• Corresponding author: Alok Kumar,E-mail address: kalok3@student.nitw.ac.inDoi: http://dx.doi.org/10.11127/ijammc2017.04.07Copyright@GRIET Publications. All rights reserved.

Advanced Materials Manufacturing & Characterization Vol. 7 Issue 1 (2017)

Advanced Materials Manufacturing & Characterization

journal home page: www.ijammc-griet.com

Fatigue analysis of welded joints

Alok Kumara* V.Suresh Babub

a,bMechanical Engineering Department, NIT Warangal, Warangal

A B S T R A C T

Welded joint is commonly used joint for industrial application and its failure

under fluctuating load (fatigue) has been the concern in recent past. Fatigue

analysis of the welded joints requires a precise knowledge of the stress

distribution in the critical regions of the weld. There are various approaches

presented by IIW to determine the stress distribution in weld region. In

present work the nonlinear peak stress which is developed at the weld

region is linearized to get actual linearized stress distribution in the weld

region. The proposed method enables us to determine linearized peak stress

at the weld toe using shell modeling. A methodology is developed to

estimate Crack initiation life of welded joints. Neuber’s rule is used to

calculate the local stress and local strain by using elastic stresses obtained

from FEA. Strain life equation is used to estimate the crack initiation life

using the local stress and strains. Keywords: Fatigue stress distribution,Weldedv joints,Life estimation,Finite element Analsis

1.Introduction

Fatigue in materials is a very complex process, as there are

many factors which effect the fatigue and these factors varies

from material to material so still the investigation is under

process to perceive the impact of the influential factors. Fatigue

in welds is even more complex as the microstructure of the

parent metal changes (HAZ) due to subsequent heating and

cooling during welding process. Moreover welds consists defects

like blow holes, slag inclusion undercuts etc. which leads to

unpredictable failure and in fact the shape of the weld and non-

welded weld gaps creates stress concentration which vary with

geometrical parameters of the weld. Residual stresses, which are

developed in the welded joints during welding due to uneven

cooling also effects the fatigue life of the weld. Due to this fatigue

analysis of the welded structures are of high practical interest

for e.g. Bridges, gas turbines, cranes etc. Various types of welded

joints are used for practical applications, among them fillet weld

is one of the commonly used welded joint so the same is used for

analysis. Fatigue cracks usually initiates at root and toe of the

weld. Mostly welds fail at toe because of high stress

concentration developed due notches and irregular weld

geometry at toe region and also due to tensile residual stresses

developed at toe region of the weld.

1.1 Fatigue analysis approaches

There are various approaches provided by IIW (International

Institute of Welding). [1]

• Nominal Stress Approach- The nominal stress approach

[1] is the simplest and the most common applied

method for estimating the fatigue life of steel

structures. This method is based on the average stress

along critical cross sections by considering overall

linear elastic beam behavior. The local stress

concentration effects of the welds and the attached

plates are neglected in stress calculations. This

approach assumes uniform stress distribution along

the throat of the weld.

• Structural hot-spot stress approach [2] - Structural

stress constitutes all notch effects of the main component but not

the notch effect caused by the weld profile itself, i.e. membrane

stress plus the linear shell bending stress, but not the non-linear

stress peak.It may be measured by strain gauges when the

assessment is based on the strains and calculated by

engineeringformulas or finite element analysis when stresses

are used as basis to do the evaluation. The structural hot-spot

stress assumes the weld is free of defects and failure (crack

initiation) will take place at toe. The structural stress is also

known as geometric stress and it considers linearized stress

without considering non-linear peak stress locally. The

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linearized stress can be obtained directly at weld toe using FEA

tool or it can also be extrapolated using the stress at the

neighboring nodes. The linearized stress obtained is the

combination of two stress i.e. membrane stress and bending

stress as shown in fig.1.

There are various recommendations provided for modelling and

meshing of weld geometry for structural stress at the weld toe

using shell elements [3][4] and solid elements [2]. To avoid

stress singularity the stress obtained from FEA model can be

compared with hotspot stress obtained by stress extrapolation

to get linearized stress at the weld toe. The equation [2] for

linear stress extrapolation is

0.48 1.01.67 0.67hs t t ……………….1

Where 0.48t and

1.0t are stresses at distances 0.4t and 1.0t

from the weld toe

• Effective notch stress approach [5] - This approach considers the local stress concentration at the toe of the weld due to notches and other irregularities as the fatigue strength of welded joints depends on their notch properties which gives rise to higher stress concentrations and lead to lower fatigue life. It captures non- linear peak stresses [1]. The FEA modelling of the notches is challenging and sometimes it gives too conservative results.

Present work is based on Structural Hot-Spot stress

approach as it is most widely used approach which provides

satisfactory results and application of this approach using

FEA software is simple. Modification is done in modelling

and meshing of weld in FEA for the prediction of accurate

value as well as location of peak stress.

1.1 Estimation of crack initiation life

Generally two methods are used for fatigue life

calculation, Stress life method and Strain life method.

The Stress life method determines the number of cycles

to failure using S-N curves .The stress values

considered in S-N curve are usually nominal stress in

which there is no adjustment for stress concentration

[6]. S-N curves are used in high- cycle fatigue cases

where the failure occurs after higher number of cycles

and the stress is considered within elastic range. As the

stress increases the fatigue life decreases progressively

and in ductile materials global plastic deformation

takes place hence analysis becomes difficult in terms of

stress. So in case of higher stress i.e. low cycle fatigue

cases Strain life method is used to calculate the fatigue

life. However even if globally the stress are within

elastic range but local plastic deformation can take

place due to stress concentration at the notches and

other geometric irregularities. In strain life method the

fatigue is cyclic strain controlled and the strain

amplitude is kept constant during cycling. A cyclic

stress-strain curve is developed on application of cyclic

load which may be described by the power law.

''( )npK ……….. 2

The total strain is the sum of elastic strain and plastic

strain. The equation [6] of cyclic stress strain is given

1

'1

2 2 2 '

n

E K

………… 3

In low cycle fatigue cases plastic stain is developed

under high stresses, Coffin and Manson [7] provided a

relationship for life estimation in low cycle fatigue case.

' (2 )2

p c

f N

………… 4

Whereas for High Cycle fatigue cases where the

nominal strains are elastic Basquin [8] provided an

expression for life estimation.

' (2 )2

bea fE N

..……….. 5

The equation valid for entire range of fatigue lives can

be obtained [9] by superposition of eq. 4 and eq. 5 '

'(2 ) (2 )2

f b c

fN NE

………... 6

The above eq.6 is valid for completely reversed loading

case, there are majority of cases where the mean stress

34

m is not zero. Morrow [10] provided an expression

considering mean stress. '

'(2 ) (2 )2

f m b c

fN NE

……….. 7

Strain life method predicts the crack initiation life at

notches or other geometrical discontinuities where

nominal stress are elastic but local stresses and strains

are inelastic. During plastic deformation both stress

concentration factor K and strain concentration

factor K needs to be considered which are linked by

Neuber’s rule [11] which states that the theoretical

stress concentration factor tK is equal to the

geometric mean of the stress and strain concentration

factors. The expression given by Neuber’s rule is 2( . )

.fK S

E

………… 8

fK (Fatigue stress concentration factor) tK . In

above eq.8, stress and strain amplitude can also be

used in place of stress and strain range.

1. Methodology and FEA Simulation

The steps followed are summarized as follows-

• Modelling and Meshing of the welded joint is done in FEA software.

• Application of boundary conditions and the load steps for fatigue loading.

• Extraction of peak elastic stresses from FEA software.• Calculation of local stress and strains using Neuber’s

rule. • Crack initiation life estimation using Strain-life

method. For the application of above methodology a fillet welded T joint

is taken for fatigue analysis. Two plates are joined using fillet

weld.

Dimension of plate 1 is 1000 x 500 x 50 and plate 2 is 550 x 500

x 50.The FEA simulation is done in ANSYS 15.0. The material

used is Structural Steel and the properties are taken by default

from ANSYS 15.0 which has referred ASME [12] for properties of

Structural Steel and it is provided as follows.

Properties Value

Yield Strength 250 MPa

Ultimate Tensile Strength 460 MPa

Fatigue Strength Coefficient 920 MPa

Fatigue Strength exponent - 0.106

Ductility Coefficient 0.213

Ductility exponent - 0.47

Cyclic Strength coefficient 1000 MPa

Cyclic strain hardening exponent 0.2

Young’s Modulus 200 GPa

Table 1. Properties of Structural Steel

Shell element (SHELL 181) is used to model the fillet weld. The

meshing is done on the basis of recommendation provided by

[3]. Tensile load is applied in X-direction i.e. xF = 500 KN and

bending load yF =100 KN. Two different load cases are used for

the application of the above methodology.

Case-1 Completely reversed stress

In completely reversed case xF = 500 KN and

yF = -100

KN is applied for one half cycle and xF = -500 KN

and yF =100 KN for another half cycle. Mean stress in zero.

Case-2 Zero-based stress

In Zero based stress onlyxF =500 KN and yF = -100 KN. Mean

stress correction should be applied using

eq. 7 as mean stress (m ) is not equal to zero.

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2. Results

The maximum stress is developed at the toe of the weld, to get conservative and safe result, first principle stress is considered for crack initiation life estimation of the weld. The max.stress obtained on upper surface is 250.539 MPa.

While modelling of weld the location of the toe in model is

shifted by (h/2) towards the root of weld from actual location of

the toe (h is the size of weld) to estimate the correct location of

hot-spot. The modelling and meshing guidelines can be referred

from [3].To check whether the hot-spot stress obtained is

linearized stress a path is defined starting at weld toe and stress

variation is plotted along the path.

From above fig. 4, it can be seen that the variation of stress is

linearized which indicates that non-linear peak stress is not

considered and stress singularity is avoided. So proceed for

crack initiation life estimation for both cases.

Case-1 Completely reversed stress condition

Mean stress = 0

Global (elastic) Stress range= 2 x 250.539 =500.78 MPa

Global (elastic) Stress amplitude (aS ) = 250.539 MPa

Using the above equations (2-8), a MATLAB program is written

to calculate local strain and Crack initiation life.

Local strain range = 0.0030 No. of cycles for crack initiation life

(N) =354844 cycles

Case-2 Zero based stress condition

Mean Stress (m ) = 125.195 MPa

Global (elastic) Stress range = 250.539 MPa

Global (elastic) Stress amplitude (aS ) = 250.539 MPa

Applying mean stress correction given in eq. 7

Local strain range = 0.001279

No. of cycles for crack initiation life (N) = 1.025 x

10^7 cycles

From the above results it can been seen that the case with

completely reversed stress has less life as compared to zero

based stress as case 1 has higher stress amplitude than case 2.

3. Conclusion

An efficient shell modelling technique has been presented for

fatigue analysis of welded joints. According to the proposed

technique the welded joints can be modelled using finite number

of shell elements which captures the hot-spot stress at the toe of

the weld. The peak stress obtained from FEA is used in strain life

method to estimate the crack initiation life of the weld. The

proposed method measures local stresses and strains for life

estimation. The methodology developed can be used for any

fatigue loading conditions as it is able to capture the effect of

mean stress. Present work can be extended to estimate the crack

propagation life as crack propagation life constitutes a major

part of total life of weld. Further the effect of residual stresses on

the life can be considered as residual stresses also has a

significant impact on fatigue life.

4. References

[1] A. Hobbacher, Recommendations for fatigue design of welded

joints and components. IIW document IIW-1823-07 ex XIII-

2151r4-07/XV-

1254r4-07- 2008

[2] Niemi E., Fricke W. and Maddox S.J. Fatigue Analysis of

Welded Components - Designer’s guide to structural hot-spot

stress approach –IIW

Doc. XIII-1819-00 / XV-1090-01, update June 2003.

Woodhead Publishing, Cambridge UK-2006

[3] A. Chattopadhyay, Glinka, M.El-Zein, J.Qian, and R.Formas:

Stress analysis and Fatigue of welded structures. Welding in the

world, Vol 55.

[4] Niemi, E., Stress determination for Fatigue Analysis of

Welded Components IIW doc. IIS/IIW-1221-93, The

International Institute of

Welding, 1995

[5] Radaj, D., Sonsino, C. M., Fricke, W.: Fatigue Assessment of

Welded Joints by Local Approaches. 2. Ed, Woodhead Publishing,

Cambridge,

2006

36

[6] George E. Dieter, Mechanical Metallurgy, 3rd Edition, Mc Graw

Hill Education-2013.

[7] L.F.Coffin, Jr, Trans. ASME, Vol. 76, pp.931-950, 1954

[8] Basquin, O.H. , The exponential law of endurance tests,

Proceedings of ASTM, Vol. 10(II), pp. 625-630, 1990

[9] S.S. Manson and M.H. Hirschberg, Fatigue : An

Interdisciplinary approach, p. 133, Syracuse University Press,

N.Y. 1964

[10] Socie, D. F. and Morrow, J. D. (1980) Review of

contemporary approaches to fatigue damage analysis. In: Risk

and Failure Analysis for

Improved Performance and Reliability (Edited by J. J. Burke & V.

Weiss), Plenum Publication Corp., New York, NY, pp. 141–194

[11] Neuber H.: Theory of stress concentration for shearstrained

prismatic bodies with arbitrary non-linear stressstrain law,

ASME Journal of

Applied Mechanics, ASME, 1961, vol. 28, pp. 544-551

[12]Fatigue Data at zero mean stress comes from 1998 ASME BPV Code, Section 8, Div 2, Table 5-110.1

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