Fatigue Life Prediction of Welded Box Structures
The objective of this study is to predict fatigue life of metal welded boxes. Experimental results of fatigue life are satisfactory predicted using an analytical scheme based on the volumetric approach. Проведено прогнозирование усталостной долговечности сварных коробчатых конструкций. Результа...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2004
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| Zitieren: | Fatigue Life Prediction of Welded Box Structures / H. Zedira, J. Gilgert, A. Boumaza, P. Jodin, Z. Azari, G. Pluvinage // Проблемы прочности. — 2004. — № 6. — С. 17-25. — Бібліогр.: 7 назв. — англ. |
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| author | Zedira, H. Gilgert, J. Boumaza, A. Jodin, P. Azari, Z. Pluvinage, G. |
| author_facet | Zedira, H. Gilgert, J. Boumaza, A. Jodin, P. Azari, Z. Pluvinage, G. |
| citation_txt | Fatigue Life Prediction of Welded Box Structures / H. Zedira, J. Gilgert, A. Boumaza, P. Jodin, Z. Azari, G. Pluvinage // Проблемы прочности. — 2004. — № 6. — С. 17-25. — Бібліогр.: 7 назв. — англ. |
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| container_title | Проблемы прочности |
| description | The objective of this study is to predict fatigue
life of metal welded boxes. Experimental results
of fatigue life are satisfactory predicted using
an analytical scheme based on the
volumetric approach.
Проведено прогнозирование усталостной долговечности сварных коробчатых конструкций.
Результаты расчета усталостной долговечности с использованием аналитической схемы,
базирующейся на объемном методе, хорошо согласуются с соответствующими экспериментальными
данными.
Проведено прогнозування довговічності зварних коробчастих конструкцій
від утомленості. Результати розрахунку довговічності від утомленості з
використанням аналітичної схеми, що базується на об’ємному методі, добре
узгоджуються з відповідними експериментальними даними.
|
| first_indexed | 2025-12-07T15:27:52Z |
| format | Article |
| fulltext |
UDC 539.4
H. Zedira,a J. Gilgert,b A. Boumaza,a P. Jodin,b Z. Azari,b and G. Pluvinageb
a Department of Mechanical Engineering, Centre University Larbi Ben M’Hidi, El
Bouaghi, Algerie
b Laboratoire de Fiabilité Mécanique, Université de Metz, France
УДК 539.4
П рогнозирование усталостной долговечности сварны х
коробчатых конструкций
X. Зедираа, Ж. Жильбер6, А. Бумазаа, П. Жодин6, 3. Азари6, Г. Плювинаж6
а Отделение машиностроения, Университетский центр Ларби Бен М’Хиди, Эль
Буахи, Алжир
б Лаборатория механической надежности, Университет г. Метц, Франция
Проведено прогнозирование усталостной долговечности сварных коробчатых конструкций.
Результаты расчета усталостной долговечности с использованием аналитической схемы,
базирующейся на объемном методе, хорошо согласуются с соответствующими экспери
ментальными данными.
Ключевые слова : сварные коробчатые конструкции, объемный метод, отно
сительный градиент напряжений, эффективное напряжение, отношение уста
лостной прочности образца без надреза к усталостной прочности образца с
надрезом.
N o t a t i o n
Fatigue Life Prediction of Welded Box Structures
to effective stress
O ̂ (x ) - normalized fatigue crack opening stress
X - relative stress gradient
Xff - effective distance
- global stress
Ф(х ) - weight function, which depends upon the distance x and the relative stress
gradient
Introduction. Unfilled boxes of square or rectangular cross sections are
usually applied in metal constructions since they combine both high stiffness and
low weight. These structural elements are susceptible to fatigue failure for various
causes (Fig. 1). Usually, the welding process is held responsible for structure
© H. ZEDIRA, J. GILGERT, A. BOUMAZA, P. JODIN, Z. AZARI, G. PLUVINAGE, 2004
ISSN 0556-171X. Проблемы прочности, 2004, N 6 17
H. Zedira, J. Gilgert, A. Boumaza, et al.
weakening and the reduced fatigue strength because of the heterogeneities created
within joined plates (Fig. 2). In fact, metal fusion followed by rapid cooling
results in residual stress generation in box walls.
Stress concentration zones are observed to be located along the weld line,
which is attributed to global geometrical discontinuities and specifically metal
filling at weld base line. Under bending loading conditions, weld line failure is
initiated as longitudinal crack at the slab intrados subjected to tensile stresses.
Life prediction of welded boxes did not retain enough research work. Insofar as
any complex structure consists of several elementary joints, it is recommended, in
order to predict the structure fatigue life, to study separately each joint’s
endurance limit. The latter is function of weld quality in terms of weld line
geometry and induced residual stress field either by the assembling process or by
inherent microscopic defects. Welded joint behavior can be precisely assessed
under cyclic loading through laboratory experiments using specimens with
representative dimensions compared to the actual structures. Based on such
experiments at constant or variable load amplitude, each type of welded joint is
then characterized by an allowable stress corresponding to structure life and
estimated service loadings.
Fig. 1. Cracked part of excavator bucket.
Fig. 2. Micrograph of the weld joint after cracking.
18 ISSN 0556-171X. npoôëeuu npouHocmu, 2004, № 6
Fatigue Life Prediction o f Welded Box Structures
1. Experimental. Welded boxes with dimensions 100 X100X 300 mm and
wall thickness 3 mm were produced from welding steel Q36 plates using SG-3 steel
as the weld metal. Chemical compositions and mechanical properties of these steels
purchased from the CPG, Algeria, are given in Tables 1 and 2, respectively. These
welded boxes simulated those used in excavator loading wheels depicted in Fig. 3.
T a b l e 1
Chemical Composition of Steels Q36 and SG-3
Material C, % max Si, % max Mn, % max P, % max S, % max Ti, % max
Q36 0.16 0.50 1.60 0.03 0.03 0 . 1 2
SG-3 0.07-0.14 0.80-1.20 1.60-1.90 - - -
T a b l e 2
Mechanical Properties of Steels Q36 and SG-3
Material Re, MPa Rm, MPa K TK cv min , T Elongation, %
Q36 355 490-690 27 25
SG-3 470 590 - 30
Fig. 3. Geometry of the welded box structures of loading wheels.
Using the Instron test machine providing the maximal tensile/compressive
load ±100 kN, welded boxes were subjected to three-point-bending cyclic loading
with frequency of 6 Hz and load ratio R = a min/ a max = 0.1 (see Fig. 4). For
construction of the experimental fatigue curve we tested 6 welded boxes.
2. Volumetric Approach. In order to take into account the notch effect, a
notion of fatigue notch factor is used [1]. The most practical definition of fatigue
notch factor k f is the ratio of the fatigue strength of smooth specimen to that of
notched specimens under the same test conditions and the same number o f cycles
a s
k f = — • (1)^ n
where о s and о n are smooth and notched specimen fatigue strength, respectively.
ISSN 0556-171X. Проблемы прочности, 2004, N 6 19
H. Zedira, J. Gilgert, A. Boumaza, et al.
Fig. 4. Three-point bending test of welded box structures.
However, no general, brief, practical and low-cost method for determination
of k f has yet been formulated [2]. Therefore, as an alternative, the volumetric
approach has been introduced [3-5] for modeling of the fatigue failure process.
The assumption made in this approach is that the fatigue failure needs a physical
volume to occur. The method is applied for an elastoplastic stress distribution
calculated using the finite element method and taking into consideration the
particular material cyclic behavior, in order to allow for the plastic and damage
relaxation. The effective stress is first determined as the stress value
corresponding to the stress distribution for the effective distance. For application
of the volumetric approach one needs the fatigue curve, the cyclic stress-strain
curve and the finite element analysis for determination of the stress distribution
near the notch tip.
2.1. G raphical M ethod of the Volumetric A pproach [3-5]. The relative
stress gradient is defined as the ratio between the first derivative of stress
distribution function and the stress value at a point:
The effective distance X f is an inflexion point, corresponding to the
minimum value of the relative stress gradient. In the volumetric approach, the
effective distance is considered to be the boundary of the stress relaxation and
fatigue process zone (see Fig. 5).
The effective stress o f is defined as the average weighted stress in the
fatigue process volume:
% o yy( x ) dx
(2 )
(3)
20 ISSN 0556-171X. npoôëeubi npounocmu, 2004, N 6
Fatigue Life Prediction o f Welded Box Structures
0.60
1000
0.10
■0.40 t=
-0.30 $
us-
- 1 . 4 0
V
1 0 0 J- - 1 . 9 0
0.1 Xeff
Fig. 5. A typical elastic-plastic fatigue crack opening stress distribution for notch root and relative
stress gradient [6].
During fatigue propagation, the crack path is always normal to the maximum
principal stress. In bending, this stress is conventionally denoted by a yy(x ). We
can write in bi-dimensional case:
2.1. Analytical M ethod of the Volumetric A pproach. In order to use the
analytical method based on the volumetric approach, it is needed to perform an
elastic or elastoplastic finite element calculation, by using the real law of behavior
of material. Material behavior equation is used taking into account the relationship
between stress and strain in the form:
The steps consist in obtaining the stress distribution as a function and
subsequently establishing the equation of the opening stress a yy(x ). A curve
fitting is then performed to assess a polynomial representation in the form:
(4)
(5)
n
(6 )
ISSN 0556-171X. npoôëeMbi npounocmu, 2004, N2 6 21
H. Zedira, J. Gilgert, A. Boumaza, et al.
Relative stress gradient %(x ) is given by the relationship
n
2
n
i—1iatx
1 do yy (x ) 1 =
x (x ) = „ r \ 1----- = ----- ----------■ (7)
o yy( x ) dx n I
Z a ix
i=0
Effective distance X f is given by [7]:
d%{x)
= 0 ^ x eff , (8)
2 2 3 3—ai 3a 3 ai —9a 3 ai + 4a 4 a 2 ai
x f ” 2 0 7 —~ 8a f + 1 6 ^ ■ (9)
Fatigue notch factor can be written as below [6 ]:
1 xeff
k f = ----- — f 0 yy (x )(1— xX)dx ,
x eff 0 g 0
Finally, k f is given by relationship (13):
1 ( a 2 2 a 3 3 3a 4 4
k f = ~ ^ a 0 — x eff — x f — x f f
(10)
0 (x) = 1 - X̂ - ( 1 1 )
For i = 4 we can write relationship (6 ) as
2 3 4o yy(x ) = ao + axx + a 2 x + a 3 x + a 4 x . ( 1 2 )
(13)
The effective stress is given by (14):
o ef f = k f o g . (14)
3. Elastoplastic FEM Analysis. In order to apply the volumetric approach to
these experimental results, finite element calculation of the stress distribution at
the welded joint has been accomplished using a multi-purpose finite element
Cast3m software developed at the CEA (French Atomic Research Center). For the
steel Q36 the following parameters of stress-strain diagram were obtained (Fig. 6 ):
■ hardening coefficient K ' = 485;
■ cyclic hardening exponent n' = 0.0794.
2 2 ISSN 0556-171X. npoôëeubi npounocmu, 2004, N2 6
Fatigue Life Prediction o f Welded Box Structures
T a b l e 3
FEM Calculation Results for Specimen under Study and the Respective Loading Conditions
ag , MPa Fmax> kN Fmm,kN R =F IFmm! max kf aef , MPa
106 90 9 0 . 1 1.33 141
485
Fig. 6 . Cyclic stress-strain curve of Q36 steel.
Fig. 7. Finite element analysis for a welded box.
5
S = S0(2N s f
S_
kr
N r
Fig. 8 . Volumetric approach procedures.
ISSN 0556-171X. Проблемы прочности, 2004, № 6 23
H. Zedira, J. Gilgert, A. Boumaza, et al.
300
250
200
'm
a.
Ф 150
tV.
(Л
100
50
o 4
103 1 04 1 05 1 06 Ю7
Number of cycles
Fig. 9. Comparison of the results.
Based on the calculated stress distribution (Fig. 7), the effective stress is
calculated according to the procedure described in Fig. 8 a and plotted versus the
experimental number of cycles to failure as shown on Fig. 8 b. In tabular form the
effective stress is given it Table 3. The effective stress obtained by volumetric
approach reported on fatigue reference curve gives directly the fatigue life of the
welded box structure (Fig. 9).
Conclusions. A simple procedure for fatigue life estimation based on
volumetric approach is illustrated, using the reference fatigue curve, the material
behavior curve, and finite element analysis. The fatigue life prediction, which is
carried out by the volumetric approach, has very good agreement with experimental
results. The advantages of the volumetric method include the possibility of
predicting fatigue life for many loading cases using notched geometry welded
structures, the absence of the empirical and ambiguous coefficients used in
traditional methods and the opportunity to obtain rapid and cost-effective results
using a finite element method. The volumetric approach makes it possible to
predict fatigue life for arbitrary structures. To apply this method, one needs only
1) reference fatigue curve and 2) cyclic stress-strain curve of the material. The
effective stress obtained by the volumetric approach superimposed on the
reference fatigue curve gives directly the fatigue life of the structure.
Acknowledgments. This work is supported by the Algerian Ministry of High
Education. The authors thank Prof. V. Sapunov from the Institute of Physics of
Moscow and Dr. Adib Ramzani from the University of Metz.
Р е з ю м е
Проведено прогнозування довговічності зварних коробчастих конструкцій
від утомленості. Результати розрахунку довговічності від утомленості з
24 ISSN 0556-171X. Проблеми прочности, 2004, № 6
Fatigue Life Prediction o f Welded Box Structures
використанням аналітичної схеми, що базується на об’ємному методі, добре
узгоджуються з відповідними експериментальними даними.
1. G. Qylafku, Z. Azari, N. Kadi, et al., “Application of a new model proposal
for fatigue life prediction on notches and keys-seats,” Int. J. Fatigue, 21,
753-760 (1999).
2. V. E. Panin, “Foundation of physical mesomechanics,” Fiz. Mesomekhanika,
No. 1, 5-22 (1998).
3. N. Kadi, M. G. Jonaj, and G. Pluvinage, “Volumetric approach of fatigue
failure of notched specimen,” in: Proc. Copernicus Annual Meeting, Miskolc,
Hungary (1997).
4. G. Qylafku, Z. Azari, M. G. Jonaj, and G. Pluvinage, “On the fatigue and
fatigue life prediction of the notched specimen,” Mater. Sci., 34, 604-618
(1999).
5. H. El Minor, M. Louah, Z. Azari, et al., “Brittle mixed-mode (I+II) fracture:
Application o f the equivalent notch stress intensity factor to cracks
emanating from notches,” Probl. Prochn., No. 6 , 61-71 (2002).
6 . H. Adib and G. Pluvinage, “Theoretical and numerical aspects of volumetric
approach for fatigue life prediction in notched components,” Int. J. Fatigue,
25, No. 1, 67-76 (2003).
7. H. Adib, Evaluation de la Durée de Vie en Fatigue par la Méthode
Volumétrique pour les Joints Soudés p a r Point, Thèse de Doctorat,
Université de Metz (2003).
Received 05. 04. 2004
ISSN 0556-171X. Проблемы прочности, 2004, № 6 25
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| id | nasplib_isofts_kiev_ua-123456789-47131 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-07T15:27:52Z |
| publishDate | 2004 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Zedira, H. Gilgert, J. Boumaza, A. Jodin, P. Azari, Z. Pluvinage, G. 2013-07-09T21:07:39Z 2013-07-09T21:07:39Z 2004 Fatigue Life Prediction of Welded Box Structures / H. Zedira, J. Gilgert, A. Boumaza, P. Jodin, Z. Azari, G. Pluvinage // Проблемы прочности. — 2004. — № 6. — С. 17-25. — Бібліогр.: 7 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/47131 539.4 The objective of this study is to predict fatigue life of metal welded boxes. Experimental results of fatigue life are satisfactory predicted using an analytical scheme based on the volumetric approach. Проведено прогнозирование усталостной долговечности сварных коробчатых конструкций. Результаты расчета усталостной долговечности с использованием аналитической схемы, базирующейся на объемном методе, хорошо согласуются с соответствующими экспериментальными данными. Проведено прогнозування довговічності зварних коробчастих конструкцій від утомленості. Результати розрахунку довговічності від утомленості з використанням аналітичної схеми, що базується на об’ємному методі, добре узгоджуються з відповідними експериментальними даними. This work is supported by the Algerian Ministry of High Education. The authors thank Prof. V. Sapunov from the Institute of Physics of Moscow and Dr. Adib Ramzani from the University of Metz. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Fatigue Life Prediction of Welded Box Structures Прогнозирование усталостной долговечности сварных коробчатых конструкций Article published earlier |
| spellingShingle | Fatigue Life Prediction of Welded Box Structures Zedira, H. Gilgert, J. Boumaza, A. Jodin, P. Azari, Z. Pluvinage, G. Научно-технический раздел |
| title | Fatigue Life Prediction of Welded Box Structures |
| title_alt | Прогнозирование усталостной долговечности сварных коробчатых конструкций |
| title_full | Fatigue Life Prediction of Welded Box Structures |
| title_fullStr | Fatigue Life Prediction of Welded Box Structures |
| title_full_unstemmed | Fatigue Life Prediction of Welded Box Structures |
| title_short | Fatigue Life Prediction of Welded Box Structures |
| title_sort | fatigue life prediction of welded box structures |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/47131 |
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