxy are valid in the vicinity of plate corners. From (16) we have

01 2 tgtg

xyy (19)

or

0..2xyyxy tgtg (20)

from where

xy

xyyytg.2

.4 22

(21)

The positive root is tgβ=0.951445444.

5. Assessing flaws using quality categories

For structural ferritic steels, each curve can be described by an equation of the form

152 J.Djubek and V. Ilanovský / Procedia Engineering 40 ( 2012 ) 148 – 153

N.3 constant (22)

For the number of cycles of the fatigue life N=2.106, the stress range is 110 MPa. Constant in equation of curve is 2.66.1012. The other constants on ferritic steel (and of aluminium alloys) are given as follows

Table 1.

Constant in equation (22)

values for steel

Stress range for 105 cycles, steels [MPa]

Stress range for 105cycles, aluminium alloys [MPa]

1.22.1012 230 77

1.02.1012 220 74

9.26.1011

5.64.1011

2.57.1011

1.64.1011

210

178

137

118

70

60

47

39

We compare the stress range for 104 cycles with the nominal values of yield strength fy [MPa]

Table 2.

Stress range for 104 cycles [3] 460 440 420 355 275 235

Nominal values of yield strength fy for hot rolled structural steel [4]

460 440 420 355 275 235

They seem to be about the same.

6. Crack in rectangular web subjected to compression

Longitudinal and transversal edges become free and remain straight in the web plane. The maximum tensile stress takes place in the middle of longitudinal edges (Fig. 1). The fatigue strength of web plate Δσy in the middle of longitudinal edges for different web slenderness is given in Table 3.

Table 3.

Web slenderness B/T 60 70 80 90 100 200

Normal stress range 1.72. Δσy 0.87. Δσy 0.74. Δσy 0.68. Δσy 0.65. Δσy 0.61. Δσy

The normal stress range (as it is different from the shear stress range) intensively depends on the web

slenderness B/T.

153 J.Djubek and V. Ilanovský / Procedia Engineering 40 ( 2012 ) 148 – 153

Fig. 1. Rectangular web subjected to compression

7. Conclusions

The critical length of crack for the number of cycles N=108 is a=8mm and cyclic stress range Δσ=27.5MPa. If a=ao, the crack geometry factor Y=0. Under repeated shear loading, the largest membrane and bending stresses are concentrated in the vicinity of corners of the web. The maximum tensile stress in the cracked rectangular web subjected to compression takes place in the middle of longitudinal edges (Table 3.). The normal stress range intensively depends on the web slenderness.

Acknowledgements

The author acknowledge support by the Slovak Scientific Grant Agency under contract No.1/1101/12.

References

[1] Djubek, J.: Assessment for fatigue of planar flaws, Building Research Journal Vol.55,No.1-2., 2007. [2] Guidance of methods for assessing acceptability of flaws in fusion welded structures (1991), PD 6493, BSI Standards [3] EN 1993-1-9 Eurocode 3: Design of steel structures. Part 1-9: Fatigue strength of steel structures. CEN Brussels. May 2005 [4] EN 1993-1-1 Eurocode 3: Design of steel structures. Part 1-1: General rules and rules for buildings. CEN Brussels. May 2005