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MODELLING OF CRACK COALESCENCE IN 2024-T351 AL ALLOY
FRICTION STIR WELDED JOINTS
Aidy Ali1, M. W. Brown2 and C. A. Rodopoulos3
1Department of Mechanical and Manufacturing Engineering, University of Putra Malaysia, 43400 Serdang, Selangor,
Malaysia.
2Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield, S1 1JD, United Kingdom.
3Department of Mechanical Engineering and Aeronautics, University of Patras, Rion-Patras, GR26500, Greece
ABSTRACT
In the present work, FSW of 2024-T351 aluminium alloys is characterised in terms of weld residual
stress and cyclic properties. A fatigue endurance of the FSW joint was also investigated and discussed.
Critical areas for natural fatigue crack initiation in FSW are pinpointed. The fatigue mechanism in FSW
is identified to follow a multiple crack coalescence nature. The numbers of cracks participate in
coalescence and the resulting crack growth rate is governed by the distance between the crack tips from
crack initiation to coalescence. The above represents a complex condition for modelling. During fatigue
bending tests, surface crack initiation and growth were monitored by means of a plastic replication
technique. Detailed analysis revealed that under that the FSW specimen failures in fatigue bending tests
are mainly a process of crack growth with initiation from defects and oxide inclusions, causing
subsurface crack formation. Multiple crack initiation sites were observed from different microstructural
regimes in the non-uniform residual stress distribution across the weld. This indicates that failure is
dominated by fatigue crack propagation from defects. Therefore mechanisms that include features such
as defect size and residual stress were considered when applying crack growth analyses to lifetime
predictions. Based on crack growth and characterisation of FSW joints, a modified version of the
Hobson-Brown is adopted. The good correlation achieved between the experimental data and the model
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predictions is presented in this paper. Satisfactory predictions of FSW lifetimes are derived from the
model.
Keywords: Friction Stir Welding (FSW), Fatigue, Crack Coalescence, Fatigue Crack Growth Modelling
Introduction
Friction stir welding (FSW) is a solid state welding process that has received the worldwide attention,
particularly for joining aluminium alloys [1, 2]. There have been numerous attempt on characterisation
in term of macrostructure, microstructure, hardness and residual stress distribution in connection with
the FSW of aluminium alloys such as 2024 [3-6], 7075 [7], 7050 [8], 6061[9], 6013 [10], 6063 [11],
1050 [12], 1100 [9, 13], 1080 and 5083 [14]. There have been also tremendous investigations on fatigue
issues concerning friction stir welding [3, 4, 6, 8]. Nevertheless there is no systematic attempt to model
the crack growth in FSW. Perhaps the existence of inhomogeneous of microstructure, hardness and
residual stress distribution in FSW was lead to complication in the process of development of the fatigue
model.
In fatigue, many attempts have been made to model the fatigue crack growth rate (FCGR) from the
simplest empirical model by Paris [15] to advanced and contemporary models such as the Weertman
[16] strain energy model, Tomkins [17] high strain model, Coffin and Manson [18] plastic strain model,
Hobson-Brown model [19] and Navarro- E. R. de Los Rios [20-22] N-R models.
Among the many types of crack growth model stated above, the Hobson-Brown model is adopted in the
present work because of its main advantage, that is simplicity, and its empirical formulation is derived
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directly from experimental results. Based on the simplicity of the Hobson-Brown model for short crack
studies, it has been demonstrated to work very well by several researchers [23-28] as a basis when
analysing their experimental results and estimating life. New advancements made by Nong Gao [28]
successfully modified the Hobson-Brown model to incorporate coalescence behaviour caused by
multiple crack initiation in his creep-fatigue test results. Based on crack growth and characterisation of
FSW joints, a modified version of the Hobson-Brown [28] is adopted. The modified model was use to
predict the fatigue life of FSW polished, FSW as welded, FSW peened as welded, FSW peened
skimmed and Parent materials specimens.
Experimental
Material and specimens
The friction stir welded plates to produce the samples were provided by Airbus UK Ltd. Plates
75x60x13mm were welded along their long edge with the weld direction parallel to the longitudinal
(rolling) orientation. Welding parameters were kept confidential to them. The friction stir welded peened
samples were produce by Metal Improvement Company. Controlled shot peening parameters were kept
confidential to them. The peening operations were carried out on two conditions of sample, peened as
welded and peened after skimmed off the top surface of the weld by 3mm thickness.
Fatigue endurance tests of FSW were carried out on longitudinal specimens of length 80mm and width
of 60mm in four point bending test in accordance with ASTM D6272 (1998). The tests configuration
was similar with in work [47]. For optical observation purposes, cross section of the welds were
mechanically polished to a ¼ micron finished lightly etched in Keller’s reagent in accordance with
ASTM E340-00. Fig. 1(a) shows a transverse macrosection of a FSW joint. The most obvious feature is
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the well-defined nugget (N) in the centre of the weld. On top of the nugget, it is evident to identify a
‘flow arm’ region between the N and the top surface on which welding was carried out. Further out
from the plate joint line (PJL) about 10mm is the thermo-mechanically affected zone (TMAZ), see Fig.
1(b). The size of this region is wide up to 4mm, on the top welding surface and narrows down through
out the thickness of 10.5mm from the plate surface. Next to the TMAZ region is the heat affected zone
(HAZ). The size of this region is narrows down to 4mm on the top welding surface and widens through
out the thickness of the plate. It is worth noting that the TMAZ region is absent on the bottom of the
weld, and regions size and shape are not symmetrical in both right and left sides, due to pin rotational
direction. The coordinate boundaries of each macrostructural phase were mapped by using optical
PolyVarMet microscopy as shown in Fig. 1(b).
Cyclic deformation behaviour test procedure
In order to investigate the cyclic deformation behaviour for each microstructural regime in FSW, fully
reversed pure cyclic bending tests were performed under displacement control for strain ranges 0.1%
and 2.5%. In these tests, the specimens were cut-off from each microstructural regime with different
cross section size as shown on Fig. 2. The specimens were numbered according to their regime as
Nugget, Composite of TMAZ and HAZ, HAZ and Parent plate with number 1, 2, 3, and 4 respectively.
Crack propagation test and measurement techniques
Crack propagation tests were performed in accordance with the standard test method for measurement of
fatigue crack growth rates describe in ASTM E 647 (2000). The tests were carried out at constant
amplitude, constant frequency of 20Hz, and constant stress ratio of R = 0.1. The polished mirror
specimens were used in order to avoid the surface irregularities of as welded specimens that could hide
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any small surface crack from detection.
The surface plastic replication on specimens in these tests was carried out using cellulose acetate sheet
of 35 microns thickness, together with acetone spread over the specimen surface. The plastic replicas
were left, during each period of replication, for about ten minutes to dry out completely. After that, they
were peeled off from the specimen surface, and mounted flat on a microscope glass slide for subsequent
microscopic examination. The replicas were placed approximately every 5000 cycles.
In the tests large acetate strips with an area of 60 mm
×
20 mm were applied at the middle of specimen,
where the highest bending stress occur, when the specimen was held under maximum stress. In this
condition, the cracks on the surface were fully open. Nevertheless, the same process was duplicating
every time, in case of bubble formation under the acetate sheet, which could deteriorate crack
information on the replicas.
The cracks on the replicas were measured from one tip to the other, in a straight line. Their length is
defined as surface crack length, s
a. The surface cracks data from replica measurement were used to
calculate the crack growth rate and life. Crack growth rate was calculated using Secant, BS DD 186
(1991), ASTM E647 of 3 and 5 point (incremental polynomial) methods.
Residual stress measurement
Residual stresses measurements were made by using the hole-drilling strain gauge techniques in
accordance with ASTM E837-99(2000). A 1.6mm nominal diameter hole was drilled at each location
with a carbide tungsten tipped inverse cone flat bottom drill driven at 300,000 rpm by an air turbine.
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High rotational speed was required in order to minimise residual stress due to drilling. The holes were
drilled at increments of 0.1 mm to a depth of 1.5 mm. Measurements of strain values around the holes
were made at each increment. Residual stresses were split in terms of longitudinal and transverse
components, according to coordinate system used relative to the weld as shown in Fig. 3. The holes were
drilled at certain location as indicated in Fig. 15 (a). In order to determine the longitudinal residual
stresses through the thickness of the weld, slicing and layer removal techniques were used with samples
that had strain gauges applied to the back of the test specimen. The longitudinal and transverse residual
stresses were calculated by the following equations [35]. The trough thickness residual stress profile can
be revealed in [36].
Results
The result of cyclic tests in pure bending
Four section of the weld have been selected to provide testing material for the evaluation of cyclic yield
stress and cyclic hardening in pure bending. The obtained results, in terms of the Ramberg-Osgood
equation are shown in Table 1. The results indicate that the TMAZ section exhibits a cyclic yield stress
value significantly lower to that of the parent material while at the same time a higher strain hardening
exponent. In contrast, the cyclic yield stress of the HAZ section demonstrates an enhanced value.
Fatigue properties of FSW
Fig. 4 shows the fatigue test data for FSW as welded, FSW polished mirror, parent material, FSW
peened as welded, and FSW peened after skimmed 3mm of 2024-T351 Al Alloy. Overall, the
superiority of the FSW peened after skimmed specimens over, FSW peened as welded, FSW polished
mirror and FSW as welded ones became more evident in the region between 106 and 107 cycles. In this
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region of endurance, FSW peened after skimmed 3mm exhibited maximum stress values approximately
8% more than FSW peened as welded, 30% more than FSW polished mirror and over 100% more than
FSW as welded joints.
Fatigue crack initiation
In the SEM investigation, the exact natural crack initiation origin in FSW 2024-T351 was influenced by
the stress level and the severity of surface irregularities. Fig. 5 shows the SEM fractograph for high
stress/LCF regime of FSW as welded. The presence of multiple cracking was confirmed causing crack
coalescence and dropping in fatigue performance. In this sample, initiation locations were observed
nucleating from –1mm from PJL (in Flow Arm) and two cracks initiated at –15mm and 17mm from PJL
(in HAZ).
As soon as the stress reduces, the crack number seems to be reduced to two cracks, rather than three
observed in low stress/HCF regime as shown in Fig. 6. In this case, crack initiation was found at –13mm
from PJL, which falls at the end of TMAZ regime, where the lip is formed. It seems the lip introduced a
stress concentrator to a cause fatigue crack to initiate. The second crack was found at 1mm from PJL (in
Flow Arm), which formed predominantly from free surface roughness of a welding beach mark.
However, when the surface roughness, irregularities were removed by mean of polishing, the initiation
site was changed from HAZ to –5.5mm and ±6mm from PJL, which are located at the end of the Flow
Arm regime, or beginning of TMAZ and underneath at the end of the Nugget regime, which can be
named as triple point position as shown in Fig. 7. Multiple cracking also has been observed in polished
specimens in LCF regime. When the stress reduces, the crack coalescence no longer occurs, when the
only single crack initiation was found in HCF of a polished specimen which mainly initiated at –3mm
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from PJL where the transition of Flow Arm to TMAZ begins. It is worth noting that, each micro-regime
in FSW seems to have a different fatigue threshold individually, so when the high stress is applied, it
overcomes threshold everywhere causing a multiple cracking phenomenon. On the other hand, once the
stress is reduced, the multiple cracking is gone, and only one crack initiates at the lowest micro-regime
threshold value, which is believed to cause the single cracking phenomenon.
Fig. 7 illustrates the initiation site in LCF FSW as welded. It is evident at high magnification that the
crack was initiated from the free surface, propagating to the triple point region, where the microstructure
caused severe fracture surface roughness. The EDX was used to analyse inclusion close to triple point
location at several positions, labelled as Point (a) as shown in Fig. 7.
Fatigue crack propagation
SEM and EDX results suggested that the fatigue initiation of FSW 2024-T351 Al Alloy was influenced
by the material defects such as inclusions and porosity. Replica images for the LCF of polished mirror in
Fig. 8 confirmed the occurrence of multiple crack initiation, causing crack coalescence and overlapping.
On the other hand, Fig. 9 shows the replica images captured from HCF of a polished sample proved a
single cracking initiation and its position until the final fracture.
When defects are likely to be present, the initiation phase is very short and the major part of fatigue life
is spent in crack propagation. Figure 12 shows the minimum crack length measured from replicas is
reasonably long, approximately 0.8 to 1mm long, indicating the crack was initiated subsurface and
measured when it appeared at the surface. An additional parameter can be tensile residual stresses
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present at the triple point, which increase the loading range and may accelerate fatigue crack
propagation.
Major cracks.
The major surface crack at failure is developed by the linkage of many individual (minor) cracks. Its net
length is therefore a function of the sum of lengths of all the individual minor cracks involved. Fig. 12
illustrates that the longest major crack (final crack), with a half-length of 20.75mm at failure for a
300MPa of maximum applied stress, was formed by the coalescence of 25 individual minor cracks. As
seen in this figure, the final crack involved a continuous growth and coalescence process which is
observed over a wide range of crack lengths for the majority of the lifetime. The major crack length, Σ
a,
is defined as the sum of the individual lengths of all the minor cracks that will eventually combine
together at failure. Figures 10 and 11 show the crack growth data versus crack length evaluated from
several calculation methods such as Secant Method, BS DD186: 1992 and ASTM E647-93: 5points.
Negative crack growth observed in Fig. 11 was a result of joining of overlapping cracks causing the
major crack length to become shorter as the cycles increase.
Crack linkage.
The formation of a major crack is illustrated schematically in Fig. 12. Because each main crack involves
the coalescence of many minor cracks, thereby directly contributing to the growth pattern of the main
crack, the behaviour of these individual cracks is critical in the whole crack growth process. The number
of minor cracks varies with the change of surface crack length. Fig. 13 displays the relationship between
the number of minor cracks that could be detected on replicas (the number probably is greater, as not
every cracks was detected on the replicas) and surface crack length at 300MPa maximum stress. It can
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be seen from Fig. 13 that two phases of the variation of the number of minor cracks
n
exist, i.e. , there is
an increase in the number of minor cracks, but eventually, after overcoming a certain critical minor
crack number, they coalesced with each other causing a decrease in the number of minor cracks.
Residual stress
Fig. 14 (a) shows the position where the hole was drilled for measuring the residual stress on the top and
bottom of the weld. Fig. 14 (b) shows the longitudinal residual stress profile along the weld measured
from the top and bottom sides of the weld. It is worth noting that the longitudinal residual stress reveals
an ‘M’ like shape which agrees with many previous findings on characterising the residual stress in
FSW. Residual stresses found on the top and the bottom surfaces of the weld were not similar. On the
top of the weld the residual stress is highly tensile at position of –12mm from PJL which is about 95MPa
and it is located in the TMAZ region. Residual tensile stress was also found at 12mm from PJL which is
about 46MPa, and its also falls in the TMAZ region.
From these two locations the tensile residual stresses decrease in the parent plate adjacent to HAZ as
well as the N, which contains compressive residual stresses of about -41MPa. With increasing distance
from the PJL, the residual stress then gradually changes into the initial stress state of the parent material
which was about zero. On the other hand, the bottom side residual stress was compressive at –17 and
17mm from PJL which about -40MPa and -50MPa respectively and it was located in HAZ region. The
maximum tensile in the bottom side was found at –7mm from PJL about 25MPa which is located in
HAZ region.
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Fig. 15 shows the longitudinal residual stress profile with the depth of the FSW peened specimens. With
two conditions of peened, peened as welded and peened after skimmed 3mm, the residual stress profile
measured at several locations shows similar patterns which were highly compressive about –200MPa at
0.4mm depth and gradually decreasing to –120MPa when its approaches to
1.6mm depth.
Lifetime Estimations
Stage I crack propagation
Stage I crack growth has been termed by Forsyth [37]. This crack growth occurs by shear in the
direction of a primary slip system when the crack and plastic zone are confined to within a few grain
diameters. These primary slip systems lead to a zigzag crack path since they have different orientations
in each grain [38]. In this stage, especially when the crack length is smaller than the grain size of the
material, the microstructure plays a dominant role in determining the extent and orientation (shape) of
the plastic zone [39]. In this situation the ratio a/rp (crack length/plastic zone size) is less than unity
initially, but increases as the crack grows considering that crack tip plasticity does not extend beyond the
first grain boundary [39]. Stage I crack has been known to propagate at rates significantly faster than
that of long cracks under the same nominal K [40-43].
Stage II crack propagation
At higher stress intensity range values there is a transition from Stage I to Stage II crack propagation. At
this stage, crack growth takes place on a plane normal to the far-field load direction. Generally, short
crack growth is a crystallographic type of growth where cracks propagate along crystallographic planes.
Due to the fact that these planes extend only to the grain boundaries, the latter act as a barrier to crack
propagation. This situation extends as long as a single family of slip planes can accommodate the crack
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tip plasticity. At longer crack lengths, crack tip plasticity becomes more intense and can only be
accommodated by multiple slip planes [44]. At this point, transition to stage II crack growth ensues and
the plastic zone extends to more than one grain. This assumption has been suggested by Yoder et. al [45]
who examined the transition from stage I to stage II growth for a number of materials. Based on above,
in [46] it was suggested that transition from stage I crack growth to stage II crack growth takes place
when the crack tip stress field is able to initiate persistent slip bands on two successive grains without
further growth of the crack. Stage II crack propagation can be easily identified by the formation of
striations. These striations are ripples on the fracture surface.
Hobson-Brown Crack Growth Model.
The early Hobson-Brown model was derived from two crack growth equations for the prediction of
fatigue crack propagation. The first considers the Stage I crack growth regime and the second the Stage
II growth regime. The first of these crack growth equations shows a microstructural dependency in the
growth rate and is expressed as [19, 32]
( ) ( ) ( )
ss
sadCadC
dN
da −=−∆= 112 2
α
ε
(1)
where dNdas is the crack growth rate, 1
ε
∆ represents the strain range Stage I, 2
Cand 2
α
were
analogous to Paris type constants. 1
C is function of the applied stress/strain range, d is the length of the
pertinent microstructural barrier and s
a is surface crack length measured from tip to tip. This equation
predicts an initial crack growth rate which decreases as the crack length increases and becomes the
minimum with value of zero at s
a=d. When the point of s
a=d is attained, the Stage I cracks may either
become non-propagating cracks (because the stress is below the fatigue limit) or become dormant before
continuing propagation due to time dependent mechanisms. If the stress exceeds the fatigue limit, cracks
change to Stage II before s
a reaches the value d.
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When s
a> d, the second equation of the Hobson-Brown model describes Stage II crack growth by a
continuum mechanics equation, namely
( )
DaGDaG
dN
da
sst
s−=−∆= 23 1
β
ε
(2)
where t
ε
∆ represents the strain range Stage II, 3
Gand 1
β
were analogous to Paris type constants 2
G
depends upon applied stress/strain and
D
represents the crack growth threshold. The fatigue lifetime in
this model is estimated by integrating the Stage I and the Stage II equations, (1) and (2) respectively, and
simply adding these lives provides the total fatigue lifetime.
Nong Gao [28] introduced crack coalescence parameters for Stage 1 and Stage II growth in the Hobson-
Brown model as follows. In Stage I, the dvalue in the case of multiple cracks, is taken as an average of
the calculated microstructural barrier distances of the entire set of minor cracks multiplied by the
number of cracks,
n, at each strain or stress range and the total crack length Σ
a replaces s
a in equation
(1). On the other hand, in Stage II, equation (2) was modified to incorporate the effect of coalescence of
minor cracks. The plot of dependence of number of minor cracks
n on the summed surface crack length
Σ
a was developed (like Fig. 13) and the approximate relationship observed for stainless steel was
presented by the following linear equation,
( )
11 +−
−
−
=Σ
c
cf
fn
aa
aa
n (3)
where
n is the number of minor cracks, f
a is the crack length at failure, Σ
a is current surface crack
length, c
a is summed crack length of all minor cracks at the start of coalescence, and c
n is the critical
number of minor cracks. Here
n decreases with an increase of surface crack length Σ
a. When the surface
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crack length is equal to the final crack length f
a, only one crack remains leading to failure, and when it
is equal to the critical crack c
athis equation gives the critical number of minor cracks c
n at the start of
the linkage process.
In equation (2) for Stage II cracks the threshold constant
D
was calculated only from the analysis of a
single crack. When a number of minor cracks
n are involved in the formation of the major crack, the
Stage II equation should be modified. Thus Eq. (2) can be written, after aggregation of the
n minor
crack growth equations, as
DnaG
dN
da −= Σ
Σ2 (4)
Substitution of Eq. (3) into Eq. (4) gives
( )
Dn
aa
aa
aG
dN
da
c
cf
f
+−
−
−
−= Σ
Σ
Σ11
2 (5)
Adoption of the Hobson-Brown model
In order to adopt Hobson-Brown model, the mechanism of fatigue crack in FSW was observed and
analysed. The smallest individual surface crack lengths detected from replication work were 0.112mm
length and 0.62mm length for 300MPa and 270MPa maximum stresses applied respectively. Since most
cracks were initiated subsurface from defects, with the length the order of 20µm, these cracks can be
considered as a long type of crack, which are propagating in the Stage II crack growth regime.
Therefore, in this study, the stage I part of the model is dropped since in these tests most cracks growing
from defects in the weld propagate immediately in Stage II, instead of starting with a Stage I
mechanism.
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Stage II Crack Growth Equation.
For determining the Stage II crack growth equation, parameters 2
G and
D
of the model should be
calculated according to the test data. To assist understanding to the model, the notation 2
G was
represented as the
B
parameter, and
B
can be written as
(
)
m
CBG
σ
∆==
2 (6)
Here
B
represents the early notation of 2
G, and it depends upon applied stress, Cand
m
were
analogous to Paris type constants.
The values of
B
in the original Hobson-Brown model [19] were calculated by fitting regression lines
through the data points of crack growth rate and mean crack length for lengths greater than 10µm which
were assumed to be unaffected by the microstructural barrier d.
In this study, the values of
B
were obtained by fitting regression line to the curves of Ln
(
)
Σ
a and Ln
(
)
s
a
and against N. The calculated values of
B
at different stress ranges are presented in Table 2. The
calculated values of
B
were then plotted against the values of stress range, and a line that passes
through the data points is expressed by the following equation
(
)
94.2
12
104
σ
∆×= −
B (7)
It was noticed that, the value of 2.94 for the slope of the fitted line,
m
is a little higher than the value 2.4
of Parent material for 2024-T351 Al alloy. Nevertheless, the crack growth data of FSW 2024-T351 Al
alloy from Bussu and Irving [3] was analysed and the values of Cand
m
Paris constants are
summarised in Table 3. Table 3 shows the Nugget has a higher
m
of 3.1 whilst HAZ exhibited the
lowest
m
value of 2.28. In this study, the
m
values obtained from crack growth data propagating
through three regimes of FSW, therefore the
m
values should be expected to have similar values of
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other regimes. As the Nugget dominates much of the growth, a value between 3.1 and 2.28 is expected
but probably closer to 3.1 for the Nugget. From (2), (4) and (7), the growth behaviour of a Stage II
crack is described by the following expression
( )
Da
dN
da
s
s−∆×= −94.2
12
104
σ
(8)
for the single crack equation and
( )
Dna
dN
da −∆×= Σ
−
Σ94.2
12
104
σ
(9)
for the multiple cracks equation, with
σ
∆
in MPa.
The threshold constant
D
is calculated by substitution of the values from the equation
(
)
( )
2
2
2
Y
K
ath
s
σπ
∆
∆
= (10)
into (8) and equating crack growth rate to zero (threshold) , where th
K
∆
= 2.8 MPa m at 1.0
=
R, the
lowest threshold value obtained from Bussu and Irving [3, 33], which was in the Nugget regime,
σ
∆
=
270MPa is chosen and
Y
is calculated from [34] for a semi elliptical surface crack tested under bending
which gives 966.0
=
Y. These give the threshold value of 6
10064.2 −
×=D mm/cycles.
The final equation for Stage II crack growth is given
( )
6
9377.2
12 10064.2104 −− ×−∆×= s
sa
dN
da
σ
(11)
in the case of single crack and
( )
( )
6
9377.2
12 10064.2104 −
Σ
−
Σ×−∆×= na
dN
da
σ
(12)
in the case of multiple cracks, for
σ
∆
in MPa and crack growth in mm/cycle.
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Life estimation procedure
In the life estimation, the crack growth and replicas were taken from the FSW polished mirror
specimens. Therefore, the FSW polished mirror S-N curve will be used to assess the accuracy of C,
m
and
D
constants. By integrating the Stage II crack growth equations of (11) and (12), the fatigue lifetime
is estimated. Equation (11) and (12) will be integrated from the initial defect size 0
a to the final crack
length of f
a.
For a single crack,
( )
−− ×−∆×
=
−
=ff a
a
s
s
a
as
s
sa
da
DBa
da
N
00 6
94.2
10 10064.2104
σ
(13)
and for multiple cracks,
( )
( )
−
Σ
−
Σ
Σ
Σ
×−∆×
=
−
=ff a
a
a
a
mna
da
DBa
da
N
00 6
94.2
10 10064.2104
σ
(14)
here s
N is fatigue life in cycles from the single crack equation, m
Nis fatigue life in cycles from the
multiple cracks equation, f
a is taken as half the width of the specimen, 30mm.
n is the number of minor
cracks calculated from Equation (3), 0
ais taken from the defect size gathered from SEM analysis. Stress
range, defined as
MinMax
σσσ
−=∆ (15)
was used in this prediction. Here Max
σ
is the maximum applied stress, and Min
σ
is the minimum applied
stress.
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Determination of defect size 0
a.
It is envisaged that the defect size 0
a is a stochastic variable, although the defect is found to be m
µ
20 in
the size, the statistical distribution is developed to give an idea the range of defect size. The normal
statistical curve distribution is developed based on the distribution of early crack size in the multiple-
crack phenomenon observed from Figure 12. The early crack lengths measured from Fig. 12 are shown
in Table 4, and the normal distribution curve developed is shown Fig. 16, with the mean value,
µ
of
169.5
m
µ
and standard deviation, S of 116.9
m
µ
.
We assume that the mean value of defect size 0
a is a size of 20 microns that we found from SEM. Now
the distribution of defects can be developed, assuming the standard deviation of defect size is scaled
from the standard deviation of initial minor crack size, the standard deviation of defects therefore can be
estimated from the following equation
m
a
a
SS
m
m
µ
=0
0 (16)
Where 0
S is the standard deviation of defect distribution, m
a0 is mean of defect size and m
ais mean of
early minor crack size. This gives the value of 0
S of 13.8
m
µ
and the Gaussian distribution curve of
defect size that has been developed is shown in Fig. 17. From this curve, the actual defect sizes will be
in the range of 0-50
m
µ
, with 98.5% probability.
Determination of critical number of minor cracks c
n.
In the multiple cracks equation, we defined c
n as the critical number of minor cracks that coalesce to
govern the life. The c
n value is taken from Fig. 18 of the linkage behaviour which is the maximum
ACCEPTED MANUSCRIPT
number of minor cracks observed on replica as suggested by Nong Gao [28] and the value chosen c
n is
17 in this study. This gives the c
a value of 14mm as shown in Fig. 18. The value c
n=17 is the measured
value in our experiment.
Sensitivity analysis.
It is usually supposed the total fatigue life is determined by the summation of the number of cycles of
Stage I and II regimes. Nevertheless, since the crack bypassed Stage I when it was initiated from a
subsurface defect, the actual life f
N of FSW polished mirror is given in Fig. 20, for Stage II alone. At
the beginning, the initial predicted life attempted was mostly a little higher than the actual fatigue life for
the single crack equation. It was improved after perform a sensitivity analysis that conducted to examine
the sensitivity of the input parameters in this model such as, defect size 0
a,
B
that gives constants Cand
m
, and threshold value
D
. From Fig. 20, having employed good fit techniques, by using trial and error
fitting the sensitivity analysis tells us that the low stress level, HCF regime is controlled by the threshold
D
and defect size 0
a, whilst the high stress level LCF regime slope is highly sensitive to value of best fit
Cand
m
constants. The new constant of C= 12
1085.2 −
× and
D
= 7
106 −
×mm/cycles were found to fit
well with the early slope of LCF and the fatigue limit respectively. Therefore the revised crack growth
equations of Stage II for single and multiple cases are
( )
7
94.2
12 1061085.2 −− ×−∆×= s
sa
dN
da
σ
(18)
in the case of single cracks and
( )
(
)
7
94.2
12 1061085.2 −
Σ
−
Σ×−∆×= na
dN
da
σ
(19)
for the multiple cracks, for
σ
∆
in MPa and
a
in mm.
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The initial C value of 12
104 −
×was obtained from just two stress levels in replication tests. This can
hardly be more than accurate to first order, without further extensive testing. Therefore the new Cvalue,
selected to fit 6 fatigue tests on the endurance curve, should provide a more accurate basis for the crack
growth rules. Future prediction of S-N curves, other than the polished mirror samples, will be genuine
predictions from these equations, rather than fitted curves.
The initial
D
value of 6
10064.2 −
×=Dmm/cycles was derived from Bussu and Irving [3,33 ]. th
K
∆
obtained by Bussu and Irving [3,33 ] was measured with the long initial crack of 1mm length, introduced
by electric discharge machine (EDM). However for the short cracks,
D
is reduced as less roughness,
less oxides packing occur and could be half or quarter the long crack value. Therefore the new
D
is used
which is approximately a quarter the calculated
D
from Bussu and Irving [3,33 ].
Incorporating residual stress influence in the Hobson-Brown-Gao crack growth equation.
In FSW, cracks are propagating in a residual stress field. Therefore in order to estimate the life, we have
to incorporate the residual stress effect in the equation for both single and multiple crack models. The
following are the steps were taken to incorporate the residual stress effect in the crack growth equation:
1) We introduced the effective stress range, eff
σ
∆ defined as
OpsMaxeff
σσσσ
−+=∆ Re (20)
if OpsMin
σσσ
≤+ Re else
σσ
∆=∆ eff
where Max
σ
is the maximum applied stress, and M in
σ
is the minimum applied stress. s
Re
σ
is the residual
stress, Op
σ
is opening stress and
σ
∆
is the stress range. Note that, the s
Re
σ
has a positive value if in
ACCEPTED MANUSCRIPT
tension or s
Re
σ
is negative value if in compression. So to obtain the correct Cfor eff
σ
∆, '
C , we assume
m
is constant or invariant,
( )
(
)
'
'm
eff
mCC
σσ
∆≅∆ (21)
for the same growth behaviour in LCF whether or not the crack closes.
m
eff
CC
∆
∆
=∴
σ
σ
' and we assume mm =
' for parallel S-N curves.
2) Before peening, with the residual stress a tensile 96MPa from experiment, the material will yield. So
we expect relaxation will occur under maximum load applied. However, after peening, the behaviour is
elastic as the stress falls from the induced residual stress value. The correct eff
σ
∆ for relaxation needs to
be calculated.
3) The opening stress ( Op
σ
) will be derived from the peened sample, if the crack closes. Peened samples
experience the greatest compression.
4) The defect size 0
awill be taken from S-N curves only if necessary, but a better size estimate will be
taken from SEM observations directly.
5) We will use a closure model to predict R (mean stress) ratio dependence.
Thus the revised crack growth equation of Stage II for single and multiple cases is
( )
7
94.2
'106 −
×−∆= seff
saC
dN
da
σ
(22)
in the case of single cracks and
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( )
( )
7
94.2
'106 −
Σ
Σ×−∆= naC
dN
da
eff
σ
(23)
for multiple cracks, for eff
σ
∆ in MPa.
Lifetime prediction input data
FSW Polished mirror.
In the life estimation of FSW Polished mirror, a tensile residual stress of 96MPa is used as an input into
the model which is obtained from the hole drilling measurement reading on the FSW Polished mirror
specimens. The initial defect size 0
a=m
µ
20 is used as measured in SEM. At the fatigue limit stress
range, MPa
fl 245=∆
σ
(at Nf
6
102 ×), which we substitute in equation (20) , to give
OpOpeff
σσσ
−=−+=∆ 36896
9
.
0
245 , where MPa
sMin 123
Re
=
+
σ
σ
. However, 368MPa exceeds the yield of
TMAZ of 272MPa, therefore the stress will be recalculated to allow for stress relaxation by using the
Ramberg-Osgood equation as follows 1266.0
1
800
368
+=
σσ
EE where the modulus of elasticity
E
=68GPa
is used as obtained from experiment, to give the actual relaxed stress MPa
8.319
=
σ
. The revised
effective stress range Opeff
σσ
−=∆ 8.319 if OpsMin
σσσ
≤+ Re , or else MPa
eff 245=∆=∆
σσ
. It is clear that
here the crack should not close, as MPa
sMin 8.74)8.319368(123
Re
=
−
−
=
+
σ
σ
. So MPa
eff 245=∆
σ
.The
opening stress ( Op
σ
) will have to be fitted from peened S-N curves. Then CC =
', and the predicted
response is shown in Figure 19.
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FSW as Welded.
In the life estimation of FSW as Welded, a tensile residual stress of 96MPa is used as an input into the
model which is obtained from the hole drilling measurement reading on the FSW Polished mirror
specimens. We assume the residual stress is unaltered during mechanical polishing. But in reality, a
slightly lower residual tensile stress should be expected in polished sample compared with FSW as
Welded. In this life estimation, the input defect size was set to be as high possible to represent the worst
case scenario 0
a=m
µ
50 . At the fatigue limit stress range, MPa
fl 150=∆
σ
(for Nf
6
102 ×), substitution in
equation (20) gives
OpOpeff
σσσ
−=−+=∆ 26396
9
.
0
150 , where MPa
sMin 7.112
Re =+
σσ
. The effective stress
range Opeff
σσ
−=∆ 263 if OpsMin
σσσ
≤+ Re else MPa
eff 150=∆=∆
σσ
. Here again, the relaxed minimum
stress is still highly tensile, so we assume the crack remains open as stress exceeds Op
σ
. The predicted S-
N curves are presented in Figure 20.
FSW Peened as Welded.
In the life estimation of FSW Peened as Welded, a compressive residual stress of 200MPa is used as an
input into the model which is obtained from the hole drilling measurement reading on the FSW Peened
specimens. The defect size, 0
a=m
µ
30 is chosen form SEM fractography. At the fatigue limit stress
range, MPa
fl 275=∆
σ
(at Nf
6
102 ×), substitution in equation (20) gives
OpOpeff
σσσ
−=−−=∆ 6.105200
9
.
0
275 , for which clearly there is no relaxation since the maximum stress is
much lower than the yielding point. So we fit the S-N curve of FSW Peened to the experimental values
of Nf
6
102 × at MPa275=∆
σ
, to give the opening stress, MPa
Op 110−=
σ
. This opening stress will be
used as an input to predict the life of FSW as Welded curves, as in Figures 21.
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FSW Peened after Skimmed.
In the life estimation of FSW Peened after Skimmed, a compressive residual stress of 200MPa is used as
an input into the model which is obtained from the hole drilling measurement reading on the FSW
Peened specimens. The defect size, 0
a=m
µ
20 is chosen, smaller than Peened as Welded, from SEM
studies. At the fatigue limit stress range, MPa
fl 301=∆
σ
(at Nf
6
102 ×)substitution in equation (20), gives
OpOpeff
σσσ
−=−−=∆ 4.134200
9
.
0
301 , for which again, clearly there is no relaxation since the maximum
stress is much lower than yielding point. So we predict the S-N curve of FSW Peened after Skimmed
with the opening stress, MPa
Op 110−=
σ
, as shown in Figure 22.
Discussion
In the present study, the Hobson-Brown-Gao Stage II crack growth model is adopted. The model
parameters are extracted from the characteristic equations and crack growth test results. This semi-
empirical model life prediction was incorporated with parameters such as, defect size, or for Stage I
microstructure size, maximum stress or stress range, multiple cracking and coalescence, and residual
stress level.
The model is used to predict the fatigue life of a) FSW Polished, b) FSW as Welded c) FSW Peened as
Welded, and FSW peened skimmed of 2024-T351 Al Alloy. The input parameters and their values for
each predicted curve are summarised in Table 5. It can be seen that, defect size and residual stress input
parameters are varied from one curve to another, to represent the difference of each of the test sample
conditions. The empirical constants C, m, D, f
a, c
aand c
n in the model were kept the same for each
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predicted curve. The opening stress Op
σ
is fitted from either of the two S-N curves from FSW Peened as
welded and Peened after Skimmed. The real value of Op
σ
needs some further investigation.
From the fitted value MPa
Op 110−=
σ
, derived for Peened as Welded test, at the fatigue limit with 300MPa
maximum stress with a compressive residual stress of MPa
s200
Re
−
=
σ
, the effective stress range was
MPa
eff 210=∆
σ
with an effective load ratio
7.1
200
300
20030 −=
−
−
=R. On the other hand, in Peened after
Skimmed, at 320MPa maximum stress with compressive residual stress of MPa
s200
Re −=
σ
, the effective
stress range was MPa
eff 230=∆
σ
and load ratio 72.0
−
=
R. Therefore with these highly negative
R
values,
the opening stress Op
σ
is expected to be negative. Nevertheless the minimum stress, with residual stress
is low enough for crack closure to take place.
The residual stress in FSW as welded and FSW Polished mirror were incorporated in the model with a
single value of 96MPa tensile residual stress where the crack initiated. Suppose the residual value used
should change as the crack approached different types of residual stress distribution in FSW joints. This
represents at different crack lengths, the crack propagating and entering different level of residual stress
values, as the gradient in the characteristics of residual stress. The effect of a crack propagating through
a non uniform residual stress can be calculated based on the Green function method, the Weight function
method or approximated by calculating the average residual stress over the crack area. However, based
on crack growth data, up to life of 2100000 cycles the crack is less than 3mm length which is still
embedded in the tensile residual stress field, close to the initiation site. When the crack propagates into a
compressive residual stress field approximately 6.7% of life remains; it is believed that the changed
residual stress will not make a significant change in the total life, if we left it out of the assessment.
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The reduction of life due to the increasing number of subcracks successfully incorporated in the model
was based on Nong Gao’s applications [28]. However, the critical subcracks number will be different to
other applications in modelling with other materials. The difference should be found from experimental
data used to derive the model. This parameter is experimentally dependent. The work suggested that the
method of determining the c
n critical crack coalescence values needs further development.
The model has demonstrated the capability of predicting of fatigue life of several Steel Alloys [19, 25-
28], however no attempt has been made on predicting the life of Aluminium alloy. The fatigue limits of
Steel generally can be observed easily from S-N curves, consistent with a flat “knee” in the high cycle
fatigue regime. However, aluminium fatigue limits are generally gradually decreasing as the cycles
increase. The fatigue limits in this model are controlled by the defect size and the threshold value, D that
is set to be constant over all fatigue lives. In order to improve the prediction of fatigue limits in
Aluminium alloy in the model, the method of calculating threshold value needs to be adjusted, so that D
can be changed with the longer lives. This will gives the gradual decrease of fatigue strength in the high
cycle fatigue regime, showing the behaviour of aluminium alloy.
Total fatigue life is composed of initiation and short and long crack propagation. The initiation stage is
assumed to be negligible in FSW as welded, peened as welded and polished predictions, because there is
evidence that local stress concentration sites from the weld scar and defects are responsible for the rapid
crack formation. When the initial crack size extended to greater than 10
m
µ
grain diameter, it became
insensitive to the microstructural barriers, beyond the short-long crack transition. This has been
demonstrated very well when the multiple cracks equation acted as a lower bound of the curve for the
LCF regime, while the single crack equation acted as an upper bound of life for LCF regime. As the
ACCEPTED MANUSCRIPT
stress reduced close to the fatigue limit, the data shows the tendency to follow the single crack equation
curve.
The input data required to apply the model are, grain size, defect size, stress or strain range, threshold,
critical crack coalescence number and length, residual stress distribution, opening stress and long crack
propagation data. Most of these data are usually available or can be obtained by short and simple tests.
Any changes to the material through alloying or surface engineering which affect the fatigue properties
can easily be assessed without resorting to an extensive experimental programme. The effects of surface
stress state altered by peening are incorporated into the model through the development of crack closure.
Conclusions
1) Overall, the good correlation achieved between the experimental data and the model predictions
suggests that the fundamentals of the model are correct. The model is successful for handling the
multiple cracks causing crack coalescence, and modelling the crack growth in random residual
stresses found in FSW joints.
2) The simplicity of the model gives credibility, and should permit the industry to adopt and simply
apply it, incorporating residual stress, defects, microstructure size and surface engineering
treatment in order to predict the fatigue life of engineering components.
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Acknowledgments
The authors wish to thank Airbus UK, Metal Improvement Company and the Malaysian Ministry of
Science for a scholarship to one of the authors (Ali). The work does not represent official views of
Airbus UK.
References
1. Williams, S.W., Welding Airframes using Friction Stir. Air and Space Europe., 3: p. 64-66(2001).
2. Dawes, C. J., An introduction to friction stir welding and its development. Welding and Metal
Fabrication, 63(1): p. 13-16(1995).
3. Bussu, G., and Irving, P. E., The role of residual stress and heat affected zone properties on fatigue
crack propagation in friction stir welded 2024-T351 aluminium joints. International Journal of
Fatigue, 25: p. 77-88(2003).
4. Booth, D. and Sinclair, I., Fatigue of friction stir welded 2024-T351 aluminium alloy. Material
Science Forum, 396-402: p. 1671-1676(2002).
5. Sutton, M. A., Yang, B, Reynolds, A. P.,Taylor, R., Microstructural studies of friction stir welds in
2024-T3 aluminium. Material Science and Engineering, A323: p. 160-166(2002).
6. Dalle Donne, D., Biallas, G., Fatigue and fracture performance of friction stir welded 2024-T3 joints.
Proceeding European Conference on Spacecraft Structure, Material and Mechanical Testing.
Braunschweig. Germany, 428: p. 309-314(1999).
7. Mahoney, M. W., Rhodes, C.G., Flintoff, J. G., Spurling, R. A., Bingel, W. H., Properties of friction
stir welded 7075 T651 Aluminum. Metallurgical and Materials Transaction A, 29A: p. 1955-
1964(1998).
8. Jata, K. V., Sankaran, K.K., Ruschau, J. J., Friction stir welding effects on microstructure and fatigue
of aluminum alloy 7050-T7451. Metallurgical and Materials Transaction A, 31(9): p. 2181-
2192(2000).
9. Murr, L. E., Li., Y., Trillo, E. A., Flores, R. D., McClure, J. C., Microstructure in friction stir welded
metals. Journal of Materials Processing and Manufacturing Science, 7: p. 145-161(1998).
ACCEPTED MANUSCRIPT
10. Heinz, B., Skrotzki, B., Eggeler, G., Microstructural and mechanical characterization of a friction
stir welded Al-alloy. Material Science Forum, 331-337: p. 1757-1762(2000).
11. S. Sato, Y. S., Kokawa, H., Distribution of tensile property and microstructure in friction stir weld of
6063 aluminium. Metallurgical and Materials Transaction A, 32A(12): p. 3023-3031(2001).
12. Kwan, Y. J., Saito, N., Shigematsu, I., Friction stir process as a new manufacturing technique of
ultrafine grained aluminium alloy. Journal of Materials Science Letters, 21: p. 1473-1476(2002).
13. Flores, O. V., Kennedy, C., Murr, L. E., Brown, D., Pappu, S., Nowak, B. M., McClure, J. C.,
Microstructural issues in a friction stir welded aluminium alloy. Scripta Materialia, 38(5): p. 703-
708(1998).
14. Sato, Y. S., Park, S.H.C., Kokawa, H., Microstructure factors governing hardness in friction stir
welds of solid solution hardenend Al alloys. Metallurgical and Materials Transaction A :Physical
Metallurgy and Materials Science, 32A(12): p. 3033-3042(2001).
15. Paris, P. C., Erdogan, F. J., A critical analysis of crack propagation law. Journal of basic engineering
trans. ASME Series D, 85(4): p. 528-535(1963).
16. Weertman, J., "Fatigue crack propagation theories" fatigue and microstructure. ASM publications, p.
279-306(1979).
17. Tomkins, B., High strain fatigue. ISPRA courses on Mechanical Science and Materials edited by L.
H. Larsson, p. 239-273(1981).
18. Coffin, L. F., The flow and fracture of a brittle material. Journal of Applied Mechanics, 17: p. 233-
248(1950).
19. Hobson, P. D., Brown, M. W., de Los Rios, E. R., Two phases of short crack growth in a medium
carbon steel. Behaviour of short fatigue crack (Edited by K. J. Miller & Eduardo R. de Los Rios), p.
441-459(1986).
20. Navarro, A., de Los Rios, E. R., A microstructurally short fatigue crack growth equation. Fatigue
and Fracture of Engineering Materials and Structure, 11(5): p. 383-396(1988).
21. Navarro, A., de Los Rios, E. R., Short and long fatigue crack growth : A unified model.
Philosophical Magazine A, 57: p. 15-36(1988).
22. Navarro, A., de Los Rios, E. R., Compact solution for a multizone BCS crack model with bounded
or unbounded end conditions. Philosophical Magazine A, 57(1): p. 43-50(1988).
23. Shaikh, Z., Initiation, propagation and coalescence of short fatigue crack in AISI 316 stainless steel
at 200C and 5500C. PhD. Thesis, Sheffield University, (1991).
ACCEPTED MANUSCRIPT
24. Grimshaw, C. S., Miller, K. J., Rees, J. M., Short fatigue crack growth under variable amplitude
loading: A theoretical approach. Short Fatigue Crack, ESISI3, Eds. K.J. Miller and E. R. de los Rios,
Mechanical Engg. Publications London, p. 449-465(1992).
25. Zhang, W., Short fatigue crack behaviour under different loading systems. PhD. Thesis, Sheffield
University, (1991).
26. Wang, C. H., The effect of mean stress on short fatigue crack growth behaviour. PhD. Thesis,
Sheffield University, (1990).
27. Akid, R., The initiation and growth of short fatigue crack in an Aqueous Saline Environment. PhD.
Thesis, Sheffield University, (1987).
28. Gao, N., Short crack coalescence and growth in 316 stainless steel subjected to cyclic and time
dependent deformation. Fatigue and Fracture Engineering Material and Structure, 18(12): p. 1423-
1441(1995).
29. Askeland, D. R., The science and engineering of materials. VNR International, 1984.
31. ASTM Standard E8M-94a (1994a) Standard tests methods for tension testing of metallic materials
(metric), Annual Book of ASTM Standards Vol 03.01.
32. Brown, M. W., Interface between short, long and non propagating cracks, In. The behaviour of short
fatigue cracks, EGF 1, Pub. Sheffield UK Eds, K. J. Miller, E. R. de Los Rios, Mech. Eng. Pub.
London, pp. 423-439(1986).
33. Bussu, G., Damage tolerance of welded aluminium aircraft structure . PhD. Thesis, Cranfield
University, (2000).
34. Murakami, Y. Stress intensity factors handbook. Committee on Fracture Mechanics, The Society of
Material Science, Japan, Pergamon Press, (1987).
35. Lu, J., Handbook of Measurement of Residual Stresses. Society for Experimental Mechanics,
Inc.(SEM), p. 33-69.(1996).
36. Ali, A, Brown, M. W., Rodopoulos, C. A., Gardiner, S., Characterization of Friction Stir Welding
2024-T351 AL Alloy, Journal of Failure Analysis and Prevention, ASM International. Volume 6 (4),
p: 83-96. ( 2006).
37. Forsyth, P.J.E., A two stage process of fatigue crack growth. In Crack Propagation: Proceedings of
Cranfield Symposium, p. 76-94. (1962).
38. Suresh, S., Fatigue of Materials, Cambridge University Press, Cambridge. (1991).
39. Miller, K. J., The three thresholds for fatigue crack propagation, Fatigue and Fracture mechanics:
27th Volume, ASTM STP 1296, p. 267-286. (1997).
ACCEPTED MANUSCRIPT
40. Pearson, S. Initiation of fatigue cracks in aluminium alloys and the subsequent propagation of very
small cracks, Engineering Fracture Mechanics, Vol.7, p.235-247.(1975).
41. Kitagawa, H. and Takahashi, S., Applicability of fracture mechanics to very small cracks or the
cracks in the early stage, In proceedings of the 2nd International Conference on Mechanical
Behaviour of Materials, Metals Park: American Society for Metals p.627-631.(1976).
42. Lankford, J. The growth of small fatigue cracks in 7075-T6 aluminium, Fatigue of Engineering
Materials and Structures, Vol. 5, No.3, p.233-248. (1982).
43. de los Rios, E. R., Hussain, J. and Miller, K. J. A micro-mechanics analysis for short fatigue crack
growth, Fatigue Fracture Engineering Materials and Structures, Vol.8, No.1, pp.49-63 (1985).
44. Doquet, V. Micromechanical simulations of microstructure-sensitive stage I fatigue crack growth,
Fatigue Fracture Engineering Materials and Structures, Vol. 22, p.215-223. (1999).
45. Yoder, G. R., Cooley, L. A. and Crooker, T. W. On microstructural control of near-threshold fatigue
crack growth in 7000-series aluminium alloys, Scripta Metall., Vol.16, p.1021-1025. (1982).
46. Curtis, S. A, Solis Romero, J., de los Rios, E. R., Rodopoulos, C. A. and Levers, A., Predicting the
behaviour of microstructurally dependent fatigue cracks in 7150-T651 aluminium alloy using the
fatigue damage map, Mater. Sci. Eng. A 344 p.79–85. (2003).
47. Ali, A, An, X., Rodopoulos, C. A. , Brown, M. W., O'Hara, P., Levers, A. and Gardiner, S. The
Effect of Controlled Shot Peening on the Fatigue Behaviour of 2024-T3 Aluminium Friction Stir
Welds - International Journal of Fatigue, Vol 29, , p:1531-1545. (2007).
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Table 1. The result of cyclic tests in pure bending
Regimes Modulus of
Elasticity (E)
Strain
Hardening
Exponent (n)
Hardening
Constant (H)
Cyclic Yield
(0
σ
) 0.02% proof cyclic
stress-strain amplitude
Parent Material 68GPa 0.086 770MPa 370MPa
HAZ 68GPa 0.05546 719MPa 448MPa
TMAZ
(Composite 35%TMAZ+65%HAZ)
68GPa 0.1266 800MPa 272MPa
Nugget 68GPa - - -
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Table 2. Calculated values of constant B for Stage II crack growth equation.
Maximum Stress Stress Range
σ
∆
Calculated Values of B
(MPa) (MPa) 5
10−
×(cycles-1)
300 270 5.373
270 243 3.943
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Table 3. C and m type of Paris constant calculated from literature [3] of FSW 2024-T351 Al alloy, with m/cycle and MPa units.
FSW Regimes m C
Parent 2.4 2.035 10
10−
×
Nugget 3.106 2.02345 10
10−
×
TMAZ 2.254 3.987 10
10−
×
HAZ 2.28 8.41 11
10−
×
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Table 4. The crack early crack length obtained from Figure 13 of multiple crack coalescence diagram.
Number Early crack name Early crack length
(2a) from Figure 106
Crack length (a)
µ
µµ
µm µ
µµ
µm
1 1a 487 243.5
2 1ba 260 130
3 1bbb 250 125
4 3aa 625 312
5 3bb 112 56
6 4bbb 164 82
7 1ca 921 460.5
8 1cba 201 100.5
9 2b 163 81.5
10 2ab 163 81.5
11 1cbba 181 90.5
12 4bba 628 314
13 1cc 351 175
14 1cbbba 199 99.5
15 2ac 261 130.5
16 2adb 239 119.9
17 4bba 628 314
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Table 5. The summary of the input values in FSW fatigue life estimation.
Predicted
Curves
Defect
Size
Final
Crack
Length
Residual
Stress
Threshold
Value
Openin
g
Stress
Critical
Crack
number
Constant
0
a
(
m
µ
)
f
a
(
mm
)
res
σ
(MPa)
D
(mm/cycle) Op
σ
(MPa)
c
n C
(cycle-1) and
m
FSW
Polished 20 30 96 7
106 −
× -110 17
12
1085.2 −
×
2.94
FSW as
Welded 50 30 96 7
106 −
× -110 17
12
1085.2 −
×
2.94
FSW
Peened as
Welded
30 30 -200 7
106 −
× -110 17
12
1085.2 −
×
2.94
FSW
Peened
Skimmed 20 30 -200 7
106 −
× -110 17
12
1085.2 −
×
2.94
ACCEPTED MANUSCRIPT
(a) (b)
Figure 1. The transverse cross section in an as-welded FSW 2024-T351 Al Alloy joint and the mapping of
boundaries between each macro structural zone.
ACCEPTED MANUSCRIPT
Figure 2. Cutting scheme for the bending cyclic test
Figure 3. Longitudinal specimen configuration and the FSW coordinate system relative to the weld.
ACCEPTED MANUSCRIPT
Figure 4. S-N data for FSW as welded, FSW polished mirror, parent material, FSW peened as welded, and
FSW peened after skimmed 3mm of 2024-T351 Al Alloy tested in four point bending test with load ratio
R=0.1.
10
4
10
5
10
6
10
7
Maximum Stress (MPa)
100
200
300
400
500
600
700
Parent Material
FSW Peened as Welded
FSW Peened after Skimmed 3mm
FSW as Welded
FSW Polished Mirror
Fatigue Life (Cycles)
ACCEPTED MANUSCRIPT
Location (a) Location (b)
Location (c)
Figure 5. SEM fractograph initiation images for LCF of 2024-T351 Al Alloy FSW as welded specimen at
292MPa maximum applied stress with load ratio R=0.1.
ACCEPTED MANUSCRIPT
Location (a)
Figure 6. SEM fractograph initiation images for HCF of 2024-T351 Al Alloy FSW polished mirror specimen at
270MPa maximum applied stress with load ratio R=0.1.
Figure 7. SEM fractograph and EDX analysis position of initiation images for HCF of 2024-T351 Al Alloy
FSW polished mirror specimen at 270MPa maximum applied stress with load ratio R=0.1.
ACCEPTED MANUSCRIPT
Figure 8. Replica images for LCF of 2024-T351 Al Alloy FSW polished mirror specimen at 300MPa
maximum applied stress with load ratio R=0.1.
Figure 9. Replicas images for HCF of 2024-T351 Al Alloy FSW polished mirror specimen at 270MPa
maximum applied stress with load ratio R=0.1.
ACCEPTED MANUSCRIPT
Figure 10. Crack growth versus total crack length for 300MPa maximum applied stress with load ratio R=0.1.
Figure 11. Crack growth versus crack length for 270MPa maximum applied stress with load ratio R=0.1.
ACCEPTED MANUSCRIPT
Figure 12. Crack coalescence diagram for 300MPa maximum applied stress.
14910484007
23082390010
29204392009
32623394023
34060396012
41500197518
Total
crack
length
(µm)
Number
of crack
(n)
Crack Name and LengthNumber of
Cycles
(Nf)
14910484007
23082390010
29204392009
32623394023
34060396012
41500197518
Total
crack
length
(µm)
Number
of crack
(n)
Crack Name and LengthNumber of
Cycles
(Nf)
Crack Coalescence Diagram
Final Crack
99221415
115511818
144813619
188024813
220436012
329857218
544978416
3900412268
62455 30014
6735640011
91171148008
95161054009
120701460012
140371766165
154201472011
15989878075
99221415
115511818
144813619
188024813
220436012
329857218
544978416
3900412268
62455 30014
6735640011
91171148008
95161054009
120701460012
140371766165
154201472011
15989878075
1
1
1
1
2
2
2
2
3
3
3
3
1 2 3 4
28500
27636
2560 3000
2100 2887
23770 1927 3507
17778 1844 3460
6147 1669 2568 4 526
1a 1b
1c
3a
4a
24b
3b
1889 1978
2295 1532
2882 817
1742 2854
1a 1ba
1ca 1cb
1bb
2a
1cc
3aa
2b
3ab
3b
4a
4ba
4bb
1171 573 1406
976
751
1482 1251
1748
163
1143
701 2373
711
971
1a 1ba
1ca 1cba
1cc
1bb
1cbb 2ab
2aa 2ac 2ad
3aa
3ab
3b 4bbb
4bba
4ba
1108 618
900 201
351
1341
1370
1709
163 1085
706
709
199 261 715 2370
231
1a 1ba
1ca 1cbb
1bba
4bbb
1bbb
2ad
3aa
3ab
3ba 3bb
4ba
4bba
1106 608
880 1043
1301 250
647
508
1569
1079
112
709
164
2094
1ba 1bba 2ad
1ca 1cbb 3aa
3ab
3ba
4ba
4bba
260 1156
818 1004
611
1280
1062
666
2017
628
1a 1bba 2ada
1ca 1cbb 2adb
2adc
3aa
3ab
3ba
4ba
487
804
991
1004 239
611 498
1209
1061
663
2000
1ca 1cbb 3aa 3ab 3ba 4ba
810 1435 1211 900 295 1980
810
1ca 1cb b 3aa 3ab 4ba
1435 1175 900 19 25
1ca 1cbba 1cbbb 4ba
917 183 1085 1715
1ca 1cbbba 1cbbbb
1cbba 3aa
3ab
4ba
998
183
162 1036
917
600
1735
1ca 1cbbba 1cbbbb 3aa 3ab
990 165 1013 625 505
1ca 1cbbba 1cbbbb
1ca 1cbbbb
4ba
4ba
4baa 4bab
984 199 1021
921 959
1448
1155
499 493
Early Crack
ACCEPTED MANUSCRIPT
Figure 13. Linkage behaviour shows changes in numbers of participating cracks at 300MPa maximum
stress, taken from Fig. 14.
(a)
(b)
Figure 14. The longitudinal residual stress profile along the FSW 2024-T351 Al alloy weld.
Distance from PJL (mm)
-30 -20 -10 0 10 20 30
Residual Stresses in Longitudinal Direction (MPa)
-60
-40
-20
0
20
40
60
80
100
Top side of the weld
Bottom side of the weld
0 10 20 30 40 50
Number of minor cracks observed
0
5
10
15
20
25
30
Number of cracks
observed on each replication
Crack coalescences + 1,
= total number of crack
Nong Gao line
Total surface crack length (mm)
ACCEPTED MANUSCRIPT
Figure 15. The longitudinal residual stress profile with depth in the FSW peened specimens.
Figure 16. Multiple early minor cracks size distribution.
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
-100 -50 0 50 100 150
Defect size (um)
Probability
ao
Figure 17. Defect size distribution
.
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0 100 200 300 400 500
Minor Cracks Size (um)
Probability
ACCEPTED MANUSCRIPT
Figure 18. Chosen critical crack number (
c
n
) and length (
c
a
).
Figure 19. Life prediction of FSW Polished mirror.
50
100
150
200
250
300
350
400
450
500
10000 100000 1000000 10000000 100000000
Fatigue life (Cycles)
Stress range (MPa)
Predicted single crack equation
Predicted multiple cracks equation
Experimental data FSW Polished
mirror
ACCEPTED MANUSCRIPT
Figure 20. Life prediction of FSW as Welded.
Figure 21. Life prediction of FSW Peened as welded.
0
50
100
150
200
250
300
350
400
450
500
10000 100000 1000000 10000000 100000000
Fatigue life (Cycles)
Stress range (MPa)
Predicted single crack equation
Predicted multiple cracks equation
Experimental data FSW as Welded
200
250
300
350
400
450
10000 100000 1000000 10000000 100000000
Fatigue life (Cycles)
Stress range (MPa)
Predicted single crack equation
Predicted multiple cracks equation
Experimental data FSW Peened as
Welded
ACCEPTED MANUSCRIPT
Figure 22. Life prediction of FSW Peened after Skimmed.
150
200
250
300
350
400
450
500
550
10000 100000 1000000 10000000 100000000
Fatigue life (Cycles)
Stress range (MPa)
Predicted single crack equation
Predicted multiple c racks equation
Experimental data FSW Peened after
Skimmed
