accidental overloading effect on the s-n …€¦ · key words: accidental fatigue overload, welded...

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International Journal of Civil Engineering and Technology (IJCIET)

Volume 8, Issue 11, November 2017, pp. 967–981, Article ID: IJCIET_08_11_096

Available online at http://http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=8&IType=11

ISSN Print: 0976-6308 and ISSN Online: 0976-6316

© IAEME Publication Scopus Indexed

ACCIDENTAL OVERLOADING EFFECT ON

THE S-N CURVE OF WELDED JOINT OF

THREE STEEL GRADES

NADJITONON Ngarmaïm

LERTI: Laboratory for Study and Research in Industrial Technology,

Faculty of Exact and Applied Sciences, University of N'Djamena (Chad).

NGARGUEUDEDJIM Kimtangar

LERTI: Laboratory for Study and Research in Industrial Technology,

Faculty of Exact and Applied Sciences, University of N'Djamena (Chad).

Faculty of Exact and Applied Sciences, University of N'Djamena, Chad PB 1027.

BIANZEUBÉ Tikri

National Polytechnic Institute of Mongo (Chad).

RIMASBE BEOSSO Sylvain

GMMA: Mechanics, Materials and Acoustics, Department of Physics,

Faculty of Science, University of Ngaoundéré PB 454 Ngaoundéré Cameroon

ABSTRACT

This paper focuses on the analysis of the fatigue behaviour of soldered points of

tree grades of steel under loading with accidental overload. For analyzing the

sensitivity of the material to accidental overloads four expressions of F-N curve are

selected. Two accidental overload ratios (1.4 and 2.3) are applied.

The experimental results and those of the four F-N models indicate the beneficial

effect of accidental overloading for the stresses greater than the level stress of the

pivot point. Below this level of stress, accidental overload is detrimental to the

material. F-N curve obtained with a ratio 2.3 shows that the breaking strength Rm of

the material is greater than that of the curve F-N ratio 1.4. But, the value D of the

endurance limit obtained with a ratio 2.3 is lower than that obtained with a ratio of

1.4.

Key words: Accidental fatigue overload, welded sheet metal, welded joints, overload

sensitivity, S-N curves.

Cite this Article: NADJITONON Ngarmaïm, NGARGUEUDEDJIM Kimtangar,

BIANZEUBÉ Tikri and RIMASBE BEOSSO Sylvain, Accidental Overloading Effect

on the S-N Curve of Welded Joint of Three Steel Grades. International Journal of

Civil Engineering and Technology, 8(11), 2017, pp. 967–981.

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=11

Accidental Overloading Effect on the S-N Curve of Welded Joint of Three Steel Grades


1. INTRODUCTION

Thanks to their excellent corrosion resistance properties, toughness and ductility the steel

HE360D, XE360D and XES are used in the automobile to achieve the hulls. The assembly of

the different parts is done by spot welding. These steels also have certain properties that

influence their behaviour and thus their cyclic fatigue resistance [1]. If the mechanical

properties of the new steels Very High Strength (THR) allow for a reduction of the plate

thickness, holding mechanical final assembly depends on the weld joints. Works on the

cyclical behaviour and fatigue resistance of the spot welding, in the presence of accidental

overload, have been the subject of studies of the team of Pascal Fatigue Institute of Clermont

Ferrand [2]. In this work, we study the sensitivity expressions of S-N curves when a periodic

accidental overload is applied. Two loading ratios (1.4 and 2.3) with respect to the base load

were used. Results of four expressions of S-N curve of their welded points and experimental,

including their sensitivity to accidental overloads, are compared in this research. The variation

of certain mechanical characteristics as the ultimate tensile strength Rm and the endurance

limit D are highlighted,

2. OBJECTIVE OF THE STUDY

The objectives of all fatigue tests on specimens welded by spot are, first the study of the

influence of accidental overloads occurring at regular intervals on their fatigue strength, and

secondly , to highlight the sensitivity of the expressions of the S-N curve overload. This study

is conducted for three different steel grades welded following a conforming adjustment to

industrial welding process. Two overload levels, from the analysis of loads, are often

encountered when driving vehicles and used for calculation of durability of automotive

components under service loading. The accidental overloads have an occurrence of an

overload cycle after 99 basic cycles. The overload ratio (maximum overload cycle on the

maximum value of the basic cycle) are equal to 1.4 or 2.3. The influence of load cycles is

analyzed in terms of life and / or maximum permissible value of the force of the basic cycles

for a life of 2.106 cycle regarded as the threshold of endurance in the automotive sector.

3. STUDY OF THE FATIGUE STRENGTH OF THE WELDED SPOT

The fatigue strength of a material is defined by the S-N curve, constructed in a stress-life

diagram (σa-N), established for a load ratio or mean stress given and constant frequency. The

endurance limit is conventionally defined to 2.106 cycles in the automotive environment. The

life N (number of cycles) is usually the sum of the numbers of cycles to initiation and

propagation of the crack to rupture. Given the difficulties to define in the critical area of the

weld points, a level representative of the constraint imposed cyclic loading, the fatigue

strength of welded point is defined by the F-N curve, where F is the maximum force applied

cycles to the test piece.

3.1. The factors of influence on the life of the welded point

Several factors influence the fatigue life of an assembly. It is essential to know and analyze

these factors well for reliable design. These key factors are recalled below.

3.2. Factors related to mechanical loading [4, 5]

3.2.1. Mean Stress

Experimental observations have shown that when a static positive stress σm is superimposed

on the cyclic loading amplitude σa the lifetime of the specimen or work piece decreases. The

reverse effect is also observed in the presence of an average compressive stress. For taking

this phenomenon into account, additional tests may be performed to establish a Haigh

NADJITONON Ngarmaïm, NGARGUEUDEDJIM Kimtangar, BIANZEUBÉ Tikri and



diagram giving for a life fixed N, the allowable alternating stress σa according to the average

stress σm. Several mathematical models of the diagram such as the straight line of Goodman,

model of CETIM and the parabola of Gerber were made.

3.2.2. Frequency

The frequency of application of charging cycles is also a mechanical parameter which should

not be overlooked. When it increases, the life generally varies in the same direction, except in

the case where this increase would result in a heating of the material. In this context, we must

avoid to load a piece at frequencies close to its natural frequency to avoid dynamic

amplification effects (resonance).

3.2.3. Nature Forces Applied

The nature of the efforts is an important parameter. Indeed, various endurance limits are

obtained depending on the type of applied stress (tensile, bending, torsion). S-N curve is thus

valid for a given type of load. In the case of a variable amplitude loading, the loading

sequence is also an important factor. For an even distribution of stress cycles, different lives

are obtained if the load blocks are applied by increasing or decreasing amplitude. This is

explained by the fact that the stresses of high amplitude have more effect on the initiation and

propagation of cracks, and the level of increase in the damages related to a given cycle

depends on the level of damage reaches when it is applied.

3.3. Materials and Specimens of the Study

3.3.1. Materials

Three steels (HE360D, XE360D and XES) were selected because of their better mechanical

characteristics in the manufacture of automobile chassis (Renault). They are developed by

ArcelorMittal in the form of hot-rolled sheet. The plate thickness of the steel HE360D is 2.5

mm while the other two sheets of steel is 1.2 mm. The specimens from these plates are made

of their delivery condition and welding settings for industrial practice. The mechanics

behaviour of welded joints of each specimen was established for monotonous tensile tests

leaded to failure.

3.3.2. Description of Test Specimens

The test specimen consists of two thin sheets of dimensions 124 x 30 (mm) with a covering

surface 38 x 30 (mm). The two sheets (of the same material) are joined by the spot welding

method. At thickness almost, specimens used for fatigue tests are similar (Figure.1).

Given the specimen geometry, two types of misalignment (concentricity defect and

angular inclination defect) may be present (Figure.2). These defects will generate static stress

and strain (proportional to the applied forces) which will be added to the stress and strain of

applied load related.



Figure 1 Definition of the specimen [2].

Figure.2: (a): concentricity defect (spacing d); (b):

angular inclination defect (θ angle) [2].

Figure.3: Test tube mounted in a stiffener

with functional games. [2].

For solving these defects, the specimens are mounted in a tightener (Figure.3).

3.4. Description Loading

The test pieces produced are loaded in corrugated tensile of load ratio R equal to 0.1. This

type of loading is often called tensile shear because these two tensile forces applied to the two

sheets assembled by a welded spot will produce a shearing of the welded spot in the plane of

contact between the sheets. Fatigue tests were carried out on servohydraulique fatigue

machine MTS 810 (maximal capacity = ± 100 kN) of Mechanical and Engineering Laboratory

of IUT of Montluçon. All tests are conducted at room temperature and at a frequency of 30

Hz under load of constant amplitude and at 20 Hz for the fatigue testing of variable amplitude.

For measuring the effect of accidental overloads on the fatigue behaviour of plates

assembled by welded point, tests at two different ratios of accidental overload have been

made (Figure.4).

(a) (b)(a) (b)




Figure 4 Description of the loading sequence comprising accidental overloading ratio R every 100

cycles.

3.5. Expressions of F-N Curves used

Four expressions of F-N curves (maximum force of the basic cycle - life) are used. They are

those of Stromeyer, Wöhler, Basquin and Nadjitonon [6 - 10]. They are presented as linear

according to the following equations.

• Model Stromeyer: DFFlogbaNlog (1)

• Model Wöhler: bFaNlog (2)

• Model Basquin: FlogbaNlog (3)

• Model Nadjitonon:

F

FloglogbaNlog m (4)

Where the parameters a and b are related to the model and specific to the materials; they

are determined by the least squares method;

Fm is the ultimate force to break, F the maximal force and FD the strength to the endurance

limit of the reference material (loaded without accidental overload).

3.6. Results Analysis Method

The analysis is performed with respect to the relative difference E(%) of the number of cycles

given by the four expressions of F-N curves selected. This relative difference E is given by

the following equation:

100N

NNE

4,1

3,24,1 (5)

Where N1.4 and N2.3 are the numbers of cycles given by the expressions of the curve F-N

corresponding to the load ratio of 1.4 and 2.3 respectively.

Equation (5) allows assessing the sensitivity of welded points of these steels to accidental

overloads which may occur in actual use parts welded points. The behaviour between the two

F-N curves for the two accidental overload ratios is analyzed.



3.7. Results and Discussion

For each case of met-loading material, the results obtained with the four F-N curve models

(Stromeyer, Wöhler, Basquin and Nadjitonon) are presented in the form of the force-number

of cycles curves, plotted in the plane (log10 (N) log10 (F)) and compared to the experimental

curve.

The Table.1 shows the test results for the three grades of steel under loading with both

accidental overload ratios.

Table 1 Experimental data of maximum load and number of cycles for the three steel grades under

accidental overload ratios R = 1.4 and R = 2.3 [2].

Material

Static loading data Fatigue loading data

Fm (N) F(N) R = 1.4 R=2.3

FD (N) N1.4 (cycles) FD (N) N2.3 (cycles)

Steel HE360D 24270

3500

3375

3 032 400

3554

3 008 600

4000 1 422 100 3 008 600

4500 727 600 718 600

5000 409 600 410 600

5500 261 800 251 800

6000 176 200 177 200

Steel XE360D 12540

3500

2634

3 033 400

2625

3 037 000

4000 1 430 100 1 469 100

4500 731 900 708 700

5000 413 600 413 600

5500 252 800 258 800

6000 172 000 178 200

Steel XES 9480

3500

2958

5 322 200

2500

4 674 100

4000 1 946 778 1 857 300

4500 887 625 886 800

5000 414 676 467 800

5500 249 796 278 800

6000 154 187 183 000

The curves of evolution of the maximum force according to the number of cycles for the

four expressions of the F-N curve in the plane (log10(N) log10(F)) have similar appearance for

the two ratios of accidental load (R = 1.4 and R = 2.3). Overall expressions Wöhler (Wo) of

Nadjitonon (Na) and Basquin (Ba) are close to the experimental (Exp). Those of Stromeyer

(Stro) are highly offset from the other; it has a high inflection as shown in Figure.5.

Figure.5: F-N Curves based on accidental overload ratios for HE360D steel.

5,1

5,3

5,5

5,7

5,9

6,1

6,3

6,5

3,54 3,59 3,64 3,69 3,74

LOG10(N)

LOG10(F)

Steel HE360DStro-R1,4

Stro-R2,3

Wo-R1,4

Wo-R2,3

Na-R1,4

Na-R2,3

Ba-R1,4

Ba-R2,3

Exp-R1,4

Exp-R2,3




Figure 6 Plots of separated F-N curves based on accidental overload ratios for HE360D steel.



Figure 7 Relative difference E (%) of cycle numbers for HE360D steel.

The plotted separate curves corresponding to the four expressions have offset downwards

of the curve accidental overload ratio of 2.3 relative to that of the curve accidental overload

ratio of 1.4, for HE360D steel (Figure.6). It is the same for the experimental curve with the

two ratios. We can say that the overloading has a detrimental effect on the fatigue strength of

soldered points of this material for all the curves because the number of cycles decreases

when the ratio of the overload moves from 1.4 to 2.3. The relative difference in terms of

number of cycles, for both reports load does not exceed 1.5% for the four expressions

(Figure.7). This evidence is mixed when looking at the experimental plots for the two ratios

because the relative difference may reach 3.8% when the load increases. A corresponding

inflection is observed also around the point where the relative difference is 3.8% when the

load ratio Fm/FD is above 1.5.




3.7.2. XE360D Steel

The evolution curves of maximum strength according to the number of cycles for the four

expressions in the plane (log10(N) log10(F)) are, like the HE360D steel, similar appearance for

the two accidental overload ratios. Again, these are the expressions of Wöhler, Nadjitonon

and Basquin which are close to experimental ones. Those of Stromeyer are strongly shifted as

shown in Figure.8.

Figure 8 Curves F-N based on accidental overload ratios for XE360D steel.



Figure 9 Plots of separated F-N curves based on accidental overload ratios for XE360D steel.

Figure 10 Relative difference E (%) of cycle numbers for XE360D steel.




Figure.10 shows that, in ascending order of the loads applied, the relative variation of the

number of cycles is between -2.5% and 0.5% for the four expressions of F-N curve. This

variation between positive and negative values shows that the F-N curve for R = 2.3, rotates

relative to the R = 1.4 in the counterclockwise (trigonometric direction).

It means that there exists a charge level defining the pivot point below which the level of

accidental overload is harmful to the welded point, and beyond the overload is beneficial. The

variation of the relative difference of cycle numbers for the experimental results is between -

3.5% and 3.5%.The curve presents an inflection around the pivot point. The accidental

overload is harmful at this point and beneficial elsewhere.

3.7.3. XES Steel

The plots evolution of the maximum force according to the number of cycles in the plane

(log10(N) log10(F)) for the four expressions have this time appearance greatly offset from

those given by the HE360D and XE360D steels for the both accidental overload ratios. Again,

these are the expressions of Wöhler, Nadjitonon and the Basquin which are close to

experimental ones. Those of Stromeyer are strongly shifted as shown in figure.11.

Figure 11 Curves F-N based on accidental overload ratios to the XES steel.

It is found that, in ascending order of the applied loads, the relative variation of the

number of cycles is contained between 0.47% to -2.3% for the four expressions of the F-N

curve. It means that the S-N curves of load ratio 2.3 rotate in the counterclockwise relative to

that of the load ratio equal 1.4. That shows that there is a charge level defining the pivot point

below which the accidental overload is beneficial, and above which the overload is

detrimental to the material.

The abscissa of the pivot point for the expressions of Wöhler, Basquin and Nadjitonon as

well as that of experimental curves is between 3.63 and 3.68. While the abscissa of pivot point

corresponding to the expression of Stromeyer is between 3.68 and 3.73.

The figure.12 presents the pivoting of the curves of the four models as well as the

experimental curves.

5

5,2

5,4

5,6

5,8

6

6,2

6,4

6,6

6,8

7

3,53 3,58 3,63 3,68 3,73 3,78

LOG10(N)

LOG10(F)

Steel XES

Stro.R=1,4

Stro.R=2,3

Wo.R=1,4

Wo.R=2,3

Na.R=1,4

Na.R=2,3

Ba.R=1,4

Ba.R=2,3

ExpR=1,4

ExpR=2,3



Figure 12 Plots of separated F-N curves based on accidental overload ratios to the XES steel.




Figure 13 Relative difference E (%) of number of cycles (R = 2.3 and R = 1.4) for the XES steel.

Accidental overload is beneficial for heavy loads greater than that corresponding to the

pivot point. From the analysis of the results of the three grades of steel, we can say that for the

high numbers of cycles (N> 106 cycles) the fatigue resistance depends essentially on the level

of hardness of the material. For the intermediate and low numbers of cycles, it is the ductility

which becomes predominant. The hard steel HE360D has a weak fatigue resistance due to its

low ductility. While for small deformations, it has better resistance. There is a reverse result

for mild steel XSE. The semi-hard steel XE360 has an intermediate behaviour.

The essential elements in the design of structures are knowledge of the behaviour of this

structure under various stresses illustrated by the F-N curve, the quantification of the gradual

degradation of the material constituting the mechanical component by damage accumulation



laws and the severity of a state of multiaxial stress (repeated or alternating fatigue limits)

compared to simple statements.

Figure 14 (a) Negative effect of overloading in fatigue (gap between the F-N curves of the two

overload ratios) on the hard steel; (b): harmful and beneficial effects (pivoting of the two F-N curves

around a pivot point) of the accidental overload level on mild and semi-hard steel.

In the case of accidental overload, the F-N curves show a change of tensile strength Rm

(Figure.14a) and the endurance limit D when accidental overload ratio varies (Figure.14b).

These two parameters have inverse variations illustrating the harmful and beneficial

effects of an accidental overload in terms of number of cycles (reducing and increasing of the

number of cycles). That seems to reflect the expressions of the F-N curve of the three grades

of steel (hard, semi-hard and mild) [5, 11].

5. CONCLUSIONS

The study of the sensitivity of the three grades of steel to periodic accidental overloads reveals

that:

- The effects of the periodic accidental overloads are detrimental to the fatigue strength for

hard steel HE360D. The effect produces a marked weakening of fatigue properties.

- The effects of these surcharges are beneficial to the fatigue strength for semi-hard steel

XE360D and mild steel XES. They can significantly increase the life.

In summary, the accidental overloads occurring at the frequency of overload every 99

basic cycles are beneficial to the fatigue strength of soldered points of mild and semi-hard

steel.

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accidental overloading effect on the s-n …€¦ · key words: accidental fatigue overload, welded...

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