Jtam-A4.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

56, 1, pp. 179-190, Warsaw 2018
DOI: 10.15632/jtam-pl.56.1.179

FATIGUE CRACK GROWTH AND PROBABILITY ASSESSMENT FOR

TRANSVERSE TIG WELDED ALUMINUM ALLOY 6013-T4

Gunawan D. Haryadi

Diponegoro University, Department of Mechanical Engineering, Semarang, Indonesia

Rando Tungga Dewa

Pukyong National University, Department of Mechanical Design Engineering, Busan, Korea

e-mail: rando.td@gmail.com

I.M.W. Ekaputra

Sanata Dharma University, Department of Mechanical Engineering, Yogyakarta, Indonesia

The aimof this study is to investigate the fatigue crack growthbehaviorwith postweld heat
treatments (T4) on transverse tungsten inert gas-welded Aluminum alloy 6013. All fatigue
tests have been carried out using center cracked tension specimens at ambient temperature
under a stress ratio of R = 0.3. The results revealed that various time of aging in T4
affects its mechanical properties, also the fatigue crack growth behavior as well. It has been
observed that in the heat treated samples the crack growth rate is lower than that in the
as-welded sample, but higher than the rate in the base metal. To be more specific, samples
with 18 hours aging exhibit the highest tensile strength and fatigue resistance compared to
the other heat treated samples. The probability assessment has also been used to determine
the fatigue crack growth rate and a good linearity has been found.

Keywords: fatigue crackgrowth,Aluminumalloy6013-T4,postweldingheat treatment,TIG
welding

1. Introduction

The aircraft and automotive industries have been long using Aluminum alloys for the prime
material construction. This material is normally used in the aerospace industry (for fuselage
skins and other applications) and automotive industry (for body panels and bumpers) due to its
excellent properties such as preferential strength, corrosion resistance, weld ability and low cost.
Various structural components in machines, pressure vessels, transport vehicles, earthmoving
equipment and spacecraft aremade of welded joints. The butt welds are themost common ones
in the fabrication and construction of many structures. The wide applications of butt welds in
various structures including offshore andnuclear ones give a large scope for researches to analyze
the behavior under different types of loading conditions. This concept was introduced after the
works of Yakubovski andValteris (1989). However, as it is well known,welded joints can exhibit
poor fatigue properties. Thus, detail design guidelines are necessary to prevent fatigue failures
in welded Aluminum alloy structures. Apart from the basic design of new structures, there is
also an increase of interest inmethods for assessing the remaining life of existing structures. The
previous author’s work also revealed the fatigue crack growth behavior of the studied material
using longitudinal direction of tungsten inert gas (TIG) welding (Haryadi and Kim, 2011).
Prompted by difficulties experienced in reaching a consensus on fatigue performance of welded
Aluminum alloys, an animated discussion has been undertaken over the past 10 years (Maddox,
2003).



180 G.D. Haryadi et al.

To produce a high quality weldment component, TIG welding is preferred rather than the
other arc welding processes due to the temperature distribution on thewelded plate, whichmay
induce distortion. Also the TIG welding process is one of the most well established processes
which has capabilities to weld all metals of industrial use. Therefore, many efforts have been
done to investigate the fatigue behavior on TIG welded Aluminum alloy joints. The weldment
components have lower impact energy and fracture tenacity compared to its parentmaterial. It is
well known that thewelded structures are also less superior to the parentmaterial as thewelding
process (thermal interaction) results inmicrostructure heterogeneity, which brings differences to
mechanical properties (Manti et al., 2008). Failure analysis of theweldment indicates that fatigue
damage have to be considered to account for most of the disruptive failures. Themain problem
is that there is an abrupt change in section due to the excess weld reinforcement, undercut,
slag inclusion and lack of penetration, and nearly 70% of fatigue cracking occurs in the welded
joint (Pakusiewicz et al., 2006). It is also well known that the heat treatment process after
welding, i.e. solution treatment and aging, can possibly overcome the degradation ofmechanical
properties.

To determine the fatigue tendency of the weld structure, the test matrix of tests is more
complex as welded joints presentmicrostructure variations over small distances, not tomention
complex distributions of residual stresses. The fatigue and fracture tests are performed in ac-
cordance with standards and codes devised by the American Society for Testing and Materials
(ASTM) E647 based on the concepts of a−N and (da/dN)−∆K for fatigue design curves.

This work deals with the dependence of constant-amplitude fatigue crack growth rates on
the center cracked tension (CCT) specimens of a material for a variety of heat-treatable thin-
-sheet Aluminum alloys. The TIGwelded 6013 Aluminum alloy transverse joint is of particular
interest. A better understanding of the relatively high variability of these rates and the role of
material parameters based on the analysis of experimental data are explored and discussed for
assessing the remaining lives of existing structures.

2. Experimental section

The material studied is Aluminum alloy 6013 with sheet thickness of 2.5mm. The chemical
composition of Aluminum alloy 6013-T4 and its filler wire Al 5356 can be found in Table 1
(Rooy, 2000). The welding process by using the TIGmethod on specimens has been performed
byAl 5356 fillerwith 3.2mmdiameter, and theweldingwasdone in the transverse direction.The
welding conditions and process parameters can be found in (Haryadi and Kim, 2011). Tensile
test specimens were made with dimensions according to the standard test ASTM B-557, and
crack propagation tests specimens according to the standard test ASTM E-647 proposed by
American Society of Mechanical Engineers (ASME) (ASTM E 647-08, 2008). The specimens
were grouped into three kinds of fracture conditions, i.e. cracks without heat treatment, cracks
in the welding simulation, and cracks in the welding simulation continued with various T82
artificial aging. The surfaces of the specimens were polished to prevent the formed notches. The
geometry and dimensions of specimens are specified in Fig. 1.

Table 1.Chemical composition of Al 6013-T4 and filler wire Al 5356 [wt%]

References Si Fe Cu Mn Mg Cr Zn Ti Al

Al 6013 0.66 0.09 0.80 0.39 1.04 0.07 0.06 0.02 Bal

Al 5356 0.25 0.40 0.10 0.10 5.55 0.20 0.10 0.20 Bal

The heat treatment (T4) on the specimen is hereafter referred to as the specimen experien-
cing the process of solution treatment (the specimen is heated until it reaches the temperature



Fatigue crack growth and probability assessment... 181

Fig. 1. Specimen configuration for tensile and fatigue crack propagation tests (all units in millimeters)

of 420◦C), followed by a process of strain hardening of 2%, and the final process is the artificial
aging in temperature of 175◦C and the aging time of 6 hours, 18 hours, and 24 hours, respec-
tively. Microhardness measurements have been conducted through fusion boundaries using a
Vickers microhardness tester. Vickers hardness measurement was carried out by using a dia-
mond indenter on ametallographically polished section of thewelded joint along the central line
at a loading of 0.2kg and loaded time of 5s. The indentations were set at an interval of 1mm
along the weld center, transverse to the direction of the base metal. The schematic illustration
of hardness testing distribution is shown in Fig. 2. The microstructures of all material types
are shown in Fig. 3. The as-welded material has a larger grain size compared to the other heat
treated samples. Coarser grained by 24 hours aging time samples relatively contained a lower
amount of grain boundary areas than the finer grained microstructure.

Fig. 2.Welding profiles and a schematic illustration of the hardness testing distribution

Initial cracks for the fatigue crack propagationCCTsamplesweremadeusingEDM(Electric
Discharge Machine) with 12mm length and 0.9mmwidth. The fatigue crack growth tests were
carried out using side grooves to ensure the crack propagation occur along a single plane. Five
different stress levels (345MPa, 225MPa, 138MPa, 202MPa, and 170MPa) were applied under
a stress ratio ofR=0.3 with a constant frequency of 5-11Hz. A travelling microscope was used
tomonitor the crack growth with an accuracy of 0.01mm. In this work, the applied stress cycle
was in the pull mode as the compressive mode usually near the fatigue crack. The data points
measured with an accuracy of 0.01mmwere fitted with a smooth curve as in the form of crack
length against the number of cycles.



182 G.D. Haryadi et al.

Fig. 3. Microstructures of as-welded and 6013-T4 samples (BM: base metal andWM: Weld metal)

3. Results and discussions

3.1. Tensile properties of 6013-T4

The tensile test results were performed on the basemetal, welding without T4, and welding
withT4 aging time variations. The results of the tensile tests aremean values ofminimum three
tests. All tensile test failures occurred in the heat affected zone (HAZ) due to coarser grains
as the cast structure of the base material. As such, the reduced section and notched specimens
weremade to characterize the failure from theweldedmetal. The yield strength results based on
0.2% offset in the load-elongation diagram and the peak maximum (ultimate tensile) strength
are reported in Fig. 4. The unwelded base metal indicates yield strength and tensile strength
values of 243MPa and 346MPa, respectively. These results are comparable to other literature
data (Heinz and Skrotzki, 2002) for 6013-T4 base metal having the yield and ultimate strength
approximately 220 and 320MPa, respectively. Thus, the transverse as-welded sample shows the
yield strengthand tensile strengthvalues of 141MPaand227MPa, respectively. Fromthis result,
we can point out that there is a 52% reduction in strength values due to theTIGwelding process
in the transverse direction. The as-welded material possesses higher strength or embrittlement,
therefore, very slight lateral displacement will result in shearing off the structure. In the case
of the as-welded samples, the transverse TIG welded samples with 6 hours aging exhibit the
lowest yield strength and tensile strength of 82MPa and 160MPa, respectively. This suggests
that there is a 42% reduction in strength due to T4with a 6 hours aging process compared to
the transverse as-welded samples. The heat treated specimens with 18 hours aging indicate the
highest yield strength and tensile strength of 107MPa and 202MPa, respectively. Though these
values are lower than those for the base metal and as-welded samples, the strength values are
comparatively higher than those of the other sampleswithT4process.The24-hour aged samples
show the yield strength and tensile strength of 102MPa and 194MPa, respectively, which is 20%
higher than the heat treated samples by 6 hours aging. To conclude all those cases, no significant
influence of the welding direction compared to the previous study (Haryadi andKim, 2011) has
been reported.

The percentage of elongation in the cross sectional area of the base material and transverse
as-welded samples can be seen in Fig. 5. The elongation in the cross sectional area of the base
metal and the transverse as-welded samples are 19.42% and 5.83%, respectively. According to



Fatigue crack growth and probability assessment... 183

Fig. 4. Results of tensile tests on the strength of various transverse TIGwelded 6013-T4 samples

Fig. 5. Reduction in area in terms of elongation [%] of transverse TIGwelded 6013-T4

the literature (Heinz and Skrotzki, 2002), the elongation for 6013-T4 basemetal is comparable,
approximating 20%. The increase of strength of the as-welded samples has been expected as
themicrostructure hardens due to the solidification process duringwelding. The transverse TIG
welded samples with T4 of 6, 18, and 24 hours exhibit 2.24%, 7.51% and 4.16% of elongation in
the cross sectional area, respectively. This suggests that there is a 60% reduction in ductility due
toT4with 6 hours agingwith respect to the transverse as-welded samples. Again, the heat aged
specimens for 18 hours indicate the highest elongation of 7.51%. The heat treatment process,
especially the 18-hour aging, can improve ductility properties significantly.

3.2. Microhardness analysis

The exact extension of the HAZ and welded region are not easily measurable, thus, each
indentation of microhardness profiles was drawn based on three average points for the best
condition obtained. Hence the mechanical characteristics of heat-treatable Aluminum alloy are
largely determined by characteristics of precipitates (i.e. size, volume fraction, composition,
distribution, etc.). Precipitates and second phase particles act as obstacles to dislocation mo-
vement, which in turn increases hardness and strength but also limits ductility of the material.
Precipitation hardening ofAl-Mg-Si alloys has also been reported to occur due to increased ener-
gy requirement to break Mg-Si bond rather than coherency strains (Haryadi and Kim, 2011).
The TIG welding process has proven to affect the original state and distribution of those pre-
cipitates. The base metal in its initial number 4-6 condition has the average hardness of about
91HVapproximately, which starts to slightly increase in theHAZ to aminimumof 100HV.The



184 G.D. Haryadi et al.

hardness is greatly reduced in the welded region irrespective of the welding processes (Fig. 6).
This is one of the reasons for location of the failure invariably at the welded region. The closer
to the center of the weld, the higher the temperature is reached, which may lead to coarsening
of the grain structure. The coarsening becomes an important aspect in the welded region due
to the thermally activated phase in this particular zone. Thus, the softening phase caused by
precipitation coarsening will also soften the material. The time aging by T4 possesses limits
the strength due to high temperatures resulting in finer grains (Effertz et al., 2016), and re-
precipitation accompanied by aging. The ductility of this Aluminum alloy can be enhanced by
a proper heat treatment process. The T4 sample aged by 6 hours indicates the lowest hardness
profiles about 50HV at the weld center. The T4 sample with 18 hours aging shows the highest
hardness of about 71HV at the welded region. It is important to emphasize that the transverse
as-welded sample has the highest hardness of about 77HV at the welded region.

Fig. 6. Vickers microhardness profile distribution across the welded zone

With the combination of tensile properties and microhardness profiles, it is also possible
to determine mechanical properties of the transverse welded butt joint with 18 hours aging,
which are the most superior compared to other aging processes. The aging by 18 hours is more
appropriate for more brittle materials (high strength). After this time of aging, the detriment
of the mechanical properties can be observed due to the over aging process.

3.3. Fatigue crack growth properties

It is well known that the growth of the fatigue crack of many materials can be divided into
three regimes as shown inFig. 7. Region I is the fatigue threshold regionwhere∆K is too low to
propagate the crack. Region II involves the rate of crack growth changes roughly linearly with
a change in the stress intensity factor (SIF). Lastly, region III with a small increase in the SIF,
produces a relatively large increase in the crack growth rate.
Considering the power law region, the experimental results for the crack length a are plot-

ted in da/dN versus ∆K, with N and ∆K being the number of cycles and SIF, respectively,
according to the following Paris equation (Paris and Erdogan, 1963)

da

dN
=C(∆K)m (3.1)

where the correlation between the exponent m and the coefficient C in the Paris equation
determines the material constants. The crack growth exponent m, which is derived from the
relationship existing between the crack growth rate da/dN and the SIF range, is an important
parameter to evaluate the fatigue crack growth behavior of materials since it decides about the
fatigue crack propagation life of the materials (Dieter, 1988).



Fatigue crack growth and probability assessment... 185

Fig. 7. Fatigue crack propagation curve

The loading variables R, ∆K, and Kmax are related in accordance with the range of the
SIFwith the following relationship (Malarvizhi et al., 2008), where σ is a uniform tensile stress
perpendicular to the crack plane and Y depends on the geometry of samples

∆K =Y
√
πa N =

af
∫

ai

1

C(∆K)m
da (3.2)

where ai and af are initial crack length and crack length at the fracture point, respectively. The
crack growth rate, da/dN for the propagation stage is calculated for the steady state growth
regime at different intervals of crack length increment, against the associated number of cycles
to propagation. The SIF values are calculated for different values of the growing fatigue crack
length 2a using the following expression for the middle tension specimen refering to the ASTM
Standard. The measured variation in the crack length 2a and the corresponding number of
cycles N endured under the action of particular applied stress range are plotted in Fig. 8.

Fig. 8. Fatigue crack propagation curve of transverse TIGwelded 6013-T4



186 G.D. Haryadi et al.

The relationship between the SIF and ∆K range and the corresponding crack growth rate
da/dN in terms of the best fit lines is shown in Figs. 9a and 9b for all samples. The data points
plotted in the graph mostly correspond to the second stage of the Paris sigmoidal relationship
(10E-6 to 10E-3mm/cycle). The exponentm, which is the slope of the line on log-log plot and
the interceptC of the line, are determined and presented in Table 2.

Fig. 9. (a) Fatigue crack growth for Al 6013-T4 (base metal) and the transverse as-welded sample.
(b)Measured fatigue crack growth for the transverse TIGwelded 6013-T4

Table 2. Fatigue crack growth parameters of transverse TIGwelded samples

References
Crack growth Coefficient
exponentm C

Al 6013 base metal 3.09 4.98E10-13

Transverse TIGwelded 4.81 1.38E10-15

After 6 hours aging 10.36 2.62E10-23

After 18 hours aging 5.55 1.14E10-16

After 24 hours aging 6.74 9.09E10-21

It can be seen from those figures that at higher crack growth rates, the measured fati-
gue crack growth rate for the base metal is 5.03E-7mm/cycle (∆Kcr = 84.2MPa

√
m), and

the measured fatigue crack growth rate for transverse as-welded samples is 1.55E-6mm/cycle
(∆Kcr =73.49MPa

√
m).Ontheotherhand, inFig. 9b forallT4samples, athigher crackgrowth

rates for 6 hours aging, 18 hours aging and 24 hours aging samples exhibit 2.2E-6mm/cycle
(∆Kcr = 42.66MPa

√
m), 9.27E-7mm/cycle (∆Kcr = 60.07MPa

√
m), and 1.31E-6mm/cycle

(∆Kcr = 68.36MPa
√
m), respectively. The unstable crack growth phase occurred and, hence,

the corresponding ∆K value is taken as the critical SIF range ∆Kcr. Furthermore, the crack
growth at a lower rate is found to be dormant, and the corresponding ∆K value is taken as
the threshold SIF (∆Kth). At a lower crack growth rate, the measured fatigue crack growth
rate for the base metal is 6.73E-8mm/cycle (∆Kth = 42.8MPa

√
m) and the measured fatigue

crack growth rate for transverse as-welded samples is 1.3E-7mm/cycle (∆Kth =42.2MPa
√
m).

Thus, at a lower crack growth rate for all T4 samples with 6 hours aging, 18 hours aging
and 24 hours aging results in 7.52E-8mm/cycle (∆Kth = 31.9MPa

√
m), 1.1E10-7mm/cycle

(∆Kth =42.73MPa
√
m), and 3.6E-8mm/cycle (∆Kth =43.01MPa

√
m), respectively.

The fatigue crack growth exponent of the Al 6013-T4 Aluminum alloy base metal is lower
than that of the transverse TIG samples. On the three heat treated samples with various aging,



Fatigue crack growth and probability assessment... 187

the 18 hours aging samples exhibit a very low fatigue crack growth exponent compared to the
other heat treated samples. Although, the fatigue crack growth exponent of 18 hours aging
samples is approximately 44% higher than in the basemetal. It is understood that the 18 hours
aging samples exhibit superior fatigue crackgrowth resistance compared to theotherheat treated
samples. If this exponent has a larger value, then the slope of the curve is higher what explains
lower resistance of thematerial to the growing fatigue crack and reduction the lifespan (Ambriz
et al., 2010; Sivaraj et al., 2014). The reasons for better fatigue crack growth resistance of the
18 hours aging samples is due to superior of mechanical properties. The crack tip plasticity is
also the reason of the higher crack growth rate, since the deformation is controlled by the yield
strength of the material and mainly concentrated in the welded metal zone. The extension of
the plastic zone size (PZS) is limited within the welded metal. This relationship indicates that
the local fatigue crack growth rate decreases when the SIF is increased, and can be estimated
by the following equation (Sohn et al., 2014)

PZS(cycle) =0.033
(∆K

σys

)2
(3.3)

Eripret and Hornet (1994) reported that as soon as the plastic zone reaches the fusion line,
plasticity keeps on developing along the interface between the parent material and the weld
metal. The triaxial state of stress is high in the weld metal and the relaxation of this stress
is poor. The crack driving force needed for this crack extension is small. Hence, the fracture
toughness of the lower strength weld metal is not high. On the other hand, if the strength of
the weld metal is more or less equal to the base metal, the plastic zone can easily extend into
the parent material.

An extensive research by Zhang et al. (2016) did not deal with probabilistic viewpoints
that define the probability of fracture. In this circumstance, a quantifiable method based on a
statistical and probabilistic approach is proposed for assessing fatigue crack growth rate data.
As mentioned above, the fatigue crack growth data followed the lognormal distribution well if
using the standard deviation σ andmean valueµ obtained from the lognormal distribution. The
probability density functions (PDF) for this distribution is

P(N, loc,scale)=
1

σ
√
2π
exp
[

−
1

2

(lnN−µ

σ

)2]

(3.4)

As an example of application, Fig. 10 shows the probability distribution on the fatigue crack
growth data for 18 hours aging samples. The fatigue crack growth life was estimated from
the initial crack length of 8.5mm to 17.6mm. To the author’s best knowledge, the lognormal
distribution provides a good agreement for the statistical distribution of fatigue crack growth
life. The confidence intervals of 90% and 10%will be the upper and lower limits of conventional
prediction for the fastest and lower fatigue crack growth rate according to the concept in the
literature (Kim et al., 2011).

To probabilistically predict the fatigue crack growth rate, the probabilistic distributions
of da/dN have been determined for various materials. Figure 11 shows a typical result for
the probability distribution of the da/dN for various materials. The relationships between the
probability and fatigue crack growth life data revealed a linear relationship in the lognormal
plot. Although, there are some variability linear equations between material types. The most
scattered and widely distributed values are revealed for the 6 hours aging samples. This also
proves that the TIG welded microstructure and the heat treatment time process could greatly
affect the fatigue crack growth life. Using these fatigue crack growth rate data, it is possible
to probabilistically predict the fatigue crack growth rate lines for this class of materials at the
operational temperature when the fatigue crack growth data is absent.



188 G.D. Haryadi et al.

Fig. 10. Probability distribution of the fatigue crack growth lifeN for 18 hours aging samples

Fig. 11. Log-normal distribution of the fatigue crack growth rate for all tested samples at
averageN values

4. Concluding remarks

This paper presents results of tensile, hardness profile, fatigue crack growth behavior and proba-
bilistic analysis of transverse TIGwelded Al 6013-T4. However, some aspects deserve attention
and are discussed in this Section. The following conclusions can be drawn:

• A 52% reduction in strength values due to the TIG welding process in the transverse
direction with respect to the base material has been observed. Thus, the heat treatment
process also can reduce the strength by about 20% in average despite the percentage of
elongation of the respected T4materials has been increased with respect to the as-welded
material.



Fatigue crack growth and probability assessment... 189

• The fatigue crack growth resistance and fatigue life of Al 6013-T4 are generally reduced
by the TIGwelding process. Of the three types of T4 samples, the 18 hours aging samples
exhibit a higher fatigue crack growth resistance compared to other heat treated samples.

• The effect of 18 hours aging showed a crack growth exponent m of 5.55 which is the
lowest value compared to the other heat treated samples.With a high∆K (SIF), it causes
a dramatic increase in the crack growth resistance compared to the other heat treated
samples.

• The relationships between probability and fatigue crack growth life data exhibit linearity
of the lognormal plot. The variability of the fatigue crack growth life is influenced by the
TIGwelded microstructures and T4 aging time.

Acknowledgements

This researchwas supported through research grant of DiponegoroUniversity andPukyongNational

University (2017).Special gratitude is granted toprof. SeonJin-Kim,PhD(PukyongNationalUniversity)

for technical discussions and supports.

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Manuscript received March 2, 2017; accepted for print August 31, 2017